Gallery of 3-SN scales

See SN scale and Rank-3 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 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)

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

2L 1M 1s = (5/4, 6/5, 16/15)

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

tempers to LLLs Dicot[4], LsLs Antitonic[4]

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

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

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

tempers to sLsLsLs Dicot[7], sLsssLs Mavila[7], LLLsLLL Enipucrop[7]

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

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

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

tempers to sLsLsLs Dicot[7], sLsssLs Pelogic[7], LLLsLLL Enipucrop[7]

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

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

16/15 75/64 5/4 4/3 10/7 3/2 8/5 128/75 15/8 as mLmmsmmLmm

tempers to sLsssssLss Srutal[10] MODMOS, LsLLsLLsLL Dicot[10],

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

2L 7M 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20)

~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as mLmmsmmLmm

tempers to sLsssssLss Pajara[10] MODMOS, LsLLsLLsLL Dicot[10]

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

2L 1M 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20)

~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as sLssMssLss

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

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

~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as sLssMssLss

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

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

~ 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

tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]

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

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

~ 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

tempers to LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]

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

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) TOP

~ 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

tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negroni[19]

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

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

~ 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

tempers to sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS, LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS, sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS

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

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

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

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

tempers to LsLsLs Augmented[6], ssLsss Enipucrop[6], LsssLs Antitonic[6] MODMOS

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

1L 2M 3s = (6/5, 75/64~7/6, 16/15~14/13)

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

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

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

tempers to sLssLssLs Augmented[9], ssssLssss Negri[9], sLsssssLs Mavila[9] MODMOS

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

1L 2M 6s = (~9/8, 35/32~49/45, 16/15~15/14)

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

tempers to sLssLssLs August[9], ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS

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

1L 2M 6s = (~9/8, 35/32~49/45~12/11, 16/15~15/14)

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

tempers to sLssLssLs August[9] , ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS

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

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

~ 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

tempers to LsLLLLLLLsLL Pajara[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]

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

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

~ 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

tempers to LsLLLLLLLsLL Pajarous[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]

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

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

~ 49/48 16/15 12/11 10/9 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as sLssLsLsLsmsLsLsLssLsL

tempers to sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, sLssLsLsLsLsLsLsLssLsL Pajarous[22], MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]

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

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

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

tempers to ssLsssLsss Srutal[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS, LsLsLsLsLs Blackwood[10]

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

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

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

tempers to ssLsssLsss Pajara[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS

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

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

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

tempers to ssLsssLsss Pajaric[10] MODMOS

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

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

tempers to LsLLLsLLsLLsLLLsL Helmholtz[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS

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

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

~ 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 LsLmLsLLsLLsLmLsL

tempers to LsLLLsLLsLLsLLLsL Garibaldi[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS

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

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) TOP

~ 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

tempers to LsLLLsLLsLLsLLLsL Andromeda[17]

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

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) TOP

~ 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

tempers to ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS, sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29], LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS

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

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) TOP

~ 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

tempers to LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS, LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31]

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

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

as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs

tempers to LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS, LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS

2.3.5 Starling

(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

tempers to LLLs Dicot[4], sLss Bug[4], 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

tempers to LsLLLsL Meantone[7], sssLsss Porcupine[7], LsLsLsL Dicot[7]

(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

tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS, LLLLLsLLLLLL Ripple[12]

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

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

~ 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

tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS

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

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

~ 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

tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS

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

7L 1m 4s = (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)

~ 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

tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS

2.5.9 Starling

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

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

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

10/9 5/4 64/45 8/5 16/9 2/1

as sMLMsM

tempers to sLLLsL, ssLsss, sLsLsL

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

1L 3M 2s = (~8/7, ~9/8, ~10/9)

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

as sMLMsM

tempers to sLLLsL, ssLsss, sLsLsL

2.5.9 Marvel

((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

tempers to ssLsss, LsLsLs, sLLLsL

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

1L 2m 3s= (~8/7, ~9/8, ~10/9)

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

as msLsms

tempers to ssLsss, LsLsLs, sLLLsL