tag:blogger.com,1999:blog-76996167242224958542024-03-05T22:32:44.107-07:00Cognition and RealityMind, Body, World: Foundations of Cognitive ScienceMichael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.comBlogger64125tag:blogger.com,1999:blog-7699616724222495854.post-91734510374968013212019-12-04T10:24:00.000-07:002019-12-04T10:24:38.881-07:00End of an embodied era
<br />
<div style="border-color: currentColor currentColor windowtext; border-style: none none solid; border-width: medium medium 1pt; mso-border-bottom-alt: solid windowtext .75pt; mso-element: para-border-div; padding: 0in 0in 1pt;">
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;">December 3 marked
what is in all likelihood the final time that I will teach ‘Embodied Cognitive
Science’ (Psyco 457) at the University of Alberta. I’ve had substantial
difficulty keeping the enrollment in that course up, and decided a few months
ago to teach an introductory Cognitive Psychology course instead of it next
year.<o:p></o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;">The course itself has
a long history. It emerged from a (failed) attempt to establish some interdisciplinary
cognitive science graduate courses in the late 1990s. (This explains why this
course has always met in the evening – this was the only time that students
from four different Departments had in common.) As graduate enrollment in that
course (INT D 554) fell, it was double-numbered as an undergraduate course, and
I began to introduce LEGO robots into its curriculum. It was then offered
(perhaps in 2001) as PSYCO 403.<o:p></o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;">The course had some
important developments over the past two decades. I received a McCalla Research
Professorship in 2007 to integrate the course with my research. This led to the
publication of a 2010 book on <a href="http://www.aupress.ca/index.php/books/120175"><span style="color: blue;">using LEGO robots to study
embodied cognitive science</span></a>. In 2013 the course received its current 457
designation.<o:p></o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;">Over the years there
has been a fair number of students who have worked through the course,
developing some very interesting robots and learning to write papers about embodied
cognitive science. One interesting success story is my current graduate student
Arturo Perez. Arturo stayed in Edmonton for a few months 7 years ago to learn
about teaching cognitive science with robots, and transported those skills to
Chile. One reason that he is back in Edmonton for graduate studies is because
of his experience with this course.<o:p></o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;">The final edition of
the course was very successful. Students developed a ‘functionally equivalent’
Grey Walter Tortoise over the term. The final class involved exploring the
behavior of three of these machines as they interacted with their environment
(and with each other). The images below reflect various stages of this project.
The index cards scaffolded the students’ building, programming, and tweaking of
their machine. The inventors of this machine pose with their work in the second
photo. A still of robots in action is provided in the third photo. The last
photois a fabulous time-lapse photo taken by Arturo illustrating robot behavior
in a fashion very reminiscent of William Grey Walter’s own work.</span></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"></span> </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1rMtCDLC6xI4q-FlDZVcWzNb5FvBV_dB1bQAwoiMrXudq94GNYwxYiy5cr-V24HItGERZi3LSy1e8m5A729jtut4LEyyCXAfnCeO_g76ChODGzAx0NluMnokz5w-zjiZVafyo3oVmWYA/s1600/Tortoise1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1560" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1rMtCDLC6xI4q-FlDZVcWzNb5FvBV_dB1bQAwoiMrXudq94GNYwxYiy5cr-V24HItGERZi3LSy1e8m5A729jtut4LEyyCXAfnCeO_g76ChODGzAx0NluMnokz5w-zjiZVafyo3oVmWYA/s320/Tortoise1.jpg" width="311" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqbMvgTp-mwWTbxsq5R4DFKnuj-qnNvT6R61pCkrl1EqM4blxtg9MHbCMrglGDLIt9bAt-BVWxZ19zOD6IHn5w4LO6AgIG8A17xk4OjmDAeMprR84rkKqoPKGNngZiqOGyEGRwlLzvl9s/s1600/Tortoise2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqbMvgTp-mwWTbxsq5R4DFKnuj-qnNvT6R61pCkrl1EqM4blxtg9MHbCMrglGDLIt9bAt-BVWxZ19zOD6IHn5w4LO6AgIG8A17xk4OjmDAeMprR84rkKqoPKGNngZiqOGyEGRwlLzvl9s/s320/Tortoise2.jpg" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0Pc7a0822Gf3dC9L7pD0NG40h-370o7EJeR1PnMnPdz-hqOQarZZP1Lchd-jdIlzyALTOAdMO1ZaRysRZc19b4AE-0Q2cRWNtCKHSieBBUfQoaRHkUqdtx8AAmU-yqBdPTispC0cSJzM/s1600/Tortoise3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0Pc7a0822Gf3dC9L7pD0NG40h-370o7EJeR1PnMnPdz-hqOQarZZP1Lchd-jdIlzyALTOAdMO1ZaRysRZc19b4AE-0Q2cRWNtCKHSieBBUfQoaRHkUqdtx8AAmU-yqBdPTispC0cSJzM/s320/Tortoise3.jpg" width="240" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw3fNjzUWV_xA1qmZPc3ins5UpgshFYAH42b2f6_EcP6GqM5mQQKO_6fRVfK6KR14JFw8Ei4R4dH_9eN-JyCpplSDN98G5I0ietY_oB1kQiB8LC7n2gj0Nvb-N5NTPYWAVTIbZiDbjtog/s1600/Tortoise4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1600" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw3fNjzUWV_xA1qmZPc3ins5UpgshFYAH42b2f6_EcP6GqM5mQQKO_6fRVfK6KR14JFw8Ei4R4dH_9eN-JyCpplSDN98G5I0ietY_oB1kQiB8LC7n2gj0Nvb-N5NTPYWAVTIbZiDbjtog/s320/Tortoise4.jpg" width="320" /></a></div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"></span> </div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"></span> </div>
<div class="MsoNormal" style="border: currentColor; line-height: normal; margin: 0in 0in 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0in 0in 1.0pt 0in; padding: 0in; text-align: justify;">
<span lang="EN-CA" style="font-family: "Arial","sans-serif"; font-size: 12pt;"></span> </div>
</div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-63748667441598069482018-08-29T10:43:00.000-06:002018-08-29T10:43:18.961-06:00Sabbatical Report: Project End
<br />
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: Calibri;">The goal of my past sabbatical was to conduct a project that
studied how simple artificial neural networks learned about uncertain
environments. This project was completed this past August 10 when I submitted a
240 page monograph for review at <i style="mso-bidi-font-style: normal;">Comparative
Cognition and Behavior Reviews</i>. The sabbatical not only involved the actual
writing this monograph, but also the collection of new results to be reported.
This involved a tremendous amount of new research activity. I developed a
number of new mathematical proofs about the relationship between simple
artificial neural networks and Bayesian probability. I conducted hundreds of
network simulations in order to collect data on how such networks behave in
uncertain environments when interactions between cues serve as signals of
reward probabilities. I also collected data from 200 Introductory Psychology
students to measure their behavior in similar environments, and to compare
human probability learning to that of my networks. There are striking
similarities between network and human performance, and one of the main goals
of my monograph is to use this relationship to support the claim that human
probability learning can potentially be modeled by very simple artificial neural
networks.</span></div>
<br />
<div style="margin: 0px 0px 10.66px;">
<span style="font-family: Calibri;">While this study of probabilistic artificial neural networks
was the primary activity of my sabbatical, I have also been able to develop a
new research project (in collaboration with Cor Baerveldt and his students in
the Department of Psychology) on the history of the Center for Advanced Study
of Theoretical Psychology at the University of Alberta. In particular, during we
have explored archival materials and used our findings to explore the
development of the Center’s flagship course ‘Seminar in Theoretical Psychology’
as well as the relationship of Center activities to Cold War social science.
Both of these projects have led to manuscripts, one that is currently under
review at <i style="mso-bidi-font-style: normal;">History of the Human Sciences</i>,
the other soon to appear in <i style="mso-bidi-font-style: normal;">History of
Psychology</i>. I also presented a poster at the 50<sup>th</sup> annual meeting
of Cheiron on the contents of the books in the collection of the Center which
are now included in the D.E. Smith Reading Room at the University of Alberta.</span></div>
<b></b><i></i><u></u><sub></sub><sup></sup><strike></strike><span style="font-family: Calibri;"></span>Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-86068714913284570062017-12-31T10:59:00.001-07:002017-12-31T10:59:46.357-07:00Sabbatical Report: Last Day of 2017
<br />
<div style="line-height: normal; margin: 0px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; margin: 0px;">With today marking
the end of 2017, I thought I would provide an end-of-year update on my current
sabbatical. <a href="http://cognitionandreality.blogspot.ca/2017/08/sabbatical-report-end-of-month-1.html" target="_blank">I provided an update at the end of its first month on August 1</a>, and
have not provided much information since then. I have been too busy writing sabbatical
projects to take the time to add to this blog!</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; margin: 0px;">The primary task
for my sabbatical is working on a new book. This book explores the
probabilistic behavior of simple artificial neural networks with a combination
of citations to classic literature in information theory, probability theory,
and cybernetics, with the reports of many formal proofs about network behavior,
with detailed presentations of many new computer simulation results, and
(eventually) with the report of the results of some new experiments on human
probability matching.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; margin: 0px;">The book is taking
shape. Today – the last day of 2017 – marked the final tweaking of Chapters 4
and 5. So, the current status of the book is very solid drafts of its first
five chapters, amounting to 145 pages that hold 73421 words. The next chapter
requires me to scrape off the programming rust and write some new neural
network code, which hopefully will not take too long. Once the new code is in
place I will proceed with a new chapter on including positive feedback in a
learning algorithm, which will then lead into a chapter in which I present the
results of an experiment with human subjects that I conducted in September. I’ve
been at the University of Alberta for 30 years, and this study marked the first
time that I used the subject pool on my own!</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; margin: 0px;">The development of
the book so far has involved collecting data from hundreds of different
networks, not to mention reading a lot of new material. Since beginning this
project I have consumed 33 books, and have to read several more to write a
sensible version of Chapter 6.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; margin: 0px;">The book project is
the primary focus of my sabbatical. However, I have been very busy with another
project as well. I have had the good luck to collaborate with my colleague Cor
Baerveldt and his graduate students on the analysis of archival material
related to the Center of Advanced Study in Theoretical Psychology, which
existed at the University of Alberta from 1965 until 1990. We have been very
busy with this project; we have two articles currently under review at
different journals, and I have built a poster that goes with an abstract that I
have submitted to Cheiron. With luck I will be able to present some new
historical material when Cheiron holds its 50<sup>th</sup> annual meeting in
June at Akron, Ohio, the home of a huge archive of psychological material.</span></div>
<br />
<div style="margin: 0px 0px 10.66px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; line-height: 107%; margin: 0px;">In short, the sabbatical project is going well, and I am
hoping that 2018 is a happy and productive new year – not just for me, but for
anyone who has taken the time to read this post.</span></div>
<br />
<div style="margin: 0px 0px 10.66px;">
<span style="color: #222222; font-family: "&quot",serif; font-size: 10pt; line-height: 107%; margin: 0px;">Happy New Year!</span></div>
<b></b><i></i><u></u><sub></sub><sup></sup><strike></strike>Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-2818116465479719732017-09-17T20:24:00.000-06:002017-09-17T20:24:25.997-06:00Psychology at the Crossroads -- Again
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">I have a
growing interest in studying the history of psychology, particularly the
history of my own Department </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"><span style="margin: 0px;">(<a href="http://www.bcp.psych.ualberta.ca/research/pdfstuff/Dawson29.pdf" target="_blank">Dawson, 2013</a>)</span></span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">. One of the surprising
consequences of this work is that I sometimes find myself viewing current Departmental
problems in a historical context.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">For
example, one Departmental debate that arises every few months, and which has
reached very high levels of administration, concerns what Faculty the
Department of Psychology should be formally part of. We are in the almost
unique position of having official status in both the Faculty of Arts and the
Faculty of Science; this unique position has been the cause of considerable
angst over the past year and a half.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Interestingly,
a little bit of history and reading indicates how this unique situation came to
be. The Department of Psychology became an independent unit at the University
of Alberta in 1960, splitting away from Philosophy. Its first Head was Joseph
R. Royce; Royce was attracted to this position because the University of
Alberta promised resources for his expensive research on behavior genetics </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"><span style="margin: 0px;">(Royce, 1978)</span></span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">. Royce was still Head
when the Faculty of Arts and Science split into two separate faculties in 1963.
In other words, it was Royce who was largely responsible for Psychology keeping
a toehold in each faculty.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Why did a
behavior geneticist make this surprising administrative decision? Why did Royce
not break away from Arts? Royce had a diverse and far-reaching vision of the
discipline of psychology. For instance, he argued that it was a mistake to
accept the general definition of psychology being ‘the science of behavior’.
Instead, Royce believed that it was better to define psychology as ‘the study
of behavior’. Replacing ‘science’ with ‘study’ opened the possibility for
psychology to use a broader range of methodologies.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Royce’s broad
vision of the discipline was presented in a 1962 talk that became the opening
chapter in his book <i>Psychology and the symbol </i></span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"><span style="margin: 0px;">(Royce, 1965)</span></span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">. Its title was
“Psychology at the Crossroads between the Sciences and the Humanities”. For
Royce, this crossroads was <i style="mso-bidi-font-style: normal;">not</i> a
moment – unlike today -- of deciding to choose one direction or the other.
Instead, the crossroads was an <i style="mso-bidi-font-style: normal;">intersection</i>,
where psychology <i style="mso-bidi-font-style: normal;">necessarily</i> had to
integrate the methods of both the sciences and the humanities. Royce recognized
that psychology is “<i>both </i>scientific and humanistic, <i>both </i>experimental
and clinical”.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Given
this position, it is hardly surprising that Royce’s also saw that it was
necessary to attach the Department of Psychology to both the Faculty of Science
and the Faculty of Arts. This remarkable decision arose naturally from Royce’s
unique and broad vision. To me, it is clear that his goal was to offer the
Department of Psychology the potential to explore broader, interdisciplinary
initiatives than would be possible in a department with a more traditional
organization.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Recently,
administrators seem to have lost sight of this possibility, focusing only on
the complications that our unique structure produces. My own hope is that my
Department is given an opportunity to stop viewing its current structure as problematic,
and instead uses its advantages to become the kind of department that Royce
imagined as its first Head. A Department that did so would be an exciting one
to be a part of, and could bring some unique opportunities to the University at
large. </span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"> </span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"><u>References </u></span></div>
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Dawson, M.R.W. (2013).
A case study in Gantt charts as historiophoty: A Century of Psychology at the
University of Alberta. <i style="mso-bidi-font-style: normal;">History of
Psychology, 16</i>(2), 145-157.</span></div>
<div style="margin: 0px 0px 0px 48px; text-indent: -0.5in;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Royce, J.R. (1965). <i style="mso-bidi-font-style: normal;">Psychology and the Symbol</i>. New York:
Random House.</span></div>
<div style="margin: 0px 0px 0px 48px; text-indent: -0.5in;">
<span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;"></span><span style="font-family: "Arial",sans-serif; font-size: 12pt; margin: 0px;">Royce, J.R. (1978). The
life style of a theory-oriented generalist in a time of empirical specialists.
In T. S. Krawiec (Ed.), <i style="mso-bidi-font-style: normal;">The Psychologists</i>
(pp. 222-259). New York: Oxford University Press.</span></div>
<br />
<div style="line-height: normal; margin: 0px;">
<br /></div>
<b></b><i></i><u></u><sub></sub><sup></sup><strike></strike>Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-66761305553380698202017-08-01T15:32:00.000-06:002017-08-01T15:38:20.618-06:00Sabbatical Report: End of Month 1<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">Today marks the end of the first month of my current year-long
sabbatical. I thought that this was as good a time as any to reflect on what I
have accomplished so far, and to consider where my research is heading.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">While the sabbatical is only officially one month old, the stage for
the project was set in the fall term of 2016. In order to be fortunate enough to
be awarded a sabbatical, one must apply for it, and part of this application
involves proposing the kind of work that will be accomplished during the
sabbatical. I have a long history of writing a book during each year-long
sabbatical that I have been awarded; the plan for the current sabbatical was no
different. I proposed using the time to draft a manuscript that extended some
recent work in my lab on simple artificial neural networks and probability
theory, and was lucky enough to be given the green light for this kind of
project from the Faculty of Arts.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">With a sabbatical plan required in the fall, it is not surprising that
I was in a position to start groundwork for the current sabbatical at the end
of the fall term. Much of that work has involved doing a lot of reading – since
marking the final exam for my fall cognitive science course, I have read 23
books on systems theory, cybernetics, information theory, and probability.
Those interested can see what I have been reading by looking through my Instagram
account (<a href="https://www.instagram.com/drmrwdawson/">https://www.instagram.com/drmrwdawson/</a>)
for pictures of covers. I use #reading to tag these posts. I have also
conducted a pretty extensive simulation study (which has involved training and
analyzing the performance of 500 different perceptrons) that explores how
networks match the probability of outcomes in a three-cue probability learning
task. In the fall, I plan to collect data from human subjects that are trained
on the same task that I have used to train the networks; I am pretty excited
about the main result that I expect to observe when networks and humans are
compared. This has meant that I have also written programs to collect this data
from humans. Importantly, I have also successfully navigated the process for
getting ethics approval for this work; I haven’t collected human data for years.
Most importantly, I have already crafted three complete chapters of a new book
manuscript (when published, it will be my eighth book) that relate networks to
probability theory and information theory, that explore the relationship
between simple networks and Bayes’ theorem in probability, and that report the
results of my simulations.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<span style="line-height: 107%;"><span style="font-family: "arial" , "helvetica" , sans-serif;">As August begins, the sabbatical project turns
to writing the opening chapter of the new book. I have enough of a ‘feel’ for
the project now that I need to put it in the context of other theories, and
need to lay out its purpose, methodology, and implications. Writing this
chapter, though, requires me to do a lot more reading than I have been doing.
Up to this point, I have been reading a book every 10 days or so, and I have to
accelerate this. In short, currently my next steps are to read, to think, and
eventually to write. Some sense of the different topics that I will be
considering will be appearing in the near future as Instagrammed book covers.</span></span>Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-57308674043855515332017-01-30T13:25:00.000-07:002017-01-30T13:25:09.338-07:00The Embodiment of Books<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">When
thinking about books, we usually focus on their content, and not on their
physical structure. However, the actual layout of a book is sometimes just as
important as the meanings of the words one finds on its pages.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">One
notable example of this is the incredible novel <i>House of Leaves</i> </span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Danielewski</Author><Year>2000</Year><RecNum>7375</RecNum><DisplayText>(Danielewski,
2000)</DisplayText><record><rec-number>7375</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza"
timestamp="1485806591">7375</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Danielewski,
Mark Z.</author></authors></contributors><titles><title>House
of leaves</title></titles><pages>xxiii, 709
p.</pages><edition>2nd</edition><dates><year>2000</year></dates><pub-location>New
York</pub-location><publisher>Pantheon
Books</publisher><isbn>0375420525 (hc)&#xD;0375410341
(hc/signed)&#xD;9781417709045&#xD;0375703764
(pbk.)</isbn><accession-num>1686650</accession-num><call-num>PS3554.A5596
H68 2000</call-num><urls><related-urls><url>Contributor
biographical information http://www.loc.gov/catdir/bios/random059/99036024.html</url><url>Publisher
description
http://www.loc.gov/catdir/description/random047/99036024.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">(Danielewski, 2000)</span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-end'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">. In many instances the pages of this book contains only a
few words, arranged in peculiar ways to mirror events occurring in the novel.
You haven’t experienced reading about a chase until you do so in this book,
flipping rapidly to the next page during a pursuit, so that the frequency of
moving to the next page reflects the increasing action unfolding in the plot.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">A nice
scholarly example of an interesting embodiment is <i>The Society of Mind</i> </span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Minsky</Author><Year>1985</Year><RecNum>449</RecNum><DisplayText>(Minsky,
1985)</DisplayText><record><rec-number>449</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza"
timestamp="0">449</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Minsky,
M.L.</author></authors></contributors><titles><title>The
Society Of Mind</title></titles><dates><year>1985</year></dates><pub-location>
New York</pub-location><publisher> Simon &amp; Schuster</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">(Minsky, 1985)</span><!--[if supportFields]><span style='font-size:
12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:field-end'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">. This book explores
the idea of cognition emerging from the interactions of numerous simple agents.
It is laid out in such a way that each chapter takes up a single page. This
encourages the reader to interpret each chapter as a simple agent, and to
consider interacting messages from chapters as delivering the rich message of
the book. I was so taken by this sort of embodiment that I drafted two whole
book manuscripts in this format </span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Dawson</Author><Year>2010</Year><RecNum>3724</RecNum><DisplayText>(Dawson,
2008; Dawson, Dupuis, &amp; Wilson, 2010)</DisplayText><record><rec-number>3724</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza"
timestamp="1272386066">3724</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Dawson,
M.R.W.</author><author>Dupuis, B.</author><author>Wilson,
M.</author></authors></contributors><titles><title>From
Bricks To Brains: The Embodied Cognitive Science Of LEGO
Robots</title></titles><dates><year>2010</year></dates><pub-location>Edmonton,
AB</pub-location><publisher>Athabasca University Press</publisher><urls><pdf-urls><url>file://F:\Reprints\D\Dawson24.pdf</url></pdf-urls></urls></record></Cite><Cite><Author>Dawson</Author><Year>2008</Year><RecNum>2131</RecNum><record><rec-number>2131</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza"
timestamp="0">2131</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Dawson,
M.R.W.</author></authors></contributors><titles><title>Connectionism
and classical conditioning</title><secondary-title>Comparative
Cognition and Behavior
Reviews</secondary-title></titles><periodical><full-title>Comparative
Cognition and Behavior
Reviews</full-title></periodical><pages>1-115</pages><volume>3
(Monograph)</volume><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">(Dawson, 2008; Dawson, Dupuis, & Wilson, 2010)</span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-end'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">. You start to write amazingly concisely when every page
has to deliver a standalone message!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">I’m
thinking about books and embodiment because I’ve just finished reading one of
the visionary books of embodied cognitive science, the influential <i>The Tree of Knowledge</i> </span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Maturana</Author><Year>1998</Year><RecNum>1335</RecNum><DisplayText>(Maturana
&amp; Varela, 1998)</DisplayText><record><rec-number>1335</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza"
timestamp="0">1335</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Maturana,
H.R.</author><author>Varela, F.J.</author></authors></contributors><titles><title>The
Tree of Knowledge</title></titles><dates><year>1998</year></dates><pub-location>Boston,
MA</pub-location><publisher>Shambhala</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">(Maturana & Varela, 1998)</span><!--[if supportFields]><span
style='font-size:12.0pt;font-family:"Arial",sans-serif'><span style='mso-element:
field-end'></span></span><![endif]--><span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">. This books provides a strong anti-representational view
of cognition, arguing instead that cognition emerges from the linked
relationships between self-organizing systems and the environments that they
act upon. What is amazing about The Tree of Knowledge is that it is laid out as
an introductory text, with a small single column of text on most pages, as well
as numerous definition boxes and figures. In keeping with this format, the book
is written in a disarmingly elementary style, even as it provides a complex and
novel view of cognition that is quite distinct from typical perspectives. That
is, the book is easy to read – but challenging to understand!<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;">Maturana
and Varela clearly had to work very hard to carry out this particular style of
writing and of presenting ideas. The afterword indicates that the book itself
was a decade in the making.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-family: "Arial",sans-serif; font-size: 12.0pt;"><b><u>References</u></b><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt;">
<br /></div>
<div class="EndNoteBibliography" style="margin: 0in 0in 0.0001pt 0.5in; text-indent: -0.5in;">
Danielewski, M.
Z. (2000). <i>House of leaves</i> (2nd ed.).
New York: Pantheon Books.<o:p></o:p></div>
<div class="EndNoteBibliography" style="margin: 0in 0in 0.0001pt 0.5in; text-indent: -0.5in;">
Dawson, M. R. W.
(2008). Connectionism and classical conditioning. <i>Comparative Cognition and Behavior Reviews, 3 (Monograph)</i>, 1-115. <o:p></o:p></div>
<div class="EndNoteBibliography" style="margin: 0in 0in 0.0001pt 0.5in; text-indent: -0.5in;">
Dawson, M. R. W.,
Dupuis, B., & Wilson, M. (2010). <i>From
Bricks To Brains: The Embodied Cognitive Science Of LEGO Robots</i>. Edmonton,
AB: Athabasca University Press.<o:p></o:p></div>
<div class="EndNoteBibliography" style="margin: 0in 0in 0.0001pt 0.5in; text-indent: -0.5in;">
Maturana, H. R.,
& Varela, F. J. (1998). <i>The Tree of
Knowledge</i>. Boston, MA: Shambhala.<o:p></o:p></div>
<div class="EndNoteBibliography" style="margin-left: 0.5in; text-indent: -0.5in;">
Minsky,
M. L. (1985). <i>The Society Of Mind</i>.
New York: Simon & Schuster.</div>
<!--[if supportFields]><span style='font-size:12.0pt;line-height:107%;
font-family:"Arial",sans-serif;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
minor-latin;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:
AR-SA'><span style='mso-element:field-end'></span></span><![endif]--><br />
<div class="EndNoteBibliography" style="margin-left: .5in; text-indent: -.5in;">
<o:p></o:p></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com1tag:blogger.com,1999:blog-7699616724222495854.post-62707701951533855472017-01-01T10:29:00.000-07:002017-01-01T10:32:27.944-07:00Science in the Service of Humanity<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">As part of an ongoing history project, I have been reading a great deal
about general systems theory and about cybernetics. Much of this reading began
with some of the major works of Ludvig von Bertalanffy (</span><i style="mso-bidi-font-style: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Problems of Life</span></i><span style="font-family: "arial" , "helvetica" , sans-serif;">, </span><i style="mso-bidi-font-style: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">General
System Theory</span></i><span style="font-family: "arial" , "helvetica" , sans-serif;">, </span><i style="mso-bidi-font-style: normal;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Robots Men and Minds</span></i><span style="font-family: "arial" , "helvetica" , sans-serif;">).
