Practical Mnemonics For The Ukulele

This is a longer than typical entry: to summarize, it provides a technique for remembering the association between finger positions and chord names on the ukulele, as well as for remembering note names in the order given by the circle of perfect fifths.  In you are interested in how to accomplish this feat, then read on!

It is that time of year again when I lecture about practical memory methods.  Last year I remembered π to 100 decimal places.  This year, I am more interested in some remembering some practical musical information. I plan to start my Thursday class by walking through the room, ukulele in hand, telling the following story:

I open the front door of my house and step into the vestibule. There on the wall I see a huge saw, obviously for cutting logs.  However, this saw is extraordinarily curved, its entire length bent around so that it takes the form of the letter ‘C’.  I cannot imagine using such a tool.

Stepping beyond the vestibule, I look into the walk-in closet. .  I am surprised; I expect to see my dog in his crate.  Instead, there is a full-grown jersey cow, cheerfully munching on tall grass-like plants that grow from the floor.  The brush-like heads of these plants take the shape of the letter ‘G’

Walking through the house, I look next into the main floor bathroom. There I see a tall, robed, bearded man – he looks like Gandalf!  I realize that he is actually Noah.  He shaves at the sink, using a large D-shaped tool, much like an oversized potato peeler.

Walking towards the kitchen, I hear a loud buzzing sound.  I stop and glance up the staircase that leads to the second floor.  On the landing, I see a large honey bee leaving a hive that is peculiarly shaped like the letter ‘A’. The buzzing bee generates the sound that attracted my attention.

Turning towards the kitchen, I continue my walk.  I glance down the basement stairs.  At the bottom landing, I see an enormous bottle of rye whiskey.  The bottle is exceedingly strange; it has three long horizontal tubes coming from its side, giving it the shape of the letter ‘E’.

I finally reach the kitchen. I see a small child, a tot, working by the gas stove.  He stands on a chair in order to reach the burners.  He skewers the letter ‘B’ onto a long stick, and toasts it over the open flame.  How will it taste?

In the middle of the kitchen is the large, yellow kitchen sink.  I glance into it.  There I see an enormous, braided, rawhide dog chew.  Someone has painstakingly shaped it into an ‘F♯’.  Ah, I think, a new musical dog chew!

At the end of the kitchen is a room that contains the refrigerator, and has a small counter upon which the cats have their containers of water and kibble.  My cat Phoebe is there, watching me.  She is wearing an enormous, long, wide black tie.  The tie has a musical theme, covered with gaudy yellow ‘C♯’s of different sizes. I think that the ‘C’ stands for cat, and the ♯ indicates ‘sharp-dressed’.

I leave the kitchen, and enter the dining room. On the table rests a large bowl filled with red juice, and decorated with the same pattern as a bottle of V8.  I look at the juice in the bowl.  On its surface, perhaps created using sour cream, I see the shape ‘G♯’.  I assume that G means that it is good for me, and that the ♯ warns me that it is very spicy.

Beside the dining room table is my Baldwin piano.  On its bench sits my mother.  She is repeatedly pounding a single, enormous, black key.  The key is ‘D♯’, her favorite note.

I pass from the dining room into the living room. There, on the couch, reclines a woman.  I only see her bare feet.  Her toes, covered in elaborate nail polish, draw my attention; each bright pink toenail has a green ‘A♯’ inscribed on top.

At the end of the living room, I notice my favorite brown recliner.  A tired policeman rests there, his feet raised.  He is in full uniform, with many decorations.  I notice a distinct ‘F’ on the sole of each of his shoes.  I realize that he is Toronto Police Chief Bill Blair, and that he has been stomping on the Fords.  This has marked his shoes.

The images in the story above are novel, bizarre, and dynamic; this makes them highly memorable. In fact, after designing the images, I learned each of them as well as their position in my ‘memory palace’ – the main floor of my house -- after only a couple of walk-throughs.

So what is the purpose of this story?  Why am I carrying my ukulele when I tell it?

