Gallery of 3-SN scales
See SN scale and Rank 3 scale.
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 (scales of even cardinality)
2.3.5; Marvel
(2/1, 3/2, 5/4)
2L 1M 1s = (5/4, 6/5, 16/15)
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]
2L 1M 4s = (75/64, 9/8, 16/15)
16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
L = M -> sLsLsLs Dicot[7]; M = s -> sLsssLs Mavila[7]; L = s -> LLLsLLL Enipucrop[7]; s = 0 -> LsL Father[3]
2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14) = (267.8165c, 200.9152c, 116.0124c) TE
~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
L = M -> sLsLsLs Dicot[7]; M = s -> sLsssLs Pelogic[7], L = s -> LLLsLLL Enipucrop[7]
2L 7m 1s = (1125/1024, 16/15, 135/128)
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 -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Mavila[9]; ; m = 0 -> LsL Father[3]
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 -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Pelogic[9]
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
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
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]
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)
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)
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)
1L 2M 3s = (6/5, 75/64, 16/15)
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]
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
1L 2M 6s = (9/8, 1125/1024, 16/15)
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]
1L 2M 6s = (~9/8, 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
1L 2M 6s = (~9/8, 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], L = s -> sLsssssLs Pelogic[9] MODMOS
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 -> LsLLLsLLLsLLs August[12]; L = s -> sssssLssssss Passion[12];
s = 0 -> LLLLsLLLLL Negri[10]; M = 0 -> LsLLLLLLsLL Pelogic[11] MODMOS
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]
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]; L = s -> MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22];
s = 0 -> LLLLsLLLLL Negri[10]
((2/1, 3/2)[5], 16/15)
2L 5m 3s = (10/9, 16/15, 135/128)
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 Srutal[10] MODMOS; L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10]; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
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 Pajara[10] MODMOS; L = m -> sLLLsLLLsL Dicot[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
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 Pajaric[10] MODMOS
10L 2M 5s = (135/128, 256/243, 2048/2025)
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]
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)
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)
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)
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
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, Luyoyo, and Ragismic
(2/1, 3/2, 6/5)
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]
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]
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]
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 Porcupine[7], L = m -> LsLLLsL Meanenneadecal[7], L = s -> LsLsLsL Flat[7]
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]
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]
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]
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
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]
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]
7L 1m 4s = (~27/25, ~25/24, 250/243~36/35) = (133.4115c, 70.5569c, 48.8911c)
~ 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]
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c)
~ 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]
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80)
~ 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
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.8546c, 27.2253c, 21.6658c)
~ 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
2.3.5; Hemifamity
((2/1, 3/2)[5], 10/9)
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]
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
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
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]
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]
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
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)
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]
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]
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
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)
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
1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c)
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c)
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
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
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
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
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
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
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)
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
1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c)
~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms
m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
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
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c)
~ 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
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55) = (163.6623c, 24.4284c, 21.4103c)
~ 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
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)
~ 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 Orwellian
(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)[12] (Orwellian)
9L 1M 2s = (~10/9, 54/49~35/32, 49/48~36/35)
~ 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 Archy[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Semaphore[5]
(2/1, 3/2, 7/6: 99/98, 385/384)[12] (Orwellian)
9L 1M 2s = (~10/9, 54/49~35/32~12/11, 49/48~36/35~33/32)
~ 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)
9L 1M 2s = (~10/9, 54/49~35/32~11/10, 49/48~36/35~45/44)
~ 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