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Gallery of 3-SN scales: Difference between revisions

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Line 1: Line 1:
See [[SN scale]] and [[Rank-3 scale]].
See [[SN scale]] and [[Rank-3 scale]].


Line 153: Line 151:
|L - M = M - s
|L - M = M - s
|sAsLsAs
|sAsLsAs
|Meantone[7] MODMOS
|[[Meantone]][7] MODMOS
|81/80
|81/80
|-
|-
Line 237: Line 235:
|L - M = M - s
|L - M = M - s
|sAsLsAs
|sAsLsAs
|Meantone[7] MODMOS
|[[Meantone]][7] MODMOS
|81/80, 126/125
|81/80, 126/125
|}
|}
Line 390: Line 388:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|2048/2025
Line 406: Line 404:
|L - m = m - s
|L - m = m - s
|sLssdssLss
|sLssdssLss
|Ampersand[10] MODMOS
|[[Ampersand]][10] MODMOS
|34171875/33554432
|34171875/33554432
|-
|-
Line 510: Line 508:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 678: Line 676:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 834: Line 832:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 1,440: Line 1,438:
|-
|-
|L = s
|L = s
|sLsssssLs
|[[OTC 2L ns|sLsssssLs]]
|[[Mavila]][9] MODMOS
|[[Mavila]][9] MODMOS
| 135/128
| 135/128
Line 1,446: Line 1,444:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orson[9] MODMOS
|[[Orson]][9] MODMOS
|2109375/2097152
|2109375/2097152
|-
|-
Line 1,538: Line 1,536:
|-
|-
|L = s
|L = s
|sLsssssLs
|[[OTC 2L ns|sLsssssLs]]
|[[Pelogic]][9] MODMOS
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
| 21/20, 135/128
Line 1,544: Line 1,542:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orwell[9] MODMOS
|[[Orwell]][9] MODMOS
|225/224, 1728/1715
|225/224, 1728/1715
|}
|}
Line 1,655: Line 1,653:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orwell[9] MODMOS
|[[Orwell]][9] MODMOS
|99/88, 121/120, 176/175
|99/88, 121/120, 176/175
|}
|}
Line 1,784: Line 1,782:
|L - M = M - s
|L - M = M - s
|LdLLLsLLLdLL
|LdLLLsLLLdLL
|Meantone[12] MODMOS
|[[Meantone]][12] MODMOS
|81/80, 126/125
|81/80, 126/125
|-
|-
Line 1,795: Line 1,793:
|LsLLLLLLsLL
|LsLLLLLLsLL
|[[Pelogic]][11] MODMOS
|[[Pelogic]][11] MODMOS
|21/20, 135/
|21/20, 135/128
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,919: Line 1,917:
|L - M = M - s
|L - M = M - s
|LdLLLsLLLdLL
|LdLLLsLLLdLL
|Meanpop[12] MODMOS
|[[Meanpop]][12] MODMOS
|81/80, 126/125, 385/384
|81/80, 126/125, 385/384
|-
|-
Line 1,998: Line 1,996:
|L - m = m - s
|L - m = m - s
|sAssAsAsAsLsAsAsAssAsA
|sAssAsAsAsLsAsAsAssAsA
|Magic[22] MODMOS
|[[Magic]][22] MODMOS
|100/99, 225/224, 245/243
|100/99, 225/224, 245/243
|-
|-
Line 2,144: Line 2,142:
|-
|-
|m = s
|m = s
|ssLsssLsss
|[[OTC 2L 8s|ssLsssLsss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|2048/2025
|-
|-
|L = m
|L = m
|sLLLsLLLsL
|[[7L 3s|sLLLsLLLsL]]
|[[Dicot family|Dicot]][10] MODMOS
|[[Dicot family|Dicot]][10] MODMOS
|25/24
|25/24
Line 2,293: Line 2,291:
|-
|-
|m = s
|m = s
|ssLsssLsss
|[[OTC 2L 8s|ssLsssLsss]]
|[[Diaschismic family#Pajara|Pajara]][10] 4M (pentachordal decatonic)
|[[Diaschismic family#Pajara|Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|50/49, 64/63
|-
|-
|L = m
|L = m
|sLLLsLLLsL
|[[OTC 7L 3s|sLLLsLLLsL]]
|[[Dicot family|Sharp]][10] MODMOS
|[[Dicot family|Sharp]][10] MODMOS
|25/24, 28/27
|25/24, 28/27
Line 2,432: Line 2,430:
|-
|-
|m = s
|m = s
|ssLsssLsss
|[[OTC 2L 8s|ssLsssLsss]]
|[[Diaschismic family#Pajaric|Pajaric]][10] 4M (pentachordal decatonic)
|[[Diaschismic family#Pajaric|Pajaric]][10] 4M (pentachordal decatonic)
|45/44, 50/49, 56/55
|45/44, 50/49, 56/55
Line 2,679: Line 2,677:
|L - M = M - s
|L - M = M - s
|LsLALsL
|LsLALsL
|Tetracot[7] MODMOS
|[[Tetracot]][7] MODMOS
|20000/19683
|20000/19683
|-
|-
Line 3,380: Line 3,378:
{| 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 family|Meantone]][12]
| [[Meantone]][12]
|81/80
| 81/80
|-
|-
|L = m
| L = m
|sLLsLLLsLLsL
| sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
| [[Diminished]][12] MODMOS
|648/625
| 648/625
|-
|-
|L = s
| L = s
|[[11L 1s|LLLLLsLLLLLL]]
| [[11L 1s|LLLLLsLLLLLL]]
|[[Ripple family|Ripple]][12]
| [[Ripple]][12]
|6561/6250
| 6561/6250
|-
|-
|L - m = m - s
| L - m = m - s
|dLLdLsLdLLdL
| dLLdLsLdLLdL
|Augmented[12] MODMOS
| [[Augmented]][12] modmos
|128/125
| 128/125
|-
|-
|s = 0
| s = 0
|[[7L 1s|LLLsLLLL]]
| [[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porcupine|Porcupine]][8]
| [[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 3,531: Line 3,530:
|L - m = m - s
|L - m = m - s
|dLLdLsLdLLdL
|dLLdLsLdLLdL
|Augene[12] MODMOS
|[[Augmented family#Augene|Augene]][12] MODMOS
|64/63, 126/125  
|64/63, 126/125  
|-
|-
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 [[Meantone family#Flattone|Flattone]][12]
| [[Meanenneadecal]][12] or [[Flattone]][12]
|45/44, 81/80
| 45/44, 81/80
|-
|-
|L = m
| L = m
|sLLsLLLsLLsL
| sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
| [[Diminished]][12] modmos
|100/99, 128/121
| 100/99, 128/121
|-
|-
|L - m = m - s
| L - m = m - s
|dLLdLsLdLLdL
| dLLdLsLdLLdL
|Augene[12] MODMOS
| [[Augene]][12] modmos
|100/99, 128/125
| 100/99, 128/125
|-
|-
|s = 0
| s = 0
|[[7L 1s|LLLsLLLL]]
| [[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porkypine|Porkypine]][8]
| [[Porcupine]][8]
|55/54, 100/99
| 55/54, 100/99
|}
|}