It has also included some biographical works about von Bertalanffy, as well as
of other scholars involved in systems thinking and cybernetics. I have also pulled
from the shelves of my library some classic works by Norbert Weiner and Gregory
Bateson and placed them on the front burner.</span></div>
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "calibri";"><span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br /></span></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">One of the striking characteristics of von Bertalanffy’s writing is his
emphasis on human values. Von Bertalanffy spent his career reacting against
mechanistic views in science, and proposing an organismic alternative. One of
his great concerns was that the mechanistic view of nature and of man
deemphasized humans as individuals, and viewed them instead as cogs in a great
machine. From his perspective, this led to many of the dark social and
political moments of the 20</span><sup><span style="font-family: "arial" , "helvetica" , sans-serif; font-size: x-small;">th</span></sup><span style="font-family: "arial" , "helvetica" , sans-serif;"> century. One Bertalanffy was
particularly critical of Weiner’s cybernetics for exactly this reason; he
viewed cybernetics as turning men into robots and leading the society into
peril by advancing military technology. In contrast, von Bertalanffy was one of
the founders (along with Kenneth Boulding, Anatol Rapaport, and Ralph Gerard)
of the Society for General Systems Research. They planted the seed for this
society in 1955 at the Center for Advanced Study in Behavioral Science. SGSR’s
initial slogan was “Science in service of humanity”.</span><br />
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">In the context of this slogan, von Bertalanffy’s criticism of the
Weiner’s mechanized cybernetics misses the mark. Weiner himself had deep
concerns about cybernetics’ technological impact on society and expressed these
concerns in many of his writings. Similar concerns are easily found in </span><span style="font-family: "arial" , "helvetica" , sans-serif;">the
writings of other cybernetic leaders such as Bateson and Margaret Mead; in
general, the cybernetic pioneers were actively sympathetic with the notion of
applying their scholarly ideas for the betterment of society.</span></div>
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br /></div>
<span style="font-family: "arial" , "helvetica" , sans-serif;">What strikes me as I read the optimistic values and goals of these
eminent researchers; as I see their deep concerns about the relationship
between science and the good of mankind; as I reflect upon their explicit goal
of improving humanity through their scientific ideas, is this: half a century
later all of these concerns seem missing from much of modern science. Nowadays
it seems that science is replaced these noble social concerns with goals of developing
products or commodities, or with solving specific problems that have been
identified by government agencies as requiring particular attention.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "arial" , "helvetica" , sans-serif;"></span><br /></span>
<br />
<div style="line-height: normal; margin: 0px;">
<span style="font-family: "arial" , "helvetica" , sans-serif;">“Science in the service of humanity” strikes me as a particularly powerful
notion, and on this first day of 2017 I resolve to explore its implementation
in my own scholarly activities.</span></div>
<b></b><i></i><u></u><sub></sub><sup></sup><strike></strike>Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-61006938108071091772015-10-09T21:12:00.000-06:002015-10-09T21:13:46.302-06:00A 'Strange Circles' Ukulele Exercise<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">In my lab
we train artificial neural networks to solve musical problems, and then examine
the structures of these networks to see how they work.<span style="mso-spacerun: yes;"> </span>Usually we do this to make discoveries about
music theory and musical cognition.<span style="mso-spacerun: yes;"> </span>However,
sometimes we stumble onto something more practical – like new ideas for exploring
chord progressions along the fretboard of a ukulele.<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">In an
earlier project </span><a href="http://cognitionandreality.blogspot.ca/2013/06/strange-circles-that-map-coltrane.html"><span style="color: blue; font-family: Arial;">we
trained a network to learn the Coltrane changes</span></a><span style="font-family: Arial;">, which is an important
progression of jazz chords.<span style="mso-spacerun: yes;"> </span>Inside this
network we discovered an interesting map, presented below, that leads from the
root note of one chord to the root note of the next.<o:p></o:p></span></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha6OvYiDVgTjth8W8ozwcgCbQtnhBBGnLEYhRG02hZ6RRqFDSQyoDIaW6vHGVom3EA2qqUQaMmBlDc3OvukSthDHxZMcwYoXHZujKNlQW-6MMlhWqCfi54W1S5qk76l-BmnbHCD0JY0w0/s1600/JoshWheel.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha6OvYiDVgTjth8W8ozwcgCbQtnhBBGnLEYhRG02hZ6RRqFDSQyoDIaW6vHGVom3EA2qqUQaMmBlDc3OvukSthDHxZMcwYoXHZujKNlQW-6MMlhWqCfi54W1S5qk76l-BmnbHCD0JY0w0/s320/JoshWheel.jpg" width="309" /></a></div>
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">The map
above has one intriguing property: its outer and inner rings of notes are
examples of what we call </span><a href="http://cognitionandreality.blogspot.ca/2015/03/strange-circles.html"><span style="color: blue; font-family: Arial;">strange
circles</span></a><span style="font-family: Arial;">.<span style="mso-spacerun: yes;"> </span>Each of these rings is a
circle of major seconds; neighboring pitch classes on the ring are a major
second, or two semitones, apart.<span style="mso-spacerun: yes;"> </span>For
instance, A is a major second away from both B and G (the outer ring), while D
is a major second away from both C and E (the inner ring).<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">One day the
map above happened to be drawn on the chalkboard when I was in the lab with my
ukulele in hand.<span style="mso-spacerun: yes;"> </span>I was noodling some
minor chords, and was pleased by the sound of moving from D minor to A
minor.<span style="mso-spacerun: yes;"> </span>As I played these two chords, I looked
at the map on the board, and noticed how it lined up these two notes.<span style="mso-spacerun: yes;"> </span>Intrigued, I played other combinations of
chords – for instance C minor and G minor – whose root notes were in similar
relationships in the map.<span style="mso-spacerun: yes;"> </span>They too were
pleasing.<span style="mso-spacerun: yes;"> </span>I then realized that a slight modified
map would produce a new picture that I could use to guide me through a progression
of twelve different chords.<span style="mso-spacerun: yes;"> </span>I drew the
map, played its succession of chords, and I really liked the sound of the
entire progression.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">I created
this new map by rotating the inner ring of notes to a different position, so
that D was aligned with A, C was aligned with G, and so on.<span style="mso-spacerun: yes;"> </span>The new map that I created is given below:<o:p></o:p></span></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9bvUaN4CSHQzDFRwUpYOgqrAEx47LVRLiQT6BhSCHe78VmbR6Xv0GFmUBSWjFugla5z15QE8x4HmdYSPBvVNjzNNWMNxafic6VQ0RpzNIbcmDcGsw2-e5NSH2UAbHuK9b1QLHkh24tis/s1600/ProgressionWheel1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="303" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9bvUaN4CSHQzDFRwUpYOgqrAEx47LVRLiQT6BhSCHe78VmbR6Xv0GFmUBSWjFugla5z15QE8x4HmdYSPBvVNjzNNWMNxafic6VQ0RpzNIbcmDcGsw2-e5NSH2UAbHuK9b1QLHkh24tis/s320/ProgressionWheel1.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">The arrows
on the map indicate how I use it to move from chord to chord.<span style="mso-spacerun: yes;"> </span>Let’s say I start with a D chord.<span style="mso-spacerun: yes;"> </span>The black arrow indicates that next an A
chord will be played.<span style="mso-spacerun: yes;"> </span>The grey arrow
shows that I next move counterclockwise to the second pair of chord roots,
beginning with the inner ring (playing a C chord) and then moving to the outer
ring (playing a G chord).<span style="mso-spacerun: yes;"> </span>I continue
this pattern moving around the map, eventually returning to where I started, at
the ‘D’ location of the inner ring.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">One example
of following this pattern is provided in the score below.<span style="mso-spacerun: yes;"> </span>This particular example plays major seventh
chords at each map position, which has (to my ear at least) a pleasing, jazzy
sound.<span style="mso-spacerun: yes;"> </span>The score uses ‘closed form
chords’, which involve pressing a finger down on each ukulele string.<span style="mso-spacerun: yes;"> </span>So playing this score is an exercise in
moving a closed form shape up and down the length of the fretboard.<span style="mso-spacerun: yes;"> </span>The Cmaj7 chord is formed at the very top of
the fretboard, while the Bmaj7 is formed with the index finger barred across
the 11<sup>th</sup> fret near the fretboard’s bottom.<span style="mso-spacerun: yes;"> </span>So, by following the new map one can perform
a progression of chords that 1) uses each of the 12 possible roots in Western
music, and 2) does so by covering the majority of the fretboard’s geometry.<o:p></o:p></span></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTBeGUsJtWruqDHr_yFvloqUXOp9ZwgmAha_TGWUb7Rdc1WZfKYYrBXPle2MRIBIQt_MsvUd5P-EJ2kBFhBrhWdnFIjekOqDNeGK_8AVRGZhCEWBt2sFHEznVU-AhvLWfL4kKa6rj7LCc/s1600/Maj7Score.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="229" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTBeGUsJtWruqDHr_yFvloqUXOp9ZwgmAha_TGWUb7Rdc1WZfKYYrBXPle2MRIBIQt_MsvUd5P-EJ2kBFhBrhWdnFIjekOqDNeGK_8AVRGZhCEWBt2sFHEznVU-AhvLWfL4kKa6rj7LCc/s320/Maj7Score.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<!--[if gte vml 1]><v:shape
id="Picture_x0020_3" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
height:336pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image005.jpg"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;"></span></span><br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">The score
above offers just a hint of the potential for using the map.<span style="mso-spacerun: yes;"> </span>Simple variations of the score involve
replacing the major seventh chords with some other closed forms, such as the
minor seventh (or major sixth), the dominant seventh, or the major.<span style="mso-spacerun: yes;"> </span>Of course, one could then use different chord
types at different points in the score.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Another
approach to varying the sound of the progression would be to follow a different
route on the map – for instance going from the inner ring to the outer ring for
the first pair of chords, but then going from the outer ring to the inner ring
for the following pair of chords.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Another
interesting approach would be to follow the same paths that are illustrated
above, but to rotate the inner ring to a different position inside the outer
one.<span style="mso-spacerun: yes;"> </span>For example, one clockwise twist of
the inner ring would line up the D with the B, the C with the A, and so
on.<span style="mso-spacerun: yes;"> </span>Changing the position of the inner
ring would change the musical distance between successive chords, and as a
result change the musicality of the progression.<o:p></o:p></span></span></div>
<br />Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-62482876440321860852015-07-01T09:45:00.001-06:002015-07-01T09:45:04.584-06:00History, Psychology, and Poster Philosophy
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">In a few
days my wife and I head to Angers, France to participate in the meeting of the
European Society for the History of the Human Sciences (</span><a href="http://www.eshhs.eu/wordpress-3.3.1/wordpress/"><span style="color: blue; font-family: Arial;">ESHHS</span></a><span style="font-family: Arial;">).<span style="mso-spacerun: yes;"> </span>She is one of the speakers in a symposium
about the recent controversy concerning the identity of Watson’s ‘Little Albert’,
while I am presenting a poster that uses Gantt charts to explore the history of
the Department of Psychology at the University of Alberta.<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">I do not
participate in many conferences, but these days when I go to a conference I
like to present a poster instead of a talk.<span style="mso-spacerun: yes;">
</span>The reason: I prefer to have conversations about research; posters facilitate
this while talks do not.<span style="mso-spacerun: yes;"> </span>But how does
one maximize the ability of a poster to initiate conversations?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">My answer
to this question is to design posters that have as few words as possible – a poster
that is almost exclusively a collection of images.<span style="mso-spacerun: yes;"> </span>Minimizing the number of words on a poster
reduces the likelihood that someone will simply come up to the poster, read it,
and move on without talking.<span style="mso-spacerun: yes;"> </span>Remove the
poster’s words; you force your audience to ask you what the poster is about –
which starts a conversation.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">My ESHHS contribution,
‘Using Gantt Charts To Explore The History Of A Canadian Psychology Department’,
is one that fully reflects my poster philosophy.<span style="mso-spacerun: yes;"> </span>It consists of 14 graphs; the only text on
the poster is its title and the various graph labels.<span style="mso-spacerun: yes;"> </span>Most of the graphs are Gantt charts like the
one described </span><a href="http://cognitionandreality.blogspot.ca/2015/06/university-of-alberta-cognition-late.html"><span style="color: blue; font-family: Arial;">in
this previous post</span></a><span style="font-family: Arial;">.<span style="mso-spacerun: yes;"> </span>Two of these
Gantt charts are gigantic – they provide the timelines for each faculty member,
or for each course offering, throughout over a century of the Department’s
history – and all of the others are derived from these two major plots.<span style="mso-spacerun: yes;"> </span>It is more of an art piece than a typical
scientific presentation. I really like the look of it, I think that it is my most striking poster ever.</span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">If you are
interested, an 11 mb version of the whole poster </span><a href="http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/ESHHS/SmallESHHS.pdf"><span style="color: blue; font-family: Arial;">can
be viewed as this PDF file</span></a><span style="font-family: Arial;">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">I like
several things about this poster, which has been ‘test driven’ over the last
couple of weeks near the main office of my Department.<span style="mso-spacerun: yes;"> </span>First, as you get closer and closer to it,
you realize that it contains a lot of information.<span style="mso-spacerun: yes;"> </span>It really draws you in.<span style="mso-spacerun: yes;"> </span>Second, the graphs are unfamiliar – Gantt charts
are not typically seen in this field.<span style="mso-spacerun: yes;"> </span>As
a result, the poster demands questions, such as 'What do these graphs show?'.<span style="mso-spacerun: yes;">
</span>On July 7 I will find out how many questions it draws out!<o:p></o:p></span></span></div>
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial;"> </span></o:p></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-90199094257894624592015-06-13T13:38:00.000-06:002015-06-13T13:38:05.293-06:00University of Alberta Cognition: Late – and Early!
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">Over the
last couple of weeks I have visited the University of Alberta Archives to pore
over their copies of past Calendars.<span style="mso-spacerun: yes;"> </span>As
part of a history project that I am presenting at the European Society for the
History of the Human Sciences (</span><a href="http://www.eshhs.eu/wordpress-3.3.1/wordpress/"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">ESHHS</span></a><span style="font-family: Arial, Helvetica, sans-serif;">) next month I
have compiled the course offering for Psychology from 1909 to 2015.<span style="mso-spacerun: yes;"> </span>This list is composed of 5089 separate
entries, which might explain why my eyes are tired and my typing fingers are
aching.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">The point
of collecting this data is to illustrate it (and later analyze it) using Gantt
charts; </span><a href="http://www.bcp.psych.ualberta.ca/research/pdfstuff/Dawson29.pdf"><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">a
previous project</span></a><span style="font-family: Arial, Helvetica, sans-serif;"> took this approach to illustrate the various faculty
members who have belonged to the Department in its existence for more than a
century.<span style="mso-spacerun: yes;"> </span>The previous project was pretty
laborious; this time around I have been able to automate a lot of it using
Excel (and VBA) to organize the data to provide to R (and the Plotrix package)
for plotting as a Gantt chart.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">This
approach can be used to provide some interesting insights into Departmental
course offerings.<span style="mso-spacerun: yes;"> </span>For instance, the
figure below provides the Gantt chart of just those courses related to modern
cognitivism:<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUwVLQIZxeB9VbMAzQWnLTCb9E6kdfQjwb4U1hAjKChh_-rMUR8nOwphNfsKk2iv_vXpFlb7yLoLeg5DEB83qhNIjb6wH5AecRoVrGM1lmP8tAyy8eIIOrd3lQwTmY8pi6JIOfuktONLY/s1600/CogGantt.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUwVLQIZxeB9VbMAzQWnLTCb9E6kdfQjwb4U1hAjKChh_-rMUR8nOwphNfsKk2iv_vXpFlb7yLoLeg5DEB83qhNIjb6wH5AecRoVrGM1lmP8tAyy8eIIOrd3lQwTmY8pi6JIOfuktONLY/s320/CogGantt.jpg" width="312" /></span></a></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p> </o:p></span><span lang="EN-US" style="mso-ansi-language: EN-US;">Examining
the Gantt chart above indicates that cognitivism arrived at the University of
Alberta in the late 1960s.<span style="mso-spacerun: yes;"> </span>The first
offering, “Topics in Cognition”, appeared in the Calendar for 1968-69.<span style="mso-spacerun: yes;"> </span>The Department’s first hiring of an ‘official’
cognitive psychologist was in 1979 when they recruited Alinda Friedman, who has
just retired after becoming the longest serving female faculty member in
Department history.<span style="mso-spacerun: yes;"> </span>Given that cognitivism
arose in the mid to late 1950s, it seems that University of Alberta was a
pretty late entrant into the cognitivist movement!<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">Interestingly,
though, this story is incomplete.<span style="mso-spacerun: yes;"> </span>One of
the earlier courses offered by the Department was ‘Legal Psychology (Psychology
56)’, which appeared in the 1922-23 Calendar, and was last offered in 1939-40.<span style="mso-spacerun: yes;"> </span>When it first appeared in the Calendar it was
described as a course about “normal and abnormal mental processes in relation
to problems of judicial procedure”, and explored topics like motivation of
crime, the discovery of guilt, mental deficiency and insanity, and
individualization of punishment.<span style="mso-spacerun: yes;"> </span>This
Calendar description was pretty much unchanged from the creation of this course
through the 1930-31 Calendar.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">However,
the Calendar description of Legal Psychology changed markedly in the 1931-32
Calendar, as the image below demonstrates.<span style="mso-spacerun: yes;">
</span>The description is split into two parts, with the second one being very
similar to the older entries.<span style="mso-spacerun: yes;"> </span>However, the
new first part is explicitly cognitive in nature: it includes the phrase “cognitive
processes”, and focuses on perception, memory, and problems arising in both of
these subtopics.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPfeufwy2GW_MtVCFjwunaCCazbZ-WLBw_1IpFPx02lNoqCwJHAG_PEyNwhxQwuuaaR_OtlhhqOgMqonWDgkPRRKjb4MnQSsFrnPIBtQ0GBCX9TyVKOZ0DdxgHbMbp7ZVSueKHym4DIh0/s1600/LegalPsych1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPfeufwy2GW_MtVCFjwunaCCazbZ-WLBw_1IpFPx02lNoqCwJHAG_PEyNwhxQwuuaaR_OtlhhqOgMqonWDgkPRRKjb4MnQSsFrnPIBtQ0GBCX9TyVKOZ0DdxgHbMbp7ZVSueKHym4DIh0/s320/LegalPsych1.jpg" width="320" /></span></a></div>
</o:p></span><span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p> </o:p></span><span lang="EN-US" style="mso-ansi-language: EN-US;">Two things
interest me about this new description of Legal Psychology.<span style="mso-spacerun: yes;"> </span>The first is that it demonstrates a very
early arrival of cognitivism at the University of Alberta.<span style="mso-spacerun: yes;"> </span>This course description is about a quarter of
a century earlier than the cognitive revolution!<span style="mso-spacerun: yes;"> </span>The second is that I cannot determine any
reason for this particular change.<span style="mso-spacerun: yes;"> </span>For
instance, there were no new faculty members in the Department whose arrival
would have led to such a change.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial, Helvetica, sans-serif;">In short,
modern cognitivism arose late at the University of Alberta, although the Gantt
chart provided above indicates that it is still healthy.<span style="mso-spacerun: yes;"> </span>It was preceded, however, by a course in
Legal Psychology that was over a quarter of a century ahead of its time.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
</div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-28390006502138360432015-06-03T08:01:00.000-06:002015-06-03T08:01:19.610-06:00On Books and BS
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">This blog
isn’t about the usual BS that my students might associate with my books –
instead it is about the kind that affects my book production: blood sugar.<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">I have been
coping with Type II diabetes since the turn of the millennium, and my control
of my blood sugar levels has been sketchy at times.<span style="mso-spacerun: yes;"> </span>When I was first diagnosed I became
well-versed in typical diabetes-related problems (kidney trouble, heart
trouble, eye trouble, infections and amputations).<span style="mso-spacerun: yes;"> </span>However, during one period in which my blood
sugar was out of control I discovered another issue while reading the
literature at my specialist’s office.<span style="mso-spacerun: yes;">
</span>Apparently </span><a href="https://uwaterloo.ca/news/news/type-2-diabetes-linked-worse-performance-cognitive-testing"><span style="color: blue; font-family: Arial;">there
are a host of cognitive deficits</span></a><span style="font-family: Arial;"> that can occur with high blood sugar
levels too.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">More
recently I encountered this problem first hand.<span style="mso-spacerun: yes;">
</span>During the fall of 2013 and the winter of 2014 I was having a great deal
of trouble concentrating.<span style="mso-spacerun: yes;"> </span>I was working
with an undergraduate student on an artificial neural networks and music
project that required interpreting the internal structure of trained networks.<span style="mso-spacerun: yes;"> </span>I was having a lot of difficulty making any
sense of any of these networks.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Not
coincidentally – although I did not realize this until later – my blood sugar
had entered a phase that required stronger control.<span style="mso-spacerun: yes;"> </span>At that time I used oral medications and an
evening injection of slow acting insulin.<span style="mso-spacerun: yes;">
</span>A visit to my specialist resulted in a new regime of pre-meal injections
of fast acting insulin.<span style="mso-spacerun: yes;"> </span>I started this
treatment in the first week of April 2014.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">What
astonished me is that within a week it seemed as if my brain suddenly turned
on.<span style="mso-spacerun: yes;"> </span>I found that my ability to
concentrate was stronger and my thinking was clearer.<span style="mso-spacerun: yes;"> </span>On April 9, 2014 I took a look at the
connection weights of a simple network that was resisting analysis, and
immediately saw how the network worked.<span style="mso-spacerun: yes;">
</span>I couldn’t believe it.<span style="mso-spacerun: yes;"> </span>I started
writing the interpretation up on April 11, in what became the first chapter of
a new book.<span style="mso-spacerun: yes;"> </span>For about a year up to that
point I had a lot of difficulty writing.<span style="mso-spacerun: yes;">
</span>After starting the new insulin regime I was working and writing daily,
and a week ago submitted a new book manuscript comprised of over 300 pages, 150
figures, 50 tables, and a whole bunch of new simulation results and network
interpretations.<span style="mso-spacerun: yes;"> </span>I don’t think that this
would have happened without the change in my treatment.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Of course
this evidence is totally anecdotal, but I now have a lot more respect for how
my blood sugar control can affect what I’m paid to do (i.e. think).<span style="mso-spacerun: yes;"> </span>I’ll apologize in advance to my students, who
will likely find more of that other BS in my new book when it comes out! I have one kind of BS under control, but have never figured out how to control the other</span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;"><o:p></o:p></span></span> </div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-19281914683274971102015-05-25T16:55:00.002-06:002015-05-25T16:55:24.703-06:00Coda: Our New Music<em><span style="font-family: Arial, Helvetica, sans-serif;">As described </span></em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><em><span style="font-family: Arial, Helvetica, sans-serif;">in this previous post</span></em></a><em><span style="font-family: Arial, Helvetica, sans-serif;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks. This particular post is the Coda for the book; the interlude that comes at the end of the main text.</span></em><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD-xaVVRPunB8h8a3N4q_LSNMPv5efAQcYQbCJajJ4OYhZEwPOu5rgWr2eNYj2dfDazJOS4gABKAnsK7QY7Zw5LJ-nkJSRStvIKlVgvadV-SR3iJl9oLZZw2Os2RKO_YaZcgBSJe4mC_0/s1600/FigureC-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="37" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD-xaVVRPunB8h8a3N4q_LSNMPv5efAQcYQbCJajJ4OYhZEwPOu5rgWr2eNYj2dfDazJOS4gABKAnsK7QY7Zw5LJ-nkJSRStvIKlVgvadV-SR3iJl9oLZZw2Os2RKO_YaZcgBSJe4mC_0/s320/FigureC-1.jpg" width="320" /></a></span></div>
<br />
<div class="WordSection1">
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial, Helvetica, sans-serif;">Figure C-1. Four key notes for the song “How
Dry I Am” used by Bernstein to illustrate the infinite variety of music.<o:p></o:p></span></strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"></span></span><div clear="all" style="mso-break-type: section-break; page-break-before: always;">
<span style="font-family: Arial, Helvetica, sans-serif;">
</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">The tonality of Western music arises from
its exclusive use of twelve pitch-classes.<span style="mso-spacerun: yes;">
</span>In spite of being constrained by this sparse set of basic musical
elements, composer Leonard Bernstein argues that Western music is infinite in
its variety </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Bernstein</Author><Year>1966</Year><RecNum>6958</RecNum><DisplayText>(Bernstein,
1966)</DisplayText><record><rec-number>6958</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6958</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Bernstein,
L.</author></authors></contributors><titles><title>The
Infinite Variety of Music</title></titles><pages>286
p.</pages><keywords><keyword>Music
appreciation.</keyword><keyword>Orchestral music Analysis,
appreciation.</keyword></keywords><dates><year>1966</year></dates><pub-location>New
York</pub-location><publisher>Simon and
Schuster</publisher><accession-num>281021</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) MT6 .B43 1966&#xD;Performing Arts
Reading Rm (Madison, LM113) - STORED OFFSITE MT6 .B43
1966</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Bernstein, 1966 #6958"><span style="color: windowtext; text-decoration: none; text-underline: none;">Bernstein,
1966</span></a>)</span></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>He observes that if one considers the twelve
pitch-classes in a single range, and computes their possible melodic combinations,
the result is 1,302,061,344.<span style="mso-spacerun: yes;"> </span>If one
extends this approach to consider both melodic and harmonic combinations of these
elements the result is 127 googols, where a googol is a digit followed by 100
zeroes.<span style="mso-spacerun: yes;"> </span>“The realm of music is an
infinity into which the composer’s mind goes wandering” (Bernstein, 1966, p.
34).<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Bernstein (1966) explores this theme with a
particular example, the four note melody that starts the song “How Dry I Am”.<span style="mso-spacerun: yes;"> </span>These four notes are provided in Figure
C-1.<span style="mso-spacerun: yes;"> </span>He notes the importance of this
pattern, and the variations of musical effects that it can produce, by noting
its presence in a huge range of compositions that begins with a French folk
song and ends with the final movement of Shostakovich’s Fifth Symphony.<span style="mso-spacerun: yes;"> </span>Bernstein ends his discussion by proposing a
variation of Figure C-1 that depicts “a motto of man’s infinite variety”
(Bernstein, 1966, pp. 46-47).<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Early in this book we saw another example
of variety from small numbers of elements.<span style="mso-spacerun: yes;">
</span>The musical signal composed by John Williams for Steven Spielberg’s 1977
movie <i style="mso-bidi-font-style: normal;">Close Encounters of the Third Kind</i>
(Figure O-1) was selected from a sample of 350 five-note compositions created
by Williams.<span style="mso-spacerun: yes;"> </span>Had Williams composed all
possible five-note melodies the movie’s signal would have been selected from
among about 134,000 possibilities.<span style="mso-spacerun: yes;"> </span>The
calculation of possibilities is conservative because it fails to take into
account rhythmic variations; not all of the notes in Williams’ signal have the
same duration.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">The infinite possibilities of Western tonal
music are reflected in music’s constant evolution.<span style="mso-spacerun: yes;"> </span>American composer Aaron Copland wrote <i style="mso-bidi-font-style: normal;">Our New Music</i> </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Copland</Author><Year>1941</Year><RecNum>6911</RecNum><DisplayText>(Copland,
1941)</DisplayText><record><rec-number>6911</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6911</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Copland,
A.</author></authors></contributors><titles><title>Our
New Music: Leading Composers in Europe and
America</title></titles><pages>xiv, 305
p.</pages><keywords><keyword>Music 20th century History and
criticism.</keyword></keywords><dates><year>1941</year></dates><pub-location>New
York ; London</pub-location><publisher>Whittlesey House,
McGraw-Hill Book Company,
Inc.</publisher><accession-num>8787203</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) ML197.C76 O8&#xD;Performing Arts Reading
Rm (Madison, LM113) - STORED OFFSITE ML197.C76
O8</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Copland, 1941 #6911"><span style="color: windowtext; text-decoration: none; text-underline: none;">Copland, 1941</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> to explain the circumstances that had led to modern classical music.<span style="mso-spacerun: yes;"> </span>His goal was to alleviate his readers’ bewilderment
with modern music.<span style="mso-spacerun: yes;"> </span>“Being unaware of the
separate steps that brought about these revolutionary changes, they are
naturally at a loss to understand the end result” (Copland, 1941, p. v).<span style="mso-spacerun: yes;"> </span>He traced modern music’s development as a
move away from a century of Germanic musical influences.<span style="mso-spacerun: yes;"> </span>This move begins with explorations of folk
music in the late 19<span style="font-size: small;"><sup>th</sup> century, proceeds through explorations of new
views of harmony, rhythm, and tonality.<span style="mso-spacerun: yes;">
</span>Copland argues that it ends by coming full circle, in Stravinsky’s
compositions of the late 1920s and early 1930s, and returning to melodic forms
from the 18<sup>th</sup> century.<o:p></o:p></span></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">The infinite possibilities of Western tonal
music make it nearly impossible to predict its future too.<span style="mso-spacerun: yes;"> </span>In the early 1940s one could analyze existing
modern music and describe a neoclassicism that had roots in the 18<span style="font-size: small;"><sup>th</sup>
century </span></span><!--[if supportFields]><span lang=EN-US><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Copland</Author><Year>1941</Year><RecNum>6911</RecNum><DisplayText>(Copland,
1941)</DisplayText><record><rec-number>6911</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6911</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Copland,
A.</author></authors></contributors><titles><title>Our
New Music: Leading Composers in Europe and America</title></titles><pages>xiv,
305 p.</pages><keywords><keyword>Music 20th century History
and
criticism.</keyword></keywords><dates><year>1941</year></dates><pub-location>New
York ; London</pub-location><publisher>Whittlesey House,
McGraw-Hill Book Company, Inc.</publisher><accession-num>8787203</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) ML197.C76 O8&#xD;Performing Arts Reading
Rm (Madison, LM113) - STORED OFFSITE ML197.C76 O8</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Copland, 1941 #6911"><span style="color: windowtext; text-decoration: none; text-underline: none;">Copland, 1941</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>However, Copland’s analysis
of modern American music does not even hint of the radical developments that
would flourish there beginning in the 1960s with, for example, the invention of
mimimalism </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Glass, 1987 #2437"><span style="color: windowtext; text-decoration: none; text-underline: none;">Glass, 1987</span></a>;
<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Griffiths, 1994 #2363"><span style="color: windowtext; text-decoration: none; text-underline: none;">Griffiths, 1994</span></a>, <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Griffiths, 1995 #2142"><span style="color: windowtext; text-decoration: none; text-underline: none;">1995</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Hartog, 1957 #2460"><span style="color: windowtext; text-decoration: none; text-underline: none;">Hartog, 1957</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Nyman, 1999 #2404"><span style="color: windowtext; text-decoration: none; text-underline: none;">Nyman, 1999</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Pleasants, 1955 #2435"><span style="color: windowtext; text-decoration: none; text-underline: none;">Pleasants, 1955</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Potter, 2000 #2244"><span style="color: windowtext; text-decoration: none; text-underline: none;">Potter, 2000</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Reich, 1974 #1941"><span style="color: windowtext; text-decoration: none; text-underline: none;">Reich, 1974</span></a>, <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Reich, 2002 #2442"><span style="color: windowtext; text-decoration: none; text-underline: none;">2002</span></a>)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Western tonal music has infinite variety
and unpredictability.<span style="mso-spacerun: yes;"> </span>However, it is
neither accidental nor unsystematic.<span style="mso-spacerun: yes;">
</span>When a composer’s mind goes wandering into the infinite musical realm,
it does not randomly move from one musical entity to another.<span style="mso-spacerun: yes;"> </span>Its search through this realm is guided by
new ideas concerning musical structure – new notions of melody, harmony, rhythm
and the like – in short, new music theory.<span style="mso-spacerun: yes;">
</span>Rather than being “dusty abstract rules of form and harmonic structure”
(Bernstein, 1966, p. 24), music theory itself seems both vast and dynamic.<span style="mso-spacerun: yes;"> </span>When violent upheaval is heard in classical
music, its root cause must be changing conceptions of music’s structure.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Does musical theory itself exhibit infinite
variety?<span style="mso-spacerun: yes;"> </span>I have no idea.<span style="mso-spacerun: yes;"> </span>However, historical examinations reveal
enormous changes in basic ideas, such as whether different inversions of a
chord are the same chord, or what is the root note of a major or minor triad </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Damschroder, 2008 #6940"><span style="color: windowtext; text-decoration: none; text-underline: none;">Damschroder,
2008</span></a>; <a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Rehding, 2003 #6466"><span style="color: windowtext; text-decoration: none; text-underline: none;">Rehding, 2003</span></a>;
<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Riemann, 1895 #6458"><span style="color: windowtext; text-decoration: none; text-underline: none;">Riemann, 1895</span></a>)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>We saw in Chapter 1 that the psychophysical
study of music that began in the late 19<span style="font-size: small;"><sup>th</sup> century faced the tension
between the physics of sound and individual differences in aesthetics that
permitted just intonation to be replaced by equal temperament </span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Hui</Author><Year>2013</Year><RecNum>6767</RecNum><DisplayText>(Hui,
2013)</DisplayText><record><rec-number>6767</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6767</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Hui,
A.</author></authors></contributors><titles><title>The
Psychophysical Ear: Muscial Experiments, Experimental Sounds,
1840-1910</title><secondary-title>Transformations : studies in the
history of science and
technology</secondary-title></titles><pages>xxii, 233
p.</pages><keywords><keyword>Psychoacoustics History 19th
century.</keyword><keyword>Psychoacoustics History 20th
century.</keyword><keyword>Sound Experiments History 19th
century.</keyword><keyword>Sound Experiments History 20th
century.</keyword><keyword>Avant-garde (Music) History 19th
century.</keyword><keyword>Avant-garde (Music) History 20th
century.</keyword></keywords><dates><year>2013</year></dates><pub-location>Cambridge,
Mass.</pub-location><publisher>MIT
Press</publisher><isbn>9780262018388 (hardcover alk. paper)</isbn><accession-num>17273197</accession-num><call-num>Jefferson
or Adams Building Reading Rooms QP461 .H85
2013</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Hui, 2013 #6767"><span style="color: windowtext; text-decoration: none; text-underline: none;">Hui, 2013</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">As well, evolving notions of consonance
have permitted new musical intervals to become accepted in music.<span style="mso-spacerun: yes;"> </span>The dissonance of the flattened seventh note
led Helmholtz to reject its use in his advice to composers </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Helmholtz</Author><Year>1863/1954</Year><RecNum>1829</RecNum><DisplayText>(Helmholtz
&amp; Ellis, 1863/1954)</DisplayText><record><rec-number>1829</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1829</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Helmholtz,
H.</author><author>Ellis, A.J.</author></authors></contributors><titles><title>On
The Sensations Of Tone As A Physiological Basis For The Theory Of
Music</title></titles><pages>xix, 576
p.</pages><edition>2d
English</edition><keywords><keyword>Sound Physiological
effect.</keyword><keyword>Music Physiological aspects.</keyword><keyword>Music
Acoustics and physics.</keyword></keywords><dates><year>1863/1954</year></dates><pub-location>New
York,</pub-location><publisher>Dover
Publications</publisher><call-num>ML3820 .H42
1954&#xD;781.1</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Helmholtz, 1863/1954 #1829"><span style="color: windowtext; text-decoration: none; text-underline: none;">Helmholtz
& Ellis, 1863/1954</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">; now it is definitive to the blues and plays a central role in Gershwin’s
classic <i style="mso-bidi-font-style: normal;">Rhapsody In Blue</i> </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Adams</Author><Year>2008</Year><RecNum>6964</RecNum><DisplayText>(Adams,
2008)</DisplayText><record><rec-number>6964</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6964</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Adams,
J.</author></authors></contributors><titles><title>Hallelujah
Junction: Composing an American Life</title></titles><pages>340
p.</pages><edition>1st</edition><keywords><keyword>Adams,
John, 1947-</keyword><keyword>Composers United States
Biography.</keyword></keywords><dates><year>2008</year></dates><pub-location>New
York</pub-location><publisher>Farrar, Straus and
Giroux</publisher><isbn>9780374281151 (hardcover alk.
