Tricesimoprimal Tetrachordal Tesseract

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for AAH

This is not really a 4-dimensional cube, but a mere triangle. This is the table of tetrachord species in 31-edo, i.e. all of the ways that a perfect 4th (13 dieses) can be broken up into three steps. Numbers indicate intervals in degrees of 31.

11-1-1 10-1-2 9-1-3 8-1-4 7-1-5 6-1-6 5-1-7 4-1-8 3-1-9 2-1-10 1-1-11
10-2-1 9-2-2 8-2-3 7-2-4 6-2-5 5-2-6 4-2-7 3-2-8 2-2-9 1-2-10
9-3-1 8-3-2 7-3-3 6-3-4 5-3-5 4-3-6 3-3-7 2-3-8 1-3-9
8-4-1 7-4-2 6-4-3 5-4-4 4-4-5 3-4-6 2-4-7 1-4-8
7-5-1 6-5-2 5-5-3 4-5-4 3-5-5 2-5-6 1-5-7
6-6-1 5-6-2 4-6-3 3-6-4 2-6-5 1-6-6
5-7-1 4-7-2 3-7-3 2-7-4 1-7-5
4-8-1 3-8-2 2-8-3 1-8-4
3-9-1 2-9-2 1-9-3
2-10-1 1-10-2

Pick an ostinato

Have a rhythm and generalized contour that you use on each tetrachord. Using the 7-note scale made up of 2 "disjunct" tetrachords (separated by a major tone), my ostinato was 0-1-2-3-2-1-0-1-2-3, 4-5-6-7-6-5-4-5-6-7, 0-1-2-3-4-5-6-7.

Pick a path

I prefer a path that is complete (hits every square exactly once) and incremental (moves by exchanges of a single diesis; in the chart, single moves of up/down, left/right, or northeast/southwest only). The path used in the first recording begins at the upper-right of the chart and zigzags left-right-left-right to the bottom left. Another fun path yet untried is a spiral triangle.

link ostinato path range tempo

(mp3 midi)

0 1 2 3 2 1

0 1 2 3

4 5 6 7 6 5

4 5 6 7

0 1 2 3 4 5 6 7

zigzag from 1-1-11 Fd2 - Fd3 eighth = 92


Start out just humming or singing along to the recording. Use the unretuned MIDI file if you want to change the tempo. Ask me for more renderings on my synth with different specifications, and I will make and upload them. I might add more renderings out of my own explorations too.

Extra credit

Sing the entire exercise with the shortspeak interval names. This chart should help:

godi gosu gosu jadi gosu leto nudi gosu mito midi gosu nuto ledi gosu jato goto gosu goto jato gosu ledi nuto gosu midi mito gosu nudi leto gosu jadi gosu gosu godi
jadi leto gosu nudi leto leto midi leto mito ledi leto nuto goto leto jato jato leto goto nuto leto ledi mito leto midi leto leto nudi gosu leto jadi
nudi mito gosu midi mito leto ledi mito mito goto mito nuto jato mito jato nuto mito goto mito mito ledi leto mito midi gosu mito nudi
midi nuto gosu ledi nuto leto goto nuto mito jato nuto nuto nuto nuto jato mito nuto goto leto nuto ledi gosu nuto midi
ledi jato gosu goto jato leto jato jato mito nuto jato nuto mito jato jato leto jato goto gosu jato ledi
goto goto gosu jato goto leto nuto goto mito mito goto nuto leto goto jato gosu goto goto
jato ledi gosu nuto ledi leto mito ledi mito leto ledi nuto gosu ledi jato
nuto midi gosu mito midi leto leto midi mito gosu midi nuto
mito nudi gosu leto nudi leto gosu nudi mito
leto jadi gosu gosu jadi leto
gosu godi gosu

Next-assignment assignment

Write a ditty in a specific or generalized tetrachord scale, and turn it into an assignment for me.

- xenjacob Jan 7, 2008