Gallery of 3-SN scales mobile

See SN scale and Rank-3 scale.

For a more thorough summary, see Gallery of 3-SN scales.

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]

2L 1M 1s = (5/4, 6/5, 16/15) = (386.3137c, 315.6413c, 111.7313c)

5/4 3/2 15/8 2/1 as LMLs

L = M -> LLLs Dicot[4]; M = s -> LsLs Antitonic[4]; s = 0 -> LsL Father[3]

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

2L 1M 4s = (75/64, 9/8, 16/15) = (274.5824c, 203.9100c, 111.7313c)

16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs

L = M -> sLsLsLs Dicot[7]; M = s -> LLLsLLL Enipucrop[7]; s = 0 -> Father[3]

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

2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14) = (267.8165c, 200.9152c, 116.0124c)

~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs

L = M -> sLsLsLs Sharp[7]; M = s -> sLsssLs Pelogic[7]; L = s -> LLLsLLL Enipucrop[7]

9-ET: (2, 1, 1); 10-ET: (2, 2, 1); 12-ET: (3, 2, 1); 19-ET: (4, 3, 2); 22-ET: (5, 4, 2); 29-ET: (6, 5, 3); 31-ET: (7, 5, 3); 41-ET: (9, 7, 4); 50-ET: (11, 8, 5); 53-ET: (12, 9, 5); 72-ET: (16, 12, 17)

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

2L 7m 1s = (1125/1024, 16/15, 135/128) = (162.8511c, 111.7313c, 92.1787c)

16/15 75/64 5/4 4/3 45/32 3/2 8/5 128/75 15/8 as mLmmsmmLmm

m = s -> sLsssssLss Srutal[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Mavila[9]; m = 0 -> LsL Father[3]

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

2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20) = (151.8041c, 116.0124c, 84.9028c) TE

~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm

m = s -> sLsssssLss Pajara[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Pelogic[9]

12-ET: (2, 1, 1); 19-ET: (2, 2, 1); 22-ET: (3, 2, 2); 29-ET: (3, 3, 2); 31-ET: (4, 3, 2); 41-ET: (5, 4, 3); 53-ET: (7, 5, 4); 72-ET: (9, 7, 5)

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

2L 1m 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) = (151.4797c, 116.1327c, 84.7519c) TE

~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm

m = s -> sLsssssLss Pajarous[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]

12e-ET: (2, 1, 1); 19-ET: (2, 2, 1); 22-ET: (3, 2, 2); 31-ET: (4, 3, 2); 41-ET: (5, 4, 3); 53-ET: (7, 5, 4) 72-ET: (9, 7, 5)

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

2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) = (150.229c, 116.7669c, 82.9601c) TE

~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm

m = s -> sLsssssLss Pajaric[10] MODMOS; L = m -> LLLLsLLLLL Negroni[10]

12-ET: (2, 1, 1); 19e-ET: (2, 2, 1); 29-ET: (3, 3, 2); 31-ET: (4, 3, 2); 41-ET: (5, 4, 3); 53e-ET: (7, 5, 4); 72-ET: (9, 7, 5)

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

10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49) = (84.9028c, 66.9013c, 31.1096c) TE

~ 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 15/8 40/21 as LsLsLMLsLsLsLMLsLsL

L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19];

s = 0 -> LLLsLLLLsLLL Pajara[12] 4M (Hexachordal Dodecatonic); m = 0 -> LsLsLLsLsLsLLsLsL Sharp [17]

22-ET: (2, 1, 0); 29-ET: (2, 1, 1); 31-ET: (2, 2, 1); 41-ET: (3, 2, 1); 50-ET: (3, 3, 2); 53-ET: (4, 3, 1); 72-ET: (5, 4, 2)

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

10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) = (84.7519c, 66.7278c, 31.3808c) TE

~ 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 15/8 40/21 as LsLsLMLsLsLsLMLsLsL

L = M -> LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19]; s = 0 -> LLLsLLLLsLLL Pajarous[12] 4M (Hexachordal Dodecatonic)

22-ET: (2, 1, 0); 31-ET: (2, 2, 1); 41-ET: (3, 2, 1); 50-ET: (3, 3, 2); 53-ET: (4, 3, 1); 72-ET: (5, 4, 2)

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

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) TE

~ 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 15/8 40/21 as LsLsLMLsLsLsLMLsLsL

L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negroni[19]; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)

