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

Pentatonic modes

MOS Modes
2L 3s 2 2 3 2 3 (2 1 1 3 2 3) ; 2 2 2 3 3
1L 4s 2 2 2 2 4

Heptatonic modes

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

Tempered commas

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
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
7-limit ratios tempered out in 12-tet, maximal benedetti height = 324
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
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
360/343 23 • 32 • 51 • 7-3 83.746 7 -83.746 2-3 • 3-2 • 5-1 • 73 343/360
405/392 2-3 • 34 • 51 • 7-2 56.482 7 -56.482 23 • 3-4 • 5-1 • 72 392/405
729/686 2-1 • 36 • 7-3 105.252 7 -105.252 21 • 3-6 • 73 686/729
729/700 2-2 • 36 • 5-2 • 7-1 70.277 7 -70.277 22 • 3-6 • 52 • 71 700/729
1296/1225 24 • 34 • 5-2 • 7-2 97.541 7 -97.541 2-4 • 3-4 • 52 • 72 1225/1296
2500/2401 22 • 54 • 7-4 69.951 7 -69.951 2-2 • 5-4 • 74 2401/2500
2560/2401 29 • 51 • 7-4 111.010 7 -111.010 2-9 • 5-1 • 74 2401/2560
2592/2401 25 • 34 • 7-4 132.516 7 -132.516 2-5 • 3-4 • 74 2401/2592
3125/3087 3-2 • 55 • 7-3 21.181 7 -21.181 32 • 5-5 • 73 3087/3125
3136/3125 26 • 5-5 • 72 6.083 7 -6.083 2-6 • 55 • 7-2 3125/3136
3200/3087 27 • 3-2 • 52 • 7-3 62.240 7 -62.240 2-7 • 32 • 5-2 • 73 3087/3200
3645/3584 2-9 • 36 • 51 • 7-1 29.218 7 -29.218 29 • 3-6 • 5-1 • 71 3584/3645
4000/3969 25 • 3-4 • 53 • 7-2 13.469 7 -13.469 2-5 • 34 • 5-3 • 72 3969/4000
4096/3969 212 • 3-4 • 7-2 54.528 7 -54.528 2-12 • 34 • 72 3969/4096
4608/4375 29 • 32 • 5-4 • 7-1 89.829 7 -89.829 2-9 • 3-2 • 54 • 71 4375/4608
5103/5000 2-3 • 36 • 5-4 • 71 35.301 7 -35.301 23 • 3-6 • 54 • 7-1 5000/5103
5120/5103 210 • 3-6 • 51 • 7-1 5.758 7 -5.758 2-10 • 36 • 5-1 • 71 5103/5120
5625/5488 2-4 • 32 • 54 • 7-3 42.687 7 -42.687 24 • 3-2 • 5-4 • 73 5488/5625
6561/6125 38 • 5-3 • 7-2 119.047 7 -119.047 3-8 • 53 • 72 6125/6561
6561/6272 2-7 • 38 • 7-2 77.988 7 -77.988 27 • 3-8 • 72 6272/6561
8192/7875 213 • 3-2 • 5-3 • 7-1 68.323 7 -68.323 2-13 • 32 • 53 • 71 7875/8192
9216/8575 210 • 32 • 5-2 • 7-3 124.805 7 -124.805 2-10 • 3-2 • 52 • 73 8575/9216
10125/9604 2-2 • 34 • 53 • 7-4 91.458 7 -91.458 22 • 3-4 • 5-3 • 74 9604/10125
13122/12005 21 • 38 • 5-1 • 7-4 154.023 7 -154.023 2-1 • 3-8 • 51 • 74 12005/13122
15876/15625 22 • 34 • 5-6 • 72 27.590 7 -27.590 2-2 • 3-4 • 56 • 7-2 15625/15876
