Gallery of 3-SN scales: Difference between revisions
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See [[SN scale]] and [[Rank-3 scale]]. | See [[SN scale]] and [[Rank-3 scale]]. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+Rank-2 temperings (mode -3) | |+Rank-2 temperings (mode -3) | ||
!Equivalence | ! Equivalence | ||
!Step pattern | ! Step pattern | ||
!Scale | ! Scale | ||
!Comma list | ! Comma list | ||
|- | |- | ||
|m = s | | m = s | ||
|[[7L 5s|sLLsLsLsLLsL]] | | [[7L 5s|sLLsLsLsLLsL]] | ||
|[[ | | [[Meantone]][12] | ||
|81/80 | | 81/80 | ||
|- | |- | ||
|L = m | | L = m | ||
|sLLsLLLsLLsL | | sLLsLLLsLLsL | ||
|[[ | | [[Diminished]][12] MODMOS | ||
|648/625 | | 648/625 | ||
|- | |- | ||
|L = s | | L = s | ||
|[[11L 1s|LLLLLsLLLLLL]] | | [[11L 1s|LLLLLsLLLLLL]] | ||
|[[ | | [[Ripple]][12] | ||
|6561/6250 | | 6561/6250 | ||
|- | |- | ||
|L - m = m - s | | L - m = m - s | ||
|dLLdLsLdLLdL | | dLLdLsLdLLdL | ||
|[[ | | [[Augmented]][12] modmos | ||
|128/125 | | 128/125 | ||
|- | |- | ||
|s = 0 | | s = 0 | ||
|[[7L 1s|LLLsLLLL]] | | [[7L 1s|LLLsLLLL]] | ||
|[[ | | [[Porcupine]][8] | ||
|250/243 | | 250/243 | ||
|} | |} | ||
=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]===== | =====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]===== | ||
{| class="wikitable" | {| class="wikitable" | ||
Line 3,803: | Line 3,802: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Rank-2 temperings (mode -3) | |+Rank-2 temperings (mode -3) | ||
!Equivalence | ! Equivalence | ||
!Step pattern | ! Step pattern | ||
!Scale | ! Scale | ||
!Comma list | ! Comma list | ||
|- | |- | ||
|m = s | | m = s | ||
|[[7L 5s|sLLsLsLsLLsL]] | | [[7L 5s|sLLsLsLsLLsL]] | ||
|[[Meanenneadecal]][12] or [[ | | [[Meanenneadecal]][12] or [[Flattone]][12] | ||
|45/44, 81/80 | | 45/44, 81/80 | ||
|- | |- | ||
|L = m | | L = m | ||
|sLLsLLLsLLsL | | sLLsLLLsLLsL | ||
|[[ | | [[Diminished]][12] modmos | ||
|100/99, 128/121 | | 100/99, 128/121 | ||
|- | |- | ||
|L - m = m - s | | L - m = m - s | ||
|dLLdLsLdLLdL | | dLLdLsLdLLdL | ||
|[[ | | [[Augene]][12] modmos | ||
|100/99, 128/125 | | 100/99, 128/125 | ||
|- | |- | ||
|s = 0 | | s = 0 | ||
|[[7L 1s|LLLsLLLL]] | | [[7L 1s|LLLsLLLL]] | ||
|[[Porcupine | | [[Porcupine]][8] | ||
|55/54, 100/99 | | 55/54, 100/99 | ||
|} | |} | ||
Line 4,592: | Line 4,591: | ||
46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11) | 46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11) | ||
===(2/1, 3/2, 100/81)=== | ==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] == | ||
====(2/1, 3/2, 100/81)[7]==== | ===((2/1, 3/2)[5], 10/9)=== | ||
=====(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)===== | ====[[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]]==== | ||
{| class="wikitable" | 5L 2M 3s = (10/9, 16/15, 81/80) | ||
!Step signature | |||
!Steps in JI | 81/80 9/8 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1 as sLMLsLMLsL | ||
!Step sizes in cents | |||
|- | L = M -> sLLLsLLLsL Dicot[10] MODMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS; | ||
|2L 1m 4s | |||
|(2500/2187~8/7, ~9/8, ~27/25) | L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS | ||
|(231.1884c, 203.974c, 133.4123c) | |||
|} | s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8] | ||
{| class="wikitable" | ====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)]]==== | ||
!Mode number | 5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE | ||
!Mode in JI | |||
!Step pattern | ~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs | ||
![[Mode height]] | |||
|- | m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; | ||
| -3 | |||
|~ 9/8 175/144 25/18 3/2 81/50 50/27 2/1 | L - m = m - s -> Garibaldi[17]; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs | ||
|msLssLs | =====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)]]===== | ||
| 0.0158 | 5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE | ||
|- | |||
| -2 | ~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs | ||
|~ 27/25 175/144 21/16 3/2 81/50 7/4 2/1 | |||
|smsLssL | m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Arnold[7]; m = 0 -> sLssLssLssLssLs | ||
| -0.0211 | ====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-24|((2/1, 3/2)[5], 10/9: 5120/5103)[24] (Hemifamity)]]==== | ||
|- | 5L 2m 17s = (~175/162, ~28/27, 81/80~64/63) = (132.1305c, 61.3411c, 24.4931c) TE | ||
| -1 | |||
|~ 8/7 100/81 25/18 3/2 12/7 50/27 2/1 | ~ 64/63 35/32 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 35/24 40/27 3/2 32/21 105/64 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss | ||
|LsmsLss | |||
| 0.037 | m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7] | ||
|- | =====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-24|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24] (Akea)]]===== | ||
