Welcome Chromatic Cube

We would like to introduce Chromatic Cube’s Blog here at the Logical Theory of Music.

Slonimsky Variations

a variation of slonimsky’s divisions of the octaves, this one is 3 octaves divided into 16 parts, or 9 half-steps divided into 4 parts. this is my first post, so i’m experimenting to see how graphic jpgs appear. i have a whole bunch of these and was curious to find out if anyone’s been working with stuff like this…

Cube 1

4 thoughts on “Welcome Chromatic Cube”

  1. David Kane says:

    To be honest, I’m not exactly sure how to read this chart. I’m familiar with the symmetric division of octaves into various parts ala Schillinger/Slonimsky/Collichio but I’m not sure what’s going on here. If you have a moment, I would appreciate a brief word on how to read this. I’m also a little confused by the division into 16 parts. I understand 3 octaves into 4 parts of 9 semitones but I don’t know where the 16 comes from. Maybe I need to reread that section 🙂

    Also, of you don’t mind me saying, you might want to experiment with some other colors as on my monitor some of them are a bit headache-inducing.
    Thanks for the post- I’m sure I’ll find it interesting once I understand it!

  2. Chromatic Cube says:


    this stuff is a wee bit outside the box for me also, so bear with me. as you say, “3 octaves into 4 parts of 9 semitones” becomes (starting on the guitar’s low E) E c# a# g1 e2, etc… if we further divide the major sixths into “whole step whole step whole step minor third” or {2,2,2,3} we end up dividing three octaves into 16 nearly equal parts, or E F# G# A# c# d# f g a# c1 d1 e1 g1 a1 b1 c2 e2, etc…

    mathematically, this can be represented as:

    3/16 or three octaves in 16 parts, or more concisely

    4/9 or four tones per none semitones.

    there are nine such groups shown in nine rows. sorry about the colors and the headaches; this is probably because i chose the brightest colors equally spaced around the RGB color wheel – i guess that would make it hard to focus on :o)

    if you’d like, i could PM you the other groups i’ve worked out as an excel spreadsheet so that you could change the colors to your liking. lemme know,


  3. Chromatic Cube says:

    sp: oops, that’s “4/9 or four tones per nine semitones”

  4. Christopher Burnett says:

    I have been working with creating alternative chord progression cycles in a parallel symmetrical fashion for the last dozen years or so. Your work looks interesting.

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