Tricesimoprimal Tetrachordal Tesseract

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
1-11-1

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

Go!

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