Gallery of 3-SN scales: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Lhearne (talk | contribs)
No edit summary
Lhearne (talk | contribs)
m Changed heading levels
Line 11: Line 11:
== 2.3.5: Marvel ==
== 2.3.5: Marvel ==


== (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 20: Line 20:
tempers to LLLs Dicot[4], LsLs Antitonic[4]
tempers to LLLs Dicot[4], LsLs Antitonic[4]


=== (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 27: Line 27:
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)


Line 34: Line 34:
tempers to sLsLsLs Dicot[7], sLsssLs Pelogic[7], LLLsLLL Enipucrop[7]
tempers to sLsLsLs Dicot[7], sLsssLs Pelogic[7], LLLsLLL Enipucrop[7]


=== (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 41: Line 41:
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 48: Line 48:
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) = (150.229c, 116.7669c, 82.9601c)  
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
~ 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 65: Line 65:
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 72: Line 72:
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) = (82.9601c, 67.2689c, 33.8068c) TOP
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


Line 79: Line 79:
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) = (49.1533c, 33.8068c, 33.4621c) TOP  
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TOP  


Line 88: Line 88:
tempers to sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS, LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS, sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS
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) ===


=== ((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)


Line 97: Line 97:
tempers to LsLsLs Augmented[6], ssLsss Enipucrop[6], LsssLs Antitonic[6] MODMOS
tempers to LsLsLs Augmented[6], ssLsss Enipucrop[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 109: Line 109:
tempers to sLssLssLs Augmented[9], ssssLssss Negri[9], sLsssssLs Mavila[9] MODMOS
tempers to sLssLssLs Augmented[9], ssssLssss Negri[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)


Line 116: Line 116:
tempers to sLssLssLs August[9], ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
tempers to sLssLssLs August[9], ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS


==== '''((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)


Line 123: Line 123:
tempers to sLssLssLs August[9] , ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
tempers to sLssLssLs August[9] , ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS


=== ((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)


Line 130: Line 130:
tempers to LsLLLLLLLsLL Pajara[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]
tempers to LsLLLLLLLsLL Pajara[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]


==== '''((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)


Line 137: Line 137:
tempers to LsLLLLLLLsLL Pajarous[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]
tempers to LsLLLLLLLsLL Pajarous[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]


=== ((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 = (~22/21, 36/35~33/32, 49/48~45/44~56/55)
9L 1m 12s = (~22/21, 36/35~33/32, 49/48~45/44~56/55)


Line 144: Line 144:
tempers to sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, sLssLsLsLsLsLsLsLssLsL Pajarous[22], MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]
tempers to sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, sLssLsLsLsLsLsLsLssLsL Pajarous[22], MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]


== ((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)


Line 153: Line 153:
tempers to ssLsssLsss Srutal[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS, LsLsLsLsLs Blackwood[10]
tempers to ssLsssLsss Srutal[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS, LsLsLsLsLs Blackwood[10]


==== '''((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)


Line 160: Line 160:
tempers to ssLsssLsss Pajara[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS
tempers to ssLsssLsss Pajara[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS


===='''((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10]'''====
====='''((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
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TOP


Line 167: Line 167:
tempers to ssLsssLsss Pajaric[10] MODMOS
tempers to ssLsssLsss Pajaric[10] MODMOS


=== ((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)


Line 174: Line 174:
tempers to LsLLLsLLsLLsLLLsL Helmholtz[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
tempers to LsLLLsLLsLLsLLLsL Helmholtz[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS


==== '''((2/1, 3/2)[5], 16/15: 225/224)[17]''' ====
====='''((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)
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63)


Line 181: Line 181:
tempers to LsLLLsLLsLLsLLLsL Garibaldi[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
tempers to LsLLLsLLsLLsLLLsL Garibaldi[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS


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


Line 188: Line 188:
tempers to LsLLLsLLsLLsLLLsL Andromeda[17]
tempers to LsLLLsLLsLLsLLLsL Andromeda[17]


