Gallery of 3-SN scales

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See SN scale and Rank-3 scale.

For more concise summary that's better for viewing on mobile devices, see Gallery of 3-SN scales mobile.

Scales are grouped by their germinations, the sequence of introduction of generators until 3 are reached, at which point the primitive 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of Pythagorean, Meantone, Superpyth, Mavila, and Father MOS (2-SN) scales is (2/1, 3/2). Germinations are grouped by their subgroup, and within that, by the first comma tempered out in scales evolved from the germination.

Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.

Tempered scales are shown in JI as their simplest symmetric pre-image.

Scales are written in JI and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without 2/1, otherwise in the inverse of the even-symmetric mode (the mode symmetric without 1/1).

2.3.5; Marvel

(2/1, 3/2, 5/4)

(2/1, 3/2, 5/4)[4]

Step signature Steps in JI Step sizes in cents
2L 1M 1s (5/4, 6/5, 16/15) (386.3137c, 315.6413c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-2 16/15 4/3 8/5 2/1 sLML -.2092
-1 5/4 4/3 5/3 2/1 LsLM -.0174
1 6/5 3/2 8/5 2/1 MLsL .0174
2 5/4 3/2 15/8 2/1 LMLs .2092
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LLLs Dicot[4] 25/24
M = s LsLs Antitonic[4] 9/8
L - M = M - s LsLd Bug[4] MODMOS 27/25
s = 0 LsL Father[3] 16/15

(2/1, 3/2, 5/4)[7]

Step signature Steps in JI Step sizes in cents
2L 1M 4s (75/64, 9/8, 16/15) (274.5824c, 203.9100c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-3 16/15 256/225 4/3 64/45 8/5 128/75 2/1 ssLsMsL -.1161
-2 16/15 6/5 32/25 3/2 8/5 128/75 2/1 sMsLssL -.0845
-1 16/15 5/4 4/3 64/45 5/3 16/9 2/1 sLssLsM -.0316
0 16/15 5/4 4/3 3/2 8/5 15/8 2/1 sLsMsLs 0
1 9/8 6/5 45/32 3/2 8/5 15/8 2/1 MsLssLs .0316
2 75/64 5/4 4/3 25/16 5/3 15/8 2/1 LssLsMs .0845
3 75/64 5/4 45/32 3/2 225/128 15/8 2/1 LsMsLss .1161
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLsLsLs Dicot[7] 25/24
M = s sLsssLs Mavila[7] 135/128
L = s LLLsLLL Enipucrop[7] 1125/1024
L - M = M - s sAsLsAs Meantone[7] MODMOS 81/80
s = 0 LsL Father[3] 16/15
(2/1, 3/2, 5/4: 225/224)[7] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
2L 1M 4s (75/64~7/6, ~9/8, 16/15~15/14) (267.8165c, 200.9152c, 116.0124c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-3 ~ 16/15 8/7 4/3 10/7 8/5 12/7 2/1 ssLsMsL -.1079
-2 ~ 16/15 6/5 9/7 3/2 8/5 12/7 2/1 sMsLssL -.0793
-1 ~ 16/15 5/4 4/3 10/7 5/3 16/9 2/1 sLssLsM -.0286
0 ~ 16/15 5/4 4/3 3/2 8/5 15/8 2/1 sLsMsLs 0
1 ~ 9/8 6/5 7/5 3/2 8/5 15/8 2/1 MsLssLs .0286
2 ~ 7/6 5/4 4/3 14/9 5/3 15/8 2/1 LssLsMs .0793
3 ~ 7/6 5/4 7/5 3/2 7/4 15/8 2/1 LsMsLss .1079
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLsLsLs Sharp[7] 25/24, 28/27
M = s sLsssLs Pelogic[7] 135/128, 21/20
L= s LLLsLLL Enipucrop[7] 35/32, 49/45
L - M = M - s sAsLsAs Meantone[7] MODMOS 81/80, 126/125
Rank-1 temperings
ET 9 10 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (4, 3, 2) (5, 4, 2) (6, 5, 3) (7, 5, 3) (9, 7, 4) (11, 8, 5) (12, 9, 5) (16, 12, 7)

(2/1, 3/2, 5/4)[10]

Step signature Steps in JI Step sizes in cents
2L 7m 1s (1125/1024, 16/15, 135/128) (162.8511c, 111.7313c, 92.1787c)
Mode number Mode in JI Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 16/15 256/225 6/5 32/25 512/375 3/2 8/5 128/75 2048/1125 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0564
-4 16/15 9/8 6/5 32/25 45/32 3/2 8/5 128/75 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0411
-3 135/128 9/8 6/5 675/512 45/32 3/2 8/5 225/128 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0258
-2 16/15 256/225 4096/3375 4/3 64/45 1024/675 8/5 128/75 2048/1125 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0230
-1 16/15 256/225 5/4 4/3 64/45 3/2 8/5 128/75 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0077
1 16/15 75/64 5/4 4/3 45/32 3/2 8/5 225/128 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0077
2 1125/1024 75/64 5/4 675/512 45/32 3/2 3375/2048 225/128 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0239
3 16/15 256/225 5/4 4/3 64/45 1024/675 5/3 16/9 256/135 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0258
4 16/15 75/64 5/4 4/3 64/45 25/16 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0411
5 1125/1024 75/64 5/4 4/3 375/256 25/16 5/3 225/128 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0564
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Srutal[10] 4M (pentachordal decatonic) 2048/2025
L = m LLLLsLLLLL Negri[10] 16875/16384
L = s LsLLsLLsLL Dicot[10] 25/24
L - m = m - s sLssdssLss Ampersand[10] MODMOS 34171875/33554432
s = 0 sLssssLss Mavila[9] 135/128
m = 0 LsL Father[3] 16/15
L = 0 LLLsLLLL Enipucrop[8] 1125/1024
(2/1, 3/2, 5/4: 225/224)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45, 16/15~15/14, 135/128~21/20) (151.8041c, 116.0124c, 84.9028c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0475
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0400
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0325
-2 ~ 16/15 8/7 60/49 4/3 10/7 32/21 8/5 12/7 64/35 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0112
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0037
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0037
2 ~ 35/32 7/6 5/4 21/16 7/5 3/2 49/30 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0112
3 ~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0325
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0400
5 ~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0475
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajara[10] 4M (pentachordal decatonic) 50/49, 64/63
L = m LLLLsLLLLL Negri[10] 49/48, 225/224
L = s LsLLsLLsLL Sharp[10] 25/24, 28/27
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 1029/1024
s = 0 sLssssLss Pelogic[9] 21/20, 135/128
Rank-1 temperings
ET 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (4, 3, 2) (5, 4, 3) (6, 5, 3) (7, 5, 4) (9, 7, 5)
(2/1, 3/2, 5/4: 225/224, 385/384)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) (151.4797c, 116.1327c, 84.7519c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 11/8 3/2 8/5 12/7 11/6 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0472
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0400
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0327
-2 ~ 16/15 8/7 11/9 4/3 10/7 32/21 8/5 12/7 11/6 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0109
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0036
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0036
2 ~ 12/11 7/6 5/4 21/16 7/5 3/2 18/11 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0109
3 ~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0327
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0400
5 ~ 12/11 7/6 5/4 4/3 16/11 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0472
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajarous[10] 4M (pentachordal decatonic) 50/49, 55/54, 64/63
L = m LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 243/242, 385/384
Rank-1 temperings
ET 12e 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 4, 3) (6, 5, 3) (7, 5, 4) (9, 7, 5)
(2/1, 3/2, 5/4: 225/224, 441/440)[10] (Prodigy)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) (150.229c, 116.7669c, 82.9601c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negroni[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0466
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0404
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0343
-2 ~ 16/15 8/7 27/22 4/3 10/7 32/21 8/5 12/7 64/35 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0092
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0031
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0031
2 ~ 35/32 7/6 5/4 21/16 7/5 3/2 44/27 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0092
3 ~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0343
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0404
5 ~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0466
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajaric[10] 4M (pentachordal decatonic) 45/44, 50/49, 56/55
L = m LLLLsLLLLL Negroni[10] 49/48, 55/54, 225/224
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 243/242, 385/384
Rank-1 temperings
ET 12 19e 29 31 41 53e 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 3, 2) (4, 3, 2) (5, 4, 3) (7, 5, 4) (9, 7, 5)

(2/1, 3/2, 5/4: 225/224)[19] (Marvel)

