Gallery of 3-SN scales: Difference between revisions

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5/4 3/2 15/8 2/1 as LMLs
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] ====
==== (2/1, 3/2, 5/4)[7] ====
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16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
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]




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==== (2/1, 3/2, 5/4)[10] ====
==== (2/1, 3/2, 5/4)[10] ====
2L 1M 7s = (1125/1024, 16/15, 135/128)
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


16/15 75/64 5/4 4/3 10/7 3/2 8/5 128/75 15/8 as sLssMssLss
tempers to sLsssssLss Srutal[10] MODMOS, LsLLsLLsLL Dicot[10]




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


2L 1M 7s = (35/32~49/45, 16/15~15/14, 135/128~21/20)
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
~ 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]
(2/1, 3/2, 5/4: 225/224, 441/440)[10]


2L 7m 1s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20~22/21)  
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
~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as sLssMssLss
Line 49: Line 65:


~ 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
~ 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]




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~ 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
~ 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] ====
==== (2/1, 3/2, 5/4: 225/224, 441/440)[31] ====
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as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm
as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm
tempers to sLssLsssLssLssLsLssLssLsssLssLs Meantone[31] MODMOS


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


==== ((2/1, 5/4)[3], 16/15)[6] ====
1L 2M 3s = (6/5, 75/64, 16/15)
1L 2M 3s = (6/5, 75/64, 16/15)


75/64 5/4 3/2 8/5 15/8 2/1 is MsLsMs
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]  
((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) ==


== (2/1, 3/2, 7/6) ==
==== ((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
 
 
((2/1, 3/2)[5], 16/15: 225/224)[29]

Revision as of 08:14, 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


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

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