First, each part of the story pairs two key images together.  One image is of a ‘peg’; this is an image that is first converted into a word, and then is converted into a number according to the famous Major Method, which maps consonant sounds into digits as follows:

Consonant Sounds	Digit
s	0
t,d	1
n	2
m	3
r	4
l	5
sh, ch, g, j	6
k	7
f,v	8
p, b	9

In the first image, the ‘peg’ is the saw, whose consonant sound is ‘s’, which is converted into a 0.  The peg of the second image is the cow, whose consonant sound is ‘k’, which is converted into a 7.  The table below lists the full set of peg images in the story.

The second image concept in each part of the story is a shape that maps into a musical note.  For instance, the shape of the saw in the first story image brings to mind the note ‘C’, while the shapes of the heads of grass in the second story image brings to mind the note ‘G’.  The table below also provides the full set of note images.

The purpose of the story is to help me remember key information about the ukulele.  Currently, I am learning ‘closed form’ chords.  These chords involve pressing down each of the four strings of the instrument.  They are practical because one can move the same chord shape up and down the fret board, playing the same kind of chord, but in a different musical key.  For instance, if I use my index finger to press down on each string along the same fret, the result will be a 6 chord.  The specific chord depends upon which fret I use: if I press on the first fret, I will play a C♯6 chord; if I press on the seventh fret, the result is a G6 chord.

Each of the twelve images in the story connects a particular number to a particular musical note, linking the root of the chord (for the subset of chords whose root comes from the C-string on the ukulele) to a fret number.  So, if I want to remember what fret to use to play a chord whose root is A (such as A6), then I remember the A-shaped beehive on the stairs, with the buzzing bee, and realize that I must use fret 9 (because bee = 9).  Each of the twelve images in the story provides musical meaning to my hand positions on the instrument!

Location	‘Peg’ Image	Image Translation	Major Method Logic	Note Image	Root
Vestibule	saw	0	S = 0	C (saw shape	C
Front Closet	cow	7	C = 7	G (grass heads)	G
Washroom	Noah	2	N = 2	D (razor)	D
Stairs	bee	9	B = 9	A (bee hive)	A
Basement stairs	rye	4	R = 4	E (bottle shape)	E
Stove	Tot	11	T T = 11	B (letter cooked)	B
Kitchen sink	chew	6	Ch = 6	F♯ (chew shape)	F♯
Cat dish beside fridge	tie	1	T = 1	C♯ (tie pattern)	C♯
Dining Room Table	v8	8	V = 8	G# (floating in bowl)	G♯
Piano	Ma	3	M = 3	D# (giant piano key)	D♯
Sofa	toes	10	T S = 10	A♯ (on toenails)	A♯
Leather Chair	law	5	L = 5	F (on soles)	F

Importantly, there is even more to the story.  I used a classic technique, the method of loci, to associate each two-concept image with a particular location in my house.  As I move through the house in my memory, I encounter these images in a particular order.  The order is deliberate: I retrieve the different notes in the same order as given by a key musical concept, the circle of perfect fifths.  That is, the G in the walk-in closet is a perfect fifth higher than the C in the vestibule; the D in the washroom is a perfect fifth higher than the G in the walk-in closet, and so on.   The image below shows the complete circle of fifths; note how it matches the order of the root notes in the rows of the tables above.  Playing chords in the order given by this circle is a standard technique in jazz, and generates particularly pleasing changes from one chord to the next.

I could practice my closed form chords – for instance, all of the 6 chords – simply by moving up one fret at a time (start with C6 (all strings open, fret 0), then C♯ (fret 1), D (fret 2), and so on).  This exercise is excellent for strengthening my index finger, but hard on the ear – it is not musically interesting.  I get the same workout, but one that is much more musical, by playing the same chords in a different order: the order given by the circle of fifths.  I start with C6 (fret 0), move on to G6 (fret 7), then to D6 (fret 2), and so on according to the table above.  By keeping my story in mind, and using its images, I play the entire chord sequence in a musical order, and learn to associate finger positions with chord names.  All without having to look at a single sheet of music!

 

How to Memorize π to 100 Decimal Places

One of my undergraduate courses introduces the foundations of cognitive science.  It first portrays three different approaches to cognition (classical, connectionist, embodied), emphasizing their differences and their mutual antagonism.  It then explores how to unify these three views. 