=== (2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] ===
==== (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
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


Line 195: Line 195:
tempers to  ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS, sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29], LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS
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] ===
==== (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  
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  


Line 202: Line 202:
tempers to LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS, LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31]
tempers to LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS, LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31]


=== (2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] ===
==== (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
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TOP


Line 211: Line 211:
== 2.3.5: Starling ==
== 2.3.5: Starling ==


== (2/1, 3/2, 6/5) ==
=== (2/1, 3/2, 6/5) ===


=== (2/1, 3/2, 6/5)[4] ===
==== (2/1, 3/2, 6/5)[4] ====
1L 2M 1s = (5/4, 6/5, 10/9)
1L 2M 1s = (5/4, 6/5, 10/9)


Line 222: Line 222:
tempers to LLLs Dicot[4], sLss Bug[4], LsLs Antitonic[4]
tempers to LLLs Dicot[4], sLss Bug[4], LsLs Antitonic[4]


=== (2/1, 3/2, 6/5)[7] ===
==== (2/1, 3/2, 6/5)[7] ====
1L 4M 2S = (9/8, 10/9, 27/25)
1L 4M 2S = (9/8, 10/9, 27/25)


Line 231: Line 231:
tempers to LsLLLsL Meantone[7], sssLsss Porcupine[7], LsLsLsL Dicot[7]
tempers to LsLLLsL Meantone[7], sssLsss Porcupine[7], LsLsLsL Dicot[7]


=== (2/1, 3/2, 6/5)[12] ===
==== (2/1, 3/2, 6/5)[12] ====
7L 1m 4s = (27/25, 25/24, 250/243)
7L 1m 4s = (27/25, 25/24, 250/243)


Line 240: Line 240:
tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS, LLLLLsLLLLLL Ripple[12]
tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS, LLLLLsLLLLLL Ripple[12]


==== (2/1, 3/2, 6/5: 126/125)[12] ====
===== (2/1, 3/2, 6/5: 126/125)[12] =====
7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27)
7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27)


Line 249: Line 249:
tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS
tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS


==== (2/1, 3/2, 6/5: 100/99)[12] ====
===== (2/1, 3/2, 6/5: 100/99)[12] =====
7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54)
7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54)


Line 258: Line 258:
tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS
tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS


==== (2/1, 3/2, 6/5: 56/55, 100/99)[12] ====
===== (2/1, 3/2, 6/5: 56/55, 100/99)[12] =====
7L 1m 4s = (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)
7L 1m 4s = (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)


Line 269: Line 269:
== 2.5.9: Starling ==
== 2.5.9: Starling ==


== ((2/1, 5/4)[3], 9/8) ==
=== ((2/1, 5/4)[3], 9/8) ===


=== ((2/1, 5/4)[3], 9/8)[6] ===
==== ((2/1, 5/4)[3], 9/8)[6] ====
1L 3M 2s = (256/225, 9/8, 10/9)  
1L 3M 2s = (256/225, 9/8, 10/9)  


Line 280: Line 280:
tempers to sLLLsL, ssLsss, sLsLsL
tempers to sLLLsL, ssLsss, sLsLsL


==== ((2/1, 5/4)[3], 9/8: 225/224)[6] ====
===== ((2/1, 5/4)[3], 9/8: 225/224)[6] =====
1L 3M 2s = (~8/7, ~9/8, ~10/9)  
1L 3M 2s = (~8/7, ~9/8, ~10/9)  


Line 291: Line 291:
== 2.5.9: Marvel ==
== 2.5.9: Marvel ==


== ((2/1, 5/4)[3], 10/9) ==
=== ((2/1, 5/4)[3], 10/9) ===


=== ((2/1, 5/4)[3], 10/9)[6] ===
==== ((2/1, 5/4)[3], 10/9)[6] ====
1L 2m 3s= (144/125, 9/8, 10/9)  
1L 2m 3s= (144/125, 9/8, 10/9)  