| 0 | 5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE | ||
|~ 27/25 100/81 4/3 3/2 81/50 50/27 2/1 | |||
|sLsmsLs | ~ 64/63 12/11 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 16/11 40/27 3/2 32/21 18/11 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss | ||
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Arnold[7] | |||
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-31|((2/1, 3/2)[5], 10/9: 5120/5103)[31] (Hemifamity)]]==== | |||
5L 2m 24s = (~1225/1152, ~49/48, 81/80~64/63) = (107.6374c, 36.848c, 24.4931c) TE | |||
~ 64/63 36/35 35/32 10/9 9/8 8/7 7/6 32/27 6/5 128/105 35/27 21/16 4/3 27/20 48/35 35/24 40/27 3/2 32/21 54/35 105/64 5/3 27/16 12/7 7/4 16/9 9/5 64/35 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss | |||
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL; | |||
s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS | |||
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-31|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31] (Akea)]]===== | |||
5L 2m 24s = (~35/33, 49/48~56/55, 81/80~64/63~55/54) = (100.7664c, 33.3269c, 26.2356c) TE | |||
~ 64/63 36/35 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 35/27 21/16 4/3 27/20 11/8 16/11 40/27 3/2 32/21 54/35 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss | |||
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL; | |||
s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss | |||
===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) === | |||
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)]]==== | |||
5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE | |||
~ 64/63 15/14 243/224 9/8 8/7 32/27 6/5 81/64 9/7 4/3 27/20 10/7 81/56 3/2 32/21 45/28 80/49 27/16 12/7 16/9 9/5 243/128 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM | |||
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12] | |||
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-24|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24] (Pele)]]===== | |||
5L 7M 12s = (135/128~35/33, 28/27~33/32, 81/80~64/63~99/98) = (97.5911c, 58.2557c, 25.3165c) TE | |||
~ 64/63 15/14 12/11 9/8 8/7 32/27 6/5 14/11 9/7 4/3 27/20 10/7 16/11 3/2 32/21 45/28 18/11 27/16 12/7 16/9 9/5 12/11 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM | |||
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12] | |||
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5013)-36|((2/1, 3/2)[12], 64/63: 5120/5013)[36] (Hemifamity)]]==== | |||
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE | |||
~ 64/63 36/35 15/14 243/224 54/49 9/8 8/7 81/70 32/27 6/5 128/105 81/64 9/7 64/49 4/3 27/20 48/35 10/7 81/56 72/49 3/2 32/21 54/35 45/28 80/49 81/49 27/16 12/7 243/140 16/9 9/5 64/35 243/128 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM | |||
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL; | |||
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS | |||
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36] (Pele)]]===== | |||
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63~99/98) = (72.2746c, 32.9392c, 25.3165c) TE | |||
~ 64/63 36/35 15/14 12/11 54/49 9/8 8/7 64/55 32/27 6/5 128/105 14/11 9/7 64/49 4/3 27/20 48/35 10/7 16/11 72/49 3/2 32/21 54/35 45/28 18/11 81/49 27/16 12/7 96/55 16/9 9/5 64/35 22/21 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM | |||
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL; | |||
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS | |||
==2.3.25== | |||
===(2/1, 3/2, 100/81)=== | |||
====(2/1, 3/2, 100/81)[7]==== | |||
=====(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)===== | |||
{| class="wikitable" | |||
!Step signature | |||
!Steps in JI | |||
!Step sizes in cents | |||
|- | |||
|2L 1m 4s | |||
|(2500/2187~8/7, ~9/8, ~27/25) | |||
|(231.1884c, 203.974c, 133.4123c) | |||
|} | |||
{| class="wikitable" | |||
!Mode number | |||
!Mode in JI | |||
!Step pattern | |||
![[Mode height]] | |||
|- | |||
| -3 | |||
|~ 9/8 175/144 25/18 3/2 81/50 50/27 2/1 | |||
|msLssLs | |||
| 0.0158 | |||
|- | |||
| -2 | |||
|~ 27/25 175/144 21/16 3/2 81/50 7/4 2/1 | |||
|smsLssL | |||
| -0.0211 | |||
|- | |||
| -1 | |||
|~ 8/7 100/81 25/18 3/2 12/7 50/27 2/1 | |||
|LsmsLss | |||
| 0.037 | |||
|- | |||
| 0 | |||
|~ 27/25 100/81 4/3 3/2 81/50 50/27 2/1 | |||
|sLsmsLs | |||
| 0 | | 0 | ||
|- | |- | ||
Line 4,646: | Line 4,730: | ||
|} | |} | ||
=====(2/1, 3/2, 100/81: 1225/1224, 1701/1700)[7]===== | =====[[SNS_(2/1,_3/2,_100/81:_1225/1224,_1701/1700)-7|(2/1, 3/2, 100/81: 1225/1224, 1701/1700)[7]]]===== | ||
{| class="wikitable" | {| class="wikitable" | ||
!Step signature | !Step signature | ||
Line 4,698: | Line 4,782: | ||
|} | |} | ||
==2.5.9; Marvel == | ==2.5.9; Marvel == | ||
=== ((2/1, 5/4)[3], 9/8)=== | === ((2/1, 5/4)[3], 9/8)=== | ||
Line 5,142: | Line 5,143: | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
{{Todo| cleanup }} |