Step signature Steps in JI Step sizes in cents (TE)
10L 2M 7s (135/128~21/20, 25/24~28/27, 64/63~50/49) (84.9028c, 66.9013c, 31.1096c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 160/147 8/7 512/441 60/49 80/63 4/3 256/189 10/7 640/441 32/21 8/5 80/49 12/7 256/147 64/35 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0464
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 35/32 147/128 7/6 49/40 5/4 21/16 441/320 7/5 189/128 3/2 63/40 49/30 441/256 7/4 147/80 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0464
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS 81/80, 126/125
M = s LsLsLsLsLsLsLsLsLsL Negri[19] 49/48, 225/224
L - M = M - s LdLdLsLdLdLdLsLdLdL Magic[19] MODMOS 225/224, 245/243
s = 0 LLLsLLLLsLLL Pajara[12] 4M (hexachordal dodecatonic) 50/49, 64/63
m = 0 LsLsLLsLsLsLLsLsL Sharp[17] 25/24, 28/27
Rank-1 temperings
ET 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 2) (4, 3, 1) (5, 4, 2)
(2/1, 3/2, 5/4: 225/224, 385/384)[19] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
10L 2M 7s (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) (84.7519c, 66.7278c, 31.3808c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 88/81 8/7 220/189 11/9 80/63 4/3 110/81 10/7 352/243 32/21 8/5 44/27 12/7 110/63 11/6 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0460
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 12/11 63/55 7/6 27/22 5/4 21/16 243/176 7/5 81/55 3/2 63/40 18/11 189/110 7/4 81/44 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0460
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS 81/80, 126/125, 385/384
M = s LsLsLsLsLsLsLsLsLsL Negri[19] 45/44, 49/48, 56/55
L - M = M - s LdLdLsLdLdLdLsLdLdL Magic[19] MODMOS 100/99, 225/224, 245/243
s = 0 LLLsLLLLsLLL Pajarous[12] 4M (hexachordal dodecatonic) 50/49, 55/54, 64/63
Rank-1 temperings
ET 22 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 1) (3, 3, 2) (4, 3, 1) (5, 4, 2)
(2/1, 3/2, 5/4: 225/224, 441/440)[19] (Prodigy)
Step signature Steps in JI Step sizes in cents (TE)
10L 2M 7s (135/128~21/20~22/21, 25/24~28/27, 64/63~50/49~45/44~56/55) (82.9601c, 67.2689c, 33.8068c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 12/11 8/7 64/55 27/22 14/11 4/3 15/11 10/7 16/11 32/21 8/5 18/11 12/7 96/55 64/35 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0428
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 35/32 55/48 7/6 11/9 5/4 21/16 11/8 7/5 22/15 3/2 11/7 44/27 55/32 7/4 11/6 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0428
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS 81/80, 99/98, 126/125
M = s LsLsLsLsLsLsLsLsLsL Negroni[19] 49/48, 55/54, 225/224
L - M = M - s LdLdLsLdLdLdLsLdLdL Witchcraft[19] MODMOS 225/224, 245/243, 441/440
s = 0 LLLsLLLLsLLL Pajaric[12] 4M (hexachordal dodecatonic) 45/44, 50/49, 56/55
Rank-1 temperings
ET 29 31 41 53e 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (4, 3, 1) (5, 4, 2)

(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)

Step signature Steps in JI Step sizes in cents (TE)
10L 19M 2s (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) (49.1533c, 33.8068c, 33.4621c)

Mode 0: ~ 50/49 22/21 16/15 12/11 9/8 8/7 7/6 6/5 27/22 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 44/27 5/3 12/7 7/4 16/9 11/6 15/8 21/11 49/25 2/1

as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm

Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
m = s sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS 225/224, 243/242, 385/384
L = m LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS 121/120, 225/224, 441/440
L = s sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS 81/80, 99/98, 126/125
s = 0 mLmmLmmLmmLmmLmLmmLmmLmmLmmLm Negroni[29] 49/48, 55/54, 225/224
m = 0 LLsLLLLLLsLL Pajaric[12] 4M (hexachordal dodecatonic) 45/44, 50/49, 56/55
Rank-1 temperings
ET 41 53e 72
Step sizes in ET (2, 1, 1) (3, 1, 2) (3, 2, 2)

((2/1, 5/4)[3], 16/15)

((2/1, 5/4)[3], 16/15)[6]

Step signature Steps in JI Step sizes in cents
1L 2M 4s (6/5, 75/64, 16/15) (315.6413c, 267.8165c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-3 16/15 5/4 4/3 25/16 5/3 2/1 sMsMsL -0.1156
-2 16/15 5/4 4/3 8/5 128/75 2/1 sMsLsM -0.0883
-1 16/15 32/25 512/375 8/5 128/75 2/1 sLsMsM -0.0609
1 75/64 5/4 375/256 25/16 15/8 2/1 MsMsLs 0.0609
2 75/64 5/4 3/2 8/5 15/8 2/1 MsLsMs 0.0883
3 6/5 32/25 3/2 8/5 15/8 2/1 LsMsMs 0.1156
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLsLs Augmented[6] 128/125
M = s ssLsss Enipucrop[6] 1125/1024
L = s LsssLs Antitonic[6] 4M 9/8
s = 0 LsL Father[3] 16/15
((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 4s 6/5, 75/64~7/6, 16/15~15/14 (316.9276c, 267.8165c, 116.0124c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-3 ~ 15/14 5/4 4/3 14/9 5/3 2/1 sMsMsL -0.1168
-2 ~ 15/14 5/4 4/3 8/5 12/7 2/1 sMsLsM -0.0840
-1 ~ 15/14 9/7 48/35 8/5 12/7 2/1 sLsMsM -0.0513
1 ~ 7/6 5/4 35/28 14/9 15/8 2/1 MsMsLs 0.0513
2 ~ 7/6 5/4 3/2 8/5 15/8 2/1 MsLsMs 0.0840
3 ~ 6/5 9/7 3/2 8/5 15/8 2/1 LsMsMs 0.1168
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLsLs August[6] 128/125
Rank-1 temperings
ET 7 9 10 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 1) (5, 4, 2) (6, 5, 2) (8, 6, 3) (8, 7, 3) (11, 9, 4) (13, 11, 5) (14, 12, 5) (19, 16, 7)

((2/1, 5/4)[3], 16/15)[9]

Step signature Steps in JI Step sizes in cents
1L 2M 6s (9/8, 1125/1024, 16/15) (203.9100c, 162.8511c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-4 16/15 256/225 5/4 4/3 64/45 25/16 5/3 16/9 2/1 ssMssMssL -0.0662
-3 16/15 256/225 5/4 4/3 64/45 8/5 128/75 2048/1125 2/1 ssMssLssM -0.0405
-2 16/15 75/64 5/4 4/3 375/256 25/16 5/3 15/8 2/1 sMssMssLs -0.0257
-1 16/15 256/225 32/25 512/375 8192/5625 8/5 128/75 2048/1125 2/1 ssLssMssM -0.0148
0 16/15 75/64 5/4 4/3 3/2 8/5 128/75 15/8 2/1 sMssLssMs 0
1 1125/1024 75/64 5/4 5625/4096 375/256 25/16 225/128 15/8 2/1 MssMssLss 0.0148
2 16/15 6/5 32/25 512/375 3/2 8/5 128/75 15/8 2/1 sLssMssMs 0.0257
3 1125/1024 75/64 5/4 45/32 3/2 8/5 225/128 15/8 2/1 MssLssMss 0.0405
4 9/8 6/5 32/25 45/32 3/2 8/5 225/128 15/8 2/1 LssMssMss 0.0662
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs Augmented[9] 128/125
M = s ssssLssss Negri[9] 16875/16384
L = s sLsssssLs Mavila[9] MODMOS 135/128
L - M = M - s sLssAssLs Orson[9] MODMOS 2109375/2097152
s = 0 LsL Father[3] 16/15
m = 0 sssLsss Enipucrop[7] 1125/1024
((2/1, 5/4)[3], 16/15: 225/224)[9] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 6s (9/8~28/25, 35/32~49/45, 16/15~15/14) (203.9100c, 162.8511c, 111.7313c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-4 ~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1 ssMssMssL -0.0633
-3 ~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 64/35 2/1 ssMssLssM -0.0326
-2 ~ 15/14 7/6 5/4 4/3 35/24 14/9 5/3 15/8 2/1 sMssMssLs -0.0307
-1 ~ 15/14 8/7 9/7 48/35 72/49 8/5 12/7 64/35 2/1 ssLssMssM -0.0019
0 ~ 15/14 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 sMssLssMs 0
1 ~ 35/32 7/6 5/4 49/36 35/24 14/9 7/4 15/8 2/1 MssMssLss 0.0019
2 ~ 15/14 6/5 9/7 48/35 3/2 8/5 12/7 15/8 2/1 sLssMssMs 0.0307
3 ~ 35/32 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1 MssLssMss 0.0326
4 ~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1 LssMssMss 0.0633
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs August[9] 36/35, 128/125
M = s ssssLssss Negri[9] 49/48, 225/224
L = s sLsssssLs Pelogic[9] MODMOS 21/20, 135/128
L - M = M - s sLssAssLs Orwell[9] MODMOS 225/224, 1728/1715
Rank-1 temperings
ET 10 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 3, 3) (5, 4, 3) (7, 5, 4) (8, 6, 5) (9, 8, 5) (12, 9, 7)

((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9] (Marvel)

Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 6s (9/8~28/25, 35/32~49/45~12/11, 16/15~15/14) (200.8846c, 151.4797c, 116.1327c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-4 ~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1 ssMssMssL -0.0632
-3 ~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 11/6 2/1 ssMssLssM -0.0324
-2 ~ 15/14 7/6 5/4 4/3 16/11 14/9 5/3 15/8 2/1 sMssMssLs -0.0309
-1 ~ 15/14 8/7 9/7 11/8 22/15 8/5 12/7 11/6 2/1 ssLssMssM -0.0015
0 ~ 15/14 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 sMssLssMs 0
1 ~ 12/11 7/6 5/4 15/11 16/11 14/9 7/4 15/8 2/1 MssMssLss 0.0015
2 ~ 15/14 6/5 9/7 11/8 3/2 8/5 12/7 15/8 2/1 sLssMssMs 0.0309
3 ~ 12/11 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1 MssLssMss 0.0324
4 ~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1 LssMssMss 0.0632
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs August[9] 36/35, 45/44, 56/55
M = s ssssLssss Negri[9] 45/44, 49/48, 56/55
L - M = M - s sLssAssLs Orwell[9] MODMOS 99/88, 121/120, 176/175
Rank-1 temperings
ET 10 12e 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 4, 3) (7, 5, 4) (8, 6, 5) (9, 8, 5) (12, 9, 7)


((2/1, 5/4)[3], 16/15: 225/224)[12] (Marvel)

Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1M 2s (16/15~15/14, 135/128~21/20, ~49/48) (116.0124c, 84.9028c, 35.7917c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-6 ~ 49/48 35/32 7/6 5/4 245/192 49/36 35/24 14/9 49/30 7/4 15/8 2/1 sLLLsLLLMLLL -0.0733
-5 ~ 15/14 35/32 7/6 5/4 4/3 49/36 35/24 14/9 5/3 7/4 15/8 2/1 LsLLLsLLLMLL -0.0433
-4 ~ 49/48 35/32 7/6 5/4 12/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1 sLLLMLLLsLLL -0.0435
-3 ~ 15/14 8/7 7/6 5/4 4/3 10/7 35/24 14/9 5/3 16/9 15/8 2/1 LLsLLLsLLLML -0.0152
-2 ~ 15/14 35/32 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LsLLLMLLLsLL -0.0145
-1 ~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1 MLLLsLLLsLLL -0.0138
1 ~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1 LLLsLLLsLLLM 0.0138
2 ~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 64/35 15/8 2/1 LLsLLLMLLLsL 0.0145
3 ~ 15/14 9/8 6/5 9/7 48/35 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LMLLLsLLLsLL 0.0152
4 ~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 8/5 12/7 64/35 96/49 2/1 LLLsLLLMLLLs 0.0435
5 ~ 15/14 8/7 6/5 9/7 48/35 72/49 3/2 8/5 12/7 64/35 15/8 2/1 LLMLLLsLLLsL 0.0443
6 ~ 15/14 8/7 60/49 9/7 48/35 72/49 384/245 8/5 12/7 64/35 96/49 2/1 LLLMLLLsLLLs 0.0733
Rank-2 temperings (mode -2)
Equivalence Step pattern Scale Comma list
L = M LsLLLLLLLsLL Pajara[12] MODMOS 50/49, 64/63
M = s LsLLLsLLLsLLs August[12] 36/35, 128/125
L = s sssssLssssss Passion[12] 64/63, 3125/3087
L - M = M - s LdLLLsLLLdLL Meantone[12] MODMOS 81/80, 126/125
s = 0 LLLLsLLLLL Negri[10] 49/48, 225/224
M = 0 LsLLLLLLsLL Pelogic[11] MODMOS 21/20, 135/
Rank-1 temperings
ET 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 0) (3, 2, 1) (4, 3, 1) (5, 3, 1) (5, 4, 2) (7, 5, 2)
((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1M 2s (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55) (116.1327c, 84.7519c, 35.347c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-6 ~ 45/44 12/11 7/6 5/4 14/11 15/11 16/11 14/9 18/11 7/4 15/8 2/1 sLLLsLLLMLLL -0.0738
-5 ~ 15/14 12/11 7/6 5/4 4/3 15/11 16/11 14/9 5/3 7/4 15/8 2/1 LsLLLsLLLMLL -0.0445
-4 ~ 45/44 12/11 7/6 5/4 12/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1 sLLLMLLLsLLL -0.0438
-3 ~ 15/14 8/7 7/6 5/4 4/3 10/7 16/11 14/9 5/3 16/9 15/8 2/1 LLsLLLsLLLML -0.0153
-2 ~ 15/14 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LsLLLMLLLsLL -0.0146
-1 ~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1 MLLLsLLLsLLL -0.0139
1 ~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1 LLLsLLLsLLLM 0.0139
2 ~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 11/6 15/8 2/1 LLsLLLMLLLsL 0.0146
3 ~ 15/14 9/8 6/5 9/7 11/8 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LMLLLsLLLsLL 0.0153
4 ~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 8/5 12/7 11/6 55/28 2/1 LLLsLLLMLLLs 0.0438
5 ~ 15/14 8/7 6/5 9/7 11/8 22/15 3/2 8/5 12/7 11/6 15/8 2/1 LLMLLLsLLLsL 0.0445
6 ~ 15/14 8/7 11/9 9/7 11/8 22/15 11/7 8/5 12/7 11/6 55/28 2/1 LLLMLLLsLLLs 0.0738
Rank-2 temperings (mode -2)
Equivalence Step pattern Scale Comma list
L = M LsLLLLLLLsLL Pajarous[12] MODMOS 50/49, 55/54, 64/63
M = s LsLLLsLLLsLL August[12] 36/35, 45/44, 56/55
L = s sssssLssssss Passion[12] 64/63, 100/99, 1375/1372
L - M = M - s LdLLLsLLLdLL Meanpop[12] MODMOS 81/80, 126/125, 385/384
s = 0 LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
Rank-1 temperings
ET 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 1) (4, 3, 1) (5, 3, 1) (5, 4, 2) (7, 5, 2)
(2/1, 5/4)[3], 16/15: 225/224, 385/384)[22] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1m 12s (~22/21, 36/35~33/32, 49/48~45/44~56/55) (80.7857c, 49.4049c, 35.347c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-7 ~ 45/44 16/15 12/11 49/44 7/6 105/88 5/4 14/11 4/3 15/11 7/5 63/44 3/2 49/32 8/5 18/11 12/7 7/4 98/55 15/8 21/11 2/1 sLssLsLsLsmsLsLsLssLsL -.0229
7 ~ 22/21 16/15 55/49 8/7 7/6 11/9 5/4 64/49 4/3 88/63 10/7 22/11 3/2 11/7 8/5 176/105 12/7 88/49 11/6 15/8 55/28 2/1 LsLssLsLsLsmsLsLsLssLs .0229
Rank-2 temperings (mode -7)
Equivalence Step pattern Scale Comma list
m = s sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS 99/98, 121/120, 176/175
L = m sLssLsLsLsLsLsLsLssLsL Pajarous[22] MODMOS 50/49, 55/54, 64/63
L = s LLLLLLLLLLsLLLLLLLLLLL Escapade[22] 99/98, 176/175, 2560/2541
L - m = m - s sAssAsAsAsLsAsAsAssAsA Magic[22] MODMOS 100/99, 225/224, 245/243
s = 0 LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
Rank-1 temperings
ET 31 41 50 53 72
Step sizes in ET (2, 1, 1) (3, 2, 1) (4, 2, 1) (3, 2, 2) (5, 3, 2)

((2/1, 3/2)[5], 16/15)

((2/1, 3/2)[5], 16/15)[10]

