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Gallery of 3-SN scales: Difference between revisions

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Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
updated the first section to tables
Line 21: Line 21:
|(5/4, 6/5, 16/15)
|(5/4, 6/5, 16/15)
|(386.3137c, 315.6413c, 111.7313c)
|(386.3137c, 315.6413c, 111.7313c)
|}Scale in JI: 5/4 3/2 15/8 2/1
|}
 
{| class="wikitable"
Step pattern: LMLs
!Mode number
!Mode in JI
!Step pattern
!Mode height
|-
| -2
|16/15 4/3 8/5 2/1
|sLML
| -.2092
|-
| -1
|5/4 4/3 5/3 2/1
|LsLM
| -.0174
|-
|1
|6/5 3/2 8/5 2/1
|MLsL
|.0174
|-
|2
|5/4 3/2 15/8 2/1
|LMLs
|.2092
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings
|+Rank-2 temperings
Line 46: Line 70:
|16/15
|16/15
|}
|}
====[[SNS (2/1, 3/2, 5/4)-7|(2/1, 3/2, 5/4)[7]]]====
====[[SNS (2/1, 3/2, 5/4)-7|(2/1, 3/2, 5/4)[7]]]====
{| class="wikitable"
{| class="wikitable"
Line 55: Line 80:
|(75/64, 9/8, 16/15)
|(75/64, 9/8, 16/15)
|(274.5824c, 203.9100c, 111.7313c)
|(274.5824c, 203.9100c, 111.7313c)
|}Scale in JI: 16/15 5/4 4/3 3/2 8/5 15/8 as
|}
 
{| class="wikitable"
Step pattern: sLsMsLs
!Mode number
!Mode in JI
!Step pattern
!Mode height
|-
| -3
|16/15 256/225 4/3 64/45 8/5 128/75 2/1
|ssLsMsL
| -.1161
|-
| -2
|16/15 6/5 32/25 3/2 8/5 128/75 2/1
|sMsLssL
| -.0845
|-
| -1
|16/15 5/4 4/3 64/45 5/3 16/9 2/1
|sLssLsM
| -.0316
|-
|0
|16/15 5/4 4/3 3/2 8/5 15/8 2/1
|sLsMsLs
|0
|-
|1
|9/8 6/5 45/32 3/2 8/5 15/8 2/1
|MsLssLs
|.0316
|-
|2
|75/64 5/4 4/3 25/16 5/3 15/8 2/1
|LssLsMs
|.0845
|-
|3
|75/64 5/4 45/32 3/2 225/128 15/8 2/1
|LsMsLss
|.1161
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings
|+Rank-2 temperings
Line 85: Line 149:
|16/15
|16/15
|}
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224)-7|(2/1, 3/2, 5/4: 225/224)[7] (Marvel)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224)-7|(2/1, 3/2, 5/4: 225/224)[7] (Marvel)]]=====
Scale in JI: ~ 16/15 5/4 4/3 3/2 8/5 15/8
Scale steps: sLsMsLs
{| class="wikitable"
{| class="wikitable"
! Step Signature
! Step Signature
Line 99: Line 161:
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -3
|~ 16/15 8/7 4/3 10/7 8/5 12/7 2/1
|ssLsMsL
| -.1079
|-
| -2
|~ 16/15 6/5 9/7 3/2 8/5 12/7 2/1
|sMsLssL
| -.0793
|-
| -1
|~ 16/15 5/4 4/3 10/7 5/3 16/9 2/1
|sLssLsM
| -.0286
|-
|0
|~ 16/15 5/4 4/3 3/2 8/5 15/8 2/1
|sLsMsLs
|0
|-
|1
|~ 9/8 6/5 7/5 3/2 8/5 15/8 2/1
|MsLssLs
|.0286
|-
|2
|~ 7/6 5/4 4/3 14/9 5/3 15/8 2/1
|LssLsMs
|.0793
|-
|3
|~ 7/6 5/4 7/5 3/2 7/4 15/8 2/1
|LsMsLss
|.1079
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Equivalence
!scale steps
!scale steps
Line 148: Line 251:
|(16, 12, 7)
|(16, 12, 7)
|}
|}
====[[SNS (2/1, 3/2, 5/4)-10|(2/1, 3/2, 5/4)[10]]]====
====[[SNS (2/1, 3/2, 5/4)-10|(2/1, 3/2, 5/4)[10]]]====
2L 7m 1s = (1125/1024, 16/15, 135/128)
{| class="wikitable"
 
! Step Signature
16/15 75/64 5/4 4/3 45/32 3/2 8/5 128/75 15/8 as mLmmsmmLmm
! Steps in JI
 
