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Gallery of 3-SN scales: Difference between revisions

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Line 28: Line 28:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -2
| -2
Line 69: Line 69:
|s = 0
|s = 0
|LsL
|LsL
|[[Father]][3]
|[[Trienstonic clan#Father|Father]][3]
|16/15
|16/15
|}
|}
Line 87: Line 87:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -3
| -3
Line 148: Line 148:
| s = 0
| s = 0
|LsL
|LsL
|[[Father]][3]
|[[Trienstonic clan#Father|Father]][3]
|16/15
|16/15
|}
|}
Line 166: Line 166:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -3
| -3
Line 269: Line 269:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -5
| -5
Line 335: Line 335:
|L = m
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[9L 1s|LLLLsLLLLL]]
|[[Negri]][10]
|[[Marvel temperaments#Negri|Negri]][10]
|16875/16384  
|16875/16384  
|-
|-
Line 350: Line 350:
|m = 0
|m = 0
|LsL
|LsL
|[[Father]][3]
|[[Trienstonic clan#Father|Father]][3]
|16/15
|16/15
|-
|-
Line 372: Line 372:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -5
| -5
Line 438: Line 438:
|L = m
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[9L 1s|LLLLsLLLLL]]
|[[Negri]][10]
|[[Marvel temperaments#Negri|Negri]][10]
|49/48, 225/224  
|49/48, 225/224  
|-
|-
Line 489: Line 489:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -5
| -5
Line 555: Line 555:
|L = m
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[9L 1s|LLLLsLLLLL]]
|[[Negri]][10]
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55  
|45/44, 49/48, 56/55  
|}
|}
Line 592: Line 592:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -5
| -5
Line 693: Line 693:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -9
| -9
Line 724: Line 724:
|M = s
|M = s
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|49/48, 225/224  
|49/48, 225/224  
|-
|-
Line 772: Line 772:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -9
| -9
Line 803: Line 803:
|M = s
|M = s
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|45/44, 49/48, 56/55
|45/44, 49/48, 56/55
|-
|-
Line 844: Line 844:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Mode height
![[Mode height]]
|-
|-
| -9
| -9
Line 962: Line 962:
===((2/1, 5/4)[3], 16/15)===
===((2/1, 5/4)[3], 16/15)===
====[[SNS ((2/1, 5/4)-3, 16/15)-6|((2/1, 5/4)[3], 16/15)[6]]]====
====[[SNS ((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) = (267.8165c, 315.6413c, 111.7313c)
{| class="wikitable"
 
! Step signature
75/64 5/4 3/2 8/5 15/8 2/1 as MsLsMs
! Steps in JI
 
!Step sizes in cents (TE tuning)
L = M -> LsLsLs Augmented[6]; M = s -> ssLsss Enipucrop[6]; L = s -> LsssLs Antitonic[6] MODMOS; s = 0 -> LsL Father[3]
|-
|2L 1M 4s
|(6/5, 75/64, 16/15)
| (315.6413c, 267.8165c, 111.7313c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
|  -3
|16/15 5/4 4/3 25/16 5/3 2/1
|sMsMsL
|  -0.1156
|-
|  -2
|16/15 5/4 4/3 8/5 128/75 2/1
|sMsLsM
|  -0.0883
|-
|  -1
|16/15 32/25 512/375 8/5 128/75 2/1
|sLsMsM
|  -0.0609
|-
|1
|75/64 5/4 375/256 25/16 15/8 2/1
|MsMsLs
|0.0609
|-
|2
|75/64 5/4 3/2 8/5 15/8 2/1
|MsLsMs
|0.0883
|-
|3
|6/5 32/25 3/2 8/5 15/8 2/1
|LsMsMs
|0.1156
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LsLsLs
|[[Augmented family|Augmented]][6]
|128/125
|-
|M = s
|ssLsss
|[[Enipucrop]][6]
|1125/1024
|-
|L = s
|LsssLs
|Antitonic[6] 4M
| 9/8
|-
|s = 0
|LsL
|[[Trienstonic clan#Father|Father]][3]
|16/15
|}
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-6|((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)]]=====
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-6|((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)]]=====
1L 2M 3s = (6/5, 75/64~7/6, 16/15~15/14) = (316.9276c, 267.8165c, 116.0124c) TE
{| class="wikitable"
 
