## Welcome Chromatic Cube

*in*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…

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!

david,

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,

schell/aka/chromatic

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

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.