paper)&#xD;0374281157 (hardcover alk.
paper)</isbn><accession-num>15266684</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) ML410.A233 A3 2008&#xD;Performing Arts
Reading Rm (Madison, LM113) - STORED OFFSITE ML410.A233 A3
2008</call-num><urls><related-urls><url>Table of
contents only
http://www.loc.gov/catdir/toc/ecip0817/2008017922.html</url><url>Contributor
biographical information http://www.loc.gov/catdir/enhancements/fy0829/2008017922-b.html</url><url>Publisher
description
http://www.loc.gov/catdir/enhancements/fy0829/2008017922-d.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Adams, 2008 #6964"><span style="color: windowtext; text-decoration: none; text-underline: none;">Adams, 2008</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Later, seasoned jazz musicians
who were completely comfortable with the flattened seventh were jarred and puzzled
by the flattened fifth interval when it was introduced to jazz via bebop </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Kelley</Author><Year>2009</Year><RecNum>6733</RecNum><DisplayText>(Kelley,
2009)</DisplayText><record><rec-number>6733</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6733</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Kelley,
R.D.G.</author></authors></contributors><titles><title>Thelonious
Monk: The Life and Times of an American
Original</title></titles><pages>xviii, 588 p., 16 p. of
plates</pages><edition>1st Free Press
hardcover</edition><keywords><keyword>Monk,
Thelonious.</keyword><keyword>Jazz musicians United States
Biography.</keyword></keywords><dates><year>2009</year></dates><pub-location>New
York</pub-location><publisher>Free
Press</publisher><isbn>9780684831909&#xD;0684831902</isbn><accession-num>15639618</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) ML417.M846 K46 2009&#xD;Reference -
Recorded Sound Reference Center (Madison, LM113) ML417.M846 K46
2009</call-num><urls><related-urls><url>Contributor
biographical information
http://www.loc.gov/catdir/enhancements/fy0906/2009008526-b.html</url><url>Publisher
description http://www.loc.gov/catdir/enhancements/fy0906/2009008526-d.html</url><url>Sample
text
http://www.loc.gov/catdir/enhancements/fy0917/2009008526-s.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Chapters/ChapsInProg/Coda.docx" title="Kelley, 2009 #6733"><span style="color: windowtext; text-decoration: none; text-underline: none;">Kelley, 2009</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Clearly there is no single, unified theory
of music.<span style="mso-spacerun: yes;"> </span>A multitude of music theories
have existed; many different theories can exist at the same time; new theories
can be invented or discovered.<span style="mso-spacerun: yes;"> </span>One approach
to composing innovative music involves taking a new musical theory an examining
the compositions that it can pick out of the infinite realm of music.<span style="mso-spacerun: yes;"> </span>Where might one find a new musical theory to
exploit in this fashion?<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">There are many, many possible answers to
this question.<span style="mso-spacerun: yes;"> </span>One reading of the
current book suggests one: train an artificial neural network to map some
musical inputs to some other musical outputs.<span style="mso-spacerun: yes;">
</span>The kind of training that we have seen in preceding chapters informs
networks about their progress, but does not inform them how to construct the
mapping.<span style="mso-spacerun: yes;"> </span>As a result, these networks can
discover new musical regularities or ideas for performing the mapping.<span style="mso-spacerun: yes;"> </span>We have seen many instances of this in the current
book, even when networks are trained on basic, traditional musical tasks.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Crucially, for a network to deliver a new
musical theory its internal structure must be explored.<span style="mso-spacerun: yes;"> </span>Artificial neural networks can only inform
the study of music if we first reject the romanticism that characterizes much
of connectionist cognitive science.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<strong><u>References</u></strong></span><br />
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Adams, J. (2008). <i style="mso-bidi-font-style: normal;">Hallelujah Junction: Composing an American Life</i> (1st ed.). New York: Farrar, Straus and Giroux.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Bernstein, L. (1966). <i style="mso-bidi-font-style: normal;">The Infinite Variety of Music</i>. New York: Simon and Schuster.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_3"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Copland, A. (1941). <i style="mso-bidi-font-style: normal;">Our New Music: Leading Composers in Europe and America</i>. New York ; London: Whittlesey House, McGraw-Hill Book Company, Inc.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_4"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Damschroder, D. (2008). <i style="mso-bidi-font-style: normal;">Thinking About Harmony: Historical Perspectives On Analysis</i>. Cambridge ; New York: Cambridge University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_5"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Glass, P. (1987). <i style="mso-bidi-font-style: normal;">Music By Philip Glass</i> (1st ed.). New York: Harper & Row.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_6"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Griffiths, P. (1994). <i style="mso-bidi-font-style: normal;">Modern Music: A Concise History</i> (Rev. ed.). New York: Thames and Hudson.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_7"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Griffiths, P. (1995). <i style="mso-bidi-font-style: normal;">Modern Music And After</i>. Oxford ; New York: Oxford University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_8"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Hartog, H. (1957). <i style="mso-bidi-font-style: normal;">European Music In The Twentieth Century</i>. London,: Routledge & Paul.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_9"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Helmholtz, H., & Ellis, A. J. (1863/1954). <i style="mso-bidi-font-style: normal;">On The Sensations Of Tone As A Physiological Basis For The Theory Of Music</i> (2d English ed.). New York,: Dover Publications.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_10"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Hui, A. (2013). <i style="mso-bidi-font-style: normal;">The Psychophysical Ear: Muscial Experiments, Experimental Sounds, 1840-1910</i>. Cambridge, Mass.: MIT Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_11"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Kelley, R. D. G. (2009). <i style="mso-bidi-font-style: normal;">Thelonious Monk: The Life and Times of an American Original</i> (1st Free Press hardcover ed.). New York: Free Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_12"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Nyman, M. (1999). <i style="mso-bidi-font-style: normal;">Experimental Music: Cage And Beyond</i> (2nd ed.). Cambridge ; New York: Cambridge University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_13"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Pleasants, H. (1955). <i style="mso-bidi-font-style: normal;">The Agony Of Modern Music</i>. New York,: Simon and Schuster.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_14"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Potter, K. (2000). <i style="mso-bidi-font-style: normal;">Four Musical Minimalists: La Monte Young, Terry Riley, Steve Reich, Philip Glass</i>. Cambridge, UK ; New York: Cambridge University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_15"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Rehding, A. (2003). <i style="mso-bidi-font-style: normal;">Hugo Riemann And The Birth Of Modern Musical Thought</i>. Cambridge ; New York: Cambridge University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_16"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Reich, S. (1974). <i style="mso-bidi-font-style: normal;">Writings About Music</i>. Halifax: Press of the Nova Scotia College of Art and Design.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_17"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Reich, S. (2002). <i style="mso-bidi-font-style: normal;">Writings On Music, 1965-2000</i>. Oxford ; New York: Oxford University Press.</span></span></a></div>
</li>
</ul>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_18"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Riemann, H. (1895). <i style="mso-bidi-font-style: normal;">Harmony simplified: Or, The Theory Of The Tonal Functions Of Chords</i>. London: Augener.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
</ul>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]-->Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-10248264954167587562015-05-16T17:24:00.000-06:002015-05-16T17:24:33.908-06:00Coltrane Changes on the Ukulele<em><span style="font-family: Arial;">As described </span></em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><em><span style="font-family: Arial, Helvetica, sans-serif;">in this previous post</span></em></a><em><span style="font-family: Arial, Helvetica, sans-serif;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<em><span style="font-family: Arial;"></span></em><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijUjKVIVhKqNaWzjCPLYumLShXBoshdupLaNkZ0M-mmzg3VyY1jvztYPPqowF4gzK0suhIVY47gQ373GKiC151vLnGIltUm_y4e88Wx-kNnInDSb_-2NLbEdwGli1MkKY8FvkyGQYEgOY/s1600/FigureI-14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijUjKVIVhKqNaWzjCPLYumLShXBoshdupLaNkZ0M-mmzg3VyY1jvztYPPqowF4gzK0suhIVY47gQ373GKiC151vLnGIltUm_y4e88Wx-kNnInDSb_-2NLbEdwGli1MkKY8FvkyGQYEgOY/s320/FigureI-14.jpg" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-14. The most basic ukulele chords
for the ii-V-I progression in the key of C major.<span style="mso-spacerun: yes;"> </span>See text for details.<o:p></o:p></span></strong></span></div>
<div class="WordSection1">
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">When investigating musical problems with
artificial neural networks, I find it useful to hear the stimuli on a musical
instrument.<span style="mso-spacerun: yes;"> </span>While I have spent a lot
time working out stimulus patterns on the keyboard of my piano, these days my
instrument of choice is the ukulele.<span style="mso-spacerun: yes;"> </span>In
this interlude I will provide the chords that I use to play the Coltrane
changes in the key of C major, developing this chord structure from variations
of the ii-V-I progression.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Figure I-14 provides the three chords that
define the simplest version of the ii-V-I progression on the ukulele.<span style="mso-spacerun: yes;"> </span>Each chord diagram illustrates the four
strings of the ukulele, and the dots on the diagram indicate the fret at which each
particular string is depressed.<span style="mso-spacerun: yes;"> </span>The
three chords that are presented are based on the assumption that the progression
involves a sequence of three triads (D minor, G major, and C major).<span style="mso-spacerun: yes;"> </span>That is, if one creates these three triads using
only the notes available in the C major scale, then one of these chords is necessarily
minor, while the other two are major (see the discussion of Figure 7-15).<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The ii-V-I progression is a staple in jazz,
and using triads doesn’t provide the jazziest sound.<span style="mso-spacerun: yes;"> </span>Jazz musicians are more likely to extend the
triads used to create the Figure I-14 chords to create tetrachords.<span style="mso-spacerun: yes;"> </span>This extension, which involves adding an
additional note to each chord from the C major scale, was also illustrated earlier
in Figure 7-15.<span style="mso-spacerun: yes;"> </span>Figure I-15 illustrates
how one would play the C major tetrachords for the ii-V-I on the ukulele.<span style="mso-spacerun: yes;"> </span>Note that the D minor has now become a D
minor seventh, the G major has become a G dominant seventh, and the C major has
become a C major seventh.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf6n3PAbAt1hMCMWFxXTKjXPXQnIY4S7HTwZiaBBs2NEb6nnD3gup-xzpnlsGLtIIPL-MYjtkOxJ_ugYNmVkW_YGQDbFWV3oLr30ipOPCLjuZFQifUoh5z1UR9q89thw60I2d80v2bc_Q/s1600/FigureI-15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="122" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf6n3PAbAt1hMCMWFxXTKjXPXQnIY4S7HTwZiaBBs2NEb6nnD3gup-xzpnlsGLtIIPL-MYjtkOxJ_ugYNmVkW_YGQDbFWV3oLr30ipOPCLjuZFQifUoh5z1UR9q89thw60I2d80v2bc_Q/s320/FigureI-15.jpg" width="320" /></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<strong><span style="font-family: Arial;"><span style="mso-ansi-language: EN-CA; mso-fareast-language: EN-CA; mso-no-proof: yes;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock><v:shape id="Picture_x0020_7" o:spid="_x0000_i1027" style="height: 75pt; mso-wrap-style: square; visibility: visible; width: 198pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg">
</v:imagedata></v:shape></v:path></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas></v:stroke></v:shapetype></span><span lang="EN-US"><o:p></o:p></span></span></strong></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-15. The ukulele tetrachords for the
ii-V-I progression in the key of C major.<span style="mso-spacerun: yes;">
</span>See text for details.<o:p></o:p></span></strong></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">All of the chords illustrated in Figures
I-14 and I-15 are called open position chords.<span style="mso-spacerun: yes;">
</span>This is because at least one ukulele string in the chord is open; that
is, it is not pressed down by a finger.<span style="mso-spacerun: yes;"> </span>The
advantage of open position chords is that they generally are easier to
play.<span style="mso-spacerun: yes;"> </span>The disadvantage of such chords is
that they are special in the sense that they cannot be moved up or down along
the ukulele fret board to play the same type of chord in a different key.<span style="mso-spacerun: yes;"> </span>This makes these chords different from the
closed form chords that were the topic of the previous interlude “Ukulele
Chords and Perceptrons”.<span style="mso-spacerun: yes;"> </span>Our next move
is to transform the Figure I-15 progression into one that uses closed position
chords.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">In order to perform this transformation, we
will use two different tricks.<span style="mso-spacerun: yes;"> </span>The first
is to replace the Dm7 and Cmaj7 chords with alternative fingerings that can be
found in a decent ukulele chord book </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Johnson</Author><Year>2005</Year><RecNum>6945</RecNum><DisplayText>(Johnson,
2005)</DisplayText><record><rec-number>6945</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6945</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Johnson,
C.</author></authors></contributors><titles><title>Hal
Leonard Ukulele Chord
Finder</title></titles><dates><year>2005</year></dates><pub-location>Milwaukee,
WI</pub-location><publisher>Hal Leonard Corporation</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(<a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude9.docx" title="Johnson, 2005 #6945"><span style="color: windowtext; text-decoration: none; text-underline: none;">Johnson, 2005</span></a>)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>For these two chords we
pick two fingerings that are related; both are barre chords that involve pressing
the index finger down across all the strings at the fifth fret.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The second trick is to take advantage of
chord substitution.<span style="mso-spacerun: yes;"> </span>In general, jazz musicians
see a chord’s name as an indicator of potential chords.<span style="mso-spacerun: yes;"> </span>For instance, when such a musician sees that
a G7 is the next chord, they would feel perfectly comfortable with substituting
a different, but related, chord.<span style="mso-spacerun: yes;"> </span>Chord
substitution conventions permit G7 to be replaced, for example, with G9 or with
G13 in order to add musical variety.<span style="mso-spacerun: yes;"> </span>We
will choose the G9 chord because the barre form of this chord places it in a similar
position on the fret board to the other closed form chords in the ii-V-I, as is
illustrated in Figure I-16. <o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilyt6r43Rb3fbkzwok-CmAHBhmyHVgRszc56LJgTpxoOBHTO3s4uGjwInUrN9xuymDb1eLCj1im1Qf9oq5H_fThkeEvuKOrAoj96cga44YDf-1u1rECfpB3adEkFCyBtf60reYG5J1d-A/s1600/FigureI-16.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="187" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilyt6r43Rb3fbkzwok-CmAHBhmyHVgRszc56LJgTpxoOBHTO3s4uGjwInUrN9xuymDb1eLCj1im1Qf9oq5H_fThkeEvuKOrAoj96cga44YDf-1u1rECfpB3adEkFCyBtf60reYG5J1d-A/s320/FigureI-16.jpg" width="320" /></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<strong><span style="font-family: Arial;"><span style="mso-ansi-language: EN-CA; mso-fareast-language: EN-CA; mso-no-proof: yes;"><v:shape id="Picture_x0020_8" o:spid="_x0000_i1026" style="height: 116.25pt; mso-wrap-style: square; visibility: visible; width: 198pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image002.jpg">
</v:imagedata></v:shape></span><span lang="EN-US"><o:p></o:p></span></span></strong></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-16. Closed form ukulele chords
for the ii-V-I progression in the key of C major.<span style="mso-spacerun: yes;"> </span>See text for details.<o:p></o:p></span></strong></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">There are three important points to make
about Figure I-16.<span style="mso-spacerun: yes;"> </span>First, the particular
chord choices that it illustrates begin quite a bit further down the fret board
(at either fret 5 or 4) than was the case in Figures I-14 or I-16.<span style="mso-spacerun: yes;"> </span>Each chord diagram has a number on the left indicating
the starting fret, and the chord diagrams have been extended more than is
typical to show where on the ukulele each chord is being played.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Second, the G9 chord that is illustrated is
not likely to be found in many ukulele chord dictionaries.<span style="mso-spacerun: yes;"> </span>This is because this form of the chord does
not include the root note G.<span style="mso-spacerun: yes;"> </span>Instead, it
uses the other four pitches that are part of G9.<span style="mso-spacerun: yes;"> </span>These four pitches actually define a minor
seventh (flat fifth) chord in a different key.<span style="mso-spacerun: yes;">
</span>G9 as illustrated in Figure I-16 is also Bm7</span></span><span lang="EN-US" style="font-family: "Arial Unicode MS","sans-serif";">♭</span><span lang="EN-US"><span style="font-family: Arial;">5.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Third, because these three chords are all
in closed form one can move these patterns up or down the fret board to play
the ii-V-I progression in a different key.<span style="mso-spacerun: yes;">
</span>For instance if one uses the same chord patterns illustrated in Figure
I-16, but moves each upwards a fret (towards the top of the page), then the result
is the ii-V-I progression in the key of B major.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">As detailed in Chapter 9, the Coltrane
changes elaborate the ii-V-I progression by using the same three chords in Figure
I-16, but also adds four additional chords that serve as lead ins.<span style="mso-spacerun: yes;"> </span>We can create the Coltrane changes by adding
these four chords to Figure I-16, attempting to choose closed form chords that
minimize movements along the fret board.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The Coltrane changes for the ukulele in key
of C major are presented in Figure I-17.<span style="mso-spacerun: yes;">
</span>Each chord is a barre chord, meaning that this figure defines chord patterns
that can be shifted to different fret board positions to generate the Coltrane
changes in a different key.<span style="mso-spacerun: yes;"> </span>For example,
shifting each chord a fret downwards (towards the bottom of the page) produces this
progression in the key of C# major.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJmuKGHhLOB5p-4SHwyOQNjXDAEI16LUUUYY-HNcp2ArZEJst02DZJCIxdpvFHFSxuddvbjFNoMq1bDvaV7qVBuh44uo20wQ74lI1NTbUtKr53F5HRpoT413dxY55j2gRRMXLbqU9tahk/s1600/FigureI-17.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJmuKGHhLOB5p-4SHwyOQNjXDAEI16LUUUYY-HNcp2ArZEJst02DZJCIxdpvFHFSxuddvbjFNoMq1bDvaV7qVBuh44uo20wQ74lI1NTbUtKr53F5HRpoT413dxY55j2gRRMXLbqU9tahk/s320/FigureI-17.jpg" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p></o:p></span> </div>
</div>
<div class="WordSection2">
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-17.<span style="mso-spacerun: yes;"> </span>Closed form ukulele chords for the Coltrane
changes in the key of C major.<o:p></o:p></span></strong></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
</div>
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span><span lang="EN-US"><span style="font-family: Arial;">Creating the chord patterns in Figure I-17
serves the primary purpose of permitting me to play the Coltrane changes on the
ukulele.<span style="mso-spacerun: yes;"> </span>However, this set of chord diagrams
suggests other uses.<span style="mso-spacerun: yes;"> </span>One of the themes
in Chapter 9 was exploring different encodings of jazz progressions for
networks.<span style="mso-spacerun: yes;"> </span>One could imagine adapting the
encoding developed in the interlude that preceded Chapter 9 to present the jazz
progressions to networks as sequences of ukulele chords.<span style="mso-spacerun: yes;"> </span>What effect might this representation have on
network complexity?<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Similarly, Figure I-17 raises the possibility
of generating alternative versions of the Coltrane changes for ukulele.<span style="mso-spacerun: yes;"> </span>For instance, might easier chord fingerings
emerge if one explores chord substitutions for the other dominant seventh
chords in the figure?</span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"></span></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"><strong><u>References</u></strong></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"></span></span> </div>
<span lang="EN-US"><span style="font-family: Arial;"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;">Johnson, C. (2005). <i style="mso-bidi-font-style: normal;">Hal Leonard Ukulele Chord Finder</i>.