!Step sizes in cents
m = s -> sLsssssLss Srutal[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Mavila[9]; m = 0 -> LsL Father[3]
|-
|2L 7m 1s
|(1125/1024, 16/15, 135/128)
| (162.8511c, 111.7313c, 92.1787c)
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -5
|16/15 256/225 6/5 32/25 512/375 3/2 8/5 128/75 2048/1125 2/1
|mmsmmLmmmL
| -.0564
|-
| -4
|16/15 9/8 6/5 32/25 45/32 3/2 8/5 128/75 15/8 2/1
|msmmLmmmLm
| -.0411
|-
| -3
|135/128 9/8 6/5 675/512 45/32 3/2 8/5 225/128 15/8 2/1
|smmLmmmLmm
| -.0258
|-
| -2
|16/15 256/225 4096/3375 4/3 64/45 1024/675 8/5 128/75 2048/1125 2/1
|mmmLmmsmmL
| -.0230
|-
| -1
|16/15 256/225 5/4 4/3 64/45 3/2 8/5 128/75 15/8 2/1
|mmLmmsmmLm
| -.0077
|-
|1
|16/15 75/64 5/4 4/3 45/32 3/2 8/5 225/128 15/8 2/1
|mLmmsmmLmm
|.0077
|-
|2
|1125/1024 75/64 5/4 675/512 45/32 3/2 3375/2048 225/128 15/8 2/1
|LmmsmmLmmm
|.0239
|-
|3
|16/15 256/225 5/4 4/3 64/45 1024/675 5/3 16/9 256/135 2/1
|mmLmmmLmms
|.0258
|-
|4
|16/15 75/64 5/4 4/3 64/45 25/16 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|.0411
|-
|5
|1125/1024 75/64 5/4 4/3 375/256 25/16 5/3 225/128 15/8 2/1
|LmmmLmmsmm
|.0564
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|m = s
|sLsssssLss
|Srutal[10] MODMOS
|2048/2025
|-
|L = m
|LLLLsLLLLL
|Negri[10]
|16875/16384
|-
|L= s
|LsLLsLLsLL
|Dicot[10]
|25/24
|-
|s = 0
|sLssssLss
|Mavila[9]
|135/128
|-
|m = 0
|LsL
|Father[3]
|16/15
|-
|L = 0
|LLLsLLLL
|Enipucrop[8]
|1125/1024
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224)-10|(2/1, 3/2, 5/4: 225/224)[10] (Marvel)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224)-10|(2/1, 3/2, 5/4: 225/224)[10] (Marvel)]]=====
2L 7M 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20) = (151.8041c, 116.0124c, 84.9028c) TE
{| class="wikitable"
 
! Step Signature
~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
! Steps in JI
 
!Step sizes in cents (TE)
m = s -> sLsssssLss Pajara[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Pelogic[9]
|-
 
|2L 7m 1s
(2, 1, 1) in 12edo, (2, 2, 1) in 19edo, (3, 2, 2) in 22edo, (3, 3, 2) in 29edo, (4, 3, 2) in 31edo, (5, 4, 3) in 41edo, (7, 5, 4) in 53edo, (9, 7, 5) in 72edo
|(35/32~49/45, 16/15~15/14, 135/128~21/20)
| (151.8041c, 116.0124c, 84.9028c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -5
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|mmsmmLmmmL
| -.0475
|-
| -4
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
| -.0400
|-
| -3
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
| -.0325
|-
| -2
|~ 16/15 8/7 60/49 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|mmmLmmsmmL
| -.0112
|-
| -1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
| -.0037
|-
|1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|.0037
|-
|2
|~ 35/32 7/6 5/4 21/16 7/5 3/2 49/30 7/4 15/8 2/1
|LmmsmmLmmm
|.0112
|-
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|mmLmmmLmms
|.0325
|-
|4
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|.0400
|-
|5
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|.0475
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|m = s
|sLsssssLss
|Pajara[10] MODMOS
|50/49, 64/63
|-
|L = m
|LLLLsLLLLL
|Negri[10]
|49/48, 225/224
|-
|L = s
|LsLLsLLsLL
|Sharp[10]
|25/24, 28/27
|-
|s = 0
|sLssssLss
|Pelogic[9]
|21/20, 135/128
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|12
|19
|22
|29
|31
|41
|50
|53
|72
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 2)
|(3, 3, 2)
|(4, 3, 2)
|(5, 4, 3)
|(6, 5, 3)
|(7, 5, 4)
|(9, 7, 5)
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-10|(2/1, 3/2, 5/4: 225/224, 385/384)[10] (Marvel)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-10|(2/1, 3/2, 5/4: 225/224, 385/384)[10] (Marvel)]]=====
2L 1M 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) = (151.4797c, 116.1327c, 84.7519c) TE
{| class="wikitable"
 