29-ET: (2, 1, 1); 31-ET: (2, 2, 1); 41-ET: (3, 2, 1); 53e-ET: (4, 3, 1); 72-ET (5, 4, 2)

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

10L 19m 2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE

~ 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

m = s -> sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS; L = m -> LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;

L = s -> sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS;

s = 0 -> mLmmLmmLmmLmmLmLmmLmmLmmLmmLm Negroni[29]; m = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)

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

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

1L 2M 3s = (6/5, 75/64, 16/15) = (315.6413c, 267.8165c, 111.7313c)

75/64 5/4 3/2 8/5 15/8 2/1 as MsLsMs

L = M -> LsLsLs Augmented[6]; M = s -> ssLsss Enipucrop[6]; L = s -> LsssLs Antitonic[6] MODMOS; s = 0 -> LsL Father[3]

((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)

1L 2M 3s = (6/5, 75/64~7/6, 16/15~15/14) = (316.9276c, 267.8165c, 116.0124c) TE

~ 7/6 5/4 3/2 8/5 15/8 2/1 as MsLsMs

L = M -> LsLsLs August[6]

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

1L 2M 6s = (9/8, 1125/1024, 16/15) = (203.9100c, 162.8511c, 111.7313c)

16/15 75/64 5/4 4/3 3/2 8/5 128/75 15/8 2/1 as sMssLssMs

L = M -> sLssLssLs Augmented[9]; M = s -> ssssLssss Negri[9]; L = s -> sLsssssLs Mavila[9] MODMOS; s = 0 -> LsL Father[3]; m = 0 -> sssLsss Eunipucrop[7]

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

1L 2M 6s = (9/8~28/25, 35/32~49/45, 16/15~15/14) = (200.9152c, 151.8041c, 116.0124c) TE

~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs

L = M -> to sLssLssLs August[9]; M = s -> ssssLssss Negri[9]; L = s -> sLsssssLs Pelogic[9] MODMOS

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

1L 2M 6s = (9/8~28/25, 35/32~49/45~12/11, 16/15~15/14) = (200.8846c, 151.4797c, 116.1327c) TE

~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs

L = M -> sLssLssLs August[9]; M = s -> ssssLssss Negri[9]

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

9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48) = (116.0124c, 84.9028c, 35.7917c) TE

~ 16/15 35/32 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as LsLLLMLLLsLL

L = M -> LsLLLLLLLsLL Pajara[12] MODMOS; M = s -> LsLLLsLLLsLL August[12]; L = s -> sssssLssssss Passion[12];

s = 0 -> LLLLsLLLLL Negri[10]; M = 0 -> LsLLLLLLsLL Pelogic[11] MODMOS

((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12] (Marvel)

9L 1M 2s = (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55) = (116.1327c, 84.7519c, 35.347c) TE

~ 16/15 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as LsLLLMLLLsLL

L = M -> LsLLLLLLLsLL Pajarous[12] MODMOS; M = s -> LsLLLsLLLsLLs August[12]; L = s -> sssssLssssss Passion[12]; s = 0 -> LLLLsLLLLL Negri[10]

((2/1, 5/4)[3], 16/15: 225/224, 385/384)[22] (Marvel)

9L 1m 12s = (~22/21, 36/35~33/32, 49/48~45/44~56/55) = (80.7857c, 49.4049c, 35.347c) TE

~ 49/48 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 as sLssLsLsLsmsLsLsLssLsL

m = s -> sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS; L = m -> sLssLsLsLsLsLsLsLssLsL Pajarous[22] MODMOS; L = s -> MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22];

s = 0 -> LLLLsLLLLL Negri[10]

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

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

2L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)

135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm

m = s -> ssLsssLsss 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10];

L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Mavila[7]; m =0 -> sLsLs Father[5]

((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)

2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE

~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm

m = s -> ssLsssLsss 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; s = 0 -> sLssLss Pelogic[7]

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)

2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE

~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm

m = s -> ssLsssLsss 4M (Pentachordal decatonic)

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

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

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; 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];

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;

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]

1L 2M 1s = (5/4, 6/5, 10/9)

6/5 3/2 9/5 2/1 as MLMs

L = M -> LLLs Dicot[4]; M = s -> sLss Bug[4]; L = s -> LsLs Antitonic[4]

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

1L 4M 2s = (9/8, 10/9, 27/25)

10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM

L = M -> LsLLLsL Meantone[7], M = s -> sssLsss Porcupine[7]; L = s -> LsLsLsL Dicot[7]; s = 0 -> ssLss Bug[5]