16128/15625 28 • 32 • 5-6 • 71 54.854 7 -54.854 2-8 • 3-2 • 56 • 7-1 15625/16128
16384/15435 214 • 3-2 • 5-1 • 7-3 103.299 7 -103.299 2-14 • 32 • 51 • 73 15435/16384
18000/16807 24 • 32 • 53 • 7-5 118.722 7 -118.722 2-4 • 3-2 • 5-3 • 75 16807/18000
18225/16807 36 • 52 • 7-5 140.228 7 -140.228 3-6 • 5-2 • 75 16807/18225
18432/16807 211 • 32 • 7-5 159.780 7 -159.780 2-11 • 3-2 • 75 16807/18432
23328/21875 25 • 36 • 5-5 • 7-1 111.336 7 -111.336 2-5 • 3-6 • 55 • 71 21875/23328
28672/28125 212 • 3-2 • 5-5 • 71 33.347 7 -33.347 2-12 • 32 • 55 • 7-1 28125/28672
32768/30625 215 • 5-4 • 7-2 117.093 7 -117.093 2-15 • 54 • 72 30625/32768
46656/42875 26 • 36 • 5-3 • 7-3 146.311 7 -146.311 2-6 • 3-6 • 53 • 73 42875/46656
50625/50176 2-10 • 34 • 54 • 7-2 15.423 7 -15.423 210 • 3-4 • 5-4 • 72 50176/50625
59049/54880 2-5 • 310 • 5-1 • 7-3 126.759 7 -126.759 25 • 3-10 • 51 • 73 54880/59049
59049/56000 2-6 • 310 • 5-3 • 7-1 91.783 7 -91.783 26 • 3-10 • 53 • 71 56000/59049
59049/57344 2-13 • 310 • 7-1 50.724 7 -50.724 213 • 3-10 • 71 57344/59049
65536/60025 216 • 5-2 • 7-4 152.069 7 -152.069 2-16 • 52 • 74 60025/65536
78125/76832 2-5 • 57 • 7-4 28.892 7 -28.892 25 • 5-7 • 74 76832/78125
81648/78125 24 • 36 • 5-7 • 71 76.360 7 -76.360 2-4 • 3-6 • 57 • 7-1 78125/81648
93312/84035 27 • 36 • 5-1 • 7-5 181.287 7 -181.287 2-7 • 3-6 • 51 • 75 84035/93312
91125/87808 2-8 • 36 • 53 • 7-3 64.193 7 -64.193 28 • 3-6 • 5-3 • 73 87808/91125
118098/109375 21 • 310 • 5-6 • 7-1 132.842 7 -132.842 2-1 • 3-10 • 56 • 71 109375/118098
125000/117649 23 • 56 • 7-6 104.927 7 -104.927 2-3 • 5-6 • 76 117649/125000
128000/117649 210 • 53 • 7-6 145.986 7 -145.986 2-10 • 5-3 • 76 117649/128000
129600/117649 26 • 34 • 52 • 7-6 167.492 7 -167.492 2-6 • 3-4 • 5-2 • 76 117649/129600
131072/117649 217 • 7-6 187.045 7 -187.045 2-17 • 76 117649/131072
131220/117649 22 • 38 • 51 • 7-6 188.998 7 -188.998 2-2 • 3-8 • 5-1 • 76 117649/131220
131072/127575 217 • 3-6 • 5-2 • 7-1 46.817 7 -46.817 2-17 • 36 • 52 • 71 127575/131072
140625/134456 2-3 • 32 • 56 • 7-5 77.663 7 -77.663 23 • 3-2 • 5-6 • 75 134456/140625
156250/151263 21 • 3-2 • 57 • 7-5 56.156 7 -56.156 2-1 • 32 • 5-7 • 75 151263/156250
160000/151263 28 • 3-2 • 54 • 7-5 97.215 7 -97.215 2-8 • 32 • 5-4 • 75 151263/160000
163840/151263 215 • 3-2 • 51 • 7-5 138.274 7 -138.274 2-15 • 32 • 5-1 • 75 151263/163840
