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Gallery of 3-SN scales

Revision as of 08:17, 10 May 2021 by Lhearne (talk | contribs)

See SN scale.

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 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).

(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], Antitonic[4] LsLs

(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

(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)

~ 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)

~ 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):

~ 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 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 1125/1024[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], 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


((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

((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 LsLLLsLLLsLLs August[12], LsLLLLLLLsLL Pajara[12] MODMOS


((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

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

9L 1M 12s = (~81/77, 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 sLssLsLsLsLsLsLsLssLsL Pajara[22] MODMOS, sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS

((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


((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

((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


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

10L 2M 5s = (135/128~21/20, 256/243, 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


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

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

~ 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

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