Milwaukee, WI: Hal Leonard Corporation.</span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Times New Roman;">
</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-no-proof: yes;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Times New Roman;">
</span><!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]--><o:p></o:p></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
</div>
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
</div>
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
</div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-21501441761047734002015-05-08T15:45:00.001-06:002015-05-08T15:45:37.722-06:00Ukulele Chords and Perceptrons<em><span style="font-family: Arial, Helvetica, sans-serif;">As described </span></em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><em><span style="font-family: Arial, Helvetica, sans-serif;">in this previous post</span></em></a><em><span style="font-family: Arial, Helvetica, sans-serif;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<em></em><span style="font-family: Arial, Helvetica, sans-serif;"> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLp5QNclBuMS3ZqUus_IRfWzoPJOblQ9vwvT__Uy_WGkUp-T9Ko8oSUOBE4zdU_GSZ_03-0-VuUCAa7kZNNfPjHJueMx4TL6ShpWa5XSGT3fG5AbBoonzTzz-mJ0ny4v8Vp5taTtcziKI/s1600/FigureI-10.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLp5QNclBuMS3ZqUus_IRfWzoPJOblQ9vwvT__Uy_WGkUp-T9Ko8oSUOBE4zdU_GSZ_03-0-VuUCAa7kZNNfPjHJueMx4TL6ShpWa5XSGT3fG5AbBoonzTzz-mJ0ny4v8Vp5taTtcziKI/s320/FigureI-10.jpg" width="320" /></span></a></div>
<div class="WordSection1">
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial, Helvetica, sans-serif;">Figure I-10. Four examples of four closed
form or moveable shapes that define major chords for the ukulele.<span style="mso-spacerun: yes;"> </span>See text for details.<o:p></o:p></span></strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span></span><br />
<div class="WordSection2">
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><h2 style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-size: small;"><span style="font-family: Arial, Helvetica, sans-serif;">Many Diagrams for One Chord<o:p></o:p></span></span></span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In music theory a tetrachord is merely a
chord comprised of four different pitch-classes.<span style="mso-spacerun: yes;"> </span>From other perspectives, however, the notion
of a tetrachord becomes more practical, and possibly more complicated.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">One such practical perspective is provided
by the ukulele, which is a small, four-stringed, guitar-like instrument
typically tuned to the notes G4, C4, E4 and A4.<span style="mso-spacerun: yes;">
</span>Any chord strummed on the ukulele is a tetrachord because it is produced
by vibrating these four strings.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Learning to play the ukulele involves studying
the finger positions that define various chords.<span style="mso-spacerun: yes;"> </span>These positions are provided in charts or
books filled with chord diagrams like the examples provided in Figure
I-10.<span style="mso-spacerun: yes;"> </span>In a chord diagram, the horizontal
lines indicate the positions of the frets on a ukulele’s fret board, and the
vertical lines represent the instrument’s four strings.<span style="mso-spacerun: yes;"> </span>The black dots in a chord diagram indicate
where, on the fret board, a finger should be pressed on the string to produce a
pitch that is part of the desired chord.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The interacting physical structures of the ukulele
and the human hand place constraints on the note combinations that constitute
playable ukulele chords.<span style="mso-spacerun: yes;"> </span>It is impossible
to play every conceivable tetrachord on the ukulele.<span style="mso-spacerun: yes;"> </span>A chord that involves placing the index
finger on the first fret of one string, and the little finger on the 12<span style="font-size: small;"><sup>th</sup>
fret of a different string, is a practical impossibility.<span style="mso-spacerun: yes;"> </span>In other words, in a playable ukulele chord
one’s fingers are not too far apart.<o:p></o:p></span></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The notes played on different ukulele
strings are not too far apart either.<span style="mso-spacerun: yes;"> </span>In
terms of tuning, the furthest distance is between the C and the A strings, but
this distance is only a major sixth (9 semitones).<span style="mso-spacerun: yes;"> </span>The G and the A strings only differ by a
major second (2 semitones).<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The relative nearness of fingers in a
playable chord, and the relative nearness of the tunings of ukulele strings, means
that relatively minor changes in finger positions can produce the same chord.<span style="mso-spacerun: yes;"> </span>This is because the changes in finger
positions invert the chord’s notes.<span style="mso-spacerun: yes;"> </span>That
is, different fingering positions can produce the same component pitches of a
chord, but on different strings.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">The upshot of this is that there is a
many-to-one relationship between fingering patterns and chords.<span style="mso-spacerun: yes;"> </span>More than one chord diagram can represent the
same ukulele chord.<span style="mso-spacerun: yes;"> </span>For example, one of
the modern bibles of ukulele chords </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Johnson</Author><Year>2005</Year><RecNum>6945</RecNum><DisplayText>(Johnson,
2005)</DisplayText><record><rec-number>6945</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6945</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Johnson,
C.</author></authors></contributors><titles><title>Hal
Leonard Ukulele Chord
Finder</title></titles><dates><year>2005</year></dates><pub-location>Milwaukee,
WI</pub-location><publisher>Hal Leonard Corporation</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude8.docx" title="Johnson, 2005 #6945"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Johnson, 2005</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> provides three different fingerings for each of the 28 chords that
it describes for each musical key, producing a book that consists of 1008
different chord diagrams.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><h2 style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-size: small;"><span style="font-family: Arial, Helvetica, sans-serif;">Chord Shapes<o:p></o:p></span></span></span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">How does a budding ukulele player even hope
to learn such an incredible diversity of possible chords?<span style="mso-spacerun: yes;"> </span>Thankfully there are some fingering patterns that
can be moved up and down the fret board.<span style="mso-spacerun: yes;">
</span>These are called closed form chords because their shape is defined by placing
a finger on each of the ukulele’s four strings.<span style="mso-spacerun: yes;">
</span>Four examples of such chords are provided in Figure I-10: these are all
closed form chords because each chord diagram contains four fingering dots.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">When a closed form chord is moved up or
down the fret board, it causes the same type of chord to be played, but in a
different key.<span style="mso-spacerun: yes;"> </span>All of the closed form
chord shapes in Figure I-10, for example, create a major chord no matter where
they are formed on the fret board.<span style="mso-spacerun: yes;"> </span>If
one is formed at one location, it produces the B</span><span lang="EN-US" style="font-family: Bach; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Bach;"><span style="mso-char-type: symbol; mso-symbol-font-family: Bach;">@</span></span><span lang="EN-US"> major
chord.<span style="mso-spacerun: yes;"> </span>The same fingering shifted to a
different position produces the C major chord.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Closed form chords are efficient for learning
the ukulele because once one learns a fingering pattern (e.g. any of the four
patterns in Figure I-10), one has really learned 12 different chords.<span style="mso-spacerun: yes;"> </span>All the player has to do is learn the name of
the chord produced (e.g. B</span><span lang="EN-US" style="font-family: Bach; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Bach;"><span style="mso-char-type: symbol; mso-symbol-font-family: Bach;">@</span></span><span lang="EN-US"> major, C major) at each location that
the same fingering pattern is used.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Of course not all ukulele chords are closed
form.<span style="mso-spacerun: yes;"> </span>Some are special cases of closed
form chords where the ukulele’s nut (the top of the fret board where the
strings end) takes the place of fingers on some of the strings.<span style="mso-spacerun: yes;"> </span>The four chord diagrams in Figure I-11
provide examples of such special cases.<span style="mso-spacerun: yes;">
</span>These chords are typically learned first, are learned with different
fingerings than the patterns in Figure I-10, and are only later related to the
more general notion of closed form chords.<span style="mso-spacerun: yes;">
</span>Still other chord forms are standalone patterns that cannot be moved
along the fret board.<span style="mso-spacerun: yes;"> </span>As a result, even
learning one kind of chord, such as a major chord, requires acquiring a number
of different chord diagrams.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Nevertheless, focusing on the shapes of the
chord diagram – the relative positions of fingers on each string – provides
efficiency.<span style="mso-spacerun: yes;"> </span>The <i style="mso-bidi-font-style: normal;">Hal Leonard Ukulele Chord Finder</i> </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Johnson</Author><Year>2005</Year><RecNum>6945</RecNum><DisplayText>(Johnson,
2005)</DisplayText><record><rec-number>6945</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6945</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Johnson,
C.</author></authors></contributors><titles><title>Hal
Leonard Ukulele Chord
Finder</title></titles><dates><year>2005</year></dates><pub-location>Milwaukee,
WI</pub-location><publisher>Hal Leonard
Corporation</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude8.docx" title="Johnson, 2005 #6945"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Johnson, 2005</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> provides at total of 36 different chord diagrams for the major
chords in each musical key.<span style="mso-spacerun: yes;"> </span>However,
from a player’s perspective, these 36 diagrams can be condensed into only 13
different chord shapes. <o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTjgYuJxCTTvo6GNUwqCiLSmWqeZ6NeWnmxnOJXIS8qiOtfYUad4f7V7V7mhGWiExunqDpVV5f5ZZZcaCV6VZQh-_N0F9sowfSrNnIHzcV4SiNWxl9P62P_CMnbZfxem-2j8fOJw2B53M/s1600/FigureI-11.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTjgYuJxCTTvo6GNUwqCiLSmWqeZ6NeWnmxnOJXIS8qiOtfYUad4f7V7V7mhGWiExunqDpVV5f5ZZZcaCV6VZQh-_N0F9sowfSrNnIHzcV4SiNWxl9P62P_CMnbZfxem-2j8fOJw2B53M/s320/FigureI-11.jpg" width="320" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><b><span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="mso-break-type: section-break; page-break-before: auto;" /><span style="font-family: Arial, Helvetica, sans-serif;">
</span></span></b><span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="WordSection4">
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial, Helvetica, sans-serif;">Figure I-11. Four special case major chord
shapes.<span style="mso-spacerun: yes;"> </span>The top fret of each of these
chord diagrams is the first fret of a ukulele; the wide horizontal black line
in each diagram is the ukulele’s nut.<span style="mso-spacerun: yes;">
</span>Each of these shapes is a special instance of each of the four general
chord shapes in Figure I-10.<span style="mso-spacerun: yes;"> </span>See text
for details.<o:p></o:p></span></strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial, Helvetica, sans-serif;"> </span></o:p></span></div>
</div>
<h2 style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-size: small;"><span style="font-family: Arial, Helvetica, sans-serif;">Towards Reverse Chord Finding<o:p></o:p></span></span></span></h2>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Chord dictionaries are organized alphabetically
by the root of the chord, and then by chord type.<span style="mso-spacerun: yes;"> </span>If you need to find out how to play a
particular chord, then you can quickly look it up by using its name.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Learning to play the ukulele is,
thankfully, more than just poring through the pages of chord dictionaries.<span style="mso-spacerun: yes;"> </span>A player can explore different fingerings
without knowing the name of the chords being played.<span style="mso-spacerun: yes;"> </span>On finding one such chord that has a
particularly pleasing sound, there may be keen interest in finding out the
chord’s name.<span style="mso-spacerun: yes;"> </span>However, chord
dictionaries are not organized by fingering patterns.<span style="mso-spacerun: yes;"> </span>This problem – known as reverse chord lookup
– does not have an easy book solution.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The reverse chord lookup problem, though,
is very similar to problems of identifying scale roots, of identifying scale
modes, and of keyfinding that have appeared earlier in this book.<span style="mso-spacerun: yes;"> </span>In those earlier problems, a set of notes was
presented to a network, and the network output some judgment about the input –
a root note, a scale mode, or both.<span style="mso-spacerun: yes;"> </span>Is
it possible to create a network that can provide the names of chords when
provided their fingering?<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">One complication that presents itself when
considering this possibility is the many-to-one relationship between chord
diagrams and chords.<span style="mso-spacerun: yes;"> </span>In our previous encounters
with scale roots and modes, the relationship between input and output was
one-to-one.<span style="mso-spacerun: yes;"> </span>Can networks adapt to the
complexities of many-to-one relationships?<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">I decided to explore this particular question
before facing the larger reverse chord lookup problem.<span style="mso-spacerun: yes;"> </span>I trained a network to decide whether a chord
was major or minor when presented the chord’s diagram.<span style="mso-spacerun: yes;"> </span>This is an interesting test case because, as
we have seen, there are many different chord diagrams that are each associated
with a major chord.<span style="mso-spacerun: yes;"> </span>Furthermore, there
is a great deal of similarity between the shapes of major and minor chord
diagrams because one can change a major chord into a minor chord by moving only
one finger.<span style="mso-spacerun: yes;"> </span>Detecting major chords is a
challenging problem.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Major chord detection is also an interesting
problem with respect to network interpretation.<span style="mso-spacerun: yes;">
</span>As discussed above, ukulele players learn chords by paying attention to
the shapes of their chord diagrams.<span style="mso-spacerun: yes;"> </span>Such
shape information is not likely to be directly available to a network whose
only window onto a chord diagram is a set of input units.<span style="mso-spacerun: yes;"> </span>If a network can detect major chord patterns,
then how does it represent their structure?<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The first problem to deal with in developing
this network is representing input patterns.<span style="mso-spacerun: yes;">
</span>I decided to represent each chord diagram as a set of activities using
20 different input units.<span style="mso-spacerun: yes;"> </span>Each of these
input units indicates a possible finger position on a chord diagram, as is
illustrated in Figure I-12.<span style="mso-spacerun: yes;"> </span>The first
five input units (labeled G1 to G5) represent five possible finger positions on
the G string.<span style="mso-spacerun: yes;"> </span>The next five input units
represent five possible finger positions on the C string, and so on.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3wTrK9lz_IAvCCoSJD1Oh45NebVfY8Alq9o9Reg2xQoWykRDHVdPd6QiN0tOQr8aPqm4XbAHdGRnKdoP60j5gnLaNDh7B_BzKBJQ3PODqRssaDoVnPXRp8RcRTUlobG8CnUTKCJgtLqA/s1600/FigureI-12.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3wTrK9lz_IAvCCoSJD1Oh45NebVfY8Alq9o9Reg2xQoWykRDHVdPd6QiN0tOQr8aPqm4XbAHdGRnKdoP60j5gnLaNDh7B_BzKBJQ3PODqRssaDoVnPXRp8RcRTUlobG8CnUTKCJgtLqA/s320/FigureI-12.jpg" width="213" /></span></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial, Helvetica, sans-serif;">Figure I-12. An array of 20 input units
used to represent finger positions in a chord diagram.<span style="mso-spacerun: yes;"> </span>See text for details.<o:p></o:p></span></strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Any of the chord diagrams in Figures I-10
or I-11 can be represented with this set of input units.<span style="mso-spacerun: yes;"> </span>If a string position is fingered in a chord
diagram, its input unit is turned on with a value of 1.<span style="mso-spacerun: yes;"> </span>Otherwise, its input unit was turned off with
a value of 0.<span style="mso-spacerun: yes;"> </span>This means that any chord
diagram can be represented as a vector of 20 different bits.<span style="mso-spacerun: yes;"> </span>For example, the representation of the A
major chord in Figure I-11 is [0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]. <o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">To explore major chord detection, I created
a training set composed of the 36 different instances of chord diagrams for
major chords on the ukulele, as well as the 36 different instances of minor
chord diagrams, from the <i style="mso-bidi-font-style: normal;">Hal Leonard
Ukulele Chord Finder</i> </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Johnson</Author><Year>2005</Year><RecNum>6945</RecNum><DisplayText>(Johnson,
2005)</DisplayText><record><rec-number>6945</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6945</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Johnson,
C.</author></authors></contributors><titles><title>Hal
Leonard Ukulele Chord
Finder</title></titles><dates><year>2005</year></dates><pub-location>Milwaukee,
WI</pub-location><publisher>Hal Leonard
Corporation</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude8.docx" title="Johnson, 2005 #6945"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Johnson, 2005</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Each of these 72 chords was
converted into a representation that could be encoded in the fashion required
by Figure I-12.<span style="mso-spacerun: yes;"> </span>I trained a network with
one output unit (a value unit with a Gaussian activation function) to turn on
when it was presented a major chord pattern, and to turn off when presented a
minor chord pattern.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">Of course, another key question to answer
concerns the nature of the network required to solve this problem.<span style="mso-spacerun: yes;"> </span>Does the many-to-one relationship between
inputs and outputs require using hidden units?<span style="mso-spacerun: yes;">
</span>It turns out that the answer to this question is no.<span style="mso-spacerun: yes;"> </span>A perceptron – a network without any hidden
units – quickly learns to identify major chords provided that it modifies the
output unit’s </span><span lang="EN-US" style="mso-bidi-font-family: Arial;">µ</span><span lang="EN-US"> during training.<span style="mso-spacerun: yes;"> </span>For
instance, the network described below solved this problem after only 397 epochs
of training with a learning rate of 0.1<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">How does this perceptron detect major chord
fingerings?<span style="mso-spacerun: yes;"> </span>Figure I-13 provides the
connection weights from each of the 20 input units to the output unit of this
perceptron.<span style="mso-spacerun: yes;"> </span>The connection weights in
this figure are arranged to correspond to the arrangement of input units in
Figure I-12.<span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="mso-bidi-font-family: Arial;">Note that the value of µ for this output
unit is equal to 1.92.<span style="mso-spacerun: yes;"> </span>In order for this
output unit to turn on and identify a major chord pattern, the signal coming
from the 20 input units must cancel this value out.<span style="mso-spacerun: yes;"> </span>In other words, the net input from a major
chord pattern must have a value that is very close to -µ, or around -1.92.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">A glance at the connection weights in
Figure I-13 does not provide any indication that the network is making explicit
patterns of the sort that are evident to a human ukulele player in the chord
diagrams of <br />
Figures I-10 or I-11.<span style="mso-spacerun: yes;"> </span>However, a closer
examination reveals that the network has carefully adapted its connection
weights to be sensitive to these patterns.<span style="mso-spacerun: yes;">
</span>The network has learned that particular combinations of input unit
activities (i.e. particular chord patterns) turn the output unit on.<span style="mso-spacerun: yes;"> </span>It assigns connection weights so that the sum
of their signals cancels </span><span lang="EN-US" style="mso-bidi-font-family: Arial;">µ out.<span style="mso-spacerun: yes;"> </span>Of particular interest,
though, is that the network chooses its weights very carefully so that it is
equally adept at dealing with the closed form patterns of Figure I-10 and the
much sparser special cases of Figure I-11.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial;"><span style="font-family: Arial, Helvetica, sans-serif;">Consider
the special cases first, because they place important constraints on the connection
weights to be assigned.<span style="mso-spacerun: yes;"> </span>The C major
chord in Figure I-11 requires that only one finger be placed on the third fret
of the A string.<span style="mso-spacerun: yes;"> </span>This means that the
connection weight from input unit A3 must be approximately equal to -µ, because
this unit must be able to turn the output unit on by itself.<span style="mso-spacerun: yes;"> </span>The weight from this unit is in fact -1.86.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3SgFG9Oh3IxO03rF4FcSw31rdcJlMZisPFWPB1_msb6SJsk5Fp1cUbANJs4yPcFhfczTM39RALDFbMYFH5bYiSr6lb9xOZMeTIwQ16epuDEfLbcbiSlW0LRV__bahHCHbFLuPEyD57O4/s1600/FigureI-13.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3SgFG9Oh3IxO03rF4FcSw31rdcJlMZisPFWPB1_msb6SJsk5Fp1cUbANJs4yPcFhfczTM39RALDFbMYFH5bYiSr6lb9xOZMeTIwQ16epuDEfLbcbiSlW0LRV__bahHCHbFLuPEyD57O4/s320/FigureI-13.jpg" width="194" /></span></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial, Helvetica, sans-serif;">Figure I-13. The connection weights from
the 20 input units to the output unit in the major chord detecting perceptron.<o:p></o:p></span></strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial;"><span style="font-family: Arial, Helvetica, sans-serif;">The A
major chord in Figure I-11 sends signals from input units G2 and C1, while the
F major chord in the same figure sends signals from input units G2 and E1.<span style="mso-spacerun: yes;"> </span>Because both sets of signals cancel out µ,
and because both sets include a signal from G2, the weight from C1 must be the
same as the weight from E1.<span style="mso-spacerun: yes;"> </span>Figure I-13
shows that both weights are equal to -3.01.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial;"><span style="font-family: Arial, Helvetica, sans-serif;">Not
surprisingly, any of the chord diagrams illustrated in the earlier figures will
produce net inputs that essentially cancel µ out and turn the output unit
on.<span style="mso-spacerun: yes;"> </span>Training the network has found a set
of weights that provide the right combinations to activate the output unit when
a major chord pattern is presented, but fail to activate it when a minor chord
pattern is given as input.<span style="mso-spacerun: yes;"> </span>The surprise
here, perhaps, is the speed with which the learning rule discovered the correct
combinations of weights to use.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial;"><span style="font-family: Arial, Helvetica, sans-serif;">The fact
that a network as simple as a perceptron can solve this problem is also
exciting because this in turn suggests that this approach can be extended.<span style="mso-spacerun: yes;"> </span>It should be possible to train networks to
detect many different types of chords, and hopefully their roots, so that one
could perform reverse chord lookup by presenting a chord’s fingering to this
network.<span style="mso-spacerun: yes;"> </span>Developing such a network is my
next step in pursuing links between artificial neural networks and the ukulele!<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><strong><u>References</u></strong> </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Johnson, C. (2005). <i style="mso-bidi-font-style: normal;">Hal Leonard Ukulele Chord Finder</i>.
Milwaukee, WI: Hal Leonard Corporation.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]-->Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-66586848685843551292015-04-28T10:08:00.000-06:002015-04-28T12:32:20.972-06:00Computing The Fit Of An MDS Solution Using R<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial;">If you want to use R<sup>2</sup> to evaluate the fit of your MDS
solution using the statistical programming language R, then read on.<span style="mso-spacerun: yes;"> </span>Some example code is given below. An R script containing the code is available here: <a href="http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/RScripts/MDS-Fit-Eg.R">http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/RScripts/MDS-Fit-Eg.R</a></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">Recently I have been doing a lot of analysis of artificial neural
networks that have been trained on a variety of musical tasks.<span style="mso-spacerun: yes;"> </span>At many times this analysis has involved
computing the distances between different processing units, where these
distances are based on connection weights.<span style="mso-spacerun: yes;">
</span>Then I perform multidimensional scaling (MDS) on the computed distances </span><!--[if supportFields]><span
style='mso-bidi-font-size:12.0pt;mso-bidi-font-family:Arial'><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Kruskal</Author><Year>1978</Year><RecNum>1233</RecNum><DisplayText>(Kruskal
&amp; Wish,
1978)</DisplayText><record><rec-number>1233</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1233</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Kruskal,
J.B.</author><author>Wish,
M.</author></authors></contributors><titles><title>Multidimensional
Scaling</title></titles><dates><year>1978</year></dates><pub-location>Beverly
Hills, CA</pub-location><publisher>Sage
Publications</publisher><urls><pdf-urls><url>file://F:\Reprints\K\Kruskal1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="mso-no-proof: yes;">(<a href="file:///F:/Work/My%20Blogs/GOF.docx" title="Kruskal, 1978 #1233"><span style="color: windowtext; text-decoration: none; text-underline: none;">Kruskal &
Wish, 1978</span></a>)</span></span><!--[if supportFields]><span
style='mso-bidi-font-size:12.0pt;mso-bidi-font-family:Arial'><span
style='mso-element:field-end'></span></span><![endif]--><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">.<span style="mso-spacerun: yes;"> </span>For
the most part I have been performing my MDS analyses in R, using the cmdscale
command.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial;">When one performs MDS one typically is doing so to reduce the
dimensionality of the distances in order to make the data more
understandable.<span style="mso-spacerun: yes;"> </span>In MDS you decide how
many dimensions you want in order to fit the data.<span style="mso-spacerun: yes;"> </span>One important aspect of this is deciding how
many dimensions are needed to give a proper fit to your distance data.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">In R cmdscale will generate, if asked, a goodness of fit measure that is
based on the eigenvalues of the MDS solution.<span style="mso-spacerun: yes;">
</span>This goodness of fit measure doesn’t make any sense to me.<span style="mso-spacerun: yes;"> </span>Being old school, I would basically like to
measure goodness of fit by taking the original distances that I analyze and
compare them to the new distances that can be determined from my MDS solution. <span style="mso-spacerun: yes;"> </span>In the old days, this was done by taking the
two matrices of distances, stringing them out into two columns, and computing
the correlation between the two columns.<span style="mso-spacerun: yes;">
</span>If you square this correlation, you get R<sup>2</sup> which measures the
proportion of variance in your original data that is accounted for by your MDS
solution.<span style="mso-spacerun: yes;"> </span>You can also compute an F
statistic from this information </span><!--[if supportFields]><span
style='mso-bidi-font-size:12.0pt;mso-bidi-font-family:Arial'><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Pedhazur</Author><Year>1982</Year><RecNum>727</RecNum><DisplayText>(Pedhazur,
1982)</DisplayText><record><rec-number>727</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">727</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Pedhazur,
E.J.</author></authors></contributors><titles><title>Multiple
Regression In Behavioral
Research</title></titles><edition>Second</edition><dates><year>1982</year></dates><pub-location>New
York, NY</pub-location><publisher>Holt, Rinehart and
Winston</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="mso-no-proof: yes;">(<a href="file:///F:/Work/My%20Blogs/GOF.docx" title="Pedhazur, 1982 #727"><span style="color: windowtext; text-decoration: none; text-underline: none;">Pedhazur,
1982</span></a>)</span></span><!--[if supportFields]><span style='mso-bidi-font-size:
12.0pt;mso-bidi-font-family:Arial'><span style='mso-element:field-end'></span></span><![endif]--><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">.<span style="mso-spacerun: yes;"> </span>F = (R<sup>2</sup>/1)/((1- R<sup>2</sup>)/(N –
2)) where N is the number of rows in your strung out distance matrix.<span style="mso-spacerun: yes;"> </span>The F can then be evaluated at 1, N – 2 degrees
of freedom.<span style="mso-spacerun: yes;"> </span>You can also use this
approach to determine if taking out another dimension accounts for a
significant increase in variance accounted for – but see Pedhazur for the
details of this approach (in the context of multiple regression).<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial;">Unfortunately R does not deliver this old school measure of fit, even
though a search of the internet for how to do so reveals that many people seek
it.<span style="mso-spacerun: yes;"> </span>These poor people, probably old
school like myself, are simply told to use the eigenvalue-based goodness of fit
that cmdscale will deliver if prompted.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: Arial;">I recently rejected this advice, and wrote some R code to compute the “old
school” goodness of fit measure.<span style="mso-spacerun: yes;"> </span>I
provide this code below; I hope that someone will find it of use!<o:p></o:p></span></span></div>
<br />
<div style="border-color: currentColor currentColor windowtext; border-style: none none solid; border-width: medium medium 1pt; mso-border-bottom-alt: solid windowtext .75pt; mso-element: para-border-div; padding: 0cm 0cm 1pt;">
<div class="MsoNormal" style="border: currentColor; margin: 0cm 0cm 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0cm 0cm 1.0pt 0cm; padding: 0cm;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
</div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#Example of calculating goodness of fit<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#for MDS via cmdscale()<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Written by Michael R.W. Dawson, spring of 2015<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#Basic idea: Do MDS on distance data with cmdscale.<span style="mso-spacerun: yes;"> </span>Use the coordinates<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#from this solution to recreate the distances.<span style="mso-spacerun: yes;"> </span>String the original<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#distances and the new distances matrices out into two columns.<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Calculate the correlation between these two columns.<span style="mso-spacerun: yes;"> </span>Square this<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#correlation to get proportion of variance accounted for.<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Compute degrees of freedom = df = n -2 where n = length of a strung out
matrix <o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Compute F = (rsquared/1)/((1 - rsquared)/df)<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Evaluate p value for F at 1,df degrees of freedom<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: "Courier New", Courier, monospace;"><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-size: x-small;">#This example uses the eurodist dataset, already a set
of distances<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#The distances between 21 European cities, standard dataset in R<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">eurodist #display the starting distance data<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;"># Perform MDS on the data using cmdscale; k determines the number of
dimensions<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">EuroMDS <- cmdscale(eurodist, eig=TRUE, k=2)<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;"># ---- Code below calculates goodness of fit ----<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;"># Copy coordinates from MDS solution into a new matrix<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">NewEuroCoords = EuroMDS$points #take coords from cmdscale solution<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#Compute a new set of distances from the MDS coordinates delivered by
cmdscale<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">NewEuroDists <- dist(NewEuroCoords, diag=TRUE, upper=TRUE)<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#String the two distance matrices out into two columns<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#and calculate the correlation between these two columns<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">r <- cor(c(eurodist), c(NewEuroDists))<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#compute and display r squared from this correlation,</span></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#this is variance
accounted for<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">rsquared <- r * r<span style="mso-spacerun: yes;"> </span>#compute<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">rsquared<span style="mso-spacerun: yes;"> </span>#display<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#compute F test on this correlation<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#degrees of freedom for numerator = 1 <o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#compute degrees of freedom for denominator = N - 2 and display<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">freedom = NROW(c(NewEuroDists)) - 2 #compute<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">freedom #display df for denominator<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#compute and display F<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">Fvalue <- rsquared /((1 - rsquared)/freedom) #compute<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">Fvalue #display<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#use pf to determine the p-value of this F at df = 1, freedom<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">pf(Fvalue, 1, freedom, lower.tail=FALSE)<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<span style="font-family: "Courier New", Courier, monospace; font-size: x-small;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">#End result: goodness of fit measured as ability to<o:p></o:p></span></span></span></div>
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#reconstruct original distances, along with<o:p></o:p></span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#a significance test of this ability</span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;"><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#Change k to see fit of a different sized</span></span></span><br />
<span style="font-family: "Courier New", Courier, monospace;"><span style="font-size: x-small;"><span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;">#solution<o:p></o:p></span></span></span><br />
<br />
<div style="border-color: currentColor currentColor windowtext; border-style: none none solid; border-width: medium medium 1pt; mso-border-bottom-alt: solid windowtext .75pt; mso-element: para-border-div; padding: 0cm 0cm 1pt;">
<div class="MsoNormal" style="border: currentColor; margin: 0cm 0cm 0pt; mso-border-bottom-alt: solid windowtext .75pt; mso-padding-alt: 0cm 0cm 1.0pt 0cm; padding: 0cm;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
</div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-bidi-font-size: 12.0pt;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-family: Arial;">References<o:p></o:p></span></u></b></div>
<br />
<a href="https://www.blogger.com/null" name="_ENREF_1"><span style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Kruskal, J. B., & Wish, M. (1978). <i style="mso-bidi-font-style: normal;">Multidimensional Scaling</i>. Beverly Hills,
CA: Sage Publications.</span></span></a><span style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Pedhazur,
E. J. (1982). <i style="mso-bidi-font-style: normal;">Multiple Regression In
Behavioral Research</i> (Second ed.). New York, NY: Holt, Rinehart and Winston.</span></span></a><span style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<!--[if supportFields]><span style='mso-element:field-end'></span><![endif]--><o:p><span style="font-family: Arial;"> </span></o:p></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com7tag:blogger.com,1999:blog-7699616724222495854.post-41954717426836950782015-04-27T14:32:00.000-06:002015-04-27T15:11:25.730-06:00Composing With Strange Circles<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<em></em><br />
<span style="font-family: Arial;">This post provides a working java program for hearing different combinations of strange circles; the program is described below and is available for free as a Java jar file at this location: </span><a href="http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/Circles/StrangeCircles.zip"><span style="color: blue; font-family: Arial;">http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/Circles/StrangeCircles.zip</span></a><span style="font-family: Arial;">.<span style="mso-spacerun: yes;"> </span></span><br />
<em></em><br />
<em>Also, this post is a<a href="http://cognitionandreality.blogspot.ca/2013/03/composing-atonal-music-using-strange.html" target="_blank"> revised version of this previous post</a> on this blog. The text is a bit different; the big difference is that at the bottom of this blog I provide a java program that lets you compose with a variety of strange circles and hear the results. Feel free to download the program and play with it. If you have any difficulties please leave a comment; this is my first attempt at distributing code in this fashion and I would be surprised if I don't make some mistakes. To run the program, download the zip file, unpack it, and double-click on the .jar file's icon. You need to have Java installed on your program for this code to function.</em><br />
<em></em><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9Mui4LxJKHxqvJktJpvAfeRkzSYq6W-Lzw2uo_4eFjIObgN5Gi7U_pHNRdQx6enRqGkh_Np0FiWbQDsC8viu5acakV0B2RwsJ7actIACjgny7eIEYINQbvoLGFDVb1nrpj1fsHccO_dw/s1600/FigureI-8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9Mui4LxJKHxqvJktJpvAfeRkzSYq6W-Lzw2uo_4eFjIObgN5Gi7U_pHNRdQx6enRqGkh_Np0FiWbQDsC8viu5acakV0B2RwsJ7actIACjgny7eIEYINQbvoLGFDVb1nrpj1fsHccO_dw/s1600/FigureI-8.jpg" height="240" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<strong><span style="font-family: Arial;">Figure I-8. The first four bars of an atonal piece composed
with some strange circles found within musical networks.<span style="mso-spacerun: yes;"> </span>See text for details.<o:p></o:p></span></strong></div>
<div class="WordSection1">
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
</div>
<span style="font-family: "Arial","sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span>
<br />
<div class="WordSection2">
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Atonal music has no discernible musical key or tonal center
because all twelve pitch-classes from Western music occur equally often.<span style="mso-spacerun: yes;"> </span>Arnold Schoenberg invented a method, called
the twelve tone technique or <i style="mso-bidi-font-style: normal;">dodecaphony</i>,
for composing atonal music.<span style="mso-spacerun: yes;"> </span>His 1923
piece <i style="mso-bidi-font-style: normal;">Fünf Klavierstücke, Opus 23</i> was
the first to be composed using this technique.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">In dodecaphony one begins a new composition by arranging all
twelve pitch-classes in some desired order; this arrangement is called the <i style="mso-bidi-font-style: normal;">tone row</i>.<span style="mso-spacerun: yes;"> </span>The first note from the tone row is then used
to begin the new piece.<span style="mso-spacerun: yes;"> </span>The duration of
this note, and whether or not it is repeated, is under the composer’s control.<span style="mso-spacerun: yes;"> </span>However, once the use of this note is
complete, dodecaphony takes control: the twelve tone method prevents the
composer from using again until all of the other eleven notes in the tone row
have first been used.<span style="mso-spacerun: yes;"> </span>Their use,