Step signature Steps in JI Step sizes in cents
2L 5m 3s (10/9, 16/15, 135/128) (182.4037c, 111.7313c, 92.1787c)
Mode number Mode in JI Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Blackwood[10] UDP Mode height
-5 16/15 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1 msmsmLmsmL sssssLsssL Dark minor sLsLsLsLsL 0|1 (5) -.0745
-4 135/128 9/8 1215/1024 81/64 45/32 3/2 405/256 27/16 15/8 2/1 smsmLmsmLm ssssLsssLs Alternate minor LsLsLsLsLs 1|0 (5) -.0592
-3 16/15 9/8 6/5 4/3 64/45 3/2 8/5 27/16 9/5 2/1 msmLmsmsmL sssLsssssL Standard minor sLsLsLsLsL 0|1 (5) -.0411
-2 135/128 9/8 5/4 4/3 45/32 3/2 405/256 27/16 15/8 2/1 smLmsmsmLm ssLsssssLs Dark major LsLsLsLsLs 1|0 (5) -.0258
-1 16/15 9/8 6/5 4/3 64/45 3/2 8/5 16/9 256/135 2/1 msmLmsmLms sssLsssLss Bright minor sLsLsLsLsL 0|1 (5) -.0077
1 135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 smLmsmLmsm ssLsssLsss Standard major LsLsLsLsLs 1|0 (5) .0077
2 16/15 32/27 512/405 4/3 64/45 3/2 8/5 16/9 256/135 2/1 mLmsmsmLms sLsssssLss Alternate major sLsLsLsLsL 0|1 (5) .0258
3 10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .0411
4 16/15 32/27 512/405 4/3 64/45 128/81 2048/1215 16/9 256/135 2/1 mLmsmLmsms sLsssLssss Dark Augmented sLsLsLsLsL 0|1 (5) .0592
5 10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1 LmsmLmsmsm LsssLsssss Bright Augmented LsLsLsLsLs 1|0 (5) .0745
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Srutal[10] 4M (pentachordal decatonic) 2048/2025
L = m sLLLsLLLsL Dicot[10] MODMOS 25/24
L = s LsLsLsLsLs Blackwood[10] 256/243
L - m = m - s sLALsLALsL Negri[10] MODMOS 16875/16384
s = 0 sLssLss Mavila[7] 135/128
m = 0 sLsLs Father[5] 16/15
((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
2L 5m 3s (10/9, 16/15~15/14, 135/128~21/20) (182.9137c, 116.0124c, 84.9028c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Blackwood[10] UDP Mode height
-5 ~ 15/14 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1 msmsmLmsmL sssssLsssL Dark minor sLsLsLsLsL 0|1 (5) -.0763
-4 ~ 21/20 9/8 189/160 81/64 7/5 3/2 63/40 27/16 15/8 2/1 smsmLmsmLm ssssLsssLs Alternate minor LsLsLsLsLs 1|0 (5) -.0688
-3 ~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1 msmLmsmsmL sssLsssssL Standard minor sLsLsLsLsL 0|1 (5) -.0400
-2 ~ 21/20 9/8 5/4 4/3 7/5 3/2 63/40 27/16 15/8 2/1 smLmsmsmLm ssLsssssLs Dark major LsLsLsLsLs 1|0 (5) -.0326
-1 ~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 40/21 2/1 msmLmsmLms sssLsssLss Bright minor sLsLsLsLsL 0|1 (5) -.0037
1 ~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 smLmsmLmsm ssLsssLsss Standard major LsLsLsLsLs 1|0 (5) .0037
2 ~ 15/14 32/27 80/63 4/3 10/7 3/2 8/5 16/9 40/21 2/1 mLmsmsmLms sLsssssLss Alternate major sLsLsLsLsL 0|1 (5) .0326
3 ~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .0400
4 ~ 15/14 32/27 80/63 4/3 10/7 128/81 320/189 16/9 40/21 2/1 mLmsmLmsms sLsssLssss Dark Augmented sLsLsLsLsL 0|1 (5) .0688
5 ~ 10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1 LmsmLmsmsm LsssLsssss Bright Augmented LsLsLsLsLs 1|0 (5) .0763
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Pajara[10] 4M (pentachordal decatonic) 50/49, 64/63
L = m sLLLsLLLsL Sharp[10] MODMOS 25/24, 28/27
L - m = m - s sLALsLALsL Negri[10] MODMOS 49/48, 225/224
s = 0 sLssLss Pelogic[7] 21/20, 135/128
((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)
Step signature Steps in JI Step sizes in cents (TE tuning)
2L 5m 3s (10/9, 16/15~15/14, 135/128~21/20~22/21) (184.0358c, 116.7669c, 82.9601c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Blackwood[10] UDP Mode height
-5 ~ 15/14 9/8 6/5 44/35 27/20 3/2 8/5 27/16 9/5 2/1 msmsmLmsmL sssssLsssL Dark minor sLsLsLsLsL 0|1 (5) -.0779
-4 ~ 21/20 9/8 33/28 44/35 7/5 3/2 11/7 27/16 15/8 2/1 smsmLmsmLm ssssLsssLs Alternate minor LsLsLsLsLs 1|0 (5) -.0718
-3 ~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1 msmLmsmsmL sssLsssssL Standard minor sLsLsLsLsL 0|1 (5) -.0405
-2 ~ 21/20 9/8 5/4 4/3 7/5 3/2 11/7 27/16 15/8 2/1 smLmsmsmLm ssLsssssLs Dark major LsLsLsLsLs 1|0 (5) -.0343
-1 ~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 21/11 2/1 msmLmsmLms sssLsssLss Bright minor sLsLsLsLsL 0|1 (5) .0031
1 ~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 smLmsmLmsm ssLsssLsss Standard major LsLsLsLsLs 1|0 (5) .0031
2 ~ 15/14 32/27 15/11 4/3 10/7 3/2 8/5 16/9 21/11 2/1 mLmsmsmLms sLsssssLss Alternate major sLsLsLsLsL 0|1 (5) .0343
3 ~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .0405
4 ~ 15/14 32/27 14/11 4/3 10/7 35/22 56/33 16/9 40/21 2/1 mLmsmLmsms sLsssLssss Dark Augmented sLsLsLsLsL 0|1 (5) .0718
5 ~ 10/9 32/27 5/4 4/3 40/27 35/22 5/3 16/9 15/8 2/1 LmsmLmsmsm LsssLsssss Bright Augmented LsLsLsLsLs 1|0 (5) .0779
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Pajaric[10] 4M (pentachordal decatonic) 45/44, 50/49, 56/55
L - m = m - s sLALsLALsL Negroni[10] MODMOS 49/48, 55/54, 225/224

((2/1, 3/2)[5], 16/15)[17]

10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)

135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL

L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]

((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)

2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE

~ 21/20 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 40/21 2/1 as MsMLMsMMsMMsMLMsM

L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;

s = 0 -> LLsLLLLLLsLL Pajara[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[17] (Prodigy)

2L 10M 5s = (256/243~35/33, 135/128~21/20~22/21, 2048/2025~50/49~64/63~45/44~56/55) = (101.0757c, 82.9601c, 33.8068c) TE

~ 22/21 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 21/11 2/1 as LsLmLsLLsLLsLmLsL

L = M -> LsLLLsLLsLLsLLLsL Andromeda[17]; s = 0 -> s = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] (Prodigy)

2L 10m 17s = (25/24~28/27, ~33/32, 2048/2025~50/49~64/63~45/44~56/55) = (67.2689c, 49.1533c, 33.8068c) TE

~ 50/49 22/21 16/15 11/10 9/8 8/7 33/28 6/5 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 5/3 56/33 7/4 16/9 20/11 15/8 21/11 49/25 2/1 as smsmssmsLsmssmsmssmsLsmssmsms

m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];

L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;

s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)

29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE

~ 50/49 33/32 22/21 16/15 12/11 11/10 9/8 8/7 7/6 32/27 40/33 11/9 5/4 14/11 128/99 21/16 4/3 15/11 11/8 7/5 10/7 16/11 22/15 3/2 32/16 99/64 11/7 8/5 18/11 33/20 27/16 12/7 7/4 16/9 20/11 11/6 15/8 21/11 64/33 49/25 2/1 as LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL

L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];

L - M = M - s -> Witchcraft[41] MODMOS

s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] (Prodigy)

29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE

as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs

L = M -> LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS;

M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;

L - M = M - s -> Compton MODMOS

s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;

m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS

2.3.5; Starling, No-7 Ptolemismic, and Ragismic

(2/1, 3/2, 6/5)

(2/1, 3/2, 6/5)[4]

Step signature Steps in JI Step sizes in cents
1L 2M 1s (5/4, 6/5, 10/9) (386.3137c, 315.6413c, 182.4037c)
Mode number Mode in JI Step pattern Mode height
-2 10/9 4/3 5/3 2/1 sMLM -0.1307
-1 6/5 4/3 8/5 2/1 MsML -0.0959
1 5/4 3/2 5/3 2/1 LMsM 0.0959
2 6/5 3/2 9/5 2/1 MLMs 0.1307
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LLLs Dicot[4] 25/24
M = s sLss Bug[4] 27/25
L = s LsLs Antitonic[4] 9/8

(2/1, 3/2, 6/5)[7]