(2/1, 3/2, 6/5: 126/125)[7] (Starling)

1L 4M 2s = (~9/8, ~10/9, 27/25~15/14) = (202.4685c, 187.562c, 123.5395c) TE

~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM

L = M -> LsLLLsL Meantone[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]

8d-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 16-ET: (2, 3, 1); 19-ET: (3, 3, 2); 27-ET: (5, 4, 3); 31-ET: (5, 5, 3); 46-ET: (8, 7, 5); 50-ET: (8, 8, 5); 58-ET: (10, 9, 6); 77-ET: (13, 12, 8)

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

1L 4M 2s = (~9/8, 10/9~11/10, 27/25~12/11) = (209.7786c, 174.0549c, 146.6352c) TE

~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as msmLmsm

m = s -> sssLsss Porkypine[7], L = m -> LsLLLsL Meanenneadecal[7], L = s -> LsLsLsL Flat[7]

8d-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 19-ET: (3, 3, 2); 22-ET: (4, 3, 3); 27e-ET: (5, 4, 3); 29-ET: (5, 4, 4); 34-ET: (6, 5, 4); 41-ET: (7, 6, 5)

(2/1, 3/2, 6/5: 56/55, 100/99)[7] (Thrasher)

1L 4M 2s = (~9/8, 10/9~11/10, 27/25~15/14~12/11) = (215.4452c, 179.0856c, 132.5782c) TE

~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM

L = M -> LsLLLsL Meanenneadecal[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]

8d-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 19-ET: (3, 3, 2); 27e-ET: (5, 4, 3); 34-ET: (6, 5, 4)

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

7L 1m 4s = (27/25, 25/24, 250/243)

250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1 as sLLsLmLsLLsL

m = s -> sLLsLsLsLLsL Meantone[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; L = s -> LLLLLsLLLLLL Ripple[12]; s = 0 -> LLLsLLLL Porcupine[8]

(2/1, 3/2, 6/5: 126/125)[12] (Starling)

7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27) = (123.5395c, 78.929c, 64.0225c) TE

~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1 as sLLsLmLsLLsL

m = s -> sLLsLsLsLLsL Meantone[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]

12-ET: (1, 1, 1); 15-ET: (2, 1, 0); 16-ET: (1, 1, 2); 19-ET: (2, 1, 1); 27-ET: (3, 2, 1); 31-ET: (3, 2, 2); 46-ET: (5, 3, 2); 50-ET: (5, 3, 3); 58-ET: (6, 4, 3); 77-ET: (8, 5, 4)

(2/1, 3/2, 6/5: 126/125, 196/195)[12]

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) TE

~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1 as sLLsLmLsLLsL

m = s -> sLLsLsLsLLsL Meanpop[12]; L = m -> sLLsLLLsLLsL MODMOS; s = 0 -> LLLsLLLL

12f-ET: (1, 1, 1); 15f-ET: (2, 1, 0); 19-ET: (2, 1, 1); 27-ET: (3, 2, 1); 31-ET: (3, 2, 2); 46-ET: (5, 3, 2); 50-ET: (5, 3, 3); 58-ET: (6, 4, 3); 77-ET: (8, 5, 4)

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

7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54) = (146.6352c, 63.1434c, 27.4197c) TE

~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1 as sLLsLmLsLLsL

m = s -> sLLsLsLsLLsL Meanenneadecal[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Porkypine[8]

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

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) TE

~ 28/27 10/9 6/5 11/9 4/3 7/5 3/2 14/9 5/3 9/5 11/6 2/1 as sLLsLmLsLLsL

m = s -> sLLsLsLsLLsL Meanenneadecal[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]

12-ET: (1, 1, 1); 15-ET: (2, 1, 0); 19-ET: (2, 1, 1); 27e-ET: (3, 2, 1); 34-ET: (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: 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;

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)

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

((2/1, 6/5)[4], 10/9)[8]

4L 3m 1s = (10/9, 27/25, 25/24)

27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1 as MLsLMLML

L=M -> LLsLLLLL Porcupine[8]; M=s -> sLsLsLsL Diminished[8]; L=s -> LsssLsLs Father[8] MODMOS; s=0 -> sLLsLsL Dicot[7]

((2/1, 6/5)[4], 10/9: 100/99)[8] =

4L 3m 1s = (10/9~11/10, 27/25~12/11, 25/24~33/32) = (174.0549c, 146.6353c, 63.1433c)

