Gallery of 3-SN scales: Difference between revisions

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~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as mLmmsmmLmm
~ 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],
tempers to sLsssssLss Pajara[10] MODMOS, LsLLsLLsLL Dicot[10]
 


(2/1, 3/2, 5/4: 225/224, 385/384)[10]
(2/1, 3/2, 5/4: 225/224, 385/384)[10]
Line 52: Line 51:


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




Line 67: Line 65:


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




Line 76: Line 75:


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




Line 152: Line 152:


tempers to sLssLsLsLsLsLsLsLssLsL Pajara[22] MODMOS, sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS
tempers to sLssLsLsLsLsLsLsLssLsL Pajara[22] MODMOS, sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS
== ((2/1, 3/2)[5], 16/15) ==
== ((2/1, 3/2)[5], 16/15) ==


Line 158: Line 159:


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




Line 166: Line 168:
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
~ 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] ====
((2/1, 3/2)[5], 16/15)[17]
 
10L 2M 5s = (135/128, 256/243, 2048/2025)
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
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




Line 179: Line 180:


~ 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
~ 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




Line 186: Line 188:


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

Revision as of 08:17, 10 May 2021

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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