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Gallery of 3-SN scales mobile: Difference between revisions

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trying to back up Gallery of 3-SN Scales because it won't save :/
 
Lhearne (talk | contribs)
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Reverted tables so this can be a mobile page for it
Line 13: Line 13:
===(2/1, 3/2, 5/4)===
===(2/1, 3/2, 5/4)===
====[[SNS (2/1, 3/2, 5/4)-4|(2/1, 3/2, 5/4)[4]]]====
====[[SNS (2/1, 3/2, 5/4)-4|(2/1, 3/2, 5/4)[4]]]====
{| class="wikitable"
2L 1M 1s = (5/4, 6/5, 16/15) = (386.3137c, 315.6413c, 111.7313c)
!Step Signature
!Steps in JI
!Step sizes in cents
|-
|2L 1M 1s
|(5/4, 6/5, 16/15)
|(386.3137c, 315.6413c, 111.7313c)
|}Scale in JI: 5/4 3/2 15/8 2/1


Step pattern: LMLs
5/4 3/2 15/8 2/1 as LMLs
{| class="wikitable"
 
|+Rank-2 temperings
L = M -> LLLs Dicot[4]; M = s -> LsLs Antitonic[4]; s = 0 -> LsL Father[3]
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|LLLs
|Dicot[4]
|25/24
|-
|M = s
|LsLs
|Antitonic[4]
|9/8
|-
|s = 0
|LsL
|Father[3]
|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"
2L 1M 4s = (75/64, 9/8, 16/15) = (274.5824c, 203.9100c, 111.7313c)
!Step Signature
 
!Steps in JI
16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
!Step sizes in cents
|-
|2L 1M 4s
|(75/64, 9/8, 16/15)
|(274.5824c, 203.9100c, 111.7313c)
|}Scale in JI: 16/15 5/4 4/3 3/2 8/5 15/8 as


Step pattern: sLsMsLs
L = M -> sLsLsLs Dicot[7]; M = s -> LLLsLLL Enipucrop[7]; s = 0 -> Father[3]
{| class="wikitable"
|+Rank-2 temperings
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|sLsLsLs
|Dicot[7]
|25/24
|-
|M = s
|sLsssLs
|Mavila[7]
|135/128
|-
|L = s
|LLLsLLL
|Enipucrop[7]
|1125/1024
|-
|s = 0
|LsL
|Father[3]
|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
2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14) = (267.8165c, 200.9152c, 116.0124c)
 
~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs


Scale steps: sLsMsLs
L = M -> sLsLsLs Sharp[7]; M = s -> sLsssLs Pelogic[7]; L = s -> LLLsLLL Enipucrop[7]
{| class="wikitable"
 
!Step Signature
(2, 1, 1) in 9ET; (2, 2, 1) in 10ET; (3, 2, 1) in 12ET; (4, 3, 2) in 19ET; (5, 4, 2) in 22ET; (6, 5, 3) in 29ET; (7, 5, 3) in 31ET; (9, 7, 4) in 41ET; (11, 8, 5) in 50ET; (12, 9, 5) in 53ET; (16, 12, 17) in 72ET
!Steps in JI
!Step sizes in cents (TE tuning)
|-
|2L 1M 4s
|(75/64~7/6, ~9/8, 16/15~15/14)
|(267.8165c, 200.9152c, 116.0124c)
|}
{| class="wikitable"
|+Rank-2 temperings
!Equivalence
!scale steps
!Scale
!Comma list
|-
|L = M
|sLsLsLs
|Sharp[7]
|25/24, 28/27
|-
|M = s
|sLsssLs
|Pelogic[7]
|135/128, 21/20
|-
|L= s
|LLLsLLL
|Enipucrop[7]
|35/32, 49/45
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|9
|10
|12
|19
|22
|29
|31
|41
|50
|53
|72
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(4, 3, 2)
|(5, 4, 2)
|(6, 5, 3)
|(7, 5, 3)
|(9, 7, 4)
|(11, 8, 5)
|(12, 9, 5)
|(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)
2L 7m 1s = (1125/1024, 16/15, 135/128) = (162.8511c, 111.7313c, 92.1787c)