! Step signature
~ 7/6 5/4 3/2 8/5 15/8 2/1 as MsLsMs
! Steps in JI
!Step sizes in cents (TE tuning)
|-
|2L 1M 4s
|6/5, 75/64~7/6, 16/15~15/14
| (316.9276c, 267.8165c, 116.0124c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
![[Mode height]]
|-
|  -3
|~ 15/14 5/4 4/3 14/9 5/3 2/1
|sMsMsL
|  -0.1156
|-
|  -2
|~ 15/14 5/4 4/3 8/5 12/7 2/1
|sMsLsM
|  -0.0883
|-
|  -1
|~ 15/14 9/7 48/35 8/5 12/7 2/1
|sLsMsM
|  -0.0609
|-
|1
|~ 7/6 5/4 35/28 14/9 15/8 2/1
|MsMsLs
|0.0609
|-
|2
|~ 7/6 5/4 3/2 8/5 15/8 2/1
|MsLsMs
|0.0883
|-
|3
|~ 6/5 9/7 3/2 8/5 15/8 2/1
|LsMsMs
|0.1156
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LsLsLs
|[[Augmented family|August]][6]
|128/125
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[7edo|7]]
|[[9edo|9]]
|[[10edo|10]]
|[[12edo|12]]
|[[19edo|19]]
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|72]]
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(5, 4, 2)
|(6, 5, 2)
|(8, 6, 3)
|(8, 7, 3)
|(11, 9, 4)
|(13, 11, 5)
|(14, 12, 5)
|(19, 16, 7)
|}
====[[SNS ((2/1, 5/4)-3, 16/15)-9|((2/1, 5/4)[3], 16/15)[9]]]====
====[[SNS ((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) = (203.9100c, 162.8511c, 111.7313c)


16/15 75/64 5/4 4/3 3/2 8/5 128/75 15/8 2/1 as sMssLssMs
{| class="wikitable"
 
! Step signature
L = M -> sLssLssLs Augmented[9]; M = s -> ssssLssss Negri[9]; L = s -> sLsssssLs Mavila[9] MODMOS; s = 0 -> LsL Father[3]; m = 0 -> sssLsss Eunipucrop[7]
! Steps in JI
!Step sizes in cents (TE tuning)
|-
|2L 1M 6s
|(9/8, 1125/1024, 16/15)
| (203.9100c, 162.8511c, 111.7313c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
| -4
|16/15 256/225 5/4 4/3 64/45 25/16 5/3 16/9 2/1
|ssMssMssL
| -0.0662
|-
|  -3
|16/15 256/225 5/4 4/3 64/45 8/5 128/75 2048/1125 2/1
|ssMssLssM
|  -0.0405
|-
|  -2
|16/15 75/64 5/4 4/3 375/256 25/16 5/3 15/8 2/1
|sMssMssLs
|  -0.0257
|-
|  -1
|16/15 256/225 32/25 512/375 8192/5625 8/5 128/75 2048/1125 2/1
|ssLssMssM
|  -0.0148
|-
|0
|16/15 75/64 5/4 4/3 3/2 8/5 128/75 15/8 2/1
|sMssLssMs
|0
|-
|1
|1125/1024 75/64 5/4 5625/4096 375/256 25/16 225/128 15/8 2/1
|MssMssLss
|0.0148
|-
|2
|16/15 6/5 32/25 512/375 3/2 8/5 128/75 15/8 2/1
|sLssMssMs
|0.0257
|-
|3
|1125/1024 75/64 5/4 45/32 3/2 8/5 225/128 15/8 2/1
|MssLssMss
|0.0405
|-
|4
|9/8 6/5 32/25 45/32 3/2 8/5 225/128 15/8 2/1
|LssMssMss
|0.0662
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 6s|sLssLssLs]]
|[[Augmented family|Augmented]][9]
|128/125
|-
|M = s
|[[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
|16875/16384
|-
|L = s
|sLsssssLs
|[[Mavila]][9] MODMOS
| 135/128
|-
|s = 0
|LsL
|[[Father]][3]
|16/15
|-
|m = 0
|[[1L 6s|sssLsss]]
|[[Enipucrop]][7]
|1125/1024
|}
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-9|((2/1, 5/4)[3], 16/15: 225/224)[9] (Marvel)]]=====
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-9|((2/1, 5/4)[3], 16/15: 225/224)[9] (Marvel)]]=====
1L 2M 6s = (~9/8, 35/32~49/45, 16/15~15/14) = (200.9152c, 151.8041c, 116.0124c) TE
{| class="wikitable"
 
