Gallery of 3-SN scales: Difference between revisions

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


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


Line 16: Line 16:
tempers to LLLs Dicot[4], Antitonic[4] LsLs
tempers to LLLs Dicot[4], Antitonic[4] LsLs


==== (2/1, 3/2, 5/4)[7] ====
=== (2/1, 3/2, 5/4)[7] ===
2L 1M 4s = (75/64, 9/8, 16/15)
2L 1M 4s = (75/64, 9/8, 16/15)


Line 23: Line 23:
tempers to sLsLsLs Dicot[7], sLsssLs Mavila[7], LLLsLLL Enipucrop[7]
tempers to sLsLsLs Dicot[7], sLsssLs Mavila[7], LLLsLLL Enipucrop[7]


'''(2/1, 3/2, 5/4: 225/224)[7]'''
==== '''(2/1, 3/2, 5/4: 225/224)[7]''' ====
 
2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14)
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
~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs


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


Line 36: Line 35:
tempers to sLsssssLss Srutal[10] MODMOS, LsLLsLLsLL Dicot[10]
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 7M 1s = (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)


Line 44: Line 42:
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]''' ====
 
2L 1M 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20)
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, 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


==== (2/1, 3/2, 5/4: 225/224)[19] ====
=== (2/1, 3/2, 5/4: 225/224)[19] ===
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49)
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49)


Line 63: Line 59:
tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]


'''(2/1, 3/2, 5/4: 225/224, 385/384)[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)
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54)


Line 71: Line 66:
tempers to LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
tempers to LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]


'''(2/1, 3/2, 5/4: 225/224, 441/440)[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)
10L 2M 7s = (135/128~21/20~22/21, 25/24~28/27, 64/63~50/49~45/44~56/55)


Line 79: Line 73:
tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negroni[19]
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] ===
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54):  
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54):  


Line 90: Line 84:
== ((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)


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tempers to LsLsLs Augmented[6], ssLsss 1125/1024[6], LsssLs Antitonic[6] MODMOS\
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)  
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
~ 7/6 5/4 3/2 8/5 15/8 2/1 as MsLsMs


==== ((2/1, 5/4)[3], 16/15)[9] ====
=== ((2/1, 5/4)[3], 16/15)[9] ===
1L 2M 6s = (9/8, 1125/1024, 16/15)
1L 2M 6s = (9/8, 1125/1024, 16/15)


Line 110: Line 103:
tempers to sLssLssLs Augmented[9], sLsssssLs Mavila[9] MODMOS
tempers to sLssLssLs Augmented[9], sLsssssLs Mavila[9] MODMOS


'''((2/1, 5/4)[3], 16/15: 225/224)[9]'''
==== '''((2/1, 5/4)[3], 16/15: 225/224)[9]''' ====
 
1L 2M 6s = (~9/8, 35/32~49/45, 16/15~15/14)
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
~ 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]'''
==== '''((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)
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
~ 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] ====
=== ((2/1, 5/4)[3], 16/15: 225/224)[12] ===
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48)
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48)


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


'''((2/1, 5/4)[3], 16/15: 225/224, 385/384)[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)
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
~ 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] ====
=== ((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)
9L 1M 12s = (~81/77, 36/35~33/32, 49/48~45/44~56/55)


Line 144: Line 134:
== ((2/1, 3/2)[5], 16/15) ==
== ((2/1, 3/2)[5], 16/15) ==


==== ((2/1, 3/2)[5], 16/15)[10] ====
=== ((2/1, 3/2)[5], 16/15)[10] ===
2L 5m 3s = (10/9, 16/15, 135/128)
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
~ 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]'''
==== '''((2/1, 3/2)[5], 16/15: 225/224)[10]''' ====
 
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20)
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
~ 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


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

Revision as of 08:25, 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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