naturally, follows the same procedure used for the first note: the composer
decides upon duration and repetition, uses the note, and then moves on to the
next note in the tone row.<span style="mso-spacerun: yes;"> </span>The final
movement of Schoenberg’s <i style="mso-bidi-font-style: normal;">Fünf Klavierstücke,
Opus 23</i> was the first to be composed using a complete (twelve note) tone
row in this fashion.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">In the preceding chapter we saw that musical pitch-classes
could be arranged in a number of different strange circles: for instance, four
different circles of major thirds ([C, E, G#], [C#, F, A], [D, F#, A#], and
[D#, E, G]) or two different circles of major seconds ([C, D, E, F#, G#, A#]
and [C#, D#, F, G, B]).<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">We also saw that when artificial neural networks are trained
to solve problems in harmony, they often use these strange circles to organize
pitch-classes into different equivalence classes.<span style="mso-spacerun: yes;"> </span>For instance, all of the pitch-classes that
belong to one circle of major seconds may all be assigned the same connection
weight (e.g. to the connection from a pitch-class input unit to a hidden unit).<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">In a musical network, the connection weight from an input
unit to a hidden unit is essentially the ‘name’ that identifies the
pitch-class.<span style="mso-spacerun: yes;"> </span>If all of the pitch-classes
belonging to a strange circle are assigned the same connection weight, then
they are all being assigned the same ‘name’.<span style="mso-spacerun: yes;">
</span>This means that the hidden unit is deaf to any differences between
members of this subset of pitch-classes.<span style="mso-spacerun: yes;">
</span>For a hidden unit that uses equivalence classes based on circles of major
seconds, there are only two pitch-classes: some ‘name’ <i style="mso-bidi-font-style: normal;">x</i> (the weight assigned to C, D, E, F#, G#, and A#) and some other
‘name’ <i style="mso-bidi-font-style: normal;">y</i> (the weight assigned to<span style="mso-spacerun: yes;"> </span>C#, D#, F, G, and B).<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Why do networks use strange circle equivalence classes to
represent musical structure?<span style="mso-spacerun: yes;"> </span>One reason
is that networks discover that notes that belong to the <i style="mso-bidi-font-style: normal;">same</i> strange circle are not typically used together to solve
musical problems, such as classifying a musical chord.<span style="mso-spacerun: yes;"> </span>Instead, the network discovers that combining
notes from <i style="mso-bidi-font-style: normal;">different</i> strange circles
is more successful.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">This use of equivalence classes -- combining pitch-classes
from different circles, but not from the same circle – suggests an alternative
approach to composing atonal music.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Imagine a musical composition constructed from a set of
different musical voices.<span style="mso-spacerun: yes;"> </span>Each of these
voices could be derived from a strange circle.<span style="mso-spacerun: yes;">
</span>The notes sung by this voice are selected by randomly choosing from the
set of pitch-classes that belong to the strange circle.<span style="mso-spacerun: yes;"> </span>For instance, if one voice was associated
with a particular circle of major thirds, then one could write its notes by
randomly choosing one note at a time from the set [C, E, G#].<span style="mso-spacerun: yes;"> </span>To make the voice more musically interesting,
one could add a randomly selected rest to the mix by selecting from the set [C,
E, G#, R] where R indicates a rest (i.e. no note is to be sung).<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">If one associated different voices with different strange
circles, and composed via random selection as described above, then one would
be following the general principle discovered by the network: pitch-classes
from different strange circles can occur together, but pitch-classes from the
same strange circle cannot.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Furthermore, one could use this method to compose atonal
music by wisely choosing which strange circles to use to create different
voices.<span style="mso-spacerun: yes;"> </span>For instance, imagine creating a
piece that included four voices, each associated with a different circle of
major thirds.<span style="mso-spacerun: yes;"> </span>This composition would be
atonal, in Schoenberg’s sense, because the four circles combine to include all
twelve possible pitch-classes.<span style="mso-spacerun: yes;"> </span>Randomly
selecting pitches from each of these circles would produce a composition that
did not have a tonal center because each of the twelve pitch-classes would
occur equally often when the composition was considered as a whole.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Figure I-8 provides a short score created by using the
approach described above.<span style="mso-spacerun: yes;"> </span>This score
includes six staves, one for each voice.<span style="mso-spacerun: yes;">
</span>Each voice is generated by randomly selecting from one strange circle (and
including rests in this sampling procedure).<span style="mso-spacerun: yes;">
</span>The top two staves, written in quarter notes, are each drawn from a
different circle of major seconds.<span style="mso-spacerun: yes;"> </span>The
bottom four staves, written in half notes, are each drawn from a different
circle of major thirds.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">The score illustrated in Figure I-8 is created by applying
two additional musical assumptions.<span style="mso-spacerun: yes;">
</span>First, while each wheel generated a pitch-class name, I decided how high
or low (in terms of octave) each note was positioned.<span style="mso-spacerun: yes;"> </span>Second, in order to ensure that all notes tended
to occur equally often in the score, I sampled the two circles of major seconds
twice as frequently relative to the other four strange circles.<span style="mso-spacerun: yes;"> </span>That is why the upper two staves use notes
that are half the duration of those in the bottom four staves.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Figure I-8 provides the first four bars of a longer
composition that can be found at this website: </span><a href="http://cognitionandreality.blogspot.ca/2013/03/composing-atonal-music-using-strange.html"><span style="color: blue; font-family: Arial;">http://cognitionandreality.blogspot.ca/2013/03/composing-atonal-music-using-strange.html</span></a><span style="font-family: Arial;">.<span style="mso-spacerun: yes;"> </span>At the bottom of this web page one can find
links that play some of the voices individually, some combinations of a small
number of the voices, and all of the voices played together.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">On listening to these samples, one discovers that individual
the strange circles are musical, but are not really musically interesting.<span style="mso-spacerun: yes;"> </span>Music that is more interesting emerges from
combining the random outputs of different circles.<span style="mso-spacerun: yes;"> </span>For instance, I enjoyed the results of
pairing the two circles of major seconds together. <span style="mso-spacerun: yes;"> </span>I was also surprised at the musicality of the
full composition.<span style="mso-spacerun: yes;"> </span>My impression of this
piece was that it is a modern, atonal composition.<span style="mso-spacerun: yes;"> </span>I am no Schoenberg, but I humbly submit that
composing music by combining strange circles provides an interesting and
alternative method to dodecaphony.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">Of course, there are other strange circles that could be
incorporated into this approach to composing, such as the three circles of
minor thirds or the six circles of tritones.<span style="mso-spacerun: yes;">
</span>What kinds of atonal pieces can be created when many different strange
circles are available?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">To answer this question, I created a Java program that uses
David Koelle’s music package jFugue <!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Koelle</Author><Year>2008</Year><RecNum>5618</RecNum><DisplayText>(Koelle,
2008)</DisplayText><record><rec-number>5618</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">5618</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Koelle,
D.</author></authors></contributors><titles><title>The
Complete Guide to JFugue: Programming Music in
Java</title></titles><dates><year>2008</year></dates><publisher>www.jfugue.org</publisher><urls><pdf-urls><url>file://F:\Reprints\K\Koelle1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span><![endif]--><span style="mso-no-proof: yes;">(</span></span><a href="file:///K:/Books/MusicNet/Interludes/Interlude7.docx" title="Koelle, 2008 #5618"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;"><span style="font-family: Arial;">Koelle, 2008</span></span></a><span style="font-family: Arial;"><span style="mso-no-proof: yes;">)</span><!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]-->.<span style="mso-spacerun: yes;"> </span>This package lets the programmer define
strings of musical notes, and then takes care of playing them.<span style="mso-spacerun: yes;"> </span>The program that I wrote lets the user choose
a composition’s tempo and length with a mouse, and then make a checkmark beside
every strange circle to be used in a piece.<span style="mso-spacerun: yes;">
</span>All fifteen circles in Figure I-9 can be used at once!<span style="mso-spacerun: yes;"> </span>The user can decide whether or not to include
rests, and set the duration and the octave (2 is lowest, 5 is highest) for each
set of circles.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">A press of the compose button leads to a pause while the
various voices are constructed, and then the piece is played through the
computer’s speakers.<span style="mso-spacerun: yes;"> </span>One can easily
explore the possibilities of strange circle composing with this program and listening
to the sounds that it creates.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;">This program is available for free as a Java jar file at
this location: </span><a href="http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/Circles/StrangeCircles.zip"><span style="color: blue; font-family: Arial;">http://www.bcp.psych.ualberta.ca/~mike/BlogStuff/Circles/StrangeCircles.zip</span></a><span style="font-family: Arial;">.<span style="mso-spacerun: yes;"> </span>Save the zip file to your computer, move it to a desired location, and unpack it. You will see a program called StrangeCircles.jar and a lib directory; these two items have to be in the same location on your computer.<span style="mso-spacerun: yes;"> </span>To run the program from a command line, when you are in the proper location type:
java –jar StrangCircles.jar.<span style="mso-spacerun: yes;"> </span>On a
windows machine, the program can also be run simply by double-clicking on the
program’s icon after it has been downloaded. The program requires that Java be installed on your program.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> </span></o:p></div>
</div>
<o:p><span style="font-family: Arial;"></span></o:p><br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="font-family: Arial;"> </span></div>
<span style="font-family: Arial;">
<br />
</span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxVLnY4GS6rWkq3_LY-kVtCq4oZS6vyfXxnMyLO-caDY9PiGXehWZ9iLFR0z0oSW538hi9h2mDB7tN1jNyHLjs0vdNNVNdOCsi-yYX_DsUm1-NYok1rOgcC0LmsEF8dR-7IxuUgXXe0I0/s1600/FigureI-9.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxVLnY4GS6rWkq3_LY-kVtCq4oZS6vyfXxnMyLO-caDY9PiGXehWZ9iLFR0z0oSW538hi9h2mDB7tN1jNyHLjs0vdNNVNdOCsi-yYX_DsUm1-NYok1rOgcC0LmsEF8dR-7IxuUgXXe0I0/s1600/FigureI-9.jpg" height="186" width="320" /></a></span></div>
<span style="font-family: Arial;">
</span><span style="font-family: "Arial","sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><br clear="all" style="mso-break-type: section-break; page-break-before: auto;" />
</span><b><span style="font-family: "Arial","sans-serif"; font-size: 9pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span></b><strong><span style="font-family: Arial;">Figure I-9. A screenshot of a Java program that randomly
selects from various strange circles to compose atonal music.<span style="mso-spacerun: yes;"> </span>In the figure, one circle of major thirds,
one circle of minor thirds, one circle of major seconds, and two circles of
tritones have been selected to be used in a four bar composition that includes
rests.<span style="mso-spacerun: yes;"> </span>See text for details.</span></strong><br />
<strong><span style="font-family: Arial;"></span></strong><br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial;"> <strong><u>References</u></strong></span></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt; text-indent: 0in;">
<!--[if supportFields]><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <![endif]--><!--[if supportFields]><span
style='mso-element:field-end'></span><![endif]--><span style="mso-bidi-font-family: Arial;"><span style="font-family: Arial;">Koelle, D. (2008). <i style="mso-bidi-font-style: normal;">The Complete Guide to JFugue: Programming Music in Java</i>:
www.jfugue.org.</span></span><span style="mso-bidi-font-family: Arial;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-77186412882762950542015-04-19T14:20:00.002-06:002015-04-19T14:20:24.388-06:00Riemannian Tonics and Symmetry<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<em></em><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6hdXMgq72FqV0FTZWaQk1X95BJNrtb6WAI65Z0x8DNYxAIk2MiYjN8_M1IELZwkXCOLJUsAv-MSzXi5h7KXPhgLlvnZxVQeK5HmpnwCc6MVIedAfwi0PPJT9yWhja4O5KRyUQSq9xIhc/s1600/FigureI-6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6hdXMgq72FqV0FTZWaQk1X95BJNrtb6WAI65Z0x8DNYxAIk2MiYjN8_M1IELZwkXCOLJUsAv-MSzXi5h7KXPhgLlvnZxVQeK5HmpnwCc6MVIedAfwi0PPJT9yWhja4O5KRyUQSq9xIhc/s1600/FigureI-6.jpg" height="149" width="320" /></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><strong><span style="font-family: Arial; font-size: x-small;"> </span></strong></o:p></span></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-6. Connection weights from input
pitch-classes to two different output units (D and D#) in a network trained to
identify Riemann’s roots for major and minor triads.<o:p></o:p></span></strong></span></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">Hugo Riemann (b. 1849, d. 1919) was one of
the most important music theorists </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Rehding</Author><Year>2003</Year><RecNum>6466</RecNum><DisplayText>(Rehding,
2003)</DisplayText><record><rec-number>6466</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6466</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Rehding,
A.</author></authors></contributors><titles><title>Hugo
Riemann And The Birth Of Modern Musical
Thought</title><secondary-title>New perspectives in music history
and criticism</secondary-title></titles><pages>x, 218
p.</pages><keywords><keyword>Riemann, Hugo, 1849-1919
Criticism and interpretation.</keyword><keyword>Music theory
History.</keyword><keyword>Musicology
History.</keyword></keywords><dates><year>2003</year></dates><pub-location>Cambridge
; New York</pub-location><publisher>Cambridge University
Press</publisher><isbn>0521820731</isbn><accession-num>12887549</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) ML423.R5 R44 2003&#xD;Performing Arts
Reading Rm (Madison, LM113) - STORED OFFSITE ML423.R5 R44
2003</call-num><urls><related-urls><url>Sample text
http://www.loc.gov/catdir/samples/cam033/2002031364.html</url><url>Publisher
description
http://www.loc.gov/catdir/description/cam031/2002031364.html</url><url>Table
of contents http://www.loc.gov/catdir/toc/cam031/2002031364.html</url><url>Contributor
biographical information
http://www.loc.gov/catdir/enhancements/fy0731/2002031364-b.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude6.docx" title="Rehding, 2003 #6466"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Rehding, 2003</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Riemann was strongly
influenced by the natural science of music that flourished in the 19<span style="font-size: small;"><sup>th</sup>
century </span></span><!--[if supportFields]><span lang=EN-US><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude6.docx" title="Burnham, 1992 #6941"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Burnham, 1992</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude6.docx" title="Hui, 2013 #6767"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hui, 2013</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">, such
as the prototypical and pioneering work of Helmholtz which was introduced in
Chapter 1.<span style="mso-spacerun: yes;"> </span>Riemann’s goal was to provide
the natural laws that governed music; he argued that these laws are rooted in
musical harmony </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Riemann</Author><Year>1895</Year><RecNum>6458</RecNum><DisplayText>(Riemann,
1895)</DisplayText><record><rec-number>6458</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6458</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Riemann,
H.</author></authors></contributors><titles><title>Harmony
simplified: Or, The Theory Of The Tonal Functions Of
Chords</title></titles><dates><year>1895</year></dates><pub-location>London</pub-location><publisher>Augener</publisher><accession-num>8162334</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) MT50.R558
B4</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude6.docx" title="Riemann, 1895 #6458"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Riemann, 1895</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>For Riemann, an
understanding of the logic of harmony was tantamount to an understanding of the
universal structure of music.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">In his own analysis of harmony, Riemann was
particularly interested in the triad.<span style="mso-spacerun: yes;"> </span>In
modern musical theory a triad is a three note chord that is built upwards from
a tonic note.<span style="mso-spacerun: yes;"> </span>For instance, the A major
triad is built upon the tonic A, and includes C# (which is a major third higher
than A) and E (which is a minor third higher than C#).<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">A minor triad can be described as a distortion
of a major triad.<span style="mso-spacerun: yes;"> </span>In general, one creates
a minor triad by lowering the middle note of a major triad by one
semitone.<span style="mso-spacerun: yes;"> </span>For instance, to produce the A
minor triad, one takes the A major triad [A, C#, E] and lowers the middle note
to create the triad [A, C, E].<span style="mso-spacerun: yes;"> </span>Another
way to consider a minor triad is that it too is built upwards from a tonic, but
using different musical intervals.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Riemann conceived triad structure in a different
fashion.<span style="mso-spacerun: yes;"> </span>He proposed an idea known as <i style="mso-bidi-font-style: normal;">harmonic dualism</i>.<span style="mso-spacerun: yes;"> </span>According to harmonic dualism, major and
minor triads are constructed from processes that are identical in
structure.<span style="mso-spacerun: yes;"> </span>However, these processes are
opposite in direction.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Harmonic dualism conceives of major triads
in the same way as modern theory: by building upwards from a tonic with a note
that is first a major third higher than the tonic, and then another note a
minor third higher than this middle note.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">However, harmonic dualism departs from
modern theory in its conception of minor triads.<span style="mso-spacerun: yes;"> </span>Harmonic dualism highlights structural
symmetry between minor and major triads.<span style="mso-spacerun: yes;">
</span>According to Riemann, minor triads are built <i style="mso-bidi-font-style: normal;">downwards</i> from the tonic using the same procedure used (in an
upwards direction) to create a major triad.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">For instance, consider the minor triad [A,
C, E].<span style="mso-spacerun: yes;"> </span>For Riemann, the tonic of this
triad is not A, but is instead E.<span style="mso-spacerun: yes;"> </span>To
create the triad, one first adds a note a major third below the tonic, and then
adds a second note a minor third below the middle note.<span style="mso-spacerun: yes;"> </span>Riemann would not call this triad A minor;
instead he would call it ‘under E’ or </span></span><span lang="EN-US" style="font-family: Symbol; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span lang="EN-US"><span style="font-family: Arial;">E.<span style="mso-spacerun: yes;"> </span>Furthermore, its symmetric structure
decreases its relationship to one major triad (A major) and increases its
relationship to another (E major).<span style="mso-spacerun: yes;"> </span>E
major and </span></span><span lang="EN-US" style="font-family: Symbol; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span lang="EN-US"><span style="font-family: Arial;">E both start from the same tonic, and have identical structure one
as moves away from this tonic.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Harmonic dualism assigns different tonics
to the minor triads than are assigned by modern music theory.<span style="mso-spacerun: yes;"> </span>Table I-1 provides each approach’s tonics for
the 12 major and 12 minor triads.<o:p></o:p></span></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxTCuRmp2YkgIdB7B54vsdmDsPnBKeWqnE-v8TH3aKUY1JzheDYxdz4RsdsCtGGC414kYRIbL9a5sDgRBwgKxR0tzhuPXFtT6dpgTXMUO4rtfwUkgbh_DFNr__7b7bUbmOoZtr6n0EYtU/s1600/Table.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxTCuRmp2YkgIdB7B54vsdmDsPnBKeWqnE-v8TH3aKUY1JzheDYxdz4RsdsCtGGC414kYRIbL9a5sDgRBwgKxR0tzhuPXFtT6dpgTXMUO4rtfwUkgbh_DFNr__7b7bUbmOoZtr6n0EYtU/s1600/Table.jpg" height="320" width="153" /></a></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Table I-1 provides two qualitatively different
theories about the tonic notes of triads.<span style="mso-spacerun: yes;">
</span>How might the differences between these theories be reflected in network
structure?<span style="mso-spacerun: yes;"> </span>Is modern theory harder or
easier for a network to learn than is harmonic dualism?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">To explore such questions, perceptrons can
be trained to identify the tonics of input triads.<span style="mso-spacerun: yes;"> </span>This requires 12 input and 12 output
units.<span style="mso-spacerun: yes;"> </span>The input units use pitch-class
representation to encode the three component pitch-classes of a triad, and the output
units use pitch-class representation to encode the triad’s tonic.<span style="mso-spacerun: yes;"> </span>The output units are all value units, and
each has its </span><span lang="EN-US" style="mso-bidi-font-family: Arial;">µ</span><span lang="EN-US"> set to 0, and a learning rate of 0.01 is employed.<span style="mso-spacerun: yes;"> </span>Two different training sets are used to teach
two different types of perceptrons: one that uses the Riemann tonics of the
input triads, the other that uses their modern tonics.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Both training sets are learned very quickly:
the Riemann tonics require an average of about 73 epochs of training, while the
modern tonics are acquired after about 65 epochs of training.<span style="mso-spacerun: yes;"> </span>This difference is not statistically
significant.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Harmonic dualism enforces symmetric
processes for constructing major and minor triads.<span style="mso-spacerun: yes;"> </span>As a result, one constructs </span></span><span lang="EN-US" style="font-family: Symbol; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span lang="EN-US"><span style="font-family: Arial;">D in exactly the same manner as one constructs D major, except in
opposite directions.<span style="mso-spacerun: yes;"> </span>This symmetry of
structure is elegantly evident in the connection weights of a perceptron
trained to detect the Riemann tonics.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Consider the left hand side of Figure I-6.<span style="mso-spacerun: yes;"> </span>It plots the connection weights from each of
the 12 pitch-class input units to the output unit that detects the Riemann
tonic of D.<span style="mso-spacerun: yes;"> </span>Note the beautiful mirror
symmetry of connection weights as you move either to the left or to the right
from the D input weight.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">How does the output unit use these weights
to detect a Riemann tonic of D?<span style="mso-spacerun: yes;"> </span>The only
positive connection weight is associated with the input pitch-class D, shown in
black in the graph.<span style="mso-spacerun: yes;"> </span>The output unit will
only activate when the signal sent through this positive connection weight is
cancelled out by two signals sent through negative connection weights.<span style="mso-spacerun: yes;"> </span>Only two pairs of signals accomplish this: signals
from A and F# (which combine with D to represent D major) and signals from A#
and G (which combine with D to represent </span></span><span lang="EN-US" style="font-family: Symbol; mso-ascii-font-family: Arial; mso-char-type: symbol; mso-hansi-font-family: Arial; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">°</span></span><span lang="EN-US"><span style="font-family: Arial;">D).<span style="mso-spacerun: yes;"> </span>These four connection
weights are also shown in black.<span style="mso-spacerun: yes;"> </span>All of
the other connection weights are so extremely negative that they turn this
output unit off if any of their associated pitch-classes are present.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Because the symmetric pattern of connection
weights emanates outwards from either side of one weight (e.g. from the left or
right of the weight for D) there must be one pitch-class that breaks this
symmetry.<span style="mso-spacerun: yes;"> </span>In this case, it is the weight
for G# which is shown in white in the figure.<span style="mso-spacerun: yes;">
</span>Importantly, this outlier weight corresponds to the pitch class that is
a tritone away from D.<span style="mso-spacerun: yes;"> </span>This means that
if one was to wrap the x-axis of the graph in a circle (i.e. the circle of
minor seconds), the connection weights would be perfectly symmetric across the
diameter from D to G# which cuts this circle in half.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Essentially the same pattern of connection
weights is found in this perceptron for the other output units.<span style="mso-spacerun: yes;"> </span>The only difference is that the pattern is
shifted to be centered on a different output unit.<span style="mso-spacerun: yes;"> </span>This is illustrated on the right side of
Figure I-6, which illustrates the weights of the connections that feed into the
output unit for D#.<span style="mso-spacerun: yes;"> </span>It provides the identical
pattern as shown on the figure’s left, but the pattern has been shifted one
pitch-class to the right.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The wonderful symmetry in the Figure I-6
connection weights is completely consistent with the symmetry that is the
foundation of harmonic dualism.<span style="mso-spacerun: yes;"> </span>Such
symmetry -- perhaps sadly -- is not found when a perceptron is trained to
generate the modern tonics of triads, as can be seen from the weights illustrated
in Figure I-7.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span><div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrSqa-75_ME3oTViu3FtWFeLq79SfhiQ-Inrg8AubJcG-oOohSr2z3vsfOvZHcHL3oQw8apyf99k8zHfujPI5mE6fP16sV2vYTvQ5Aas9sUGNiAsRdqupo-iuwYzKRoysmVgnMpgkW29Q/s1600/FigureI-7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrSqa-75_ME3oTViu3FtWFeLq79SfhiQ-Inrg8AubJcG-oOohSr2z3vsfOvZHcHL3oQw8apyf99k8zHfujPI5mE6fP16sV2vYTvQ5Aas9sUGNiAsRdqupo-iuwYzKRoysmVgnMpgkW29Q/s1600/FigureI-7.jpg" height="310" width="320" /></a></span></div>
<br />
<br />
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-7. The connection weights from the input units to the output unit representing the tonic D in a perceptron trained to detect modern tonics.<o:p></o:p></span></strong></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"></span></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Figure I-7 provides the connection weights
that feed into the D output unit of a perceptron trained on modern tonics.<span style="mso-spacerun: yes;"> </span>Its bars are colored according to the same
scheme used in Figure I-6: black bars show pitch-classes involved in turning
this output unit on, grey bars show pitch-classes involved in turning this
output unit off, and the white bar is associated with the pitch-class a tritone
away from D.<span style="mso-spacerun: yes;"> </span>These weights function in a
fashion similar to those of Figure I-6: A signal from D and two other input
units produce a net input close enough to zero to turn the output unit on.<span style="mso-spacerun: yes;"> </span>The combinations are [D, F#, A] for D major
and [D, F, A] for D minor.<span style="mso-spacerun: yes;"> </span>This identical
pattern is found for other output units, once again shifted along the x-axis.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The symmetry that is present in Figure I-6,
and missing from Figure I-7, is enchanting.<span style="mso-spacerun: yes;">
</span>There are clearly additional properties to be gleaned from the Figure
I-6 weights that involve considering the relationships between pairs of
pitch-classes that are assigned the same weight.<span style="mso-spacerun: yes;"> </span>These relationships, for instance, could be
considered in the context of Riemann’s theories about tonal relationships.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">In short, training networks to detect regularities
defined by opposing musical theories provides a new paradigm – network interpretation
– that could be applied to consider their advantages and disadvantages.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"><strong><u>References</u></strong></span></o:p></span></div>
<br />
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Burnham, S. (1992). Method and motivation in Hugo Riemann's history of harmonic theory. <i style="mso-bidi-font-style: normal;">Music Theory Spectrum, 14</i>(1), 1-14.</span></span></a></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Hui, A. (2013). <i style="mso-bidi-font-style: normal;">The Psychophysical Ear: Muscial Experiments, Experimental Sounds, 1840-1910</i>. Cambridge, Mass.: MIT Press.</span></span></a></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_3"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rehding, A. (2003). <i style="mso-bidi-font-style: normal;">Hugo Riemann And The Birth Of Modern Musical Thought</i>. Cambridge ; New York: Cambridge University Press.</span></span></a></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_4"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Riemann, H. (1895). <i style="mso-bidi-font-style: normal;">Harmony simplified: Or, The Theory Of The Tonal Functions Of Chords</i>. London: Augener.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
</ul>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
</div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-29772300800009007372015-04-15T16:47:00.000-06:002015-04-15T16:47:35.412-06:00Keyfinding Logistics<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The networks described up to this point in
the book have used the Gaussian activation function in their output or hidden
units.<span style="mso-spacerun: yes;"> </span>One reason for this is that using
value units leads to networks that are often easier to interpret, largely
because they are tuned to respond to a very narrow range of net inputs </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <EndNote><Cite><Author>Berkeley</Author><Year>1995</Year><RecNum>4</RecNum><DisplayText>(Berkeley,
Dawson, Medler, Schopflocher, &amp; Hornsby,
1995)</DisplayText><record><rec-number>4</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">4</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Berkeley,
I.S.N.</author><author>Dawson,
M.R.W.</author><author>Medler, D.A.</author><author>Schopflocher,
D.P.</author><author>Hornsby, L.</author></authors></contributors><titles><title>Density
plots of hidden value unit activations reveal interpretable
bands</title><secondary-title>Connection
Science</secondary-title></titles><periodical><full-title>Connection
Science</full-title></periodical><pages>167-186.</pages><volume>7</volume><dates><year>1995</year></dates><urls><pdf-urls><url>file://F:%5CReprints%5CB%5CBerkeley1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Berkeley, 1995 #4"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Berkeley, Dawson, Medler, Schopflocher, & Hornsby, 1995</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Most of connectionist cognitive science,
however, uses networks whose processors compute activity with the logistic
function.<span style="mso-spacerun: yes;"> </span>Let us take a moment to
consider one such network of integration devices, and to explore its performance
on a keyfinding task.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The logistic activation function has a long
history of being used in the study of populations and in economics </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Cramer</Author><Year>2003</Year><RecNum>6942</RecNum><DisplayText>(Cramer,
2003)</DisplayText><record><rec-number>6942</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6942</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Cramer,
J.S.</author></authors></contributors><titles><title>Logit
Models From Economics and Other
Fields</title></titles><pages>x, 173
p.</pages><keywords><keyword>Econometric
models.</keyword><keyword>Logits.</keyword></keywords><dates><year>2003</year></dates><pub-location>Cambridge,
UK ; New York</pub-location><publisher>Cambridge University
Press</publisher><isbn>0521815886</isbn><accession-num>13017692</accession-num><call-num>Jefferson
or Adams Building Reading Rooms - STORED OFFSITE HB141 .C722
2003</call-num><urls><related-urls><url>Table of
contents
http://www.loc.gov/catdir/toc/cam031/2002041450.html</url><url>Publisher
description
http://www.loc.gov/catdir/description/cam031/2002041450.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Cramer, 2003 #6942"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Cramer, 2003</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>It was first invented and
named by Pierre-Fran</span><span lang="EN-US" style="mso-bidi-font-family: Arial;">ҫ</span><span lang="EN-US">ois Verhulst in the 19<span style="font-size: small;"><sup>th</sup> century as a mathematical model
of growth.<span style="mso-spacerun: yes;"> </span>It was independently
rediscovered on more than one occasion in the early 20<sup>th</sup> century.<o:p></o:p></span></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">In connectionism, the logistic function is
particularly famous for being used as a continuous approximation of the
threshold function; this in turn permitted researchers to use calculus to
derive learning rules for multilayer perceptrons </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Rumelhart</Author><Year>1986</Year><RecNum>261</RecNum><DisplayText>(Rumelhart,
Hinton, &amp; Williams,
1986)</DisplayText><record><rec-number>261</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">261</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Rumelhart,
D.E.</author><author>Hinton,
G.E.</author><author>Williams,
R.J.</author></authors></contributors><titles><title>Learning
representations by back-propagating errors</title><secondary-title>Nature</secondary-title></titles><periodical><full-title>Nature</full-title></periodical><pages>533-536</pages><volume>323</volume><dates><year>1986</year></dates><urls><pdf-urls><url>file://F:\Reprints\R\Rumelhart2.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Rumelhart, 1986 #261"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Rumelhart, Hinton, & Williams,
1986</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>However, this equation has
other important roles in connectionism as well.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">For instance, the logistic equation permits
network responses to be translated into probability theory </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>McClelland</Author><Year>1998</Year><RecNum>6734</RecNum><DisplayText>(McClelland,
1998)</DisplayText><record><rec-number>6734</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6734</key></foreign-keys><ref-type
name="Book
Section">5</ref-type><contributors><authors><author>McClelland,
J.</author></authors><secondary-authors><author>Oaksford,
M.</author><author>Chater, N.</author></secondary-authors></contributors><titles><title>Connectionist
models and Bayesian inference</title><secondary-title>Rational
Models of
Cognition</secondary-title></titles><pages>21-53</pages><dates><year>1998</year></dates><pub-location>Oxford</pub-location><publisher>Oxford
University
Press</publisher><urls><pdf-urls><url>file://F:\Reprints\M\McClelland2.pdf</url><url>file://F:\Reprints\M\McClelland3.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="McClelland, 1998 #6734"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">McClelland, 1998</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>As a result, the responses
of a network that has integration devices in its output layer can literally be
interpreted as being conditional probabilities </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Dawson</Author><Year>2012</Year><RecNum>5701</RecNum><DisplayText>(Dawson
&amp; Dupuis, 2012; Dawson, Dupuis, Spetch, &amp; Kelly,
2009)</DisplayText><record><rec-number>5701</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">5701</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Dawson,
M.R.W.</author><author>Dupuis,
B.</author></authors></contributors><titles><title>Equilibria
of perceptrons for simple contingency
problems</title><secondary-title>IEEE Transactions On Neural
Networks And Learning
Systems</secondary-title></titles><periodical><full-title>IEEE
Transactions On Neural Networks And Learning
Systems</full-title></periodical><volume>in
press</volume><dates><year>2012</year></dates><urls><pdf-urls><url>file://F:\Reprints\D\Dawson25.pdf</url></pdf-urls></urls></record></Cite><Cite><Author>Dawson</Author><Year>2009</Year><RecNum>2752</RecNum><record><rec-number>2752</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">2752</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Dawson,
M.R.W.</author><author>Dupuis,
B.</author><author>Spetch, M. L.</author><author>Kelly,
D.
M.</author></authors></contributors><titles><title>Simple
artificial networks that match probability and exploit and explore when
confronting a multiarmed bandit</title><secondary-title>IEEE
Transactions on Neural
Networks</secondary-title></titles><periodical><full-title>Ieee
Transactions on Neural Networks</full-title><abbr-1>Ieee T Neural
Networ</abbr-1></periodical><pages>1368-1371</pages><volume>20</volume><number>8</number><dates><year>2009</year></dates><urls><pdf-urls><url>file://F:\Reprints\D\Dawson21.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Dawson, 2012 #5701"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson & Dupuis, 2012</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Dawson, 2009 #2752"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson, Dupuis,
Spetch, & Kelly, 2009</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">From this perspective, training an integration
device network on a keyfinding task is appealing.<span style="mso-spacerun: yes;"> </span>Imagine that this network has 24 different
output units, one for each possible major and minor key in Western tonal
music.<span style="mso-spacerun: yes;"> </span>The activity in each of these
output units would indicate probability judgments: each activity would indicate
the probability that some musical event belonged to a particular musical key.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">In Chapter 5 we described a network of
value units that was trained on a set of pitch-class patterns that implied
particular musical keys </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Handelman</Author><Year>2013</Year><RecNum>6663</RecNum><DisplayText>(Handelman
&amp; Sigler,
2013)</DisplayText><record><rec-number>6663</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6663</key></foreign-keys><ref-type
name="Book Section">5</ref-type><contributors><authors><author>Handelman,
E.J.</author><author>Sigler,
A.</author></authors><secondary-authors><author>Yust,
J.</author><author> Wild, J.</author><author>Burgoyne,
J.A.</author></secondary-authors></contributors><titles><title>Key
induction and key mapping using pitch-class set
assertions</title><secondary-title>Mathematics and Computation in
Music</secondary-title></titles><pages>115-127</pages><dates><year>2013</year></dates><pub-location>New
York</pub-location><publisher>Springer</publisher><urls><pdf-urls><url>file://F:\Reprints\H\Handelman1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Handelman, 2013 #6663"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Handelman & Sigler, 2013</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>This network’s ability to
judge the musical keys of 152 different Nova Scotian folk songs </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Creighton</Author><Year>1932</Year><RecNum>6709</RecNum><DisplayText>(Creighton,
1932)</DisplayText><record><rec-number>6709</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6709</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Creighton,
H.</author></authors></contributors><titles><title>Songs
And Ballads From Nova Scotia</title></titles><pages>xxii, 333,
1 p.</pages><keywords><keyword>Folk songs, English Nova
Scotia.</keyword><keyword>Ballads, English Nova
Scotia.</keyword><keyword>Canadian poetry Nova
Scotia.</keyword><keyword>Nova Scotia Songs and
music.</keyword></keywords><dates><year>1932</year></dates><pub-location>Toronto,
Canada</pub-location><publisher>J. M.
