Porcupine/Chords

Below are listed the dyadic chords of 11-limit porcupine temperament that do not have generator steps 7 or 13 as dyads. Typing the chords requires consideration of the fact that porcupine conflates 10/9, 11/10 and 12/11 and also 16/9 and 7/4. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only 64/63 tempering are marked archytas, by 100/99 ptolemismic, by 121/120 biyatismic, 176/175 valinorsmic, and by 385/384 keenanismic. Chords that require 64/63 and 176/175 tempering are marked ares, 100/99 and 385/384 tempered chords are supermagic, and 176/175 and 385/384 tempered chords are marked zeus. Chords that receive tempering by three independent commas above are labeled porcupine.

Triads

Chord	Transversal	Type
0-1-2	1-11/10-6/5	otonal
0-1-3	1-10/9-4/3	otonal
0-2-3	1-11/9-4/3	otonal
0-1-4	1-12/11-16/11	otonal
0-2-4	1-6/5-22/15	otonal
0-3-4	1-4/3-22/15	otonal
0-1-5	1-11/10-8/5	otonal
0-2-5	1-6/5-8/5	otonal
0-3-5	1-4/3-8/5	utonal
0-4-5	1-22/15-8/5	otonal
0-1-6	1-10/9-16/9	otonal
0-2-6	1-11/9-16/9	otonal
0-3-6	1-4/3-16/9	ambitonal
0-4-6	1-16/11-16/9	utonal
0-5-6	1-8/5-16/9	utonal
0-2-8	1-6/5-16/15	otonal
0-3-8	1-4/3-16/15	ambitonal
0-4-8	1-22/15-16/15	otonal
0-5-8	1-8/5-16/15	ambitonal
0-6-8	1-16/9-16/15	utonal
0-1-9	1-11/10-7/6	valinorsmic
0-3-9	1-4/3-7/6	otonal
0-4-9	1-16/11-7/6	keenanismic
0-5-9	1-8/5-7/6	keenanismic
0-6-9	1-7/4-7/6	utonal
0-8-9	1-16/15-7/6	valinorsmic
0-1-10	1-12/11-14/11	otonal
0-2-10	1-6/5-14/11	valinorsmic
0-4-10	1-16/11-14/11	otonal
0-5-10	1-8/5-14/11	valinorsmic
0-6-10	1-7/4-14/11	utonal
0-8-10	1-16/15-14/11	valinorsmic
0-9-10	1-7/6-14/11	utonal
0-1-11	1-11/10-7/5	otonal
0-2-11	1-6/5-7/5	otonal
0-3-11	1-4/3-7/5	archytas
0-5-11	1-8/5-7/5	otonal
0-6-11	1-7/4-7/5	utonal
0-8-11	1-16/15-7/5	archytas
0-9-11	1-7/6-7/5	utonal
0-10-11	1-14/11-7/5	utonal
0-1-12	1-10/9-14/9	otonal
0-2-12	1-11/9-14/9	otonal
0-3-12	1-4/3-14/9	otonal
0-4-12	1-16/11-14/9	keenanismic
0-6-12	1-16/9-14/9	otonal
0-8-12	1-16/15-14/9	keenanismic
0-9-12	1-7/6-14/9	utonal
0-10-12	1-14/11-14/9	utonal
0-11-12	1-7/5-14/9	utonal
0-2-14	1-6/5-28/15	otonal
0-3-14	1-4/3-28/15	otonal
0-4-14	1-22/15-28/15	otonal
0-5-14	1-8/5-28/15	otonal
0-6-14	1-7/4-28/15	utonal
0-8-14	1-16/15-28/15	otonal
0-9-14	1-7/6-28/15	utonal
0-10-14	1-14/11-28/15	utonal
0-11-14	1-7/5-28/15	utonal
0-12-14	1-14/9-28/15	utonal

Tetrads

Chord	Transversal	Type
0-1-2-3	1-10/9-11/9-4/3	otonal
0-1-2-4	1-11/10-11/9-22/15	utonal
0-1-3-4	1-10/9-4/3-22/15	ptolemismic
0-1-2-5	1-11/10-6/5-8/5	otonal
0-1-3-5	1-11/10-4/3-8/5	ptolemismic
0-1-4-5	1-11/10-16/11-8/5	biyatismic
0-2-3-5	1-6/5-4/3-8/5	ambitonal
0-2-4-6	1-6/5-16/11-7/4	supermagic
0-3-6-9	1-4/3-7/4-7/6	archytas
0-4-8-12	1-16/11-16/15-14/9	zeus

Pentads

Chord	Transversal	Type
0-1-2-3-6	1-10/9-11/9-4/3-16/9	otonal
0-2-3-4-6
0-3-4-5-6
0-2-4-6-8	1-6/5-16/11-7/4-16/15	porcupine
0-3-6-9-12	1-4/3-7/4-7/6-14/9	archytas