I end the course with a lecture on memory, because this topic is one that promotes theoretical unification.  Mnemonic techniques for converting numbers into words are clearly in the realm of classical cognitive scientists interested in symbol manipulation.  Techniques that assert associations between memories, so that a recalled item cues the recall of the next item, have definite connectionist attributes.  Techniques that promote the use of the real world, such as using well-known locations to store to-be-remembered material, evoke embodied cognitive science’s interest in cognitive scaffolding.   

I set the stage for my lecture by performing a feat of memory.  Recently I recalled π to 100 decimal places under the watchful eyes of my students. (As I wrote the digits across the board in front of the class, they used the internet to track my progress – without me asking!)   This performance is not particularly notable – world record holder Lu Chau has recited π to 67,890 digits – but it is grand enough for me, and it possibly impresses my students. 

Surprisingly, anyone interested in performing this memory feat who peruses the internet for how-to advice is often steered in inefficient and laborious directions.  Some websites recommend learning π by repetition:  “Repeat 4 digits out loud at least 20 times” says one.  Other sites recommend looking for numerical patterns within a block of digits, and then for other patterns that link one block to the next.  Others provide piems – poems that represent the desired digits – for memorization, and for later decoding.  A handful of sites refer to classic mnemonics for converting digits to words; but cautions the reader about difficulties;  the words have to be linked together into a (memorisable) story in order to recite π’s digits in the right order, which is quite challenging because the required words do not typically come in meaningful patterns! 

My own technique for this memory feat seems more efficient.  I employ two different mnemonic techniques in concert.  First, I use a standard technique for converting digits into words.  However, I deal with the sequencing of the words using a second technique, the ancient method of loci, in which I move from location to location in a ‘memory palace’, placing to-be-remembered images at each location.  Several of my ‘π words’ are chunked together in a single image.  My memory palace is a very familiar place – my house – and I can memorize 100 digits of π using only 16 different images.  To perform my feat, I simply walk through my memory palace, retrieving the stored images in the necessary order.  Each image recalls a phrase; I (knowing the Major method described below) translate the phrase into numbers; I then write out the numbers in front of the class. 

Of course, as this memory feat is part of a lecture, I am compelled to explain my methods to my students.  I begin by telling them the following story, which illustrates my use of the method of loci.  If you read the story, concentrating on creating each image (placing it in your own memory palace), then you will be able to perform this memory feat as well: 

I begin at the front sidewalk to my house. I look at the sidewalk, covered in snow, and place upon it an image of a running car motor resting on top of a red tulip; the tulip vibrates from the action of the engine. This image represents the concept Motor-Tulip. 

Next, I see the top of the stairs that lead to my front door. I imagine seeing NBA star Steve Nash limping down the stairs as he leaves my house. I place that image on the stairs, standing for the sports headline Nash! Lame! Leave! 

I open the front door, step into the vestibule. There I imagine an unknown person throwing a pickaxe (instead of a dart) to choose one of a number of nametags stuck to the wall. Each tag holds the name of a poem. This dynamic image conveys the meaning Pick-Poem-Name. 

Stepping beyond the vestibule, I look into the walk-in closet. I imagine seeing automatic conveyor of the type used by drycleaners; many fur coats hang from this device. My image activates, and the coats spin round and round the closet. This is clearly a Fur-Changer. 

Moving along, I look into the main floor bathroom. I add to this room an image of my mother in an incoherent rage, so angry that volumes of foam spew from her mouth. Yes, I see Mom-Foaming. 

The next room that I reach is the kitchen. On the counter, I see a large, overflowing bowl of dog kibble. I imagine making each of these kibbles even smaller by cutting them into pieces using a large, sharp knife. Setting this image into motion encodes Kibbles-Knife. 

Moving towards the end of the kitchen, I peer into the back entry and notice the upright freezer. I imagine opening the freezer, gazing inside; in my mind’s eye, I see an aluminum bucket being flipped up and down on a hot frying pan. To me, this image means Fried-Bucket. 

Beside the back entry is a pantry connected to the kitchen. On the small counter within it, I imagine seeing an old, torn, dirty roadmap; attached to the map is a lit fuse with its bright spark moving dangerously close to the end. This is a strange device, perhaps invented by one of my cats; it is a Shabby-Map-Bomb. 

I leave the kitchen, and enter the dining room. I imagine that the dining room table supports a large cooler of ice. On this ice are many of seal fins, eerily flipping up and down on their own. Tonight, dinner appears to be Cooled-Seal-Fins. 

