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Gallery of 3-SN scales: Difference between revisions

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→2.3.5; Hemifamity: Changed 'tempers to'; added tempering steps to 0
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→((2/1, 5/4)[3], 9/8): changed 'tempers to' to add when steps go to zero, added Category Rank-3 scales on page
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9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs
9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs


tempers to LsLLLs, sssLss, LsLsLs
L = M -> LsLLLs; M = s -> sssLss; L =s -> LsLsLs


===== [[SNS ((2/1, 5/4)-3, 9/8: 225/224)-6|((2/1, 5/4)[3], 9/8: 225/224)[6]]] =====
=====[[SNS ((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, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c)  
1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c)  


~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs


tempers to LsLLLs, sssLss, LsLsLs
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs


===== [[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-6|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6]]] =====
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-6|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6]]]=====
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c)  
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c)  


~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs


tempers to LsLLLs, sssLss, LsLsLs
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs


==== [[SNS ((2/1, 5/4)-3, 9/8)-10|((2/1, 5/4)[3], 9/8)[10]]] ====
====[[SNS ((2/1, 5/4)-3, 9/8)-10|((2/1, 5/4)[3], 9/8)[10]]]====
6L 1M 3s = (10/9, 128/125, 81/80)  
6L 1M 3s = (10/9, 128/125, 81/80)  


10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,  
10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,  


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL; L = 0 -> ssms (i.e., Elimination MOS scale)


===== [[SNS ((2/1, 5/4)-3, 9/8: 225/224)-10|((2/1, 5/4)[3], 9/8: 225/224)[10]]] =====
===== [[SNS ((2/1, 5/4)-3, 9/8: 225/224)-10|((2/1, 5/4)[3], 9/8: 225/224)[10]]]=====
6L 1M 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE  
6L 1M 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE  


~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
m = s -> LsLLsLsLsLMODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL; L = 0 -> ssms (i.e., Elimination MOS scale)


===== [[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-10|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10]]] =====
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-10|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10]]]=====
6L 1M 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE  
6L 1M 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE  


~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL; L = 0 -> ssms (i.e., Elimination MOS scale)


==== [[SNS ((2/1, 5/4)-3, 9/8)-17|((2/1, 5/4)[3], 9/8)[17]]] ====
====[[SNS ((2/1, 5/4)-3, 9/8)-17|((2/1, 5/4)[3], 9/8)[17]]]====
6L 10m 1s = (800/729, 81/80, 2048/2025)  
6L 10m 1s = (800/729, 81/80, 2048/2025)  


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tempers to sLsLssLsssLssLsLs MODMOS, LLLLLLLLsLLLLLLLL, sLsLssLsLsLssLsLs
tempers to sLsLssLsssLssLsLs MODMOS, LLLLLLLLsLLLLLLLL, sLsLssLsLsLssLsLs


===== [[SNS ((2/1, 5/4)-3, 9/8: 225/224)-17|((2/1, 5/4)[3], 9/8: 225/224)[17]]] =====
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-17|((2/1, 5/4)[3], 9/8: 225/224)[17]]]=====
6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE  
6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE  


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tempers to sLsLssLsssLssLsLs MODMOS, sLsLssLsLsLssLsLs, LLLLLLLLsLLLLLLLL
tempers to sLsLssLsssLssLsLs MODMOS, sLsLssLsLsLssLsLs, LLLLLLLLsLLLLLLLL


===== [[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-17|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17]]] =====
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-17|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17]]] =====
6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE  
6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE  


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tempers to sLsLssLsssLssLsLs Machine[17] MODMOS, LLLLLLLLsLLLLLLLL, sLsLssLsLsLssLsLs
tempers to sLsLssLsssLssLsLs Machine[17] MODMOS, LLLLLLLLsLLLLLLLL, sLsLssLsLsLssLsLs


== 2.5.9; Starling ==
==2.5.9; Starling ==


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


==== [[SNS ((2/1, 5/4)-3, 10/9)-6|((2/1, 5/4)[3], 10/9)[6]]] ====
==== [[SNS ((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)  


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tempers to ssLsss, LsLsLs, sLLLsL
tempers to ssLsss, LsLsLs, sLLLsL


===== [[SNS ((2/1, 5/4)-3, 10/9: 126/125)-6|((2/1, 5/4)[3], 10/9: 126/125)[6]]] =====
=====[[SNS ((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, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c)  
1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c)  


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tempers to ssLsss, LsLsLs, sLLLsL
tempers to ssLsss, LsLsLs, sLLLsL
==== [[SNS ((2/1, 5/4)-3, 10/9)-9|((2/1, 5/4)[3], 10/9)[9]]] ====
====[[SNS ((2/1, 5/4)-3, 10/9)-9|((2/1, 5/4)[3], 10/9)[9]]]====
6L 1m 2s = (10/9, 648/625, 81/80)  
6L 1m 2s = (10/9, 648/625, 81/80)  


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tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL
tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL


===== [[SNS ((2/1, 5/4)-3, 10/9: 126/125)-9|((2/1, 5/4)[3], 10/9: 126/125)[9]]] =====
=====[[SNS ((2/1, 5/4)-3, 10/9: 126/125)-9|((2/1, 5/4)[3], 10/9: 126/125)[9]]]=====
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c)  
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c)  


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tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL
tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL


==== ((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16] ====
====((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16]====
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55)
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55)


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tempers to sLssLsLsssLsLssL, sLssLsLsLsLsLssL, LLLLLLLLsLLLLLLL
tempers to sLssLsLsssLsLssL, sLssLsLsLsLsLssL, LLLLLLLLsLLLLLLL


===== ((2/1, 5/4)[3], 10/9: 91/90, 126/125, 325/324)[16] =====
=====((2/1, 5/4)[3], 10/9: 91/90, 126/125, 325/324)[16]=====
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143)
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143)


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[[Category:Scales]]
[[Category:Scales]]
[[Category:Step-Nested Scales]]
[[Category:Step-Nested Scales]]
[[Category:Rank-3 scales]]
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"