16/15 75/64 5/4 4/3 45/32 3/2 8/5 128/75 15/8 as mLmmsmmLmm
16/15 75/64 5/4 4/3 45/32 3/2 8/5 128/75 15/8 as mLmmsmmLmm
Line 155: Line 39:
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]
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]
=====[[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
2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20) = (151.8041c, 116.0124c, 84.9028c) TE


~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
Line 161: Line 45:
m = s -> sLsssssLss Pajara[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Pelogic[9]
m = s -> sLsssssLss Pajara[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]; L = s -> LsLLsLLsLL Dicot[10]; s = 0 -> sLssssLss Pelogic[9]


(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
(2, 1, 1) in 12ET, (2, 2, 1) in 19ET, (3, 2, 2) in 22ET, (3, 3, 2) in 29ET, (4, 3, 2) in 31ET, (5, 4, 3) in 41ET, (7, 5, 4) in 53ET, (9, 7, 5) in 72ET
=====[[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
2L 1m 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) = (151.4797c, 116.1327c, 84.7519c) TE


~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
Line 169: Line 53:
m = s -> sLsssssLss Pajarous[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]
m = s -> sLsssssLss Pajarous[10] MODMOS; L = m -> LLLLsLLLLL Negri[10]


(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
(2, 2, 1) in 19ET, (3, 2, 2) in 22ET, (4, 3, 2) in 31ET, (5, 4, 3) in 41ET, (7, 5, 4) in 53ET, (9, 7, 5) in 72ET
=====[[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
2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) = (150.229c, 116.7669c, 82.9601c) TE
Line 177: Line 61:
m = s -> sLsssssLss Pajaric[10] MODMOS; L = m -> LLLLsLLLLL Negroni[10]
m = s -> sLsssssLss Pajaric[10] MODMOS; L = m -> LLLLsLLLLL Negroni[10]


(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
(2, 1, 1) in 12ET, (2, 2, 1) in 19eET, (3, 3, 2) in 29ET, (4, 3, 2) in 31ET, (5, 4, 3) in 41ET, (9, 7, 5) in 72ET
====[[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
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49) = (84.9028c, 66.9013c, 31.1096c) TE
Line 186: Line 70:


s = 0 -> LLLsLLLLsLLL Pajara[12] 4M (Hexachordal Dodecatonic); m = 0 -> LsLsLLsLsLsLLsLsL Sharp [17]
s = 0 -> LLLsLLLLsLLL Pajara[12] 4M (Hexachordal Dodecatonic); m = 0 -> LsLsLLsLsLsLLsLsL Sharp [17]
(2, 1, 0) in 22ET; (2, 1, 1) in 29ET; (2, 2, 1) in 31ET; (3, 2, 1) in 41ET; (3, 3, 2) in 50ET; (4, 3, 1) in 53ET; (5, 4, 2) in 72ET
=====[[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
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) = (84.7519c, 66.7278c, 31.3808c) TE
Line 192: Line 78:


L = M -> LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19]; s = 0 -> LLLsLLLLsLLL Pajarous[12] 4M (Hexachordal Dodecatonic)
L = M -> LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negri[19]; s = 0 -> LLLsLLLLsLLL Pajarous[12] 4M (Hexachordal Dodecatonic)
(2, 1, 0) in 22ET; (2, 2, 1) in 31ET; (3, 2, 1) in 41ET; (3, 3, 2) in 50ET; (4, 3, 1) in 53ET; (5, 4, 2) in 72ET
=====[[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
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
Line 198: Line 86:


L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negroni[19]; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
L = M -> LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS; M = s -> LsLsLsLsLsLsLsLsLsL Negroni[19]; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
(2, 1, 1) in 29ET; (2, 2, 1) in 31ET; (3, 2, 1) in 41ET; (4, 3, 1) in 53eET; (5, 4, 2) in 72ET
====[[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
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