Xenharmonic Wiki

Gallery of 3-SN scales: Difference between revisions

← Older editNewer edit →
VisualWikitext
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,636 edits
Line 2,570: Line 2,570:
|}
|}
=====[[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)]]=====
7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27) = (123.5395c, 78.929c, 64.0225c) TE
{| class="wikitable"
 
!Step signature
~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1 as sLLsLmLsLLsL
!Steps in JI
 
!Step sizes in cents (TE)
m = s -> sLLsLsLsLLsL Meantone[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]
|-
 
|7L 1m 4s
12-ET: (1, 1, 1); 15-ET: (2, 1, 0); 16-ET: (1, 1, 2); 19-ET: (2, 1, 1); 27-ET: (3, 2, 1); 31-ET: (3, 2, 2); 46-ET: (5, 3, 2); 50-ET: (5, 3, 3); 58-ET: (6, 4, 3); 77-ET: (8, 5, 4)
|(27/25~15/14, 25/24~21/20, 250/243~28/27)
|(123.5395c, 78.929c, 64.0225c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 28/27 10/9 280/243 56/45 4/3 112/81 40/27 14/9 5/3 140/81 28/15 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|  -0.0440
|-
|  -5
|~ 28/27 10/9 7/6 5/4 35/27 7/5 3/2 14/9 5/3 140/81 28/15 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|  -0.0417
|-
|  -4
|~ 28/27 10/9 6/5 56/45 4/3 112/81 40/27 8/5 224/135 16/9 28/15 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|  -0.0237
|-
|  -3
|~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|  -0.0214
|-
|  -2
|~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0191
|-
|  -1
|~ 15/14 10/9 6/5 56/45 4/3 10/7 40/27 8/5 5/3 9/5 28/15 2/1
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|  -0.0011
|-
|1
|~ 15/14 10/9 6/5 5/4 27/20 7/5 3/2 45/28 5/3 9/5 28/15 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0011
|-
|2
|~ 15/14 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0191
|-
|3
|~ 15/14 10/9 6/5 9/7 4/3 10/7 3/2 45/28 5/3 9/5 27/14 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0214
|-
|4
|~ 15/14 9/8 135/112 5/4 27/20 81/56 3/2 45/28 5/3 9/5 27/14 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0237
|-
|5
|~ 15/14 81/70 6/5 9/7 4/3 10/7 54/35 8/5 12/7 9/5 27/14 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0417
|-
|6
|~ 15/14 81/70 6/5 9/7 27/20 81/56 3/2 45/28 243/140 9/5 27/14 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0440
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family|Meantone]][12]
|81/80, 126/125
|-
|L = m
|sLLsLLLsLLsL
|[[Diminished]][12] MODMOS
|36/35, 50/49
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 126/125
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[16edo|16]]
|[[19edo|19]]
|[[27edo|27]]
|[[31edo|31]]
|[[46edo|46]]
|[[50edo|50]]
|[[58edo|58]]
|[[77edo|77]]
|-
!Step sizes in ET
|(2, 1, 0)
|(1, 1, 2)
|(2, 1, 1)
|(3, 2, 1)
|(3, 2, 2)
|(5, 3, 2)
|(5, 3, 3)
|(6, 4, 3)
|(8, 5, 4)
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]]=====
=====[[SNS (2/1, 3/2, 6/5: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]]=====
7L 1m 4s = (27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63) = (123.5395c, 78.929c, 64.0225c) TE
{| class="wikitable"
 
!Step signature
~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1 as sLLsLmLsLLsL
!Steps in JI
 
