In an
earlier project we
trained a network to learn the Coltrane changes, which is an important
progression of jazz chords. 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.
The map above has one intriguing property: its outer and inner rings of notes are examples of what we call strange circles. Each of these rings is a circle of major seconds; neighboring pitch classes on the ring are a major second, or two semitones, apart. 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).
One day the
map above happened to be drawn on the chalkboard when I was in the lab with my
ukulele in hand. I was noodling some
minor chords, and was pleased by the sound of moving from D minor to A
minor. As I played these two chords, I looked
at the map on the board, and noticed how it lined up these two notes. Intrigued, I played other combinations of
chords – for instance C minor and G minor – whose root notes were in similar
relationships in the map. They too were
pleasing. 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. I drew the
map, played its succession of chords, and I really liked the sound of the
entire progression.
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. The new map that I created is given below:
The arrows
on the map indicate how I use it to move from chord to chord. Let’s say I start with a D chord. The black arrow indicates that next an A
chord will be played. 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). I continue
this pattern moving around the map, eventually returning to where I started, at
the ‘D’ location of the inner ring.
One example
of following this pattern is provided in the score below. This particular example plays major seventh
chords at each map position, which has (to my ear at least) a pleasing, jazzy
sound. The score uses ‘closed form
chords’, which involve pressing a finger down on each ukulele string. So playing this score is an exercise in
moving a closed form shape up and down the length of the fretboard. The Cmaj7 chord is formed at the very top of
the fretboard, while the Bmaj7 is formed with the index finger barred across
the 11th fret near the fretboard’s bottom. 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.
The score
above offers just a hint of the potential for using the map. 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. Of course, one could then use different chord
types at different points in the score.
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.
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. 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. 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.
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