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I do not have much background in music or linear algebra or group theory. I am just trying to delve deeper.

I came across the answer on circle division by chords over here. The series is intriguing in its own right. It goes like...

1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ...

where 256 is the last power of 2. This pattern can be understood in terms of pascal's rule/triangle.

(n) + (n) + (n) = (n−1) + (n−1) + (n−1) + (n−1) + (n−1).
 0     2     4      0       1       2       3       4

Could possibly music theory have anything remotely close to it?

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    I'm not sure why you would think that the term chord as used by geometers has anything to do with the term chord as used by musicians. The two terms have different etymologies. The geometry term comes from the Latin word chorda for bowstring, and the music term comes from the English word cord, a shortening of accord. – David Bowling Mar 31 '18 at 6:18
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    @DavidBowling Guess that is an answer already. Just place a "no" in front :) – Arsak Mar 31 '18 at 6:22
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    Adding to David's - a geometrical chord joins two points, a musical chord needs three notes (although some believe two is sufficient). 'Accord' is a sort of blending.Odd that the Latin also meant a string. On which a chord cannot be played... Unless it gets stretched out to a string of notes... The English language has been bastardised over many centuries, and meanings lost in the mist of time. No real connection here - only spurious ones! – Tim Mar 31 '18 at 6:23
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    You may want to consider checking out A Geometry of Music by Dmitri Tymoczko. – Richard Mar 31 '18 at 11:49
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    @topomorto -- I wasn't sure that my earlier comment really qualified as a complete answer, but I have tried to expand it to one. – David Bowling Mar 31 '18 at 13:35
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The term chord as used by geometers has an entirely different meaning and etymology from the term chord as used by musicians. The geometry term comes from the Latin chorda for bowstring, while the musical term comes from the Middle English cord, itself a shortening of accord.

So the chords of music and the chords of geometry are unrelated in that sense. Sometimes musicians talk about the Circle of Fifths, but this isn't a circle in the geometric sense; it is a way of visually organizing the 12 tones of the chromatic scale. Even if you used circle division for (musical) chords on the Circle of Fifths, I am not sure that anything useful would arise. Geometric patterns found by constructing (geometric) chords on a (geometric) circle laid atop the Circle of Fifths may or may not correspond to musical patterns, and this is as good a means as any for generating ideas, but this doesn't mean that it is a deeply meaningful theoretical notion.

That said, there is a long tradition of applying mathematics, including geometry, to music. I happen to have a copy of Tymoczko's A Geometry of Music, mentioned by @Richard in the comments. I must confess to not having read it, but only having skimmed over it a bit. It does look interesting, and is on my list of books to read more carefully. Looking in it again I see that Tymoczko develops a concept of pitch space, and a concept of a circular pitch-class space that is not organized in the same way as the Circle of Fifths. In a chapter entitled "A Geometry of Chords" he develops a concept of chord space that uses two-, three-, and higher-dimensional spaces. I don't see anything directly related to circle division or connecting geometric chords to musical chords here, though. You might also be interested in reading about negative harmony.

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