Gallery of 3-SN scales: Difference between revisions

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See [[SN scale]].
See [[SN 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).


Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.
Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.
Line 5: Line 7:
Tempered scales are shown in JI as their simplest symmetric pre-image.
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).
Scales are written in JI and as step patterns in their symmetric mode, for scales of odd cardinality, or in the mode symmetric without 2/1 for scales of even cardinality.


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

Revision as of 14:53, 10 May 2021

See SN 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).

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, for scales of odd cardinality, or in the mode symmetric without 2/1 for scales of even cardinality.

(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

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 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

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

((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 Pajarous[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

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 sLssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssL

tempers to sLssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssL Marvolo[72] MODMOS, sLssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssL Miracle[72] MODMOS,

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