Line 4,591: Line 4,590:


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)
==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
===((2/1, 3/2)[5], 10/9)===
===((2/1, 3/2)[5], 10/9)===
Line 4,674: Line 4,674:


s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
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
|-
|  1
|~ 27/25 7/6 4/3 36/25 81/50 7/4 2/1
|ssLsmsL
|  -0.037
|-
|  2
|~ 8/7 100/81 4/3 32/21 288/175 50/27 2/1
|LssLsms
|  0.0211
|-
|  3
|~ 27/25 100/81 4/3 36/25 288/175 16/9 2/1
|sLssLsm
|  -0.0158
|}
=====[[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"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 1m 4s
|(2500/2187~8/7, ~9/8, ~27/25)
|(231.5807c, 203.8094c, 133.2573c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
|  -3
|~ 9/8 17/14 25/18 3/2 34/21 50/27 2/1
|msLssLs
|  0.0157
|-
|  -2
|~ 27/25 17/14 21/16 3/2 34/21 7/4 2/1
|smsLssL
|  -0.0214
|-
|  -1
|~ 8/7 21/17 25/18 3/2 12/7 50/27 2/1
|LsmsLss
|  0.0371
|-
|  0
|~ 27/25 21/17 4/3 3/2 34/21 50/27 2/1
|sLsmsLs
|  0
|-
|  1
|~ 27/25 7/6 4/3 36/25 34/21 7/4 2/1
|ssLsmsL
|  -0.0371
|-
|  2
|~ 8/7 21/17 4/3 32/21 28/17 50/27 2/1
|LssLsms
|  0.0214
|-
|  3
|~ 27/25 21/17 4/3 36/25 28/17 16/9 2/1
|sLssLsm
|  -0.0157
|}
==2.5.9; Marvel ==
==2.5.9; Marvel ==
=== ((2/1, 5/4)[3], 9/8)===
=== ((2/1, 5/4)[3], 9/8)===
Line 5,031: Line 5,139:


53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
[[Category:Gallery]]
[[Category:Step-nested scales]]
[[Category:Step-nested scales]]
[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:Rank 3]]
[[Category:Rank 3]]
{{Todo| cleanup }}
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"