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Gallery of 3-SN scales: Difference between revisions

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m Added tables for... black...ville
Line 1,203: Line 1,203:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|1L 2M 4s
|1L 2M 4s
Line 1,365: Line 1,365:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|1L 2M 6s
|1L 2M 6s
Line 2,025: Line 2,025:
=== ((2/1, 3/2)[5], 16/15)===
=== ((2/1, 3/2)[5], 16/15)===
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
2L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)
{| class="wikitable"
 
!Step signature
135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
!Steps in JI
 
!Step sizes in cents
m = s -> ssLsssLsss Srutal[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10];
|-
 
|2L 5m 3s
L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
|(10/9, 16/15, 135/128)
| (182.4037c, 111.7313c, 92.1787c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
|  -5
|16/15 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0745
|-
|  -4
|135/128 9/8 1215/1024 81/64 45/32 3/2 405/256 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0592
|-
|  -3
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0411
|-
|  -2
|135/128 9/8 5/4 4/3 45/32 3/2 405/256 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0258
|-
|  -1
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0077
|-
|1
|135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0077
|-
|2
|16/15 32/27 512/405 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0258
|-
|3
|10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|LsssssLss
|Bright major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0411
|-
|4
|16/15 32/27 512/405 4/3 64/45 128/81 2048/1215 16/9 256/135 2/1
|mLmsmLmsms
|sLsssLssss
|Dark Augmented
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0592
|-
|5
|10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1
|LmsmLmsmsm
|LsssLsssss
|Bright Augmented
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0745
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|ssLsssLsss
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|-
|L = m
|sLLLsLLLsL
|Dicot[10] MODMOS
|25/24
|-
|L = s
|[[5L 5s|LsLsLsLsLs]]
|[[Limmic temperaments#5-limit .28blackwood.29|Blackwood]][10]
|256/243
|-
|L - m = m - s
|sLALsLALsL
|Negri[10] MODMOS
|16875/16384
|-
|s = 0
|[[2L 5s|sLssLss]]
|[[Mavila]][7]
|135/128
|-
|m = 0
|[[2L 3s|sLsLs]]
|[[Trienstonic clan#Father|Father]][5]
|16/15
|}
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE
{| class="wikitable"
 
!Step signature
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
!Steps in JI
 
!Step sizes in cents (TE tuning)
m = s -> ssLsssLsss Pajara[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
|-
|2L 5m 3s
|(10/9, 16/15~15/14, 135/128~21/20)
| (182.9137c, 116.0124c, 84.9028c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
|  -5
|~ 15/14 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0763
|-
|  -4
|~ 21/20 9/8 189/160 81/64 7/5 3/2 63/40 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0688
|-
|  -3
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0400
|-
|  -2
|~ 21/20 9/8 5/4 4/3 7/5 3/2 63/40 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0326
|-
|  -1
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0037
|-
|1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0037
|-
|2
|~ 15/14 32/27 80/63 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0326
|-
|3
|~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|LsssssLss
|Bright major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0400
|-
|4
|~ 15/14 32/27 80/63 4/3 10/7 128/81 320/189 16/9 40/21 2/1
|mLmsmLmsms
|sLsssLssss
|Dark Augmented
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0688
|-
|5
|~ 10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1
|LmsmLmsmsm
|LsssLsssss
|Bright Augmented
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0763
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|ssLsssLsss
|[[Diaschismic family#Pajara|Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|-
|L = m
|sLLLsLLLsL
|[[Dicot family|Sharp]][10] MODMOS
|25/24, 28/27
|-
|L - m = m - s
|sLALsLALsL
|[[Marvel temperaments#Negri|Negri]][10] MODMOS
|49/48, 225/224
|-
|s = 0
|[[2L 5s|sLssLss]]
|[[Pelogic family#Pelogic|Pelogic]][7]
|21/20, 135/128
|}
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-10|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-10|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)]]=====
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE
{| class="wikitable"
 
!Step signature
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
!Steps in JI
 
!Step sizes in cents (TE tuning)
m = s -> ssLsssLsss Pajaric[10] 4M (Pentachordal decatonic); L - m = m - s -> sLALsLALsL Negroni[10] MODMOS
|-
|2L 5m 3s
|(10/9, 16/15~15/14, 135/128~21/20~22/21)
| (184.0358c, 116.7669c, 82.9601c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
|  -5
|~ 15/14 9/8 6/5 44/35 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0779
|-
|  -4
|~ 21/20 9/8 33/28 44/35 7/5 3/2 11/7 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0718
|-
|  -3
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0405
|-
|  -2
|~ 21/20 9/8 5/4 4/3 7/5 3/2 11/7 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0343
|-
|  -1
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 21/11 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
| .0031
|-
|1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0031
|-
|2
|~ 15/14 32/27 15/11 4/3 10/7 3/2 8/5 16/9 21/11 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0343
|-
|3
|~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|LsssssLss
|Bright major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0405
|-
|4
|~ 15/14 32/27 14/11 4/3 10/7 35/22 56/33 16/9 40/21 2/1
|mLmsmLmsms
|sLsssLssss
|Dark Augmented
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0718
|-
|5
|~ 10/9 32/27 5/4 4/3 40/27 35/22 5/3 16/9 15/8 2/1
|LmsmLmsmsm
|LsssLsssss
|Bright Augmented
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0779
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|ssLsssLsss
|[[Diaschismic family#Pajaric|Pajaric]][10] 4M (pentachordal decatonic)
|45/44, 50/49, 56/55
|-
|L - m = m - s
|sLALsLALsL
|[[Marvel temperaments#Negroni|Negroni]][10] MODMOS
|49/48, 55/54, 225/224
|}
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)
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