I pass from the dining room into the living room. There, in my imagination, an unknown woman works, taking a black hockey puck and laboriously winding colorful ribbons around it. I do not know who this woman is, but I do know her role in the household: She is the Puck-Wrapper. 

I turn away from the living room, and begin to climb the stairs to the second floor. At the first stairs landing I imagine seeing a person with a very large earlobe from which dangles a strange earring. The earring consists of several different gnomes and a cup of coffee. To me the image represents Earlobe-Gnomes-Coffee. 

I climb the second flight of stairs, turn left and gaze into the laundry room. There I imagine a number of my former teachers all standing around using cloths to polish the nose of a large fish. Thus in the laundry room I place the concept Teachers-Shine-Fish-Nose. 

Beside the laundry room is a linen closet. I open it and imagine seeing a beehive from which swim a number of long, lanky pipefish. Apparently, the linen closet contains a Hive o’ Pipefish.  

The next room that I enter is a second floor office. There I imagine seeing Knives Chau, a character from the movie Scott Pilgrim vs. the World. She is using a hammer to smash all my old LPs into bits. The concept in this room is Knives-Hammer-Vinyl. 

The office leads into the master bedroom. I imagine seeing on the bed a desert island surrounded by ocean. The island is small, but covered with a mass of moving ticks. The bed contains Marooned-Ticks. 

My final stop is the bathroom attached to the master bedroom. On the bathroom floor, I imagine seeing a single shoe that has the appearance of a cob of corn. This is my missing Shoe-Cob. 

I designed the images in the story above to be novel, bizarre, and dynamic in order to make them easy to remember. In fact, after selecting the images, I learned each of them as well as their position in my memory palace after only a couple of imaginary walk-throughs. 

I selected the words encoded by the images with a different mnemonic technique in mind. This technique was the Major method, for converting digits into consonant sounds. For instance, the consonant sound n is associated with the digit 2 because n has two downward strokes; the consonant sound m is associated with the digit 3 because m has three downward strokes. The table below provides the full Major method; I highly recommend reading about it in Lorayne, H. and J. Lucas (1974). The Memory Book. New York, Stein and Day. 

To use the Major method to remember a long number, take the number, convert its digits into consonant sounds, and then add vowels to make meaningful words and expressions. To recall the number, recall the expression – then work backwards to convert its consonant sounds back into digits. 

Consonant Sounds	Digit
s	0
t,d	1
n	2
m	3
r	4
l	5
sh, ch, g, j	6
k	7
f,v	8
p, b	9

 The images that I placed in the various loci in the story that I told above now make perfect sense: each represents words to translate into digits of π with the aid of the Major method, as shown in the table below:  

Words From Image	Consonants	Digits
Motor-Tulip	m-t-r-l-p	3.14159
Nash! Lame! Leave	n-sh-l-m-l-v	265358
Pick-Poem-Name	p-k-p-m-n-m	979323
Fur-Changer	f-r-ch-n-g-r	846264
Mom-Foaming	m-m-f-m-n	33832
Kibbles-Knife	k-b-l-s-n-f	795028
Fried-Bucket	f-r-d-b-k-t	841971
Shabby-Map-Bomb	sh-b-m-p-b-m	693993
Cooled-Seal-Fins	c-l-d-s-l-f-n-s	75105820
Puck-Wrapper	p-k-r-p-r	97494
Earlobe-Gnomes-Coffee	r-l-b-n-m-s-k-f	45923078
Teachers-Shine-Fish-Nose	t-ch-r-s-sh-n-f-sh-n-s	1640628620
Hive O’ Pipefish	v-p-p-f-sh	89986
Knives-Hammer-Vinyl	n-v-s-m-r-v-n-l	28034825
Marooned-Ticks	m-r-n-d-t-k-s	3421170
Shoe-Cob	sh-k-b	679

 

With a little practice using the Major method – I usually do so by memorizing the digits of license plates on other cars as I drive – converting words into digits becomes automatic.  This ability, combined with the method of loci and vivid mental imagery, permits you to perform memory feats like mine without too much effort.  However, if I ever want to reach Lu Chau’s level of performance, then I will have to move into a much, much larger memory palace!