~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1 as MLsLMLML

((2/1, 6/5)[4], 10/9: 100/99, 144/143)[8]

4L 3m 1s = (10/9~11/10, 27/25~12/11~13/12, 25/24~33/32) = (175.892c, 142.775c, 66.766c)

~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1 as MLsLMLML

((2/1, 6/5)[4], 10/9: 325/324)[8]

4L 3m 1s = (10/9, 27/25~13/12, 25/24)

~ 27/25 6/5 5/4 18/13 3/2 5/3 9/5 2/1 as MLsLMLML

((2/1, 6/5)[4], 10/9)[15]

4L 8m 3s = (16/15, 25/24, 648/625)

25/24 10/9 125/108 6/5 5/4 4/3 25/18 36/25 3/2 8/5 5/3 216/125 48/25 2/1 as mLmsmLmsmLmsmLm

m=s -> sLsssLsssLsssLs Hanson[15]; L = m -> LLLsLLLsLLLsLLL Augmented[15] mod; L=s -> sLsLsLsLsLsLsLs; Porcupine[15]; s=0 -> sLssLssLssLs Diminished[12]

((2/1, 6/5)[4], 10/9: 100/99)[15]

4L 3m 8s = (~16/15, 648/625, 25/24~33/32)

~ 25/24 10/9 55/48 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 72/55 48/25 2/1 as sLsmsLsmsLsmsLs

((2/1, 6/5)[4], 10/9: 100/99, 144/143)[15]

4L 3m 8s = (~16/15, 26/25, 25/24~33/32~27/26) = (109.1256c, 76.00911c, 66.76626c)

~ 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 48/25 2/1 as sLsmsLsmsLsmsLsm

((2/1, 6/5)[4], 10/9: 325/324)[15]

4L 3m 8s = (~16/15, 26/25, 25/24~27/26)

~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 48/25 2/1 as sLsmsLsmsLsmsLsm

((2/1, 6/5)[4], 10/9: 325/324)[22]

15L 4M 3s = (25/24~27/26, 128/125, 676/675) LMLLsLLMLLsLLMLLsLLMLL

~ 25/24 16/15 10/9 15/13 (52/45) 6/5 5/4 32/25 4/3 18/13 (104/75) 13/9 3/2 192/125 8/5 5/3 (208/125) 26/15 65/36 416/225 48/25 2/1

L=M -> LLLLsLLLLLsLLLLLsLLLLL Magic[22] MODMOS; M=s -> LsLLsLLsLLsLLsLLsLLsLL Porcupine[22]; L=s -> sLsssssLsssssLsssssLss; s=0 -> LsLLLLsLLLLsLLLLsLL Hanson[19]

((2/1, 6/5)[4], 10/9: 100/99, 144/143)[22]

15L 4M 3s = (25/24~33/32~27/26, 128/125, 676/675) LMLLsLLMLLsLLMLLsLLMLL

~ 25/24 16/15 10/9 15/13 (52/45) 6/5 5/4 32/25 4/3 11/8 (104/75) 13/9 3/2 192/125 8/5 5/3 (208/125) 26/15 65/36 416/225 48/25 2/1

L=M -> LLLLsLLLLLsLLLLLsLLLLL Magic[22] MODMOS; M=s -> LsLLsLLsLLsLLsLLsLLsLL Porcupine[22]; L=s -> sLsssssLsssssLsssssLss; s=0 -> LsLLLLsLLLLsLLLLsLL Hanson[19]

((2/1, 6/5)[4], 10/9: 100/99, 144/143, 225/224)[22]

15L 4M 3s = (25/24~33/32~27/26~28/27, 128/125~36/35, 169/168) LMLLsLLMLLsLLMLLsLLMLL

~ 25/24 16/15 10/9 15/13 (52/45) 6/5 5/4 32/25 4/3 11/8 (39/28) 13/9 3/2 54/35 8/5 5/3 (117/71) 26/15 65/36 13/7 48/25 2/1

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] MOSMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[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; 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[7]; 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[7]; 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[22]; 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[22]; 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[22]

(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, 7/6)[4], 12/11) Orwellian

MsMsMsML

12/11 7/6 14/11 11/8 3/2 8/5 96/55~26/15 2/1

sM

((2/1, 7/6)[4], 11/10) Guanyin

11/10 7/6 77/60 15/11 3/2 8/5 44/25 2/1