Dent</publisher><accession-num>9697530</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) M1678.C91 S6</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Creighton, 1932 #6709"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Creighton, 1932</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> was then examined.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Now let us consider a network that deals
with the keys of these folk songs in a much more direct manner – by being
trained to judge the keys of a subset of these songs.<span style="mso-spacerun: yes;"> </span>After this training, we can then examine the
network’s performance on the songs that it was <i style="mso-bidi-font-style: normal;">not</i> presented during learning.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The network to be discussed uses 24 output
units to represent the possible musical keys, 8 hidden units, and 12 input
units that represent pitch-classes.<span style="mso-spacerun: yes;"> </span>Each
of the 152 folk songs is represented in terms of their use of the 12 possible
pitch-classes as was described in detail in Section 5.7.1.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">A subset of 114 of these songs – 75% of the
Creighton collection – is randomly selected to be used for training
purposes.<span style="mso-spacerun: yes;"> </span>The multilayer perceptron is
trained on these songs for 10,000 epochs to ensure that overall error is as low
as possible.<span style="mso-spacerun: yes;"> </span>The desired output for each
input song is the musical key selected for it by the Krumhansl and Schmuckler
keyfinding algorithm </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Krumhansl</Author><Year>1990</Year><RecNum>1718</RecNum><DisplayText>(Krumhansl,
1990)</DisplayText><record><rec-number>1718</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1718</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Krumhansl,
C.L.</author></authors></contributors><titles><title>Cognitive
Foundations Of Musical Pitch</title><secondary-title>Oxford psychology
series ; no. 17</secondary-title></titles><pages>x, 307
p.</pages><keywords><keyword>Music Psychological
aspects.</keyword><keyword>Musical
pitch.</keyword><keyword>Cognitive psychology.</keyword></keywords><dates><year>1990</year></dates><pub-location>New
York</pub-location><publisher>Oxford University
Press</publisher><isbn>019505475X (alk.
paper)</isbn><call-num>MUS ML3830.K76 1990&#xD;Lewis Music
Library ML3830.K76 1990</call-num><urls><pdf-urls><url>file://F:\Reprints\K\Krumhansl6.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Krumhansl, 1990 #1718"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Krumhansl, 1990</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>After this training, the
total sum of squared error (summed over 114 patterns with 24 different outputs
for each pattern) is only 5.39.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Next, the remaining 38 folk songs (the 25%
of all of the songs that were randomly selected to <i style="mso-bidi-font-style: normal;">not</i> be part of network training) are presented to the network to
determine whether its learned keyfinding abilities generalize to novel stimuli.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">When all of the data for network training
and generalization is obtained, network outputs are considered as
probabilities.<span style="mso-spacerun: yes;"> </span>Standard methods </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Duda</Author><Year>2001</Year><RecNum>6280</RecNum><DisplayText>(Duda,
Hart, &amp; Stork, 2001)</DisplayText><record><rec-number>6280</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6280</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Duda,
R.O.</author><author>Hart, P.E.</author><author>Stork,
D.G.</author></authors></contributors><titles><title>Pattern
Classification</title></titles><pages>xx, 654
p.</pages><edition>2nd</edition><keywords><keyword>Pattern
recognition systems.</keyword><keyword>Statistical
decision.</keyword></keywords><dates><year>2001</year></dates><pub-location>New
York</pub-location><publisher>Wiley</publisher><isbn>0471056693
(alk. paper)</isbn><accession-num>2630878</accession-num><call-num>Jefferson
or Adams Building Reading Rooms Q327; .D83 2001&#xD;Jefferson or Adams
Building Reading Rooms - STORED OFFSITE Q327; .D83
2001</call-num><urls><related-urls><url>http://www.loc.gov/catdir/bios/wiley041/99029981.html</url><url>http://www.loc.gov/catdir/description/wiley032/99029981.html</url><url>http://www.loc.gov/catdir/toc/onix03/99029981.html</url></related-urls><pdf-urls><url>file://F:\Reprints\D\Duda1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Duda, 2001 #6280"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Duda, Hart, & Stork, 2001</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> are now used to convert these probabilities into a keyfinding
judgment for each song.<span style="mso-spacerun: yes;"> </span>This is done by
finding the output unit that has the maximum activity, and assigning that
output unit’s key to the input song.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">For the training set of 114 folk songs,
there is a very high degree of correspondence between the judgments made by
this network of integration devices and the judgments made by the
Krumhansl/Schmuckler algorithm.<span style="mso-spacerun: yes;"> </span>The network
generates the same judgment for 113 of these songs, or over 99% of the training
set.<span style="mso-spacerun: yes;"> </span>The two only disagree on the key assignment
for the “Crocodile Song”, which the network judges to be in the key of C major,
while the Krumhansl algorithm judges it to be in the key of F major.<span style="mso-spacerun: yes;"> </span>The second highest activity in the network’s
response for this song is found in the F major output unit, suggesting that the
network’s error is not too radical!<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">How does the network perform on the 38
songs that were not presented to it during learning?<span style="mso-spacerun: yes;"> </span>The network agrees with the
Krumhansl/Schmuckler algorithm on 32 of these songs (84% agreement).<span style="mso-spacerun: yes;"> </span>This, as well as the 99% agreement on the
training set, demonstrates a much stronger agreement between the two approaches
than was evident in Chapter 5.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Is there anything special about the six
songs for which the network and the Krumhansl/Schmuckler algorithm do not agree?<span style="mso-spacerun: yes;"> </span>It seems that these songs may be difficult to
correctly keyfind, even for the standard algorithm.<span style="mso-spacerun: yes;"> </span>This suggests that failing to agree on these
particular songs may not be surprising.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">To be more precise, using the
Krumhansl/Schmuckler algorithm on the Nova Scotian folk songs is accomplished using
the HumDrum software package </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Huron</Author><Year>1999</Year><RecNum>6712</RecNum><DisplayText>(Huron,
1999)</DisplayText><record><rec-number>6712</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6712</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Huron,
D.</author></authors></contributors><titles><title>Music
Research Using Humdrum: A User&apos;s Guide.
</title></titles><dates><year>1999</year></dates><pub-location>Stanford,
California</pub-location><publisher>Center for Computer Assisted
Research in the Humanities</publisher><urls><pdf-urls><url>file://F:\Reprints\H\Huron2.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude5.docx" title="Huron, 1999 #6712"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Huron, 1999</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>For each key assignment,
this software package generates a confidence value.<span style="mso-spacerun: yes;"> </span>When this value is high, the algorithm’s
ability to keyfind is clear, which means that the key selected by the
Krumhansl/Schmuckler algorithm generates a high match, and no other possible
keys generate matches that are nearly that high.<span style="mso-spacerun: yes;"> </span>As confidence decreases, more than one key is
a possible choice, because several different keys generate similarly valued
matches.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">For the 32 songs that receive the same key
from both the network and from the Krumhansl/Schmuckler algorithm, the average
confidence is 54.34%.<span style="mso-spacerun: yes;"> </span>However, for the 6
songs for which the two disagree, the average confidence is only 14.03%.<span style="mso-spacerun: yes;"> </span>In other words, when generalizing to new
songs, the network tends to disagree with the Krumhansl/Schmuckler algorithm
only on songs for which this algorithm itself is not confident.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Clearly this approach to using networks of
integration devices for keyfinding demonstrates a great deal of promise.<span style="mso-spacerun: yes;"> </span>This promise, in turn, suggests further
research questions.<span style="mso-spacerun: yes;"> </span>How well does
learning about the keys of these folk songs generalize to other musical
stimuli?<span style="mso-spacerun: yes;"> </span>What is the relationship
between the internal structure of this network and the mechanics of the
Krumhansl/Schmuckler algorithm?<span style="mso-spacerun: yes;"> </span>How
might the network’s structure (e.g. number of hidden units) be altered to
improve performance?<span style="mso-spacerun: yes;"> </span>The allure of
studying musical networks is that their successes lead to promising future
research projects!<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"><strong><u> References</u></strong></span></o:p></span></div>
<br />
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Berkeley, I. S. N., Dawson, M. R. W., Medler, D. A., Schopflocher, D. P., & Hornsby, L. (1995). Density plots of hidden value unit activations reveal interpretable bands. <i style="mso-bidi-font-style: normal;">Connection Science, 7</i>, 167-186.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Cramer, J. S. (2003). <i style="mso-bidi-font-style: normal;">Logit Models From Economics and Other Fields</i>. Cambridge, UK ; New York: Cambridge University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_3"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Creighton, H. (1932). <i style="mso-bidi-font-style: normal;">Songs And Ballads From Nova Scotia</i>. Toronto, Canada: J. M. Dent.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_4"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., & Dupuis, B. (2012). Equilibria of perceptrons for simple contingency problems. <i style="mso-bidi-font-style: normal;">IEEE Transactions On Neural Networks And Learning Systems, in press</i>.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_5"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., Dupuis, B., Spetch, M. L., & Kelly, D. M. (2009). Simple artificial networks that match probability and exploit and explore when confronting a multiarmed bandit. <i style="mso-bidi-font-style: normal;">IEEE Transactions on Neural Networks, 20</i>(8), 1368-1371.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_6"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Duda, R. O., Hart, P. E., & Stork, D. G. (2001). <i style="mso-bidi-font-style: normal;">Pattern Classification</i> (2nd ed.). New York: Wiley.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_7"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Handelman, E. J., & Sigler, A. (2013). Key induction and key mapping using pitch-class set assertions. In J. Yust, J. Wild & J. A. Burgoyne (Eds.), <i style="mso-bidi-font-style: normal;">Mathematics and Computation in Music</i> (pp. 115-127). New York: Springer.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_8"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Huron, D. (1999). <i style="mso-bidi-font-style: normal;">Music Research Using Humdrum: A User's Guide. </i>. Stanford, California: Center for Computer Assisted Research in the Humanities.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_9"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Krumhansl, C. L. (1990). <i style="mso-bidi-font-style: normal;">Cognitive Foundations Of Musical Pitch</i>. New York: Oxford University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_10"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">McClelland, J. (1998). Connectionist models and Bayesian inference. In M. Oaksford & N. Chater (Eds.), <i style="mso-bidi-font-style: normal;">Rational Models of Cognition</i> (pp. 21-53). Oxford: Oxford University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_11"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. <i style="mso-bidi-font-style: normal;">Nature, 323</i>, 533-536.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
</ul>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-45041973870491620142015-04-05T11:46:00.000-06:002015-04-05T11:46:26.957-06:00Multiple Realizations and Music<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<em></em><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX1HK1dgcWcRFFELW1LtF1KJUJMX8R2o1mCBR1fw7dkWQZQC-CMXmVPTJs28UEGJWgUBDkrsudhqCHf8UBr3uAoE9pqjjOGZlrTyGseQgTyrA_xzdJKO9a1ggNIjwlb6ZXRiE4z_DtP7M/s1600/FigureI-5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX1HK1dgcWcRFFELW1LtF1KJUJMX8R2o1mCBR1fw7dkWQZQC-CMXmVPTJs28UEGJWgUBDkrsudhqCHf8UBr3uAoE9pqjjOGZlrTyGseQgTyrA_xzdJKO9a1ggNIjwlb6ZXRiE4z_DtP7M/s1600/FigureI-5.jpg" height="160" width="320" /></a></div>
<div class="WordSection1">
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-5. Two very different theories
can be used to define a major scale.<span style="mso-spacerun: yes;">
</span>One, on the left, involves identifying patterns of musical intervals
between adjacent scale pitches.<span style="mso-spacerun: yes;"> </span>Another,
on the right, involves measuring tritone balance – a property that major scales
have little of.<o:p></o:p></span></strong></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"></span> </div>
</div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">When the cognitive revolution occurred,
researchers used the digital computer as a metaphor to provide insight into the
workings of the mind.<span style="mso-spacerun: yes;"> </span>Their working
hypothesis was that thinking involved the same kind of operations involved when
computers performed computations.<span style="mso-spacerun: yes;"> </span>As a
result, one could attempt to explain cognition in exactly the same way that one
explains how a computer works.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">How does one explain a computer?<span style="mso-spacerun: yes;"> </span>From the perspective of a science grounded in
physical, causal laws one might expect to explain computing by describing the
workings of the various physical or electronic components from which a computer
is constructed.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">However, computer explanations are not
merely physical, but are also more abstract and functional </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Cummins</Author><Year>1983</Year><RecNum>359</RecNum><DisplayText>(Cummins,
1983)</DisplayText><record><rec-number>359</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">359</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Cummins,
R.</author></authors></contributors><titles><title>The
Nature Of Psychological
Explanation</title></titles><dates><year>1983</year></dates><pub-location>
Cambridge, MA.</pub-location><publisher> MIT
Press</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Cummins, 1983 #359"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Cummins, 1983</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>That is, explaining a
computer does not focus exclusively on the stuff it is made of.<span style="mso-spacerun: yes;"> </span>Instead, it focuses on what this stuff does.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">For instance, one might detail the algorithm
or program that is being carried out by a computer.<span style="mso-spacerun: yes;"> </span>This involves describing the function of
various processing operations (first the program reads in some data, then it
transforms the data according to this formula, and finally it prints the
results).<span style="mso-spacerun: yes;"> </span>This sort of account rarely
involves explaining how the various operations of a computer are brought to
life by the intricacies of its hardware.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Similarly, one might provide a very general
account of the information processing problem that a computer solves when it
runs a particular program.<span style="mso-spacerun: yes;"> </span>For instance,
perhaps the program’s purpose is determining the minimum value of some
equation.<span style="mso-spacerun: yes;"> </span>Again, this kind of account
does not appeal to hardware.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">David Marr is best known for his convincing
arguments that a complete account of an information processing system like a computer
requires three different levels of analysis, each of which answers different
kinds of questions using distinct vocabularies and methods </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Marr</Author><Year>1982</Year><RecNum>439</RecNum><DisplayText>(Marr,
1982)</DisplayText><record><rec-number>439</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">439</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Marr,
D.</author></authors></contributors><titles><title>Vision</title></titles><dates><year>1982</year></dates><pub-location>San
Francisco, Ca.</pub-location><publisher>W.H.
Freeman</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Marr, 1982 #439"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Marr, 1982</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>At the computational level,
mathematical proofs are used to answer the question “What information processing
problem is the system solving?”<span style="mso-spacerun: yes;"> </span>At the
algorithmic level, experiments are conducted to answer the question “What information
processing steps are being used to solve the information processing
problem?”<span style="mso-spacerun: yes;"> </span>At the implementational level,
physical properties are examined to answer the question “What physical
properties are responsible for bringing particular information processing steps
to life in a specific information processing device?”<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Central to Marr’s (1982) theory is that a
complete explanation of an information processor requires examining at the
computational, algorithmic, and the implementational levels of analysis.<span style="mso-spacerun: yes;"> </span>Furthermore, systematic links between each
level of analysis must also be established.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">Establishing the links between levels is
what makes explaining information processing both challenging and
exciting.<span style="mso-spacerun: yes;"> </span>Imagine that it has been
established at the computational level that a particular system is solving
Problem X.<span style="mso-spacerun: yes;"> </span>It turns out that there are
many different algorithms that can be used to solve this problem.<span style="mso-spacerun: yes;"> </span>In other words, there is a many-to-one
relationship from the algorithmic level to the computational level.<span style="mso-spacerun: yes;"> </span>Similarly, any one of these algorithms can be
brought to life on computing machines based on very different physical
principles </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Hillis</Author><Year>1998</Year><RecNum>3288</RecNum><DisplayText>(Hillis,
1998)</DisplayText><record><rec-number>3288</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">3288</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Hillis,
W.D.</author></authors></contributors><titles><title>The
Pattern on the Stone</title><secondary-title>Science
masters</secondary-title></titles><pages>xi, 164
p.</pages><edition>1st</edition><keywords><keyword>Computers.</keyword></keywords><dates><year>1998</year></dates><pub-location>New
York</pub-location><publisher>Basic Books</publisher><isbn>0465025951
(hc)</isbn><accession-num>727580</accession-num><call-num>Jefferson
or Adams Building Reading Rooms QA76.5; .H4918 1998&#xD;Jefferson or Adams
Building Reading Rooms - STORED OFFSITE QA76.5; .H4918
1998</call-num><urls><related-urls><url>http://www.loc.gov/catdir/enhancements/fy0833/98038888-d.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Hillis, 1998 #3288"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hillis, 1998</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>There is a many-to-one relationship
from the implementational level to the algorithmic level.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The phrase ‘multiple realizations’ is often
used when many-to-one relationships are at play.<span style="mso-spacerun: yes;"> </span>That is, one computation can be realized by
multiple algorithms, while one algorithm can be realized by multiple physical
systems.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">One exciting aspect of interpreting the internal
structure of a musical network is that one might be confronted with multiple
realizations.<span style="mso-spacerun: yes;"> </span>That is, while one might
expect that identifying some musical property involves one procedure,
interpreting a network can reveal a completely different approach.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The scale mode network provides an example
of this.<span style="mso-spacerun: yes;"> </span>Its task is to turn its output
unit on when it is presented a major scale.<span style="mso-spacerun: yes;">
</span>Traditional music theory dictates that a major scale is defined by a
particular pattern of musical intervals between adjacent pitches in a scale, as
illustrated on the right side of Figure I-5.<span style="mso-spacerun: yes;">
</span>However, the interpretation of the multilayer perceptron for this task revealed
that it uses a completely different musical property, tritone balance, which major
scales (unlike harmonic minor scales) tend not to exhibit.<span style="mso-spacerun: yes;"> </span>This alternative theory is depicted on the
left side of Figure I-5.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Multiple realizations in music should not
be surprising.<span style="mso-spacerun: yes;"> </span>The history of music, and
in particular the history of musical analysis, reveals that musical theory is
constantly evolving.<span style="mso-spacerun: yes;"> </span>As a result, one
can find many different theoretical accounts of the same musical phenomenon.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">For instance, in modern music theory it is
typical to view that different inversions of a chord are all instances of the
same chord.<span style="mso-spacerun: yes;"> </span>However, prior to 1771 music
theory held that different inversions of a chord were all different chords </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Damschroder</Author><Year>2008</Year><RecNum>6940</RecNum><DisplayText>(Damschroder,
2008)</DisplayText><record><rec-number>6940</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6940</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Damschroder,
D.</author></authors></contributors><titles><title>Thinking
About Harmony: Historical Perspectives On
Analysis</title></titles><pages>ix, 331
p.</pages><keywords><keyword>Musical analysis History 19th
century.</keyword><keyword>Harmony
History.</keyword><keyword>Music History and criticism.</keyword></keywords><dates><year>2008</year></dates><pub-location>Cambridge
; New York</pub-location><publisher>Cambridge University
Press</publisher><isbn>052188814X&#xD;9780521888141</isbn><accession-num>15386393</accession-num><call-num>Performing
Arts Reading Room (Madison, LM113) MT90 .D36 2008&#xD;Performing Arts
Reading Rm (Madison, LM113) - STORED OFFSITE MT90 .D36
2008</call-num><urls><related-urls><url>Contributor
biographical information
http://www.loc.gov/catdir/enhancements/fy0838/2008298014-b.html</url><url>Publisher
description http://www.loc.gov/catdir/enhancements/fy0838/2008298014-d.html</url><url>Table
of contents only
http://www.loc.gov/catdir/enhancements/fy0838/2008298014-t.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Damschroder, 2008 #6940"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Damschroder, 2008</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Similarly, in modern music
theory it is accepted that the A major triad (built from the pitch-classes A,
C#, E) and the A minor triad (built from the pitch-classes A, C, E) both have
the same tonic – the pitch-class A.<span style="mso-spacerun: yes;"> </span>However,
according to the music theory of Hugo Riemann, the root of the A major triad is
A, but the root of the A minor triad is E </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Rehding, 2003 #6466"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Rehding, 2003</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude4.docx" title="Riemann, 1895 #6458"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Riemann, 1895</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">There are two key points to highlight
here.<span style="mso-spacerun: yes;"> </span>The first is that current theories
of Western tonal music are not the only ones possible; alternative theories
exist, and many have been proposed at various times in history.<span style="mso-spacerun: yes;"> </span>The second is that artificial neural networks
are not constrained by current theories of music, and therefore may be quite
capable of discovering viable and interesting alternatives.<span style="mso-spacerun: yes;"> </span>In short, musical multiple realizations
exist, and artificial neural networks may be able to reveal them.<o:p></o:p></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> <strong><u>References</u></strong></span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
<ul>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Cummins, R. (1983). <i style="mso-bidi-font-style: normal;">The Nature Of Psychological Explanation</i>. Cambridge, MA.: MIT Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Damschroder, D. (2008). <i style="mso-bidi-font-style: normal;">Thinking About Harmony: Historical Perspectives On Analysis</i>. Cambridge ; New York: Cambridge University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_3"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Hillis, W. D. (1998). <i style="mso-bidi-font-style: normal;">The Pattern on the Stone</i> (1st ed.). New York: Basic Books.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_4"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Marr, D. (1982). <i style="mso-bidi-font-style: normal;">Vision</i>. San Francisco, Ca.: W.H. Freeman.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_5"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rehding, A. (2003). <i style="mso-bidi-font-style: normal;">Hugo Riemann And The Birth Of Modern Musical Thought</i>. Cambridge ; New York: Cambridge University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<a href="https://www.blogger.com/null" name="_ENREF_6"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Riemann, H. (1895). <i style="mso-bidi-font-style: normal;">Harmony simplified: Or, The Theory Of The Tonal Functions Of Chords</i>. London: Augener.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
</li>
</ul>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]-->Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-8838246103905331172015-03-29T17:52:00.001-06:002015-03-29T17:52:12.111-06:00Scale Tonics and Strange Circles<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em><br />
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPC7cqYXu5Mg90wJFPNEfWbQsYZrvotJljEgednmydWKoDIateVr8vJKcuu-9CV1afkXcx_I-eJHvWYkJR4yNyDdCLxo1NLieS76wgw7B_BSVp1JubjwxDxMLNsSLI3J_YHTd4SMw4NJg/s1600/FigureI-2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPC7cqYXu5Mg90wJFPNEfWbQsYZrvotJljEgednmydWKoDIateVr8vJKcuu-9CV1afkXcx_I-eJHvWYkJR4yNyDdCLxo1NLieS76wgw7B_BSVp1JubjwxDxMLNsSLI3J_YHTd4SMw4NJg/s1600/FigureI-2.jpg" height="320" width="284" /></a></div>
<br />
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-2. The pattern of weights from
the input units of the scale tonic perceptron to one of its output units are
presented at the top.<span style="mso-spacerun: yes;"> </span>The bottom
illustrates the two circles of major seconds.<o:p></o:p></span></strong></span></div>
<br />
<span lang="EN-US"><span style="font-family: Arial;">An earlier interlude noted that interpretations
of musical networks often reveal strange circles.<span style="mso-spacerun: yes;"> </span>However, in many respects the interpretation
of the weights of the scale tonic perceptron (a pattern like the upper part of
Figure I-2) seems very conventional.<span style="mso-spacerun: yes;"> </span>It
was argued (using Figures 3-5 and 3-6) the weights in the upper part of Figure
I-2 contains the pattern of musical intervals that defines a major scale as
well as the pattern of musical intervals that defines a harmonic minor scale.<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">In this interlude, we discover that from
another perspective the weights of the scale tonic perceptron also lead to
strange circles.<span style="mso-spacerun: yes;"> </span>An analysis of these
weights reveals the presence of the two circles of major seconds that are
presented in the bottom half of Figure I-2.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The tonal hierarchy </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Krumhansl</Author><Year>1990</Year><RecNum>1718</RecNum><DisplayText>(Krumhansl,
1990)</DisplayText><record><rec-number>1718</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1718</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Krumhansl,
C.L.</author></authors></contributors><titles><title>Cognitive
Foundations Of Musical Pitch</title><secondary-title>Oxford
psychology series ; no.
17</secondary-title></titles><pages>x, 307 p.</pages><keywords><keyword>Music
Psychological aspects.</keyword><keyword>Musical
pitch.</keyword><keyword>Cognitive
psychology.</keyword></keywords><dates><year>1990</year></dates><pub-location>New
York</pub-location><publisher>Oxford University Press</publisher><isbn>019505475X
(alk. paper)</isbn><call-num>MUS ML3830.K76 1990&#xD;Lewis
Music Library ML3830.K76
1990</call-num><urls><pdf-urls><url>file://F:\Reprints\K\Krumhansl6.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude3.docx" title="Krumhansl, 1990 #1718"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Krumhansl, 1990</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"> discussed in Chapter 1 was a theory about the relationships between
pitch-classes.<span style="mso-spacerun: yes;"> </span>Krumhansl explored the
structure of the tonal hierarchy using a statistical technique called
multidimensional scaling or MDS </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Kruskal</Author><Year>1978</Year><RecNum>1233</RecNum><DisplayText>(Kruskal
&amp; Wish,
1978)</DisplayText><record><rec-number>1233</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1233</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Kruskal,
J.B.</author><author>Wish,
M.</author></authors></contributors><titles><title>Multidimensional
Scaling</title></titles><dates><year>1978</year></dates><pub-location>Beverly
Hills, CA</pub-location><publisher>Sage Publications</publisher><urls><pdf-urls><url>file://F:\Reprints\K\Kruskal1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude3.docx" title="Kruskal, 1978 #1233"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Kruskal & Wish, 1978</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>MDS takes a matrix of
similarity relationships between objects and creates a map.<span style="mso-spacerun: yes;"> </span>In this map, each object is represented by a
point at particular coordinates of the space.<span style="mso-spacerun: yes;">
</span>The distance between a pair of points in the space indicates the
similarity between two objects.<span style="mso-spacerun: yes;"> </span>The
closer the two points are, the higher is the similarity.<span style="mso-spacerun: yes;"> </span>MDS attempts to build a map involving all of
the objects, placing them at locations that provide the best fit to the raw
similarity measures between them.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The scale tonic perceptron has twelve
different output units, each representing a pitch-class.<span style="mso-spacerun: yes;"> </span>Each of these units has its own pattern of
weights between it and the
twelve input units used to present scales to the network.<span style="mso-spacerun: yes;"> </span>It stands to reason that if two different
output units represent scale tonics that are related in some way, then they
should have a similar pattern of connection weights.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">One can use connection weights to compute a
measure of similarity between two output units in this network.<span style="mso-spacerun: yes;"> </span>Each output unit is a point in a
twelve-dimensional space; its coordinates are given by its twelve connection
weights.<span style="mso-spacerun: yes;"> </span>The similarity between two
output units is determined by measuring the distance between the two points in
this twelve-dimensional space.<span style="mso-spacerun: yes;"> </span>This can
be done by computing the Euclidean distance between the coordinates of the two
points.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">A twelve-dimensional space is too large to
understand; it would be better if a smaller space could be used to render the
similarity relationships between the output units more easily
understandable.<span style="mso-spacerun: yes;"> </span>This is the purpose of
MDS.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">We provided the matrix of connection
weights from the network to the statistical programming language R.<span style="mso-spacerun: yes;"> </span>R converted this matrix into a matrix of
distances between pairs of output units by computing Euclidean distances
between twelve-dimensional coordinates.<span style="mso-spacerun: yes;">
</span>R was then used to perform MDS on this distance data.<span style="mso-spacerun: yes;"> </span>The best fitting solution to this data
requires a six- or seven-dimensional space.<span style="mso-spacerun: yes;">
</span>However, the first three dimensions of the MDS solution – which capture
more structure in the distances than do later dimensions – reveal some very interesting
structure.</span></span></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<strong><span style="font-family: Arial;"><span style="mso-ansi-language: EN-CA; mso-fareast-language: EN-CA; mso-no-proof: yes;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock><v:shape id="Picture_x0020_3" o:spid="_x0000_i1026" style="height: 173.25pt; mso-wrap-style: square; visibility: visible; width: 198pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\User\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg">
</v:imagedata></v:shape></v:path></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas></v:stroke></v:shapetype></span></span></strong></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQVaozhMT0kuYjvg0iSW34RVu1DLug3nW17H4xrXx1-CaiYIrDjAhsRZHHnQIYfBwfX6GXrHjUqkUR7u1vDe9hdhCo6d_J0c_rK80vZYvkZJ6lZ3MOmmTT1HAyL6TGFH9isd-LyNR5JLQ/s1600/FigureI-3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQVaozhMT0kuYjvg0iSW34RVu1DLug3nW17H4xrXx1-CaiYIrDjAhsRZHHnQIYfBwfX6GXrHjUqkUR7u1vDe9hdhCo6d_J0c_rK80vZYvkZJ6lZ3MOmmTT1HAyL6TGFH9isd-LyNR5JLQ/s1600/FigureI-3.jpg" height="280" width="320" /></a></div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;"></span></strong></span> </div>
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-3.<span style="mso-spacerun: yes;"> </span>The plot of the two-dimensional MDS analysis
of the scale tonic perceptron weights.<o:p></o:p></span></strong></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> F</span></o:p></span><span lang="EN-US"><span style="font-family: Arial;">igure I-3 presents the plot of the
two-dimensional MDS of the scale tonic perceptron’s weights.<span style="mso-spacerun: yes;"> </span>One obvious property of this graph is that
the output unit pitch-classes are clearly organized into two different groups,
one to the left of the dashed line in the middle of the plot and the other to
its right.<span style="mso-spacerun: yes;"> </span>An examination of these two
groups indicates a striking musical property: all of the pitch-classes in one
side of the plot belong to one of the circles of major seconds in Figure I-2,
while those on the other side of the plot belong to the other circle of major
seconds.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">A better fit to data requires performing a
higher dimensional MDS analysis.<span style="mso-spacerun: yes;"> </span>Figure
I-4 presents the three-dimensional analysis.<span style="mso-spacerun: yes;">
</span>Note that the first two dimensions of this solution (provided by the x
and y axes) pull the pitch-classes apart in terms of membership in the two
circles of major seconds.<span style="mso-spacerun: yes;"> </span>The position
of the pitch-classes in the third dimension arranges them into patterns that
are very suggestive of the two circles in Figure I-2, though the correspondence
between the two figures is not perfect. <o:p></o:p></span></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiCbEbif6ZY3j0tqB7wPBFKmiGHaklvqoIePSqP4_FqdyBIbBNzOjFA6cWYUHIh0UghDJ5IpEyi9kRfyoblzmDUrVRMEh9sQwRnFexqSKinUYFWSTFg8veleenkgfw-hmkPXlRf6qSGu4/s1600/FigureI-4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiCbEbif6ZY3j0tqB7wPBFKmiGHaklvqoIePSqP4_FqdyBIbBNzOjFA6cWYUHIh0UghDJ5IpEyi9kRfyoblzmDUrVRMEh9sQwRnFexqSKinUYFWSTFg8veleenkgfw-hmkPXlRf6qSGu4/s1600/FigureI-4.jpg" height="266" width="320" /></a></div>
<br />
<div class="MsoCaption" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><strong><span style="font-family: Arial;">Figure I-4.<span style="mso-spacerun: yes;"> </span>The plot of the three-dimensional MDS
analysis of the scale tonic perceptron weights.<o:p></o:p></span></strong></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">In summary, the pattern of connection
weights that emerges in the scale tonic perceptron contains some interesting
musical relationships that cannot be understood simply by inspecting a table of connection weights.<span style="mso-spacerun: yes;"> </span>There is systematic structure that
suggests that output units that represent tonics that belong to the same circle
of major seconds are more similar to one another than to an output unit that
represents a tonic that belongs to the other circle.<span style="mso-spacerun: yes;"> </span>Furthermore, the closer two tonics are to one
another in the same circle of major seconds, the more similar they are to one
another.<span style="mso-spacerun: yes;"> </span>In short, multivariate analyses
of the scale tonic perceptron reveals that it uses strange circles to organize
musical inputs.</span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"></span></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;"><strong><u>References:</u></strong></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Krumhansl, C. L. (1990). <i style="mso-bidi-font-style: normal;">Cognitive Foundations Of Musical Pitch</i>.