Step signature Steps in JI Step sizes in cents
1L 4M 2s (9/8, 10/9, 27/25) (203.9100c, 182.4037c, 133.2376c)
Mode number Mode in JI Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 27/25 6/5 4/3 36/25 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0529
-2 10/9 6/5 4/3 40/27 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0316
-1 27/25 6/5 27/20 3/2 81/50 9/5 2/1 sMLMsMM sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0213
0 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 10/9 100/81 4/3 40/27 5/3 50/27 2/1 MMsMLMs LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0213
2 9/8 5/4 27/20 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0316
3 10/9 5/4 25/18 3/2 5/3 50/27 2/1 MLMsMMs LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0529
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meantone[7] 81/80
M = s sssLsss Porcupine[7] 250/243
L = s LsLsLsL Dicot[7] 25/24
L - M = M - s LsLALsL Tetracot[7] MODMOS 20000/19683
s = 0 ssLss Bug[5] 27/25
(2/1, 3/2, 6/5: 126/125)[7] (Starling)
Step signature Steps in JI Step sizes in cents (TE)
1L 4M 2s (~9/8, ~10/9, 27/25~15/14) (202.4685c, 187.562c, 123.5395c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0616
-2 ~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1 sMLMsMM sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0314
-1 ~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0302
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 ~ 9/8 5/4 27/20 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0302
2 ~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1 MMsMLMs LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0314
3 ~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1 MLMsMMs LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0616
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meantone[7] 81/80, 126/125
M = s sssLsss Opossum[7] 28/27, 126/125
L = s LsLsLsL Flat[7] 21/20, 25/24
Rank-1 temperings
ET 8d 12 15 16 19 27 31 46 50 58 77
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (2, 3, 1) (3, 3, 2) (5, 4, 3) (5, 5, 3) (8, 7, 5) (8, 8, 5) (10, 9, 6) (13, 12, 8)
(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
1L 4m 2s (9/8~25/22, 10/9~11/10, 27/25~12/11) (209.7786c, 174.0549c, 146.6352c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 smmsmLm sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0427
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 msmmsmL LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0374
-1 ~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1 smLmsmm sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0053
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 msmLmsm LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 mmsmLms LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0053
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 Lmsmmsm LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0374
3 ~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1 mLmsmms LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0427
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
m = s sssLsss Porkypine[7] 55/54, 100/99
L = m LsLLLsL Meanenneadecal[7] or Flattone[7] 45/44, 81/80
L = s LsLsLsL Flat[7] 25/24, 33/32
L - m = m - s LsLALsL Tetracot[7] MODMOS 100/99, 243/242
Rank-1 temperings
ET 8 12 15 19 22 26 27e 29 34 37 41
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (4, 3, 3) (4, 4, 3) (5, 4, 3) (5, 4, 4) (6, 5, 4) (7, 5, 5) (7, 6, 5)
(2/1, 3/2, 6/5: 56/55, 100/99)[7] (Thrasher)
Step signature Steps in JI Step sizes in cents (TE)
1L 4M 2s (9/8~25/22, 10/9~11/10, 27/25~15/14~12/11) (215.4452c, 179.0856c, 132.5782c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Porcupine[7] UDP Porcupine mode Diatonic mode Mode height
-3 ~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 sssssLs 1|5 Dark diminished Lochrian -0.0591
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 ssssssL 0|6 Magical seventh Aeolian -0.0433
-1 ~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1 sMLMsMM sLLLsLL 1|5 ssLssss 4|2 Bright minor Phrygian -0.0158
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 sssLsss 3|3 Dark minor Dorian 0
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 MMsMLMs LLsLLLs 5|1 ssssLss 2|4 Bright diminished Ionian 0.0158
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Lssssss 6|0 Bright major Mixolydian 0.0433
3 ~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1 MLMsMMs LLLsLLs 6|0 sLsssss 5|1 Dark major Lydian 0.0591
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meanenneadecal[7] 45/44, 56/55, 81/80
M = s sssLsss Opossum[7] 28/27, 55/54, 77/75
L = s LsLsLsL Flat[7] 21/20, 25/24, 33/32
Rank-1 temperings
ET 8d 12 15 19 27e 34
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (5, 4, 3) (6, 5, 4)
(2/1, 3/2, 6/5: 100/99, 144/143)[7] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
1L 4m 2s (9/8~25/22, 10/9~11/10, 27/25~12/11~13/12) (209.5416c, 175.8918c, 142.7754c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 12/11 6/5 4/3 13/9 8/5 9/5 2/1 smmsmLm sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 msmmsmL LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh
-1 ~ 12/11 6/5 15/11 3/2 13/8 9/5 2/1 smLmsmm sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 msmLmsm LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 mmsmLms LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 Lmsmmsm LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major
3 ~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1 mLmsmms LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
m = s sssLsss Porcupine[7] 40/39, 55/54, 66/65
L = m LsLLLsL Flattone[7] 45/44, 65/64, 81/80
L - m = m - s LsLALsL Tetracot[7] MODMOS 100/99, 144/143, 243/242
Rank-1 temperings
ET 8 12 15 19 22f 26 27e 34 41
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (4, 3, 3) (4, 4, 3) (5, 4, 3) (6, 5, 4) (7, 6, 5)

(2/1, 3/2, 6/5)[12]

