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
Tetra	2 5 2 3
Penta MOS	2 2 3 2 3
Penta b7 9	3 3 2 2 2
Penta #5 9 #11	2 2 4 2 2

Blues scales (tempering out 2048/2025)

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

All commas tempered out thoughout 5-odd-limit series with all notes distinct

Ratio	Factorization	Cents	Limit	- Cents	1 / Factorization	1 / Ratio
531441/524288	2-19 • 312	23.460	3	-23.460	219 • 3-12	524288/531441
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
32805/32768	2-15 • 38 • 51	1.954	5	-1.954	215 • 3-8 • 5-1	32768/32805
82944/78125	210 • 34 • 5-7	103.624	5	-103.624	2-10 • 3-4 • 57	78125/82944
262144/253125	218 • 3-4 • 5-5	60.611	5	-60.611	2-18 • 34 • 55	253125/262144
531441/500000	2-5 • 312 • 5-6	105.578	5	-105.578	25 • 3-12 • 56	500000/531441
2125764/1953125	22 • 312 • 5-9	146.637	5	-146.637	2-2 • 3-12 • 59	1953125/2125764
10616832/9765625	217 • 34 • 5-10	144.683	5	-144.683	2-17 • 3-4 • 510	9765625/10616832
33554432/31640625	225 • 3-4 • 5-8	101.670	5	-101.670	2-25 • 34 • 58	31640625/33554432
53747712/48828125	213 • 38 • 5-11	166.189	5	-166.189	2-13 • 3-8 • 511	48828125/53747712