! Step Signature
~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
! Steps in JI
 
!Step sizes in cents (TE)
m = s -> sLsssssLss Pajarous[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]
|-
 
|2L 7m 1s
(2, 2, 1) in 19edo, (3, 2, 2) in 22edo, (4, 3, 2) in 31edo, (5, 4, 3) in 41edo, (7, 5, 4) in 53edo, (9, 7, 5) in 72edo
|(35/32~49/45~12/11, 16/15~15/14, 135/128~21/20)
| (151.4797c, 116.1327c, 84.7519c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -5
|~ 16/15 8/7 6/5 9/7 11/8 3/2 8/5 12/7 11/6 2/1
|mmsmmLmmmL
| -.0472
|-
| -4
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
| -.0400
|-
| -3
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
| -.0327
|-
| -2
|~ 16/15 8/7 11/9 4/3 10/7 32/21 8/5 12/7 11/6 2/1
|mmmLmmsmmL
| -.0109
|-
| -1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
| -.0036
|-
|1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|.0036
|-
|2
|~ 12/11 7/6 5/4 21/16 7/5 3/2 18/11 7/4 15/8 2/1
|LmmsmmLmmm
|.0109
|-
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|mmLmmmLmms
|.0327
|-
|4
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|.0400
|-
|5
|~ 12/11 7/6 5/4 4/3 16/11 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|.0472
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|m = s
|sLsssssLss
|Pajarous[10] MODMOS
|50/49, 55/54, 64/63
|-
|L = m
|LLLLsLLLLL
|Negri[10]
|45/44, 49/48, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|19
|22
|31
|41
|50
|53
|72
|-
!Step sizes in ET
|(2, 2, 1)
|(3, 2, 2)
|(4, 3, 2)
|(5, 4, 3)
|(6, 5, 3)
|(7, 5, 4)
|(9, 7, 5)
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-10|(2/1, 3/2, 5/4: 225/224, 441/440)[10] (Prodigy)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-10|(2/1, 3/2, 5/4: 225/224, 441/440)[10] (Prodigy)]]=====
2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) = (150.229c, 116.7669c, 82.9601c) TE
{| class="wikitable"
 
! Step Signature
~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
! Steps in JI
 
!Step sizes in cents (TE)
m = s -> sLsssssLss Pajaric[10] MODMOS; L = m -> LLLLsLLLLL Negroni[10]
|-
 
|2L 7m 1s
(2, 1, 1) in 12edo, (2, 2, 1) in 19e, (3, 3, 2) in 29edo, (4, 3, 2) in 31edo, (5, 4, 3) in 41edo, (9, 7, 5) in 72edo
|(35/32~49/45, 16/15~15/14, 135/128~21/20~22/21)
| (150.229c, 116.7669c, 82.9601c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -5
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|mmsmmLmmmL
| -.0466
|-
| -4
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
| -.0404
|-
| -3
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
| -.0343
|-
| -2
|~ 16/15 8/7 27/22 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|mmmLmmsmmL
| -.0092
|-
| -1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
| -.0031
|-
|1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|.0031
|-
|2
|~ 35/32 7/6 5/4 21/16 7/5 3/2 44/27 7/4 15/8 2/1
|LmmsmmLmmm
|.0092
|-
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|mmLmmmLmms
|.0343
|-
|4
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|.0404
|-
|5
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|.0466
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|m = s
|sLsssssLss
|Pajaric[10] MODMOS
|45/44, 50/49, 56/55
|-
|L = m
|LLLLsLLLLL
|Negroni[10]
|49/48, 55/54, 225/224
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|12
|19e
|29
|31
|41
|72
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 3, 2)
|(4, 3, 2)
|(5, 4, 3)
|(9, 7, 5)
|}
====[[SNS (2/1, 3/2, 5/4: 225/224)-19|(2/1, 3/2, 5/4: 225/224)[19] (Marvel)]]====
====[[SNS (2/1, 3/2, 5/4: 225/224)-19|(2/1, 3/2, 5/4: 225/224)[19] (Marvel)]]====
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49) = (84.9028c, 66.9013c, 31.1096c) TE
{| class="wikitable"
! Step Signature
! Steps in JI
!Step sizes in cents (TE)
|-
|10L 2M 7s
|(135/128~21/20, 25/24~28/27, 64/63~50/49)
| (84.9028c, 66.9013c, 31.1096c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -9
|~ 50/49 16/15 160/147 8/7 512/441 60/49 80/63 4/3 256/189 10/7 640/441 32/21 8/5 80/49 12/7 256/147 64/35 40/21 2/1
|sLsLsLMLsLsLLsLsLML
| -.0464
|-
|0
|~ 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 2/1
|LsLsLMLsLsLsLMLsLsL
|0
|-
|9
|~ 21/20 35/32 147/128 7/6 49/40 5/4 21/16 441/320 7/5 189/128 3/2 63/40 49/30 441/256 7/4 147/80 15/8 49/25 2/1
|LMLsLsLLsLsLMLsLsLs
|.0464
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|LsLsLLLsLsLsLLLsLsL
|Meantone[19] MODMOS
|81/80, 126/125
|-
|M = s
|LsLsLsLsLsLsLsLsLsL
|Negri[19]
|49/48, 225/224
|-
|s = 0
|LLLsLLLLsLLL
|Pajara[12] 4M (Hexachordal Dodecatonic)
|50/49, 64/63
|-
|m = 0
|LsLsLLsLsLsLLsLsL
|Sharp[17]
|25/24, 28/27
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|22
|29
|31
|41
|50
|53
|72
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 2)
|(4, 3, 1)
|(5, 4, 2)
|}


