User:Contribution/Exploring Selected Modes in 12-EDO

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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
Selected 7-limit commas tempered out in 12-tet
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
6561/6400 2-8 • 38 • 5-2 43.013 5 -43.013 28 • 3-8 • 52 6400/6561
16384/15625 214 • 5-6 82.118 5 -82.118 2-14 • 56 15625/16384
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
419904/390625 26 • 38 • 5-8 125.130 5 -125.130 2-6 • 3-8 • 58 390625/419904
531441/500000 2-5 • 312 • 5-6 105.578 5 -105.578 25 • 3-12 • 56 500000/531441
531441/512000 2-12 • 312 • 5-3 64.519 5 -64.519 212 • 3-12 • 53 512000/531441
2097152/1953125 221 • 5-9 123.177 5 -123.177 2-21 • 59 1953125/2097152
2125764/1953125 22 • 312 • 5-9 146.637 5 -146.637 2-2 • 3-12 • 59 1953125/2125764
4194304/4100625 222 • 3-8 • 5-4 39.105 5 -39.105 2-22 • 38 • 54 4100625/4194304
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
43046721/39062500 2-2 • 316 • 5-10 168.143 5 -168.143 22 • 3-16 • 510 39062500/43046721
43046721/40000000 2-9 • 316 • 5-7 127.084 5 -127.084 29 • 3-16 • 57 40000000/43046721
43046721/40960000 2-16 • 316 • 5-4 86.025 5 -86.025 216 • 3-16 • 54 40960000/43046721
43046721/41943040 2-23 • 316 • 5-1 44.966 5 -44.966 223 • 3-16 • 51 41943040/43046721
53747712/48828125 213 • 38 • 5-11 166.189 5 -166.189 2-13 • 3-8 • 511 48828125/53747712
67108864/66430125 226 • 3-12 • 5-3 17.599 5 -17.599 2-26 • 312 • 53 66430125/67108864
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