164025/153664 2-6 • 38 • 52 • 7-4 112.964 7 -112.964 26 • 3-8 • 5-2 • 74 153664/164025
165888/153125 211 • 34 • 5-5 • 7-2 138.600 7 -138.600 2-11 • 3-4 • 55 • 72 153125/165888
200000/194481 26 • 3-4 • 55 • 7-4 48.445 7 -48.445 2-6 • 34 • 5-5 • 74 194481/200000
204800/194481 213 • 3-4 • 52 • 7-4 89.504 7 -89.504 2-13 • 34 • 5-2 • 74 194481/204800
236196/214375 22 • 310 • 5-4 • 7-3 167.817 7 -167.817 2-2 • 3-10 • 54 • 73 214375/236196
253125/235298 2-1 • 34 • 55 • 7-6 126.433 7 -126.433 21 • 3-4 • 5-5 • 76 235298/253125
250047/250000 2-4 • 36 • 5-6 • 73 0.325 7 -0.325 24 • 3-6 • 56 • 7-3 250000/250047
256000/250047 211 • 3-6 • 53 • 7-3 40.733 7 -40.733 2-11 • 36 • 5-3 • 73 250047/256000
262144/250047 218 • 3-6 • 7-3 81.792 7 -81.792 2-18 • 36 • 73 250047/262144
295245/268912 2-4 • 310 • 51 • 7-5 161.734 7 -161.734 24 • 3-10 • 5-1 • 75 268912/295245
331776/300125 212 • 34 • 5-3 • 7-4 173.575 7 -173.575 2-12 • 3-4 • 53 • 74 300125/331776
321489/312500 2-2 • 38 • 5-7 • 72 49.096 7 -49.096 22 • 3-8 • 57 • 7-2 312500/321489
321489/320000 2-9 • 38 • 5-4 • 72 8.037 7 -8.037 29 • 3-8 • 54 • 7-2 320000/321489
327680/321489 216 • 3-8 • 51 • 7-2 33.022 7 -33.022 2-16 • 38 • 5-1 • 72 321489/327680
390625/388962 2-1 • 3-4 • 58 • 7-4 7.386 7 -7.386 21 • 34 • 5-8 • 74 388962/390625
395136/390625 27 • 32 • 5-8 • 73 19.878 7 -19.878 2-7 • 3-2 • 58 • 7-3 390625/395136
401408/390625 213 • 5-8 • 72 47.142 7 -47.142 2-13 • 58 • 7-2 390625/401408
413343/390625 310 • 5-8 • 71 97.866 7 -97.866 3-10 • 58 • 7-1 390625/413343
413343/400000 2-7 • 310 • 5-5 • 71 56.807 7 -56.807 27 • 3-10 • 55 • 7-1 400000/413343
413343/409600 2-14 • 310 • 5-2 • 71 15.748 7 -15.748 214 • 3-10 • 52 • 7-1 409600/413343
472392/420175 23 • 310 • 5-2 • 7-5 202.793 7 -202.793 2-3 • 3-10 • 52 • 75 420175/472392
458752/455625 216 • 3-6 • 5-4 • 71 11.841 7 -11.841 2-16 • 36 • 54 • 7-1 455625/458752
531441/470596 2-2 • 312 • 7-6 210.505 7 -210.505 22 • 3-12 • 76 470596/531441
531441/480200 2-3 • 312 • 5-2 • 7-4 175.529 7 -175.529 23 • 3-12 • 52 • 74 480200/531441
524288/496125 219 • 3-4 • 5-3 • 7-2 95.587 7 -95.587 2-19 • 34 • 53 • 72 496125/524288
531441/490000 2-4 • 312 • 5-4 • 7-2 140.553 7 -140.553 24 • 3-12 • 54 • 72 490000/531441
531441/501760 2-11 • 312 • 5-1 • 7-2 99.494 7 -99.494 211 • 3-12 • 51 • 72 501760/531441
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