Line 302: Line 302:
tempers to ssLsss, LsLsLs, sLLLsL
tempers to ssLsss, LsLsLs, sLLLsL


==== ((2/1, 5/4)[3], 10/9: 126/125)[6] ====
===== ((2/1, 5/4)[3], 10/9: 126/125)[6] =====
1L 2m 3s= (~8/7, ~9/8, ~10/9)  
1L 2m 3s= (~8/7, ~9/8, ~10/9)  



Revision as of 17:35, 20 May 2021

See SN scale and Rank-3 scales.

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). Germinations are grouped by their subgroup, and within that, by the first comma tempered out in scales evolved from the germination.

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 (scales of odd cardinality) or in the even-symmetric mode: the mode symmetric without 2/1 (scales of even cardinality).

2.3.5: Marvel

(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], LsLs Antitonic[4]

(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 LsLLLLLLLsLL Pajara[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[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)

~ 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 LsLLLLLLLsLL Pajarous[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]

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

9L 1m 12s = (~22/21, 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 sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, sLssLsLsLsLsLsLsLssLsL Pajarous[22], MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]

((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 LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs

tempers to LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS, LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS

2.3.5: Starling

(2/1, 3/2, 6/5)

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

1L 2M 1s = (5/4, 6/5, 10/9)

6/5 3/2 9/5 2/1

as MLMs

tempers to LLLs Dicot[4], sLss Bug[4], LsLs Antitonic[4]

(2/1, 3/2, 6/5)[7]

1L 4M 2S = (9/8, 10/9, 27/25)

10/9 6/5 4/3 3/2 5/3 9/5 2/1

as MsMLMsM

tempers to LsLLLsL Meantone[7], sssLsss Porcupine[7], LsLsLsL Dicot[7]

(2/1, 3/2, 6/5)[12]

7L 1m 4s = (27/25, 25/24, 250/243)

250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1

as sLLsLmLsLLsL

tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS, LLLLLsLLLLLL Ripple[12]

(2/1, 3/2, 6/5: 126/125)[12]

7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27)

~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1

as sLLsLmLsLLsL

tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS

(2/1, 3/2, 6/5: 100/99)[12]

7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54)

~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1

as sLLsLmLsLLsL

tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS

(2/1, 3/2, 6/5: 56/55, 100/99)[12]

7L 1m 4s = (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)

~ 28/27 10/9 6/5 11/9 4/3 7/5 3/2 14/9 5/3 9/5 11/6 2/1

as sLLsLmLsLLsL

tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS

2.5.9: Starling

((2/1, 5/4)[3], 9/8)

((2/1, 5/4)[3], 9/8)[6]

1L 3M 2s = (256/225, 9/8, 10/9)

10/9 5/4 64/45 8/5 16/9 2/1

as sMLMsM

tempers to sLLLsL, ssLsss, sLsLsL

((2/1, 5/4)[3], 9/8: 225/224)[6]

1L 3M 2s = (~8/7, ~9/8, ~10/9)

~ 10/9 5/4 10/7 8/5 16/9 2/1

as sMLMsM

tempers to sLLLsL, ssLsss, sLsLsL

2.5.9: Marvel

((2/1, 5/4)[3], 10/9)

((2/1, 5/4)[3], 10/9)[6]

1L 2m 3s= (144/125, 9/8, 10/9)

9/8 5/4 36/25 8/5 9/5 2/1

as msLsms

tempers to ssLsss, LsLsLs, sLLLsL

((2/1, 5/4)[3], 10/9: 126/125)[6]

1L 2m 3s= (~8/7, ~9/8, ~10/9)

~ 9/8 5/4 10/7 8/5 9/5 2/1

as msLsms

tempers to ssLsss, LsLsLs, sLLLsL