Gallery of 3-SN scales

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 32/21 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 32/21 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 32/21 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, 135/128

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
-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
-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
-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
-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
-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

2.3.25

(2/1, 3/2, 100/81)

(2/1, 3/2, 100/81)[7]

(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)

Step signature	Steps in JI	Step sizes in cents
2L 1m 4s	(2500/2187~8/7, ~9/8, ~27/25)	(231.1884c, 203.974c, 133.4123c)

Mode number	Mode in JI	Step pattern	Mode height
-3	~ 9/8 175/144 25/18 3/2 81/50 50/27 2/1	msLssLs	0.0158
-2	~ 27/25 175/144 21/16 3/2 81/50 7/4 2/1	smsLssL	-0.0211
-1	~ 8/7 100/81 25/18 3/2 12/7 50/27 2/1	LsmsLss	0.037
0	~ 27/25 100/81 4/3 3/2 81/50 50/27 2/1	sLsmsLs	0
1	~ 27/25 7/6 4/3 36/25 81/50 7/4 2/1	ssLsmsL	-0.037
2	~ 8/7 100/81 4/3 32/21 288/175 50/27 2/1	LssLsms	0.0211
3	~ 27/25 100/81 4/3 36/25 288/175 16/9 2/1	sLssLsm	-0.0158

(2/1, 3/2, 100/81: 1225/1224, 1701/1700)[7]

Step signature	Steps in JI	Step sizes in cents
2L 1m 4s	(2500/2187~8/7, ~9/8, ~27/25)	(231.5807c, 203.8094c, 133.2573c)

Mode number	Mode in JI	Step pattern	Mode height
-3	~ 9/8 17/14 25/18 3/2 34/21 50/27 2/1	msLssLs	0.0157
-2	~ 27/25 17/14 21/16 3/2 34/21 7/4 2/1	smsLssL	-0.0214
-1	~ 8/7 21/17 25/18 3/2 12/7 50/27 2/1	LsmsLss	0.0371
0	~ 27/25 21/17 4/3 3/2 34/21 50/27 2/1	sLsmsLs	0
1	~ 27/25 7/6 4/3 36/25 34/21 7/4 2/1	ssLsmsL	-0.0371
2	~ 8/7 21/17 4/3 32/21 28/17 50/27 2/1	LssLsms	0.0214
3	~ 27/25 21/17 4/3 36/25 28/17 16/9 2/1	sLssLsm	-0.0157

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)

Gallery of 3-SN scales

2.3.5; Marvel

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

(2/1, 3/2, 5/4: 225/224)[7] (Marvel)

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

(2/1, 3/2, 5/4: 225/224, 385/384)[10] (Marvel)

(2/1, 3/2, 5/4: 225/224, 441/440)[10] (Prodigy)

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

(2/1, 3/2, 5/4: 225/224, 385/384)[19] (Marvel)

(2/1, 3/2, 5/4: 225/224, 441/440)[19] (Prodigy)

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

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

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

2.3.5; Starling, No-7 Ptolemismic, and Ragismic

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

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

(2/1, 3/2, 6/5: 100/99, 144/143)[12] (No-7 Ptolemismic)

(2/1, 3/2, 6/5: 100/99, 385/384)[12] (Supermagic)

(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12] (Supermagic)

(2/1, 3/2, 6/5: 56/55, 91/90, 100/99)[12] (Thrasher)

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

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

2.3.5; Hemifamity

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

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

2.3.25

(2/1, 3/2, 100/81)

(2/1, 3/2, 100/81)[7]

(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)

2.5.9; Marvel

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

2.5.9; Starling

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

2.3.7; Orwellismic

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

((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]

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

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

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

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

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

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

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

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

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

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

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

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

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

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