Step signature Steps in JI Step sizes in cents
7L 1m 4s (27/25, 25/24, 250/243) (133.2376c, 70.6724c, 49.1661c)
Mode number Mode in JI Step pattern Meantone[12] UDP Mode height
-6 250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0622
-5 250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0587
-4 250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0338
-3 250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0302
-2 25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9 -0.0267
-1 27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5 -0.0018
1 27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6 0.0018
2 27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0267
3 27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0302
4 27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4 0.0338
5 27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0 0.0587
6 27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1 0.0622
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meantone[12] 81/80
L = m sLLsLLLsLLsL Diminished[12] MODMOS 648/625
L = s LLLLLsLLLLLL Ripple[12] 6561/6250
L - m = m - s dLLdLsLdLLdL Augmented[12] MODMOS 128/125
s = 0 LLLsLLLL Porcupine[8] 250/243
(2/1, 3/2, 6/5: 126/125)[12] (Starling)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14, 25/24~21/20, 250/243~28/27) (123.5395c, 78.929c, 64.0225c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 28/27 10/9 280/243 56/45 4/3 112/81 40/27 14/9 5/3 140/81 28/15 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0440
-5 ~ 28/27 10/9 7/6 5/4 35/27 7/5 3/2 14/9 5/3 140/81 28/15 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0417
-4 ~ 28/27 10/9 6/5 56/45 4/3 112/81 40/27 8/5 224/135 16/9 28/15 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0237
-3 ~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0214
-2 ~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 28/15 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9 -0.0191
-1 ~ 15/14 10/9 6/5 56/45 4/3 10/7 40/27 8/5 5/3 9/5 28/15 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5 -0.0011
1 ~ 15/14 10/9 6/5 5/4 27/20 7/5 3/2 45/28 5/3 9/5 28/15 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6 0.0011
2 ~ 15/14 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0191
3 ~ 15/14 10/9 6/5 9/7 4/3 10/7 3/2 45/28 5/3 9/5 27/14 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0214
4 ~ 15/14 9/8 135/112 5/4 27/20 81/56 3/2 45/28 5/3 9/5 27/14 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4 0.0237
5 ~ 15/14 81/70 6/5 9/7 4/3 10/7 54/35 8/5 12/7 9/5 27/14 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0 0.0417
6 ~ 15/14 81/70 6/5 9/7 27/20 81/56 3/2 45/28 243/140 9/5 27/14 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1 0.0440
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meantone[12] 81/80, 126/125
L = m sLLsLLLsLLsL Diminished[12] MODMOS 36/35, 50/49
L - m = m - s dLLdLsLdLLdL Augene[12] MODMOS 64/63, 126/125
s = 0 LLLsLLLL Opossum[8] 28/27, 126/125
Rank-1 temperings
ET 15 16 19 27 31 46 50 58 77
Step sizes in ET (2, 1, 0) (1, 1, 2) (2, 1, 1) (3, 2, 1) (3, 2, 2) (5, 3, 2) (5, 3, 3) (6, 4, 3) (8, 5, 4)
(2/1, 3/2, 6/5: 126/125, 196/195)[12]
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63) (123.5395c, 78.929c, 64.0225c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 28/27 10/9 52/45 26/21 4/3 104/75 40/27 14/9 5/3 26/15 13/7 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0465
-5 ~ 28/27 10/9 7/6 5/4 13/10 7/5 3/2 14/9 5/3 26/15 13/7 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0433
-4 ~ 28/27 10/9 6/5 26/21 4/3 104/75 40/27 8/5 104/63 16/9 13/7 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0256
-3 ~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 13/7 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0225
-2 ~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 13/7 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9 -0.0193
-1 ~ 14/13 10/9 6/5 26/21 4/3 10/7 40/27 8/5 5/3 9/5 13/7 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5 -0.0016
1 ~ 14/13 10/9 6/5 5/4 27/20 7/5 3/2 21/13 5/3 9/5 13/7 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6 0.0016
2 ~ 14/13 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0193
3 ~ 14/13 10/9 6/5 9/7 4/3 10/7 3/2 21/13 5/3 9/5 27/14 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0225
4 ~ 14/13 9/8 63/52 5/4 27/20 75/52 3/2 21/13 5/3 9/5 27/14 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4 0.0256
5 ~ 14/13 15/13 6/5 9/7 4/3 10/7 20/13 8/5 12/7 9/5 27/14 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0 0.0433
6 ~ 14/13 15/13 6/5 9/7 27/20 75/52 3/2 21/13 45/26 9/5 27/14 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1 0.0465
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanpop[12] 81/80, 105/104, 126/125
Rank-1 temperings
ET 15f 19 27 31 46 50 58 77
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 2, 1) (3, 2, 2) (5, 3, 2) (5, 3, 3) (6, 4, 3) (8, 5, 4)
(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11, 25/24~33/32, 250/243~55/54~121/120) (146.6352c, 63.1434c, 27.4197c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0899
-5 ~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0819
-4 ~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0510
-3 ~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0430
-2 ~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9 -0.0349
-1 ~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5 -0.0040
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6 0.0040
2 ~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0349
3 ~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 18/11 5/3 9/5 108/55 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0430
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 108/55 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4 0.0510
5 ~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0 0.0819
6 ~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 18/11 216/121 9/5 108/55 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1 0.0899
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanenneadecal[12] or Flattone[12] 45/44, 81/80
L = m sLLsLLLsLLsL Diminished[12] MODMOS 100/99, 128/121
L - m = m - s dLLdLsLdLLdL Augene[12] MODMOS 100/99, 128/125
s = 0 LLLsLLLL Porkypine[8] 55/54, 100/99
Rank-1 temperings
ET 15 19 22 26 27e 29 34 37 41
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (3, 2, 1) (4, 1, 0) (4, 2, 1) (5, 2, 0) (5, 2, 1)
(2/1, 3/2, 6/5: 100/99, 144/143)[12] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11~13/12, 25/24~33/32~27/26, 250/243~55/54~121/120~40/39) (142.77537c, 66.76626c, 33.11646c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 40/39 10/9 44/39 11/9 4/3 110/81 22/15 20/13 5/3 22/13 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10
-5 ~ 40/39 10/9 15/13 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-4 ~ 40/39 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7
-3 ~ 40/39 10/9 6/5 11/9 4/3 11/8 3/2 20/13 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8
-2 ~ 25/24 9/8 15/13 5/4 15/11 11/8 3/2 20/13 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9
-1 ~ 12/11 10/9 6/5 11/9 4/3 13/9 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 13/8 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6
2 ~ 12/11 10/9 6/5 13/10 4/3 13/9 22/15 8/5 26/15 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2
3 ~ 12/11 10/9 6/5 13/10 4/3 13/9 3/2 13/8 5/3 9/5 39/20 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 13/8 5/3 9/5 39/20 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4
5 ~ 12/11 13/11 6/5 13/10 4/3 13/9 52/33 8/5 26/15 9/5 39/20 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0
6 ~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 13/8 39/22 9/5 39/20 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 65/64, 81/80
s = 0 LLLsLLLL Porcupine[8] 40/39, 55/54, 66/65
Rank-1 temperings
ET 15 19 22f 26 27e 34 41
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (3, 2, 1) (4, 2, 1) (5, 2, 1)
(2/1, 3/2, 6/5: 100/99, 385/384)[12] (Supermagic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120) (149.51592c, 58.8799c, 23.6254c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10
-5 ~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-4 ~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7
-3 ~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8
-2 ~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 32/21 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9
-1 ~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6
2 ~ 12/11 10/9 6/5 21/16 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2
3 ~ 12/11 10/9 6/5 21/16 4/3 16/11 3/2 18/11 5/3 9/5 63/32 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4
5 ~ 12/11 144/121 6/5 21/16 4/3 16/11 192/121 8/5 7/4 9/5 63/32 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0
6 ~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 81/80, 385/384
s = 0 LLLsLLLL Porcupine[8] 55/54, 64/63, 100/99
Rank-1 temperings
ET 15 19 22 26 34 41 104
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (4, 2, 1) (5, 2, 1) (13, 5, 2)
(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12] (Supermagic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11~13/12~35/32, 25/24~27/26~33/32, 250/243~40/39~55/54~64/63~121/120) (145.47082c, 58.39270c, 30.85183c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 40/39 10/9 44/39 11/9 4/3 110/81 22/15 20/13 5/3 22/13 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10
-5 ~ 40/39 10/9 8/7 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-4 ~ 40/39 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7
-3 ~ 40/39 10/9 6/5 11/9 4/3 11/8 3/2 20/13 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8
-2 ~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 20/13 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9
-1 ~ 12/11 10/9 6/5 11/9 4/3 13/9 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 13/8 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6
2 ~ 12/11 10/9 6/5 13/10 4/3 13/9 22/15 8/5 7/4 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2
3 ~ 12/11 10/9 6/5 13/10 4/3 13/9 3/2 13/8 5/3 9/5 39/20 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 13/8 5/3 9/5 39/20 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4
5 ~ 12/11 13/11 6/5 13/10 4/3 13/9 52/33 8/5 7/4 9/5 39/20 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0
6 ~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 13/8 39/22 9/5 39/20 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 65/64, 78/77, 81/80
s = 0 LLLsLLLL Porcupine[8] 40/39, 55/54, 64/63, 66/65
Rank-1 temperings
ET 15 19 22f 26 34 41
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (4, 2, 1) (5, 2, 1)
(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54) (132.5782c, 82.867c, 46.5074c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 28/27 10/9 121/108 11/9 4/3 110/81 22/15 14/9 5/3 121/72 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0671
-5 ~ 28/27 10/9 7/6 5/4 121/96 11/8 3/2 14/9 5/3 121/72 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0526
-4 ~ 28/27 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0445
-3 ~ 28/27 10/9 6/5 11/9 4/3 11/8 3/2 14/9 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0299
-2 ~ 21/20 9/8 7/6 5/4 15/11 11/8 3/2 14/9 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9 -0.0154
-1 ~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5 -0.0073
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6 0.0073
2 ~ 12/11 10/9 6/5 9/7 4/3 16/11 22/15 8/5 12/7 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0154
3 ~ 12/11 10/9 6/5 9/7 4/3 16/11 3/2 18/11 5/3 9/5 27/14 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0299
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 27/14 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4 0.0445
5 ~ 12/11 144/121 6/5 9/7 4/3 16/11 192/121 8/5 12/7 9/5 27/14 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0 0.0526
6 ~ 12/11 144/121 6/5 9/7 15/11 81/55 3/2 81/50 216/121 9/5 27/14 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1 0.0671
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanenneadecal[12] 45/44, 56/55, 81/80
L = m sLLsLLLsLLsL Diminished[12] MODMOS 36/35, 50/49, 56/55
s = 0 LLLsLLLL Opossum[8] 28/27, 55/54, 77/75
Rank-1 temperings
ET 15 19 27e 34
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 2, 1) (4, 2, 1)
(2/1, 3/2, 6/5: 56/55, 91/90, 100/99)[12] (Thrasher)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14~12/11~13/12, 25/24~21/20~33/32~27/26, 250/243~28/27~55/54~40/39)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 28/27 10/9 44/39 11/9 4/3 110/81 22/15 14/9 5/3 22/13 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10
-5 ~ 28/27 10/9 7/6 5/4 33/26 11/8 3/2 14/9 5/3 121/72 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-4 ~ 28/27 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7
-3 ~ 28/27 10/9 6/5 11/9 4/3 11/8 3/2 14/9 5/3 9/5 11/6 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8
-2 ~ 21/20 9/8 7/6 5/4 15/11 11/8 3/2 14/9 5/3 9/5 11/6 2/1 mLsLLsLsLLsL sLsLLsLsLLsL 2|9
-1 ~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1 LsLsLLsLmLsL LsLsLLsLsLsL 6|5
1 ~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1 LsLmLsLLsLsL LsLsLsLLsLsL 5|6
2 ~ 12/11 10/9 6/5 9/7 4/3 16/11 22/15 8/5 12/7 16/9 48/25 2/1 LsLLsLsLLsLm LsLLsLsLLsLs 9|2
3 ~ 12/11 10/9 6/5 9/7 4/3 16/11 3/2 18/11 5/3 9/5 27/14 2/1 LsLLsLmLsLLs LsLLsLsLsLLs 8|3
4 ~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 27/14 2/1 LmLsLLsLsLLs LsLsLLsLsLLs 7|4
5 ~ 12/11 13/11 6/5 9/7 4/3 16/11 192/121 8/5 12/7 9/5 27/14 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0
6 ~ 12/11 13/11 6/5 9/7 15/11 81/55 3/2 81/50 39/22 9/5 27/14 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Vincenzo[12] 45/44, 56/55, 65/64, 81/80
s = 0 LLLsLLLL Opossum[8] 28/27, 40/39, 55/54, 66/65
Rank-1 temperings
ET 15 19 27e 34
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 2, 1) (4, 2, 1)
(2/1, 3/2, 6/5: 4375/4374)[12] (Ragismic)

7L 1m 4s = (~27/25, ~25/24, 250/243~36/35) = (133.4115c, 70.5569c, 48.8911c) TE

~ 27/25 10/9 6/5 35/27 4/3 36/25 3/2 81/50 5/3 9/5 35/18 2/1 as LsLLsLmLsLLs

m = s -> LsLLsLsLsLLs Falttone[12]; L = m -> LsLLsLLLsLLs MODMOS; L = s -> LLLLLLsLLLLL; s = 0 -> LLLLsLLL Hystrix[8]

19-ET: (2, 1, 1); 53-ET: (6, 3, 2); 72-ET: (8, 4, 3); 99-ET: (11, 6, 4); 118-ET: (13, 7, 5); 152-ET: (17, 9, 6); 171-ET: (19, 10, 7); 224-ET: (25, 13, 9); 270-ET: (30, 16, 11); 441-ET: (49, 26, 18); 494-ET: (55, 29, 20); 612-ET: (68, 36, 25)