New York: Oxford University Press.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Kruskal, J. B., & Wish, M. (1978). <i style="mso-bidi-font-style: normal;">Multidimensional
Scaling</i>. Beverly Hills, CA: Sage Publications.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]-->Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-59160224027529066502015-03-22T09:40:00.003-06:002015-03-22T09:40:41.729-06:00Shallow Networks for Deeper Understanding?<span style="font-family: Arial;"><span lang="EN-US"><span style="font-family: Times New Roman;"><em>As described </em></span><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><span style="font-family: Times New Roman;"><em>in this previous post</em></span></a><em><span style="font-family: Times New Roman;">, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</span></em></span></span><br />
<br />
<span style="font-family: Arial;"><span lang="EN-US">In the first half of the 20<span style="font-size: small;"><sup>th</sup>
century, the notion of an artificial neural network composed of many different
layers of processors was born </span></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>McCulloch</Author><Year>1943</Year><RecNum>654</RecNum><DisplayText>(McCulloch
&amp; Pitts, 1943)</DisplayText><record><rec-number>654</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">654</key></foreign-keys><ref-type
name="Journal Article">17</ref-type><contributors><authors><author>McCulloch,
W.S.</author><author>Pitts, W.</author></authors></contributors><titles><title>A
logical calculus of the ideas immanent in nervous
activity</title><secondary-title>Bulletin of Mathematical
Biophysics</secondary-title></titles><pages>115-133</pages><volume>5</volume><dates><year>1943</year></dates><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="McCulloch, 1943 #654"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">McCulloch & Pitts, 1943</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>These networks were very
powerful, but had to be hand wired because a learning rule capable of training
them had not yet been invented.<o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The first learning rule for artificial
neural networks was discovered around the time of the cognitive revolution </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Rosenblatt</Author><Year>1958</Year><RecNum>2194</RecNum><DisplayText>(Rosenblatt,
1958, 1962)</DisplayText><record><rec-number>2194</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">2194</key></foreign-keys><ref-type
name="Journal Article">17</ref-type><contributors><authors><author>Rosenblatt,
F.</author></authors></contributors><titles><title>The
perceptron: A probabilistic model for information storage and organization in
the brain</title><secondary-title>Psychological
Review</secondary-title></titles><periodical><full-title>Psychological
Review</full-title></periodical><pages>386-408</pages><volume>65</volume><number>6</number><dates><year>1958</year></dates><isbn>0033-295X</isbn><accession-num>ISI:A1958WG40900006</accession-num><urls><related-urls><url>&lt;Go
to
ISI&gt;://A1958WG40900006</url></related-urls><pdf-urls><url>file://F:\Reprints\R\Rosenblatt1.pdf</url></pdf-urls></urls><language>English</language></record></Cite><Cite><Author>Rosenblatt</Author><Year>1962</Year><RecNum>473</RecNum><record><rec-number>473</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">473</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Rosenblatt,
F.</author></authors></contributors><titles><title>Principles
Of
Neurodynamics</title></titles><dates><year>1962</year></dates><pub-location>Washington</pub-location><publisher>Spartan
Books</publisher><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Rosenblatt, 1958 #2194"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Rosenblatt, 1958</span></a><span style="mso-no-proof: yes;">, </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Rosenblatt, 1962 #473"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">1962</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>However, this rule could
not train networks that contained hidden units.<span style="mso-spacerun: yes;">
</span>As a result this learning rule could only train perceptrons, which are
networks of limited capability </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Minsky</Author><Year>1969</Year><RecNum>4537</RecNum><DisplayText>(Minsky
&amp; Papert,
1969)</DisplayText><record><rec-number>4537</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">4537</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Minsky,
M.L.</author><author>Papert,
S.</author></authors></contributors><titles><title>Perceptrons:
An Introduction To Computational
Geometry</title></titles><pages>258 p.</pages><edition>1st</edition><keywords><keyword>Perceptrons.</keyword><keyword>Geometry
Data processing.</keyword><keyword>Parallel processing (Electronic
computers)</keyword><keyword>Machine
learning.</keyword></keywords><dates><year>1969</year></dates><pub-location>Cambridge,
Mass.,</pub-location><publisher>MIT Press</publisher><accession-num>1707551</accession-num><call-num>Jefferson
or Adams Building Reading Rooms Q327; .M55&#xD;Jefferson or Adams Building
Reading Rooms - STORED OFFSITE Q327;
.M55</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Minsky, 1969 #4537"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Minsky & Papert, 1969</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The rise of modern connectionism began with
the discovery of supervised learning rules for networks with hidden units </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Ackley, 1985 #46"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Ackley, Hinton, & Sejnowski, 1985</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Amari, 1967 #4555"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Amari, 1967</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Anderson, 1995 #4554"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Anderson, 1995</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Rumelhart, 1986 #261"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Rumelhart, Hinton, & Williams,
1986</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Werbos, 1994 #6936"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Werbos, 1994</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Researchers could now teach networks that had
enormous computational power (in principle).<span style="mso-spacerun: yes;">
</span>Networks like the multilayer perceptron became the staple of
connectionist cognitive science.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">In the early decades of the 21<span style="font-size: small;"><sup>st</sup>
century some researchers expressed concern with the limitations of the
supervised training of multilayer perceptrons.<span style="mso-spacerun: yes;">
</span>While such networks can learn to perform a variety of complicated tasks,
researchers often encounter practical problems in their use.<span style="mso-spacerun: yes;"> </span>Some have pointed out that the incredible
power of the human brain arises from its use of many, many different layers of
hidden neurons </span></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Bengio</Author><Year>2009</Year><RecNum>6935</RecNum><DisplayText>(Bengio,
2009)</DisplayText><record><rec-number>6935</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6935</key></foreign-keys><ref-type
name="Journal Article">17</ref-type><contributors><authors><author>Bengio,
Y.</author></authors></contributors><titles><title>Learning
deep architectures for AI</title><secondary-title>Foundations and
Trends in Machine Learning</secondary-title></titles><periodical><full-title>Foundations
and Trends in Machine
Learning</full-title></periodical><pages>1-127</pages><volume>2</volume><number>1</number><dates><year>2009</year></dates><urls><pdf-urls><url>file://F:\Reprints\B\Bengio2.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Bengio, 2009 #6935"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Bengio, 2009</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>However, when 20<span style="font-size: small;"><sup>th</sup>
century supervised learning rules are used, networks of many layers are
enormously difficult to train.<span style="mso-spacerun: yes;"> </span>The old approaches
to network training face practical obstacles that prevent the in principle
power of multilayer networks from being exploited.<o:p></o:p></span></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">Modern researchers have discovered new
types of learning rules that permit networks with many layers of hidden units
to be trained </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Bengio, 2013 #6934"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Bengio, Courville, & Vincent, 2013</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2007 #6933"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton, 2007</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2006 #6925"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton, Osindero,
& Teh, 2006</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2006 #6924"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton &
Salakhutdinov, 2006</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Larochelle, 2012 #6930"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Larochelle, Mandel,
Pascanu, & Bengio, 2012</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>These new rules, often called <i style="mso-bidi-font-style: normal;">deep learning</i>, now permit researchers to
train <i style="mso-bidi-font-style: normal;">deep belief networks</i> to
accomplish tasks far beyond the capabilities of shallow, late 20<span style="font-size: small;"><sup>th</sup>
century networks.<span style="mso-spacerun: yes;"> </span>Deep learning has produced
networks for classification tasks involving natural language, image classification,
and the processing of sound </span></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2007 #6933"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton, 2007</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2006 #6925"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton et al., 2006</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Mohamed, 2012 #6927"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Mohamed, Dahl, & Hinton, 2012</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Sarikaya, 2014 #6922"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Sarikaya, Hinton, & Deoras, 2014</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Daily news reports reveal deep learning
applications are being employed by various companies such as Google, Facebook
and PayPal; deep learning rules are widely available </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Fischer, 2014 #6931"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Fischer & Igel, 2014</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Testolin, 2013 #6921"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Testolin, Stoianov, De Grazia, &
Zorzi, 2013</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data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w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The networks studied in the current book
are clearly antiquated in comparison to modern deep belief networks.<span style="mso-spacerun: yes;"> </span>What is the point of using older, less
powerful, networks to investigate music?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">The primary motivation for exploring music
with older architectures is the frequent disconnect between the technology of
neural networks and the cognitive science of neural networks </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Dawson</Author><Year>1994</Year><RecNum>7</RecNum><DisplayText>(Dawson
&amp; Shamanski, 1994)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">7</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Dawson,
M.R.W.</author><author>Shamanski, K.S.</author></authors></contributors><titles><title>Connectionism,
confusion and cognitive science</title><secondary-title>Journal of
Intelligent
Systems</secondary-title></titles><pages>215-262</pages><volume>4</volume><dates><year>1994</year></dates><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Dawson, 1994 #7"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson & Shamanski, 1994</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>The development of
artificial neural networks occurs in many different disciplines, and these
different disciplines often have different goals. <span style="mso-spacerun: yes;"> </span>For instance, deep learning is emerging from
computer science, and current research on it focuses on developing new procedures
for accomplishing deep learning efficiently </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Bengio</Author><Year>2009</Year><RecNum>6935</RecNum><DisplayText>(Bengio,
2009)</DisplayText><record><rec-number>6935</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6935</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Bengio,
Y.</author></authors></contributors><titles><title>Learning
deep architectures for AI</title><secondary-title>Foundations and
Trends in Machine
Learning</secondary-title></titles><periodical><full-title>Foundations
and Trends in Machine Learning</full-title></periodical><pages>1-127</pages><volume>2</volume><number>1</number><dates><year>2009</year></dates><urls><pdf-urls><url>file://F:\Reprints\B\Bengio2.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Bengio, 2009 #6935"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Bengio, 2009</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>In other words, deep
learning is being developed from a technological perspective; its developers
are concerned with successfully training networks to perform extremely complex
pattern classification tasks.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">The cognitive science of deep learning is
lagging far behind its technology.<span style="mso-spacerun: yes;"> </span>Some
researchers have expressed concern that while deep learning produces networks
that solve problems worthy of human neural processing, these networks are not
themselves providing any insight about the workings of the human brain or the
human mind.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">One reason for this is that most deep
learning advances are currently quantitative, not qualitative </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Erhan</Author><Year>2010</Year><RecNum>6939</RecNum><DisplayText>(Erhan,
Courville, &amp; Bengio, 2010)</DisplayText><record><rec-number>6939</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6939</key></foreign-keys><ref-type
name="Report">27</ref-type><contributors><authors><author>Erhan,
D.</author><author>Courville,
A.</author><author>Bengio, Y.</author></authors></contributors><titles><title>Understanding
Representations Learned in Deep Architectures. Technical Report
1355</title></titles><number>1355</number><dates><year>2010</year></dates><publisher>Departement
d’Informatique et Recherche Operationnelle, Universite de
Montreal</publisher><urls><pdf-urls><url>file://F:\Reprints\E\Erhan1.pdf</url></pdf-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Erhan, 2010 #6939"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Erhan, Courville, & Bengio, 2010</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Techniques for interpreting the internal
structure of deep belief networks are in their infancy.<span style="mso-spacerun: yes;"> </span>If a network cannot be interpreted, then it
likely cannot contribute to cognitive science </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>McCloskey</Author><Year>1991</Year><RecNum>207</RecNum><DisplayText>(McCloskey,
1991)</DisplayText><record><rec-number>207</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">207</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>McCloskey,
M</author></authors></contributors><titles><title>Networks
and theories:<span style='mso-spacerun:yes'> </span>The place of connectionism
in cognitive science</title><secondary-title>Psychological
science</secondary-title></titles><periodical><full-title>Psychological
Science</full-title></periodical><pages>387-395</pages><volume>2</volume><dates><year>1991</year></dates><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="McCloskey, 1991 #207"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">McCloskey, 1991</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>Without interpretation,
deep belief networks are magnificent artifacts, but are neither cognitive nor
biological theories.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">Of course, this is not to say that researchers
are not interested in interpreting the internal structure of deep belief
networks </span><!--[if supportFields]><span lang=EN-US><span style='mso-element:
field-begin'></span><span style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Erhan</Author><Year>2010</Year><RecNum>6939</RecNum><DisplayText>(Erhan
et al., 2010; Hinton et al.,
2006)</DisplayText><record><rec-number>6939</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6939</key></foreign-keys><ref-type
name="Report">27</ref-type><contributors><authors><author>Erhan,
D.</author><author>Courville,
A.</author><author>Bengio,
Y.</author></authors></contributors><titles><title>Understanding
Representations Learned in Deep Architectures. Technical Report
1355</title></titles><number>1355</number><dates><year>2010</year></dates><publisher>Departement
d’Informatique et Recherche Operationnelle, Universite de
Montreal</publisher><urls><pdf-urls><url>file://F:\Reprints\E\Erhan1.pdf</url></pdf-urls></urls></record></Cite><Cite><Author>Hinton</Author><Year>2006</Year><RecNum>6925</RecNum><record><rec-number>6925</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6925</key></foreign-keys><ref-type
name="Journal Article">17</ref-type><contributors><authors><author>Hinton,
G. E.</author><author>Osindero, S.</author><author>Teh,
Y.</author></authors></contributors><titles><title>A
fast learning algorithm for deep belief nets</title><secondary-title>Neural
Computation</secondary-title></titles><periodical><full-title>Neural
Computation</full-title><abbr-1>Neural
Comput</abbr-1></periodical><pages>1527-1554</pages><volume>18</volume><number>7</number><dates><year>2006</year><pub-dates><date>Jul</date></pub-dates></dates><isbn>0899-7667</isbn><accession-num>WOS:000237698100002</accession-num><urls><related-urls><url>&lt;Go
to
ISI&gt;://WOS:000237698100002</url></related-urls><pdf-urls><url>file://F:\Reprints\H\Hinton2.pdf</url></pdf-urls></urls><electronic-resource-num>10.1162/neco.2006.18.7.1527</electronic-resource-num></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Erhan, 2010 #6939"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Erhan et al., 2010</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Hinton, 2006 #6925"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Hinton et al., 2006</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>For instance, in the very
first publication describing a method for deep learning Hinton et al. (2006)
look into a network’s “mind” by observing responses of network processors to
various stimuli in hope of discovering the abstract features that are detected
by hidden layers.<span style="mso-spacerun: yes;"> </span>However, few
sophisticated techniques for interpreting deep networks exist.<span style="mso-spacerun: yes;"> </span>Erhan et al. (2010) observe that typically
researchers only visually examine the receptive field (i.e. the connection
weights) that feed into processors in the first hidden layer of a deep belief
network.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">One reason to explore older architectures
in the current book is because there are many more procedures in existence for
interpreting their internal structure.<span style="mso-spacerun: yes;">
</span>This in turn permits them to be more likely contributors to a cognitive
science of music.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial;"><span lang="EN-US">A second reason to focus on older artificial
neural network architectures is the goal of seeking the simplest network that
is required to solve a particular task.<span style="mso-spacerun: yes;">
</span>For example, in the next chapter we will see that no hidden units are
required at all to identify the tonic of a scale.<span style="mso-spacerun: yes;"> </span>If such a simple network can accomplish this
task, then why would we examine it with a deep belief network?<span style="mso-spacerun: yes;"> </span>Indeed, though very old architectures like
the perceptron <span style="mso-spacerun: yes;"> </span>are extraordinarily
simple, they can easily be used to contribute to a variety of topics in modern
cognitive science </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE <span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE.DATA <![if gte mso 9]><xml>
<w:data>3C456E644E6F74653E3C436974653E3C417574686F723E446177736F6E3C2F417574686F723E3C596561723E323031323C2F596561723E3C5265634E756D3E353730313C2F5265634E756D3E3C446973706C6179546578743E28446177736F6E2C20323030383B20446177736F6E2026616D703B204475707569732C20323031323B20446177736F6E2C204475707569732C205370657463682C2026616D703B204B656C6C792C20323030393B20446177736F6E2C204B656C6C792C205370657463682C2026616D703B204475707569732C2032303130293C2F446973706C6179546578743E3C7265636F72643E3C7265632D6E756D6265723E353730313C2F7265632D6E756D6265723E3C666F726569676E2D6B6579733E3C6B6579206170703D22454E222064622D69643D22766570783970786573356678616265777064787866303230643261326676397376647A61223E353730313C2F6B65793E3C2F666F726569676E2D6B6579733E3C7265662D74797065206E616D653D224A6F75726E616C2041727469636C65223E31373C2F7265662D747970653E3C636F6E7472696275746F72733E3C617574686F72733E3C617574686F723E446177736F6E2C204D2E522E572E3C2F617574686F723E3C617574686F723E4475707569732C20422E3C2F617574686F723E3C2F617574686F72733E3C2F636F6E7472696275746F72733E3C7469746C65733E3C7469746C653E457175696C6962726961206F662070657263657074726F6E7320666F722073696D706C6520636F6E74696E67656E63792070726F626C656D733C2F7469746C653E3C7365636F6E646172792D7469746C653E49454545205472616E73616374696F6E73204F6E204E657572616C204E6574776F726B7320416E64204C6561726E696E672053797374656D733C2F7365636F6E646172792D7469746C653E3C2F7469746C65733E3C706572696F646963616C3E3C66756C6C2D7469746C653E49454545205472616E73616374696F6E73204F6E204E657572616C204E6574776F726B7320416E64204C6561726E696E672053797374656D733C2F66756C6C2D7469746C653E3C2F706572696F646963616C3E3C766F6C756D653E696E2070726573733C2F766F6C756D653E3C64617465733E3C796561723E323031323C2F796561723E3C2F64617465733E3C75726C733E3C7064662D75726C733E3C75726C3E66696C653A2F2F463A5C52657072696E74735C445C446177736F6E32352E7064663C2F75726C3E3C2F7064662D75726C733E3C2F75726C733E3C2F7265636F72643E3C2F436974653E3C436974653E3C417574686F723E446177736F6E3C2F417574686F723E3C596561723E323031303C2F596561723E3C5265634E756D3E333032373C2F5265634E756D3E3C7265636F72643E3C7265632D6E756D6265723E333032373C2F7265632D6E756D6265723E3C666F726569676E2D6B6579733E3C6B6579206170703D22454E222064622D69643D22766570783970786573356678616265777064787866303230643261326676397376647A61223E333032373C2F6B65793E3C2F666F726569676E2D6B6579733E3C7265662D74797065206E616D653D224A6F75726E616C2041727469636C65223E31373C2F7265662D747970653E3C636F6E7472696275746F72733E3C617574686F72733E3C617574686F723E446177736F6E2C204D2E522E572E3C2F617574686F723E3C617574686F723E4B656C6C792C20442E204D2E3C2F617574686F723E3C617574686F723E5370657463682C204D2E204C2E3C2F617574686F723E3C617574686F723E4475707569732C20422E3C2F617574686F723E3C2F617574686F72733E3C2F636F6E7472696275746F72733E3C7469746C65733E3C7469746C653E5573696E672070657263657074726F6E7320746F206578706C6F7265207468652072656F7269656E746174696F6E207461736B3C2F7469746C653E3C7365636F6E646172792D7469746C653E436F676E6974696F6E3C2F7365636F6E646172792D7469746C653E3C2F7469746C65733E3C706572696F646963616C3E3C66756C6C2D7469746C653E436F676E6974696F6E3C2F66756C6C2D7469746C653E3C2F706572696F646963616C3E3C70616765733E3230372D3232363C2F70616765733E3C766F6C756D653E3131343C2F766F6C756D653E3C6E756D6265723E323C2F6E756D6265723E3C64617465733E3C796561723E323031303C2F796561723E3C2F64617465733E3C75726C733E3C7064662D75726C733E3C75726C3E66696C653A2F2F463A5C52657072696E74735C445C446177736F6E32322E7064663C2F75726C3E3C2F7064662D75726C733E3C2F75726C733E3C2F7265636F72643E3C2F436974653E3C436974653E3C417574686F723E446177736F6E3C2F417574686F723E3C596561723E323030393C2F596561723E3C5265634E756D3E323735323C2F5265634E756D3E3C7265636F72643E3C7265632D6E756D6265723E323735323C2F7265632D6E756D6265723E3C666F726569676E2D6B6579733E3C6B6579206170703D22454E222064622D69643D22766570783970786573356678616265777064787866303230643261326676397376647A61223E323735323C2F6B65793E3C2F666F726569676E2D6B6579733E3C7265662D74797065206E616D653D224A6F75726E616C2041727469636C65223E31373C2F7265662D747970653E3C636F6E7472696275746F72733E3C617574686F72733E3C617574686F723E446177736F6E2C204D2E522E572E3C2F617574686F723E3C617574686F723E4475707569732C20422E3C2F617574686F723E3C617574686F723E5370657463682C204D2E204C2E3C2F617574686F723E3C617574686F723E4B656C6C792C20442E204D2E3C2F617574686F723E3C2F617574686F72733E3C2F636F6E7472696275746F72733E3C7469746C65733E3C7469746C653E53696D706C65206172746966696369616C206E6574776F726B732074686174206D617463682070726F626162696C69747920616E64206578706C6F697420616E64206578706C6F7265207768656E20636F6E66726F6E74696E672061206D756C746961726D65642062616E6469743C2F7469746C653E3C7365636F6E646172792D7469746C653E49454545205472616E73616374696F6E73206F6E204E657572616C204E6574776F726B733C2F7365636F6E646172792D7469746C653E3C2F7469746C65733E3C706572696F646963616C3E3C66756C6C2D7469746C653E49656565205472616E73616374696F6E73206F6E204E657572616C204E6574776F726B733C2F66756C6C2D7469746C653E3C616262722D313E496565652054204E657572616C204E6574776F723C2F616262722D313E3C2F706572696F646963616C3E3C70616765733E313336382D313337313C2F70616765733E3C766F6C756D653E32303C2F766F6C756D653E3C6E756D6265723E383C2F6E756D6265723E3C64617465733E3C796561723E323030393C2F796561723E3C2F64617465733E3C75726C733E3C7064662D75726C733E3C75726C3E66696C653A2F2F463A5C52657072696E74735C445C446177736F6E32312E7064663C2F75726C3E3C2F7064662D75726C733E3C2F75726C733E3C2F7265636F72643E3C2F436974653E3C436974653E3C417574686F723E446177736F6E3C2F417574686F723E3C596561723E323030383C2F596561723E3C5265634E756D3E323133313C2F5265634E756D3E3C7265636F72643E3C7265632D6E756D6265723E323133313C2F7265632D6E756D6265723E3C666F726569676E2D6B6579733E3C6B6579206170703D22454E222064622D69643D22766570783970786573356678616265777064787866303230643261326676397376647A61223E323133313C2F6B65793E3C2F666F726569676E2D6B6579733E3C7265662D74797065206E616D653D224A6F75726E616C2041727469636C65223E31373C2F7265662D747970653E3C636F6E7472696275746F72733E3C617574686F72733E3C617574686F723E446177736F6E2C204D2E522E572E3C2F617574686F723E3C2F617574686F72733E3C2F636F6E7472696275746F72733E3C7469746C65733E3C7469746C653E436F6E6E656374696F6E69736D20616E6420636C6173736963616C20636F6E646974696F6E696E673C2F7469746C653E3C7365636F6E646172792D7469746C653E436F6D706172617469766520436F676E6974696F6E20616E64204265686176696F7220526576696577733C2F7365636F6E646172792D7469746C653E3C2F7469746C65733E3C706572696F646963616C3E3C66756C6C2D7469746C653E436F6D706172617469766520436F676E6974696F6E20616E64204265686176696F7220526576696577733C2F66756C6C2D7469746C653E3C2F706572696F646963616C3E3C70616765733E312D3131353C2F70616765733E3C766F6C756D653E3320284D6F6E6F6772617068293C2F766F6C756D653E3C64617465733E3C796561723E323030383C2F796561723E3C2F64617465733E3C75726C733E3C2F75726C733E3C2F7265636F72643E3C2F436974653E3C2F456E644E6F74653E</w:data>
</xml><![endif]><span style='mso-element:field-end'></span><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Dawson, 2008 #2131"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson, 2008</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Dawson, 2012 #5701"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson & Dupuis,
2012</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Dawson, 2009 #2752"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson, Dupuis, Spetch, & Kelly,
2009</span></a><span style="mso-no-proof: yes;">; </span><a href="file:///C:/Users/User/Documents/My%20Work/My%20Books/MusicNet/Interludes/Interlude2.docx" title="Dawson, 2010 #3027"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson, Kelly, Spetch, & Dupuis,
2010</span></a><span style="mso-no-proof: yes;">)</span><!--[if gte mso 9]><xml>
<w:data>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</w:data>
</xml><![endif]--></span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial;">Of course, the proof of the pudding is in
the eating.<span style="mso-spacerun: yes;"> </span>Thus in order to defend the
claim that older network architectures can contribute to musical cognition, we
must actually demonstrate their utility.<span style="mso-spacerun: yes;">
</span>The goal of the remaining chapters in this book is to do exactly that.<span style="mso-spacerun: yes;"> </span>Can we show that training shallow networks
can provide a deeper understanding of music?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"><strong><u> Cited Literature</u></strong>:</span></o:p></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"></span></o:p></span> </div>
<ul>
<li>
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985). A learning algorithm for Boltzman machines. <i style="mso-bidi-font-style: normal;">Cognitive Science, 9</i>, 147-169.</span></span></li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Amari, S. (1967). A theory of adaptive pattern classifiers. <i style="mso-bidi-font-style: normal;">IEEE Transactions on Electronic Computers, Ec16</i>(3), 299-307.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Anderson, J. A. (1995). <i style="mso-bidi-font-style: normal;">An Introduction to Neural Networks</i>. Cambridge, Mass.: MIT Press.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Bengio, Y. (2009). Learning deep architectures for AI. <i style="mso-bidi-font-style: normal;">Foundations and Trends in Machine Learning, 2</i>(1), 1-127.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Bengio, Y., Courville, A., & Vincent, P. (2013). Representation learning: A review and new perspectives. <i style="mso-bidi-font-style: normal;">IEEE Transactions on Pattern Analysis and Machine Intelligence, 35</i>(8), 1798-1828.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W. (2008). Connectionism and classical conditioning. <i style="mso-bidi-font-style: normal;">Comparative Cognition and Behavior Reviews, 3 (Monograph)</i>, 1-115.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., & Dupuis, B. (2012). Equilibria of perceptrons for simple contingency problems. <em>IEEE Transactions On Neural Networks And Learning Systems, </em><span style="font-family: Arial;"><span style="font-family: Arial;"><i>23(8)</i></span></span><span style="font-family: Arial;"><span style="font-family: Arial;">, 1340-1344</span></span>.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., Dupuis, B., Spetch, M. L., & Kelly, D. M. (2009). Simple artificial networks that match probability and exploit and explore when confronting a multiarmed bandit. <i style="mso-bidi-font-style: normal;">IEEE Transactions on Neural Networks, 20</i>(8), 1368-1371.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., Kelly, D. M., Spetch, M. L., & Dupuis, B. (2010). Using perceptrons to explore the reorientation task. <i style="mso-bidi-font-style: normal;">Cognition, 114</i>(2), 207-226.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Dawson, M. R. W., & Shamanski, K. S. (1994). Connectionism, confusion and cognitive science. <i style="mso-bidi-font-style: normal;">Journal of Intelligent Systems, 4</i>, 215-262.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Erhan, D., Courville, A., & Bengio, Y. (2010). <i style="mso-bidi-font-style: normal;">Understanding Representations Learned in Deep Architectures. Technical Report 1355</i>: Departement d’Informatique et Recherche Operationnelle, Universite de Montreal.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Fischer, A., & Igel, C. (2014). Training restricted Boltzmann machines: An introduction. <i style="mso-bidi-font-style: normal;">Pattern Recognition, 47</i>(1), 25-39.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Hinton, G. E. (2007). Learning multiple a layers of representation. <i style="mso-bidi-font-style: normal;">Trends in Cognitive Sciences, 11</i>(10), 428-434.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Hinton, G. E., Osindero, S., & Teh, Y. (2006). A fast learning algorithm for deep belief nets. <i style="mso-bidi-font-style: normal;">Neural Computation, 18</i>(7), 1527-1554.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. <i style="mso-bidi-font-style: normal;">Science, 313</i>(5786), 504-507.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Larochelle, H., Mandel, M., Pascanu, R., & Bengio, Y. (2012). Learning algorithms for the classification restricted Boltzmann machine. <i style="mso-bidi-font-style: normal;">Journal of Machine Learning Research, 13</i>, 643-669.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">McCloskey, M. (1991). Networks and theories:<span style="mso-spacerun: yes;"> </span>The place of connectionism in cognitive science. <i style="mso-bidi-font-style: normal;">Psychological science, 2</i>, 387-395.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. <i style="mso-bidi-font-style: normal;">Bulletin of Mathematical Biophysics, 5</i>, 115-133.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Minsky, M. L., & Papert, S. (1969). <i style="mso-bidi-font-style: normal;">Perceptrons: An Introduction To Computational Geometry</i> (1st ed.). Cambridge, Mass.,: MIT Press.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Mohamed, A., Dahl, G. E., & Hinton, G. E. (2012). Acoustic modeling using deep belief networks. <i style="mso-bidi-font-style: normal;">IEEE Transactions on Audio Speech and Language Processing, 20</i>(1), 14-22.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. <i style="mso-bidi-font-style: normal;">Psychological Review, 65</i>(6), 386-408.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rosenblatt, F. (1962). <i style="mso-bidi-font-style: normal;">Principles Of Neurodynamics</i>. Washington: Spartan Books.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. <i style="mso-bidi-font-style: normal;">Nature, 323</i>, 533-536.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Sarikaya, R., Hinton, G. E., & Deoras, A. (2014). Application of deep belief networks for natural language understanding. <i style="mso-bidi-font-style: normal;">IEEE-Acm Transactions on Audio Speech and Language Processing, 22</i>(4), 778-784.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Testolin, A., Stoianov, I., De Grazia, M., & Zorzi, M. (2013). Deep unsupervised learning on a desktop PC: a primer for cognitive scientists. <i style="mso-bidi-font-style: normal;">Frontiers in Psychology, 4</i>.</span></span></div>
</li>
<li><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-indent: 0cm;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial;">Werbos, P. J. (1994). <i style="mso-bidi-font-style: normal;">The Roots of Backpropagation: From Ordered Derivatives to Neural Networks and Political Forecasting</i>. New York: Wiley.</span></span></div>
</li>
</ul>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-30754018479511532872015-03-15T20:50:00.000-06:002015-03-15T20:50:16.341-06:00Strange Circles<em>As described </em><a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank"><em>in this previous post</em></a><em>, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</em><br />
<em></em><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTBsi7zXaHX2U_jbG-DlsILol0kRmDM-To3S76fu_PJsaWKraftq-YmCVd8eXoXQuKD1vXjptCZm7CCFkWwVU5zJ9J0LVlYf1-xhy_6imlkTTjNXVBxWabm0IdnWqpVHZ3Wz4u12sfSLY/s1600/FigureI-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTBsi7zXaHX2U_jbG-DlsILol0kRmDM-To3S76fu_PJsaWKraftq-YmCVd8eXoXQuKD1vXjptCZm7CCFkWwVU5zJ9J0LVlYf1-xhy_6imlkTTjNXVBxWabm0IdnWqpVHZ3Wz4u12sfSLY/s1600/FigureI-1.jpg" height="255" width="320" /></a></div>
<br />
<div style="text-align: center;">
<span lang="EN-US"><strong><span style="font-size: x-small;"><span style="font-family: Arial;">Figure I-1. Three different types of
circles of pitch classes.<o:p></o:p></span></span></strong></span></div>
<div class="WordSection1">
<span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;">
</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span lang="EN-US">In the novel <i style="mso-bidi-font-style: normal;">Us Conductors</i> </span><!--[if supportFields]><span lang=EN-US><span
style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Michaels</Author><Year>2014</Year><RecNum>6920</RecNum><DisplayText>(Michaels,
2014)</DisplayText><record><rec-number>6920</rec-number><foreign-keys><key
app="EN" db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">6920</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Michaels,
S.</author></authors></contributors><titles><title>Us
Conductors</title></titles><keywords><keyword>Scientists
Russia (Federation) Fiction.</keyword><keyword>Women musicians
Fiction.</keyword><keyword>Theremin Fiction.</keyword><keyword>FICTION
/ Literary.</keyword><keyword>Love
stories.</keyword></keywords><dates><year>2014</year></dates><pub-location>New
York</pub-location><publisher>Random House
Canada</publisher><isbn>9781935639817
(pbk.)</isbn><accession-num>17957534</accession-num><call-num>Jefferson
or Adams Building Reading Rooms PR9199.4.M527 U8
2014</call-num><urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Desktop/Interlude1.docx" title="Michaels, 2014 #6920"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Michaels, 2014</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">, protagonist Lev Termen reflects that “it was not that I was
careless in my calculations; it was that I was seeking the wrong sum” (p. 161).<span style="mso-spacerun: yes;"> </span>A parallel situation arose when I first began
to train artificial neural networks on musical problems.<span style="mso-spacerun: yes;"> </span>My goal was to create a clean example of how to
interpret a trained network to include in a book on connectionist modeling </span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.CITE
<EndNote><Cite><Author>Dawson</Author><Year>2004</Year><RecNum>1635</RecNum><DisplayText>(Dawson,
2004)</DisplayText><record><rec-number>1635</rec-number><foreign-keys><key
app="EN"
db-id="vepx9pxes5fxabewpdxxf020d2a2fv9svdza">1635</key></foreign-keys><ref-type
name="Book">6</ref-type><contributors><authors><author>Dawson,
M.R.W.</author></authors></contributors><titles><title>Minds
And Machines: Connectionism And Psychological
Modeling</title></titles><keywords><keyword>Connectionism.</keyword><keyword>Cognitive
science.</keyword></keywords><dates><year>2004</year></dates><pub-location>Malden,
MA</pub-location><publisher>Blackwell
Pub.</publisher><isbn>1405113480 (hardcover alk.
