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Octave Tessellation?


I was fooling around with sieves trying to find something that would’nt repeat pitch classes for certain numbers of octaves, and i kind of failed…i ended up trying to find them by hand and this is the best i got:

(this are intervals with the semitone as the unit)

1 6 2 5 1 5 2 6 1 6 (this covers up 4 octaves)

now i realized that what i was basically doing is tiling a 1-dimensional plane in modulo 12 (i think :laughing:)

i was wondering, is there any way to make a patch that would return this kinds of structures, maybe with intervals of my choosing? I know there’s CNMAT’s Tessellate but i found it pretty confusing and not sure if it would help me with this particular problem :confused:


I’m working in a patch to trying to construct symmetrical twelve-tone chords based in some hexachords (this was mainly used by the composer Magnus Lindberg and he selected 13 hexachords). I’ve included some others hexachords recently and i’m running some tests.
The patch basically generates 1440 symmetrical twelve-tone chords based on M.L. hexachords (forms AB and BA) and 720 based on the others hexachords.
There is another way in the patch to find a symmetrical twelve-tone chord. You only have to insert a list with eleven intervals, the lowest note and to choose one type of hexachord. Then evaluate the subpatch Brute-Force-STTCH. The program will try to find a symmetrical twelve-tone chord based on the intervals of the original chord.

Thats it. Maybe it will be helpful for you.

P.S.: The patch uses the OMTristan and OMPitchField libraries. I’m not expert in LISP, so it is a lit bit slow.

Raposo-Workspace.zip (1.2 MB)

Best Regards,

Paulo Raposo

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Wow, awesome patch! I’ll keep looking at it for a while, thank you so much!

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