(2/1, 3/2, 6/5: 100/99, 144/143)[20] (No-7 Ptolemismic)

7L 12m 1s = (~189/176, 250/243~55/54~121/120~40/39, 81/80~45/44~65/64) =

(2/1, 3/2, 6/5: 100/99, 385/384)[20] (Supermagic)

7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE

40/39 12/11 10/9 32/27 6/5 11/9 13/10 4/3 11/8 22/15 3/2 20/13 13/8 5/3 16/9 9/5 11/6 39/20 2/1

(2/1, 3/2, 6/5: 4375/4374)[20] (Ragismic)

7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c) TE

~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm

m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;

L - m = m - s -> Unidec[20] MODMOS

s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]

19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)

(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)

7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE

~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm

m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;

s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL

19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)

(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)

7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE

~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms

m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs

46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)

2.3.5; Hemifamity

((2/1, 3/2)[5], 10/9)

((2/1, 3/2)[5], 10/9)[10]

5L 2M 3s = (10/9, 16/15, 81/80)

81/80 9/8 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1 as sLMLsLMLsL

L = M -> sLLLsLLLsL Dicot[10] MODMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;

L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS

s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]

((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)

5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE

~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs

m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss;

L - m = m - s -> Garibaldi[17]; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)

5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE

~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs

m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Arnold[7]; m = 0 -> sLssLssLssLssLs

((2/1, 3/2)[5], 10/9: 5120/5103)[24] (Hemifamity)

5L 2m 17s = (~175/162, ~28/27, 81/80~64/63) = (132.1305c, 61.3411c, 24.4931c) TE

~ 64/63 35/32 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 35/24 40/27 3/2 32/21 105/64 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss

m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24] (Akea)

5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE

~ 64/63 12/11 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 16/11 40/27 3/2 32/21 18/11 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss

m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Arnold[7]

((2/1, 3/2)[5], 10/9: 5120/5103)[31] (Hemifamity)

5L 2m 24s = (~1225/1152, ~49/48, 81/80~64/63) = (107.6374c, 36.848c, 24.4931c) TE

~ 64/63 36/35 35/32 10/9 9/8 8/7 7/6 32/27 6/5 128/105 35/27 21/16 4/3 27/20 48/35 35/24 40/27 3/2 32/21 54/35 105/64 5/3 27/16 12/7 7/4 16/9 9/5 64/35 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss

m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;

s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31] (Akea)

5L 2m 24s = (~35/33, 49/48~56/55, 81/80~64/63~55/54) = (100.7664c, 33.3269c, 26.2356c) TE

~ 64/63 36/35 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 35/27 21/16 4/3 27/20 11/8 16/11 40/27 3/2 32/21 54/35 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss

m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;

s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss

((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63)

((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)

5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE

~ 64/63 15/14 243/224 9/8 8/7 32/27 6/5 81/64 9/7 4/3 27/20 10/7 81/56 3/2 32/21 45/28 80/49 27/16 12/7 16/9 9/5 243/128 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM

L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]

((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24] (Pele)

5L 7M 12s = (135/128~35/33, 28/27~33/32, 81/80~64/63~99/98) = (97.5911c, 58.2557c, 25.3165c) TE

~ 64/63 15/14 12/11 9/8 8/7 32/27 6/5 14/11 9/7 4/3 27/20 10/7 16/11 3/2 32/21 45/28 18/11 27/16 12/7 16/9 9/5 12/11 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM

L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]

((2/1, 3/2)[12], 64/63: 5120/5013)[36] (Hemifamity)

5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE

~ 64/63 36/35 15/14 243/224 54/49 9/8 8/7 81/70 32/27 6/5 128/105 81/64 9/7 64/49 4/3 27/20 48/35 10/7 81/56 72/49 3/2 32/21 54/35 45/28 80/49 81/49 27/16 12/7 243/140 16/9 9/5 64/35 243/128 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM

L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;

s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS

((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36] (Pele)

5L 7M 12s = (~25/24, ~49/48, 81/80~64/63~99/98) = (72.2746c, 32.9392c, 25.3165c) TE

~ 64/63 36/35 15/14 12/11 54/49 9/8 8/7 64/55 32/27 6/5 128/105 14/11 9/7 64/49 4/3 27/20 48/35 10/7 16/11 72/49 3/2 32/21 54/35 45/28 18/11 81/49 27/16 12/7 96/55 16/9 9/5 64/35 22/21 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM

L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;

s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS

2.5.9; Marvel

((2/1, 5/4)[3], 9/8)

((2/1, 5/4)[3], 9/8)[6]

1L 3M 2s = (256/225, 9/8, 10/9)

9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8: 225/224)[6] (Marvel)

1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c) TE

~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6] (Apollo)

1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c) TE

~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8)[10]

6L 1m 3s = (10/9, 128/125, 81/80)

10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,

m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8: 225/224)[10] (Marvel)

6L 1m 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE

~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL

m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10] (Apollo)

6L 1m 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE

~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL

m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8)[17]

6L 10m 1s = (800/729, 81/80, 2048/2025)

81/80 10/9 9/8 100/81 5/4 81/64 25/18 45/32 64/45 36/18 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as mLmLmmLmsmLmmLmLm

m = s -> sLsLssLsssLssLsLs MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL

((2/1, 5/4)[3], 9/8: 225/224)[17] (Marvel)

6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE

~ 81/80 10/9 9/8 100/81 5/4 81/64 25/18 7/5 10/7 36/25 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as sLsLssLsmsLssLsLs

m = s -> sLsLssLsssLssLsLs MODMOS; L = m -> sLsLssLsLsLssLsLs; L = s -> LLLLLLLLsLLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLsLssLssLssLsLs MODMOS

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17] (Apollo)

6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE

~ 56/55 10/9 9/8 11/9 5/4 14/11 11/8 7/5 10/7 16/11 11/7 8/5 11/9 16/9 9/5 55/28 2/1 as mLmLmmLmsmLmmLmLm

m = s -> sLsLssLsssLssLsLs Machine[17] MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL

2.5.9; Starling

((2/1, 5/4)[3], 10/9)

((2/1, 5/4)[3], 10/9)[6]

1L 2m 3s = (144/125, 9/8, 10/9)

9/8 5/4 36/25 8/5 9/5 2/1 as msLsms

m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL

((2/1, 5/4)[3], 10/9: 126/125)[6]

1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c) TE

~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms

m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL

((2/1, 5/4)[3], 10/9)[9]

6L 1m 2s = (10/9, 648/625, 81/80)

10/9 9/8 5/4 25/18 36/25 8/5 16/9 9/5 2/1 as LsLLmLLsL

m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS

((2/1, 5/4)[3], 10/9: 126/125)[9]

6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c) TE

~ 10/9 9/8 5/4 7/5 10/7 8/5 16/9 9/5 2/1 as LsLLmLLsL

m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS

((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16]

6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55) = (163.6623c, 24.4284c, 21.4103c) TE

~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 81/50 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL

m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL

((2/1, 5/4)[3], 10/9: 91/90, 126/125, 896/891)[16]

6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143) = (160.4106c, 30.0969c, 23.0825c) TE

~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 13/8 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL

m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL

2.3.7; Orwellismic

(2/1, 3/2, 7/6)

(2/1, 3/2, 7/6)[4]

1L 2m 1s = (9/7, 7/6, 8/7)

7/6 3/2 7/4 2/1 as mLms

m = s -> sLss Sempahore[4]

(2/1, 3/2, 7/6)[7]

4L 1M 2s = (8/7, 9/8, 49/48)

8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL

L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]

(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)

4L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE

~ 8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL

L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)

4L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE

~ 36/35 8/7 7/6 6/5 4/3 48/35 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[12] (Orwellian)

4L 1M 7s = (~10/9, 54/49~35/32~12/11, 49/48~36/35~33/32) = (185.7619, 155.4288c, 155.4288c) TE

~ 33/32 8/7 7/6 6/5 4/3 11/8 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Suprapyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[12] (Guanyin)

4L 1M 7s = (~10/9, 54/49~35/32~11/10, 49/48~36/35~45/44) = (183.8734c, 162.5743c, 43.0239c) TE

~ 36/35 8/7 7/6 6/5 4/3 15/11 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS

(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)

4L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 48/35 35/24 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[17] (Orwellian)

4L 1M 12s = (~160/147, 15/14~35/33, 49/48~36/35~33/32) = (142.5744c, 112.2413c, 43.1875c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 11/8 16/11 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Suprapyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[17] (Guanyin)

4L 1M 12s = (~88/81, 15/14~77/72, 49/48~36/35~45/44) = (140.8495c, 119.5504c, 43.0239c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 15/11 22/15 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs

(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)

4L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 48/35 7/5 35/24 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs

m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[22] (Orwellian)

4L 1m 17s = (~200/189, 25/24~80/77, 49/48~36/35~33/32) = (99.3869c, 69.0538c, 43.1875c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 11/8 7/5 16/11 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs

m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Suprapyth[17]; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[22] (Guanyin)