paper)&#xD;1405113499 (pbk. alk. paper)</isbn><call-num>BF311
.D345
2003&#xD;153</call-num><urls><related-urls><url>http://www.loc.gov/catdir/toc/ecip041/2003005918.html</url></related-urls></urls></record></Cite></EndNote><span
style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-US"><span style="mso-no-proof: yes;">(</span><a href="file:///C:/Users/User/Desktop/Interlude1.docx" title="Dawson, 2004 #1635"><span style="color: windowtext; mso-no-proof: yes; text-decoration: none; text-underline: none;">Dawson, 2004</span></a><span style="mso-no-proof: yes;">)</span></span><!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-US">.<span style="mso-spacerun: yes;"> </span>I felt that it should be
quite straightforward to train a network on a well-defined music problem, and
then be able to pull the theory that defined the problem right out of the
network’s internal structure.<span style="mso-spacerun: yes;"> </span>I was
wrong.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The task that I investigated was chord
classification.<span style="mso-spacerun: yes;"> </span>The input units of the
network represented the keys of a small piano.<span style="mso-spacerun: yes;">
</span>These inputs were used to present tetrachords – chords built from four
notes – to the network.<span style="mso-spacerun: yes;"> </span>The network learned
to classify each chord as belonging to one of four types: major, minor,
dominant, or diminished.<span style="mso-spacerun: yes;"> </span>Traditional
music theory defines each of these tetrachord types in terms of the presence of
particular musical intervals within the chord.<span style="mso-spacerun: yes;">
</span>To make the problem more challenging chords were presented in different
musical keys and in different inversions.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In order to learn this problem, the network
required four hidden units.<span style="mso-spacerun: yes;"> </span>After learning
was completed, the task was to make sense of the network’s internal
structure.<span style="mso-spacerun: yes;"> </span>In particular, the question
of interest concerned what musical features were being detected by each hidden
unit.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The first attempt at answering this question
involved examining hidden unit activities to the various input chords.<span style="mso-spacerun: yes;"> </span>It was expected (from traditional music
theory) that each hidden unit would be sensitive to a musical interval involved
in defining tetrachords of a particular type, and that the network would solve
the problem by combining these different intervals.<span style="mso-spacerun: yes;"> </span>However, there was no evidence that supported
this approach.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">After a number of false starts, I simply
looked at the weights of the connections from each input unit (i.e. each ‘piano
key’) to each hidden unit.<span style="mso-spacerun: yes;"> </span>This approach
revealed two very interesting regularities.<span style="mso-spacerun: yes;">
</span>First, there was a regular mapping between weights and note names. <span style="mso-spacerun: yes;"> </span>For instance, different input units that
represented the note A at different octaves had exactly the same connection
weight feeding into the same hidden unit.<span style="mso-spacerun: yes;">
</span>In other words, if one views a connection weight as the network’s name
for a note, then these notes encoded pitch-class instead of pitch.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Second, more than one pitch-class was given
the same name – the same connection weight – by the network.<span style="mso-spacerun: yes;"> </span>For instance, one hidden unit assigned the
same connection weight to the pitch-classes C, D, E, F#, G#, and A#.<span style="mso-spacerun: yes;"> </span>Another hidden unit assigned the same
connection weight to the pitch-classes C, E, and G#.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In considering the various pitch-classes
that were given the same connection weights in the network, it became evident
that the network had discovered a new way of solving the chord classification
task: using what I call strange circles.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Traditional music theory employs circular
representations of pitch-classes.<span style="mso-spacerun: yes;"> </span>For
example, most music students are exposed to the circle of perfect fifths that
is illustrated on the left of Figure I-1.<span style="mso-spacerun: yes;">
</span>In this circle one can find each of the twelve possible pitch-classes;
nearest neighbors in the circle are a perfect fifth (seven semitones)
apart.<span style="mso-spacerun: yes;"> </span>This circle is not strange;
students use it (for example) to determine how many sharps or flats are required
in a written key signature.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The tetrachord classification network discovered
that it needed circles of pitch-classes, but based them on musical intervals
other than the perfect fifth.<span style="mso-spacerun: yes;"> </span>For instance,
one hidden unit named pitch-classes using the two circles of major seconds that
are illustrated in the middle of Figure I-1.<span style="mso-spacerun: yes;">
</span>In either of these circles, nearest neighbors are a major second (two
semitones) apart.<span style="mso-spacerun: yes;"> </span>If a pitch-class
belonged to one circle, it was given one connection weight.<span style="mso-spacerun: yes;"> </span>If it belonged to the other circle, it was
given a different connection weight.<span style="mso-spacerun: yes;"> </span>Any
pitch-class that belonged to the same circle of major seconds was given the
same connection weight.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Similarly, another hidden unit named
pitch-classes using the four circles of major thirds that are illustrated on
the right of Figure I-1. In each of these circles, nearest neighbors are a
major third (four semitones) apart.<span style="mso-spacerun: yes;"> </span>When
these circles were used, pitch-classes that fell into the same circle of major
thirds were given identical connection weights; pitch-classes that belonged to
different circles of major thirds were assigned different connection weights.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">One way in which circles of major seconds
and circles of major thirds are strange circles for this network is that they
define weird equivalence classes for pitch.<span style="mso-spacerun: yes;">
</span>Traditional Western tonal music recognizes twelve distinct
pitch-classes.<span style="mso-spacerun: yes;"> </span>However, a hidden unit
that organizes inputs using circles of major seconds only recognizes two
distinct pitch-classes (one for each circle).<span style="mso-spacerun: yes;">
</span>A hidden unit that organizes input using circles of major thirds only
recognizes four distinct pitch-classes (one for each circle).<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">A second way in which these circles are
strange is that they are not typical topics of music theory.<span style="mso-spacerun: yes;"> </span>Students learn the circle of perfect fifths
because of its utility; students do not learn strange circles, because their
utility is much less evident.<span style="mso-spacerun: yes;"> </span>This is
not to say that these strange circles are removed from traditional theory,
because this theory defines the musical intervals which in turn define each
circle.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">This leads to the third way in which these
circles are strange.<span style="mso-spacerun: yes;"> </span>How is it possible
to use circles of major seconds and circles of major thirds to represent the
differences between major, minor, dominant, and diminished tetrachords?<span style="mso-spacerun: yes;"> </span>We will postpone the answer to this question
until Chapter 7 which examines chord classification networks in detail.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">For now, the key point is that even when
traditional music theory defines the input/output mapping for a task, this
theory is the only means for mapping inputs into outputs.<span style="mso-spacerun: yes;"> </span>Artificial neural networks are capable of
finding alternative music theories.<span style="mso-spacerun: yes;"> </span>However,
to find such surprises one must examine the internal structure of trained
networks.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In short, supervised learning of standard
musical problems might lead a researcher to expect to find the network solves
the problem in a particular way.<span style="mso-spacerun: yes;">
</span>However, networks can easily defy such expectations.<span style="mso-spacerun: yes;"> </span>It is not that a researcher’s expectations
are careless.<span style="mso-spacerun: yes;"> </span>It is just that a network
can compute different sums.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<!--[if supportFields]><span
lang=EN-US><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>ADDIN EN.REFLIST <span style='mso-element:
field-separator'></span></span><![endif]--><a href="https://www.blogger.com/null" name="_ENREF_1"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Dawson, M. R. W. (2004). <i style="mso-bidi-font-style: normal;">Minds And Machines: Connectionism And
Psychological Modeling</i>. Malden, MA: Blackwell Pub.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; text-indent: -36pt;">
<a href="https://www.blogger.com/null" name="_ENREF_2"><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><span style="font-family: Arial, Helvetica, sans-serif;">Michaels, S. (2014). <i style="mso-bidi-font-style: normal;">Us Conductors</i>.
New York: Random House Canada.</span></span></a><span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-bidi-font-family: Arial; mso-no-proof: yes;"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
<!--[if supportFields]><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
12.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA'><span style='mso-element:field-end'></span></span><![endif]--><br />
<br />
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-30202728221320638942015-03-08T19:47:00.000-06:002015-03-08T19:47:18.239-06:00Overture: Alien Music
<em>As described <a href="http://cognitionandreality.blogspot.ca/2015/03/a-prelude-to-some-interludes.html" target="_blank">in this previous post</a>, the text below is a draft of one of several "interludes" to be included in a book that I am working on concerned with music and artificial neural networks.</em><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3xRnUhTOUj89519sLpV3ERL307o-ipPkP27pJf_cw4banw7gCRdAu3xxYk8ldKgf0H_8WOgapG5VuGCkYixpxvrKxzFu__2w_mrH1prdqubas8uzNhHnzq0KoDw5m4mksZpnoK38MzaU/s1600/FigO-1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3xRnUhTOUj89519sLpV3ERL307o-ipPkP27pJf_cw4banw7gCRdAu3xxYk8ldKgf0H_8WOgapG5VuGCkYixpxvrKxzFu__2w_mrH1prdqubas8uzNhHnzq0KoDw5m4mksZpnoK38MzaU/s1600/FigO-1.jpg" height="43" width="320" /></a></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;"><span style="font-size: x-small;"></span></span></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;"><span style="font-size: x-small;"><span lang="EN-US" style="font-family: "Arial","sans-serif"; font-size: 10pt; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 12.0pt; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: EN-US;"><strong>Figure O-1. The musical signal composed by John
Williams for <i style="mso-bidi-font-style: normal;">Close Encounters of the
Third Kind</i>.</strong></span></span></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"></span> </div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Steven Spielberg’s 1977 movie <i style="mso-bidi-font-style: normal;">Close Encounters of the Third Kind</i>
declares that we are not alone, and we should not be afraid.<span style="mso-spacerun: yes;"> </span>The film follows ordinary people after they
experience a close encounter with an unidentified flying object.<span style="mso-spacerun: yes;"> </span>After this experience, the protagonist of the
movie, Roy Neary (played by Richard Dreyfuss), becomes obsessed with seeing the
UFO again, as well as with creating sculptures (from mashed potatoes and other
materials) of a shape that has a deep meaning that he cannot quite fathom.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Eventually it is revealed that this shape represents
a monolith of rock (Devil’s Tower, Wyoming) marking the selected location for
first contact between humans and aliens.<span style="mso-spacerun: yes;">
</span>The obsessions of Neary and others are produced by an implanted
invitation from the aliens to journey with them. <span style="mso-spacerun: yes;"> </span>The invitees recognize the shape from
television news broadcasts concerning a story about a (hoax) anthrax outbreak
in Wyoming.<span style="mso-spacerun: yes;"> </span>They spend the latter part
of movie traveling to Devil’s Tower and dodging the efforts of the authorities
to stop them.<span style="mso-spacerun: yes;"> </span>In the final scene of the
movie only Neary succeeds; he is welcomed by alien children as he ventures
aboard their mother ship.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">A simple musical signal plays a key role in
the film, and is presented in the musical score above (Figure O-1).<span style="mso-spacerun: yes;"> </span>It was composed by John Williams.<span style="mso-spacerun: yes;"> </span>He strove to write a signal that it was long
enough to be set apart from the simplest musical elements (e.g. a chord or an
interval), but not so long to exist on its own as a melody.<span style="mso-spacerun: yes;"> </span>He decided that these goals would be achieved
by a theme that was only five notes in length, and composed about 350 different
five-note permutaitons.<span style="mso-spacerun: yes;"> </span>Spielberg liked
the one presented in Figure O-1 the best, and it became one of the most famous
musical themes in film history.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The musical theme is first encountered in
the film being sung by hundreds of pilgrims at Dharmsala, India.<span style="mso-spacerun: yes;"> </span>When asked where they first heard it, they
all point, in unison, to the sky.<span style="mso-spacerun: yes;"> </span>In a
later scene, scientists broadcast the tones into space, and receive the
coordinates of Devil’s Tower in return.<span style="mso-spacerun: yes;"> </span>At
the climax of the film, the signal is performed on an ARP 2500 synthesizer
located on a massive runway constructed atop Devil’s Tower.<span style="mso-spacerun: yes;"> </span>The music greets, and communicates with, the
alien visitors.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In this final scene the keyboard is played
by a young, fresh-faced Phillip Dodds.<span style="mso-spacerun: yes;">
</span>Dodds was in fact the engineer that ARP sent to set up the synthesizer used
in the movie.<span style="mso-spacerun: yes;"> </span>When the original actor who
was to play it became sick, Spielberg saw Dodds working on the machine, liked
his look, and cast him in the role.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">As the scene unfolds Dodds is instructed to
play the musical signal faster and louder while the chief scientist (Lacombe,
played by Francois Truffault) strides out along the runway.<span style="mso-spacerun: yes;"> </span>Eventually the enormous mother ship arrives,
hovers over the runway, and begins to loudly copy the notes that Dodds
plays.<span style="mso-spacerun: yes;"> </span>This musical mimicing quickly erupts
into an interstellar jam session of increasing tempo and complexity.<span style="mso-spacerun: yes;"> </span>Awestruck and wide eyed, Dodds exclaims “What
are we saying to each other?”<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">This is a very deep question indeed.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">The intended message in the film is that
music is – literally – a <i style="mso-bidi-font-style: normal;">universal</i>
language, one shared by all intelligent life forms.<span style="mso-spacerun: yes;"> </span>That the alien ship generates the same notes,
and that it jams with Dodds’ character in the same musical system, supports
this optimistic view.<span style="mso-spacerun: yes;"> </span>To answer Dodds’
question a scientist standing beside him says “Seems they’re trying to teach us
a basic tonal vocabulary.”<span style="mso-spacerun: yes;"> </span>Another
immediately adds “It’s the first day of school, fellas.”<o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">However, other intriguing scenarios exist;
there are alternative musical possibilities that Spielberg did not explore in
his film.<span style="mso-spacerun: yes;"> </span>Does the fact that both the
ARP 2500 and the mother ship generate the same basic tonal vocabulary imply
that the humans and the aliens share the same underlying musical theory?<span style="mso-spacerun: yes;"> </span>Or instead is it possible that a completely
different musical theory – an alien music theory that is dramatically different
from our own – is still capable of generating the same patterns of musical
notes?<span style="mso-spacerun: yes;"> </span>Perhaps all these fellas know
they are attending the first day of school, but are not aware of the lecture
topic!<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In many respects, my aim in this book is to
explore the possibility of such alien music.<span style="mso-spacerun: yes;">
</span>However, instead of requiring a close encounter of the third kind for
this exploration, I am fortunately able to adopt a much more terrestrial
approach.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">This method involves teaching a particular
type of computer simulation to generate responses that are consistent with
Western musical theory.<span style="mso-spacerun: yes;"> </span>For instance,
the computer simulation can be presented the tones that define a particular
scale, and can learn to respond with the tonic note of that scale, or to
identify that scale as being major or minor.<span style="mso-spacerun: yes;">
</span>From this perspective, similar to the alien encounter at the end of
Spielberg’s movie, the computer simulation and I are saying something to each
other, and are learning to use a basic tonal vocabulary.<span style="mso-spacerun: yes;"> </span>Our inputs and outputs are consistent.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span lang="EN-US"></span></span><br />
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">However, the particular type of computer
simulation that is being trained in this fashion is called an artificial neural
network, and while it learns to generate the correct outputs to various musical
inputs, it is not taught – or constrained by – traditional Western music
theory.<span style="mso-spacerun: yes;"> </span>Many researchers in what is known
as connectionist cognitive science argue that the internal workings of
artificial neural networks are quite distinct from the clear formal properties
found in logic, mathematics, or music theory.<span style="mso-spacerun: yes;">
</span>As a result it is possible that the artificial neural network can
discover a completely novel approach – and alien music theory – that generates
the same input/output relationships that are defined by Western music theory.<o:p></o:p></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">In order to determine whether this is possible,
after a network is trained we have to examine its internal structure to
discover how it is able to generate its musical responses.<span style="mso-spacerun: yes;"> </span>As is explained in more detail in Chapters 1
through 3, an artificial neural network is a messy collection of different
processors (analogous to neurons) that send signals to one another through a
larger and messier collection of weighted connections (analogous to synapses
between neurons).<span style="mso-spacerun: yes;"> </span>The musical knowledge
of a trained network is represented in its internal patterns of
connectivity.<span style="mso-spacerun: yes;"> </span>The messiness of such patterns
– called distributed representations – is what makes the existence of an alien
music theory plausible.<span style="mso-spacerun: yes;"> </span>We can use a
variety of techniques to make sense of a network’s internal structure, and in
so doing can reveal the musical regularities that the network has learned, on
its own, to exploit.<span style="mso-spacerun: yes;"> </span>Of key interest is
whether the theory that the network has learned is the same as our own.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><span style="font-family: Arial, Helvetica, sans-serif;">Interestingly, and as will be detailed in the
chapters that follow, artificial neural networks can discover novel musical
theories that seem completely alien.<span style="mso-spacerun: yes;">
</span>This has interesting implications for music, insofar as it reveals
alternative musical formalisms.<span style="mso-spacerun: yes;"> </span>This
also has important implications for the study of musical cognition, because it
reveals a variety of different kinds of representations that the human brain
might use to process music.<o:p></o:p></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US"><o:p><span style="font-family: Arial; font-size: x-small;"> </span></o:p></span></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-12263875998957780252015-03-08T19:30:00.000-06:002015-03-08T19:30:19.022-06:00A Prelude To Some InterludesThis blog has not been active since April, 2014, but for a very good reason: I am hard at work on a new book that describes some research that uses artificial neural networks to study music. Last April, for a variety of reasons that may be discussed in a future blog, this research started to advance nicely. One consequence is that I began to write book chapters -- the first 9 are in solid form, with only a couple more to go, and amount to well over 100,000 words of new prose. Striking the book while the iron was hot meant putting other writing (aka work on this blog) on hold.<br />
<br />
Part of my book writing involves creating short "interludes" between chapters; short pieces that highlight some general theme, and move the reader's focus away from the technical details of a particular chapter to the bigger picture. I thought that these pieces might serve well as posts on this blog, so over the next few weeks (as more and more get created) I will test drive them here. I will post the first (the "overture" entitled "Alien Music") here later this evening.<br />
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0tag:blogger.com,1999:blog-7699616724222495854.post-63710996295063469772014-04-07T09:41:00.000-06:002014-04-07T09:41:20.785-06:00Coarse Coding and Coarse Behavior
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">I confess
that I am fascinated with the ongoing saga of Toronto Mayor Rob Ford’s
scandalous behavior, his bid for reelection, and the coverage of it all by the
Toronto, Canadian, and international media.<span style="mso-spacerun: yes;">
</span>I am particularly intrigued when the same event is described completely
differently by different news outlets (with competing political aims in their
editorial policies).<span style="mso-spacerun: yes;"> </span>At the Leafs home
game on April 5, was the key story about </span><a href="http://www.torontosun.com/2014/04/06/ford-frenzy-as-mayor-mobbed-by-fans-at-acc"><span style="color: blue; font-family: Arial;">a
happy, lucid, sober Mr. Ford mobbed by a frenzy of adoring supporters</span></a><span style="font-family: Arial;">?<span style="mso-spacerun: yes;"> </span>Or was the news instead about </span><a href="http://www.thestar.com/news/gta/2014/04/05/belligerent_rob_ford_warned_by_security_at_air_canada_centre.html"><span style="color: blue; font-family: Arial;">a
belligerent, irate, possibly drinking Mayor being warned about his behavior by
security</span></a><span style="font-family: Arial;">? <o:p></o:p></span></span><br />
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Regarding
this most recent incident, it is of particular interest that social media provided
the most detailed account of the Mayor’s evening out.<span style="mso-spacerun: yes;"> </span>Posts on Twitter, several including links to
video and photographs, tracked his movements from the start of the hockey game
to his confrontation with security, alerted followers to his late night visit
to City Hall (What was that mysterious burning rubber smell detected by
security there? Why is that not mentioned in the traditional media?), and
established his early morning presence at the Muzik nightclub.<span style="mso-spacerun: yes;"> </span>In this case, it seemed that Twitter was
breaking the news, and that the traditional media were playing catchup.<span style="mso-spacerun: yes;"> </span>As reports appeared in the media the next day
some posts on Twitter accused traditional outlets of not telling the complete
story!<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">All of this
made me think of Twitter as representing reality in what connectionist
cognitive scientists call a <u>coarse code</u>.<span style="mso-spacerun: yes;">
</span>Many artificial neural networks generate highly accurate responses by
pooling the signals of individual elements, where each individual element has noisy,
sketchy, or inaccurate information about what is going on.<span style="mso-spacerun: yes;"> </span>The ‘coarseness’ of this type of
representation is reflected in the fact that every processor inside the network
is an inaccurate detector.<span style="mso-spacerun: yes;"> </span>The surprising
power of this representation comes from the fact that if you combine all of
these poor measures together, a highly accurate measure is generated.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">For coarse coding
to work, the individual (inaccurate) measures generally require two different
properties.<span style="mso-spacerun: yes;"> </span>First, different measuring
elements must have overlapping sensitivity: many of them will be measuring
similar things.<span style="mso-spacerun: yes;"> </span>Second, different
measuring elements must also have to have different perspectives on what is
being detected.<span style="mso-spacerun: yes;"> </span>In short, their
sensitivities overlap, but are <u>not</u> identical.<span style="mso-spacerun: yes;"> </span>When these two properties are true high
accuracy can be produced by combining measures.<span style="mso-spacerun: yes;">
</span>This is because if each detector has a different perspective, it will be
providing different ‘noise’ than is provided another.<span style="mso-spacerun: yes;"> </span>Combining the different noise from different
detectors will tend to cancel it all out.<span style="mso-spacerun: yes;">
</span>What remains is the amplified ‘signal’ – the ‘truth’ – that is also
being sensed to a limited extent by the various processors in the network (due
to their overlapping sensitivities).<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Each
individual tweet on Twitter can be viewed as some information being provided by
an inaccurate detector.<span style="mso-spacerun: yes;"> </span>If the sources
of a large number of these tweets have slightly different perspectives, or
provide different kinds of information (statements vs pictures vs videos), then
their combined effect provides information that has a strong sense of accuracy.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">Not
surprisingly, researchers interested in Big Data are actively exploring this
characteristic of social media.<span style="mso-spacerun: yes;"> </span>For
instance, some researchers are using the content of tweets </span><a href="http://www.washingtonpost.com/opinions/how-twitter-can-predict-an-election/2013/08/11/35ef885a-0108-11e3-96a8-d3b921c0924a_story.html"><span style="color: blue; font-family: Arial;">to
predict the results of elections</span></a><span style="font-family: Arial;">, although the accuracy of this approach is
subject to a healthy debate.<span style="mso-spacerun: yes;">
</span>Importantly, the accuracy of such predictions requires that the two key
properties of coarse coding (presenting information that is similar, but
different) be true.<span style="mso-spacerun: yes;"> </span>When these
properties are not true – for instance, when many people retweet the same
information, so that different perspectives are <u>not</u> provided – social media
can misinform, as shown by Twitter being a continual source of celebrity death
hoaxes.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">To me, the
parallel between tweets and successful coarse coding in artificial neural
networks clearly indicates that Twitter can be a source of a great deal of
accurate information, and makes me reflect on how neural network paradigms
might be tweaked to explore tweet contents.<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><span style="font-family: Arial;">The
parallel also makes me think that if I was a politician seeking reelection –
particularly one who is such a notorious celebrity that my frequent encounters
with the public immediately appear on social media – I would strive to be on my
best behavior.<span style="mso-spacerun: yes;"> </span>The image of me emerging
from all of those Tweets might be more accurate and telling than the one that
the traditional news media feels safe to publish!<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US" style="mso-ansi-language: EN-US;"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
Michael R.W. Dawsonhttp://www.blogger.com/profile/08970484174229230816noreply@blogger.com0