~ 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
L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19];
s = 0 -> LLLsLLLLsLLL Pajara[12] 4M (Hexachordal Dodecatonic); m = 0 -> LsLsLLsLsLsLLsLsL Sharp [17]
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-19|(2/1, 3/2, 5/4: 225/224, 385/384)[19] (Marvel)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-19|(2/1, 3/2, 5/4: 225/224, 385/384)[19] (Marvel)]]=====
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) = (84.7519c, 66.7278c, 31.3808c) TE
{| class="wikitable"
 
! Step Signature
~ 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
! Steps in JI
!Step sizes in cents (TE)
|-
|10L 2M 7s
|(135/128~21/20, 25/24~28/27, 64/63~50/49~55/54)
| (84.7519c, 66.7278c, 31.3808c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -9
|~ 50/49 16/15 88/81 8/7 220/189 11/9 80/63 4/3 110/81 10/7 352/243 32/21 8/5 44/27 12/7 110/63 11/6 40/21 2/1
|sLsLsLMLsLsLLsLsLML
| -.0460
|-
|0
|~ 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 2/1
|LsLsLMLsLsLsLMLsLsL
|0
|-
|9
|~ 21/20 12/11 63/55 7/6 27/22 5/4 21/16 243/176 7/5 81/55 3/2 63/40 18/11 189/110 7/4 81/44 15/8 49/25 2/1
|LMLsLsLLsLsLMLsLsLs
|.0460
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|LsLsLLLsLsLsLLLsLsL
|Meanpop[19] MODMOS
|81/80, 126/125, 385/384
|-
|M = s
|LsLsLsLsLsLsLsLsLsL
|Negri[19]
|45/44, 49/48, 56/55
|-
|s = 0
|LLLsLLLLsLLL
|Pajarous[12] 4M (Hexachordal Dodecatonic)
|50/49, 55/54, 64/63
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|22
|31
|41
|50
|53
|72
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 2)
|(4, 3, 1)
|(5, 4, 2)
|}


L = M -> LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19]; s = 0 -> LLLsLLLLsLLL Pajarous[12] 4M (Hexachordal Dodecatonic)
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-19|(2/1, 3/2, 5/4: 225/224, 441/440)[19] (Prodigy)]]=====
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-19|(2/1, 3/2, 5/4: 225/224, 441/440)[19] (Prodigy)]]=====
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) TE
{| class="wikitable"
 
! Step Signature
~ 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
! Steps in JI
!Step sizes in cents (TE)
|-
|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)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode height
|-
| -9
|~ 50/49 16/15 12/11 8/7 64/55 27/22 14/11 4/3 15/11 10/7 16/11 32/21 8/5 18/11 12/7 96/55 64/35 40/21 2/1
|sLsLsLMLsLsLLsLsLML
| -.0428
|-
|0
|~ 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 2/1
|LsLsLMLsLsLsLMLsLsL
|0
|-
|9
|~ 21/20 35/32 55/48 7/6 11/9 5/4 21/16 11/8 7/5 22/15 3/2 11/7 44/27 55/32 7/4 11/6 15/8 49/25 2/1
|LMLsLsLLsLsLMLsLsLs
|.0428
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|LsLsLLLsLsLsLLLsLsL
|Meantone[19] MODMOS
|81/80, 99/98, 126/125
|-
|M = s
|LsLsLsLsLsLsLsLsLsL
|Negroni[19]
|49/48, 55/54, 225/224
|-
|s = 0
|LLLsLLLLsLLL
|Pajaric[12] 4M (Hexachordal Dodecatonic)
|45/44, 50/49, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|29
|31
|41
|72
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(5, 4, 2)
|}


L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negroni[19]; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)]]====
====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)]]====
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE
10L 19m 2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE


~ 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
~ 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
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