4L 1m 17s = (~200/189, 25/24~22/21, 49/48~36/35~45/44) = (97.8256c, 76.5265c, 43.0239c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 27/22 35/27 4/3 15/11 7/5 22/15 3/2 54/27 63/40 5/3 12/7 7/4 9/5 81/44 35/18 2/1 as ssLssssLsssmsssLssssLs

m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]

(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)

4L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE

~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 48/35 7/5 10/7 35/24 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM

L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; M = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[27] (Orwellian)

4L 22M 1s = (~250/243, 49/48~36/35~33/32, 50/49~100/99) = (56.1994c, 43.1875c, 25.8663c) TE

~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 11/8 7/5 10/7 16/11 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM

L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartz[27]; M = s -> ssLsssssLsssssssssLsssssLss Myno[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Suprapyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[27] (Guanyin)

4L 22M 1s = (~250/243, 49/48~36/35~45/44, 50/49~55/54) = (54.8017c, 43.0239c, 33.5026c) TE

~ 36/35 21/20 88/81 10/9 8/7 7/6 6/5 27/22 80/63 35/27 4/3 15/11 7/5 10/7 22/15 3/2 54/27 63/40 44/27 5/3 12/7 7/4 9/5 81/44 40/21 35/18 2/1 as mmLmmmmmLmmmmsmmmmLmmmmmLmm

m = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = m -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS

(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)

27L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE

~ 50/49 36/35 360/343 21/20 15/14 27/25 54/49 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 48/35 480/343 7/5 10/7 343/240 35/24 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 49/27 50/27 28/15 40/21 343/180 35/18 49/25 2/1 as LsLsLsLsLMLsLsLsLsLsLMLsLsLsLsLMLsLsLsLsLsLMLsLsLsLsL

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53]; L = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss

s = 0 -> LLLLLsLLLLLLsLLLLLsLLLLLLsLLLLL Myna[31] MODMOS; M = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49];

L = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS

(2/1, 3/2, 7/6: 99/98, 385/384)[53] (Orwellian)

4L 27M 22s = (64/63~245/243~55/54, 50/49~100/99, 126/125~2401/2400) = (30.3331c, 25.8663c, 17.3212c) TE

~ 50/49 36/35 80/77 21/20 15/14 27/25 12/11 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 11/8 480/343 7/5 10/7 343/240 16/11 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 11/6 50/27 28/15 40/21 77/40 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartz[53];

s = 0 -> sssssLssssssLsssssLssssssLsssss Myno[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS;

L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Suprapyth[49]

(2/1, 3/2, 7/6: 176/175, 540/539)[53] (Guanyin)

4L 27M 22s = (64/63~245/243~100/99, 50/49~55/54, 126/125~2401/2400~441/440) = (33.5026c, 21.2991c, 9.5213c) TE

~ 50/49 36/35 22/21 21/20 15/14 27/25 11/10 243/220 9/8 8/7 125/108 7/6 25/21 6/5 11/9 27/22 5/4 63/50 9/7 162/125 21/16 4/3 110/81 15/11 88/63 7/5 10/7 63/44 22/15 81/55 3/2 32/16 125/81 14/9 100/63 8/5 44/27 18/11 5/3 42/25 12/7 216/125 7/4 16/9 440/243 20/11 50/27 40/21 21/11 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss Kleiboh[53] MODMOS; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53];

s = 0 -> sssssLssssssLsssssLssssssLsssss Myna[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Fleetwood[22] MODMOS;

L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49]

((2/1, 3/2)[12], 49/48) or ((2/1, 3/2)[12], 36/35)

((2/1, 3/2)[12], 36/35: 1728/1715)[24] (Orwellian)

2.3.7 Sensamagic

(2/1, 3/2, 9/7)

(2/1, 3/2, 9/7)[4]

2L 1M 1s = (9/7, 7/6, 28/27) = (435.0841c, 266.8709c, 62.9609c)

9/7 3/2 27/14 2/1 as LMLs

L = M -> LLLs; M = s -> LsLs; s = 0 -> LsL

(2/1, 3/2, 9/7: 245/243)[7] Sensamagic

2L 1m 4s = (~5/4, ~9/8, 28/27~36/35)

~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 as sLsmsLs

m = s -> sLsssLs; s = 0 -> LsL

5-ET: (2, 1, 0); 14c-ET: (4, 2, 1); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22-ET: (7, 4, 1) 24-ET: (8, 4, 1); 27-ET: (9, 5, 1); 41-ET: (13, 7, 2); 46-ET: (15, 8, 2); 68-ET: (22, 12, 3); 87-ET: (28, 15, 4)

(2/1, 3/2, 9/7: 245/243)[10] Sensamagic

2L 1m 7s = (~135/112, ~35/32, 28/27~36/35)

~ 28/27 5/4 9/7 4/3 35/24 3/2 14/9 15/8 27/14 2/1 as sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic

2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)

~ 28/27 5/4 9/7 4/3 16/11 3/2 14/9 15/8 27/14 2/1 as sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 63-ET: (18, 8, 3); 68-ET: (19, 9, 3); 87-ET: (24, 11, 4)

(2/1, 3/2, 9/7: 245/243)[13] Sensamagic

2L 1m 10s = (~75/64, ~135/128, 28/27~36/35)

~ 28/27 16/15 5/4 9/7 4/3 48/35 35/24 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss

m = s -> ssLsssssssLss Pycnic[13] MODMOS; s = 0 -> LsL

14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic

2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)

~ 28/27 16/15 5/4 9/7 4/3 11/8 16/11 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 63-ET: (15, 5, 3); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[16] Sensamagic

2L 13m 1s = (~25/22, 28/27~36/35~33/32, ~45/44)

~ 28/27 16/15 40/33 5/4 9/7 4/3 11/8 45/32 16/11 3/2 14/9 8/5 20/11 15/8 27/14 2/1 as mmLmmmmsmmmmLmmm

m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss

17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 22-ET: (4, 1, 1) 24-ET: (5, 1, 1); 27-ET: (6, 1, 2); 41-ET: (7, 2, 1); 46-ET: (9, 2, 2); 63-ET: (12, 3, 2); 68-ET: (13, 3, 3); 87-ET: (16, 4, 3)

(2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic

2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)

~ 45/44 28/27 35/33 16/15 12/11 11/10 9/8 154/135 7/6 9/7 405/308 4/3 15/11 11/8 45/32 64/45 16/11 22/15 3/2 616/405 14/9 12/7 135/77 16/9 20/11 11/6 15/8 66/35 27/14 88/45 2/1 as msmsmsmsmLmsmsmsmsmsmLmsmsmsmsm

m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS

41-ET: (6, 1, 1); 46-ET: (7, 2, 0); 63-ET: (10, 2, 1); 68-ET: (10, 3, 0); 87-ET: (13, 3, 1)

(2/1, 3/2, 9/7: 729/728)[7]

2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)

~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs

m = s -> sLsssLs; s = 0 -> LsL

5-ET: (2, 1, 0); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22f-ET: (7, 4, 1) 24-ET: (8, 4, 1); 36-ET: (11, 6, 2); 41-ET: (13, 7, 2); 53-ET: (16, 9, 3); 58-ET: (18, 10, 3); 77-ET: (24, 13, 4); 94-ET: (29, 16, 5)

(2/1, 3/2, 9/7: 729/728)[10]

2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)

~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22f-ET: (6, 3, 1) 24-ET: (7, 3, 1); 36-ET: (9, 4, 2); 41-ET: (11, 5, 2); 53-ET: (13, 6, 3); 58-ET: (15, 7, 3); 77-ET: (20, 9, 4); 94-ET: (24, 11, 5)

(2/1, 3/2, 9/7: 729/728)[13]

2L 1m 10s = (~169/147, ~117/112, 28/27~27/26)

~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)

(2/1, 3/2, 9/7: 351/350, 676/675)[13]

2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)

~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 24-ET: (6, 2, 1); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 111-ET: (22, 7, 6); 130-ET: (26, 8, 7)

(2/1, 3/2, 9/7: 351/350, 676/675)[16]

2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)

~ 26/25 14/13 25/21 26/21 9/7 4/3 18/13 39/28 13/9 3/2 14/9 21/13 25/14 13/7 23/13 2/1 as mmLmmmmsmmmmLmmm

m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss

17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 24-ET: (5, 1, 1); 53-ET: (7, 3, 0); 58-ET: (9, 3, 1); 77-ET: (12, 4, 1); 111-ET: (16, 6, 1); 130-ET: (19, 7, 1)

(2/1, 3/2, 9/7: 351/350, 676/675)[31]

2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)

~169/168 26/25 117/112 14/13 13/12 28/25 9/8 378/325 7/6 9/7 325/252 4/3 75/56 18/13 39/28 56/39 13/9 112/75 3/2 14/9 12/7 325/189 16/9 25/14 24/13 13/7 224/117 25/13 336/169 2/1 as smsmsmsmsLsmsmsmsmsmsLsmsmsmsms

m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS

53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)