User:Contribution/Exploring Selected Modes in 12-EDO

Modes

Modes of limited transposition

Period	Modes
1\12	1
2\12	2
3\12	3 ; 1 2
4\12	4 ; 1 3 ; 1 1 2
6\12	6 ; 1 5 ; 2 4 ; 1 1 4 ; 1 2 3 ; 1 3 2 ; 1 1 1 3 ; 1 1 2 2 ; 1 1 1 1 2
12\12	12

Nonatonic modes (tempering out 32805/32768)

Alteration	Modes
Schisma	2 2 1 1 1 2 1 1 1

Heptatonic modes (tempering out 5120/5103)

Alteration	Modes
Ion	2 2 1 2 2 2 1
Ion b3	2 1 2 2 2 2 1
Ion b6	2 2 1 2 1 3 1
Ion b3 b6	2 1 2 2 1 3 1
Ion b2	1 3 1 2 2 2 1
Ion b2 b3	1 2 2 2 2 2 1
Ion b2 b6	1 3 1 2 1 3 1
Ion b2 b3 b6	1 2 2 2 1 3 1

Pentatonic modes (tempering out 81/80)

Alteration	Modes
Penta	2 2 3 2 3
Penta b5	3 3 2 2 2
Penta b5 b6	2 2 2 4 2

Blues scales (tempering out 2048/2025)

Added notes	Modes
None	2 2 3 2 3
b3	2 1 1 3 2 3
#1	1 1 2 3 2 3
#1 b3	1 1 1 1 3 2 3
#1 b3 #5/b6	1 1 1 1 3 1 1 3

Tempered commas

Selected 7-limit commas tempered out in 12-tet

Ratio	Factorization	Cents	Limit	- Cents	1 / Factorization	1 / Ratio
81/80	2-4 • 34 • 5-1	21.506	5	-21.506	24 • 3-4 • 51	80/81
128/125	27 • 5-3	41.059	5	-41.059	2-7 • 53	125/128
648/625	23 • 34 • 5-4	62.565	5	-62.565	2-3 • 3-4 • 54	625/648
2048/2025	211 • 3-4 • 5-2	19.553	5	-19.553	2-11 • 34 • 52	2025/2048
6561/6250	2-1 • 38 • 5-5	84.071	5	-84.071	21 • 3-8 • 55	6250/6561
6561/6400	2-8 • 38 • 5-2	43.013	5	-43.013	28 • 3-8 • 52	6400/6561
36/35	22 • 32 • 5-1 • 7-1	48.770	7	-48.770	2-2 • 3-2 • 51 • 71	35/36
50/49	21 • 52 • 7-2	34.976	7	-34.976	2-1 • 5-2 • 72	49/50
64/63	26 • 3-2 • 7-1	27.264	7	-27.264	2-6 • 32 • 71	63/64
126/125	21 • 32 • 5-3 • 71	13.795	7	-13.795	2-1 • 3-2 • 53 • 7-1	125/126
225/224	2-5 • 32 • 52 • 7-1	7.712	7	-7.712	25 • 3-2 • 5-2 • 71	224/225
256/245	28 • 5-1 • 7-2	76.034	7	-76.034	2-8 • 51 • 72	245/256