! Step signature
~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
! Steps in JI
 
!Step sizes in cents (TE tuning)
L = M -> to sLssLssLs August[9]; M = s -> ssssLssss Negri[9]; L = s -> sLsssssLs Pelogic[9] MODMOS
|-
|2L 1M 6s
|(9/8~28/25, 35/32~49/45, 16/15~15/14)
| (203.9100c, 162.8511c, 111.7313c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
| -4
|~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1
|ssMssMssL
| -0.0662
|-
|  -3
|~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 64/35 2/1
|ssMssLssM
|  -0.0405
|-
|  -2
|~ 15/14 7/6 5/4 4/3 35/24 14/9 5/3 15/8 2/1
|sMssMssLs
|  -0.0257
|-
|  -1
|~ 15/14 8/7 9/7 48/35 72/49 8/5 12/7 64/35 2/1
|ssLssMssM
|  -0.0148
|-
|0
|~ 15/14 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1
|sMssLssMs
|0
|-
|1
|~ 35/32 7/6 5/4 49/36 35/24 14/9 7/4 15/8 2/1
|MssMssLss
|0.0148
|-
|2
|~ 15/14 6/5 9/7 48/35 3/2 8/5 12/7 15/8 2/1
|sLssMssMs
|0.0257
|-
|3
|~ 35/32 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1
|MssLssMss
|0.0405
|-
|4
|~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1
|LssMssMss
|0.0662
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 6s|sLssLssLs]]
|[[August]][9]
|36/35, 128/125
|-
|M = s
|[[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
|49/48, 225/224
|-
|L = s
|sLsssssLs
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
|}
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-9|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9] (Marvel)]]=====
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-9|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9] (Marvel)]]=====
1L 2M 6s = (~9/8, 35/32~49/45~12/11, 16/15~15/14) = (200.8846c, 151.4797c, 116.1327c) TE


~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
{| class="wikitable"
 
! Step signature
L = M -> sLssLssLs August[9]; M = s -> ssssLssss Negri[9], L = s -> sLsssssLs Pelogic[9] MODMOS
! Steps in JI
!Step sizes in cents (TE tuning)
|-
|2L 1M 6s
|(9/8~28/25, 35/32~49/45~12/11, 16/15~15/14)
| (200.8846c, 151.4797c, 116.1327c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
| -4
|~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1
|ssMssMssL
| -0.0662
|-
|  -3
|~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 11/6 2/1
|ssMssLssM
|  -0.0405
|-
|  -2
|~ 15/14 7/6 5/4 4/3 16/11 14/9 5/3 15/8 2/1
|sMssMssLs
|  -0.0257
|-
|  -1
|~ 15/14 8/7 9/7 11/8 22/15 8/5 12/7 11/6 2/1
|ssLssMssM
|  -0.0148
|-
|0
|~ 15/14 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1
|sMssLssMs
|0
|-
|1
|~ 12/11 7/6 5/4 15/11 16/11 14/9 7/4 15/8 2/1
|MssMssLss
|0.0148
|-
|2
|~ 15/14 6/5 9/7 11/8 3/2 8/5 12/7 15/8 2/1
|sLssMssMs
|0.0257
|-
|3
|~ 12/11 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1
|MssLssMss
|0.0405
|-
|4
|~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1
|LssMssMss
|0.0662
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 6s|sLssLssLs]]
|[[August]][9]
|36/35, 45/44, 56/55
|-
|M = s
|[[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
|45/44, 49/48, 56/55
|}
====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-12|((2/1, 5/4)[3], 16/15: 225/224)[12] (Marvel)]]====
====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-12|((2/1, 5/4)[3], 16/15: 225/224)[12] (Marvel)]]====
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48) = (116.0124c, 84.9028c, 35.7917c) TE
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48) = (116.0124c, 84.9028c, 35.7917c) TE
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"