!Step sizes in cents (TE)
m = s -> sLLsLsLsLLsL Meanpop[12]; L = m -> sLLsLLLsLLsL MODMOS; s = 0 -> LLLsLLLL
|-
 
|7L 1m 4s
12f-ET: (1, 1, 1); 15f-ET: (2, 1, 0); 19-ET: (2, 1, 1); 27-ET: (3, 2, 1); 31-ET: (3, 2, 2); 46-ET: (5, 3, 2); 50-ET: (5, 3, 3); 58-ET: (6, 4, 3); 77-ET: (8, 5, 4)
|(27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63)
|(123.5395c, 78.929c, 64.0225c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 28/27 10/9 52/45 26/21 4/3 104/75 40/27 14/9 5/3 26/15 13/7 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|  -0.0465
|-
|  -5
|~ 28/27 10/9 7/6 5/4 13/10 7/5 3/2 14/9 5/3 26/15 13/7 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|  -0.0433
|-
|  -4
|~ 28/27 10/9 6/5 26/21 4/3 104/75 40/27 8/5 104/63 16/9 13/7 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|  -0.0256
|-
|  -3
|~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 13/7 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|  -0.0225
|-
|  -2
|~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 13/7 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0193
|-
|  -1
|~ 14/13 10/9 6/5 26/21 4/3 10/7 40/27 8/5 5/3 9/5 13/7 2/1
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|  -0.0016
|-
|1
|~ 14/13 10/9 6/5 5/4 27/20 7/5 3/2 21/13 5/3 9/5 13/7 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0016
|-
|2
|~ 14/13 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0193
|-
|3
|~ 14/13 10/9 6/5 9/7 4/3 10/7 3/2 21/13 5/3 9/5 27/14 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0225
|-
|4
|~ 14/13 9/8 63/52 5/4 27/20 75/52 3/2 21/13 5/3 9/5 27/14 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0256
|-
|5
|~ 14/13 15/13 6/5 9/7 4/3 10/7 20/13 8/5 12/7 9/5 27/14 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0433
|-
|6
|~ 14/13 15/13 6/5 9/7 27/20 75/52 3/2 21/13 45/26 9/5 27/14 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0465
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanpop]][12]
|81/80, 105/104, 126/125
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|15f
|[[19edo|19]]
|[[27edo|27]]
|[[31edo|31]]
|[[46edo|46]]
|[[50edo|50]]
|[[58edo|58]]
|[[77edo|77]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 2, 1)
|(3, 2, 2)
|(5, 3, 2)
|(5, 3, 3)
|(6, 4, 3)
|(8, 5, 4)
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
{| class="wikitable"
{| class="wikitable"
Line 2,646: Line 2,914:
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
Line 2,660: Line 2,928:
|-
|-
|3
|3
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 81/50 5/3 9/5 108/55 2/1
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 18/11 5/3 9/5 108/55 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
Line 2,667: Line 2,935:
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 81/50 5/3 9/5 108/55 2/1
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 108/55 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
Line 2,681: Line 2,949:
|-
|-
|6
|6
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 81/50 216/121 9/5 108/55 2/1
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 18/11 216/121 9/5 108/55 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
Line 2,731: Line 2,999:
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)]]=====
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)]]=====
7L 1m 4s = (27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54) = (132.5782c, 82.867c, 46.5074c) TE
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)
|(132.5782c, 82.867c, 46.5074c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 28/27 10/9 121/108 11/9 4/3 110/81 22/15 14/9 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|  -0.0671
|-
|  -5
|~ 28/27 10/9 7/6 5/4 121/96 11/8 3/2 14/9 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|  -0.0526
|-
|  -4
|~ 28/27 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|  -0.0445
|-
|  -3
|~ 28/27 10/9 6/5 11/9 4/3 11/8 3/2 14/9 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|  -0.0299
|-
|  -2
|~ 21/20 9/8 7/6 5/4 15/11 11/8 3/2 14/9 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0154
|-
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|  -0.0073
|-
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0073
|-
|2
|~ 12/11 10/9 6/5 9/7 4/3 16/11 22/15 8/5 12/7 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0154
|-
|3
|~ 12/11 10/9 6/5 9/7 4/3 16/11 3/2 18/11 5/3 9/5 27/14 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0299
|-
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 27/14 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0445
|-
|5
|~ 12/11 144/121 6/5 9/7 4/3 16/11 192/121 8/5 12/7 9/5 27/14 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0526
|-
|6
|~ 12/11 144/121 6/5 9/7 15/11 81/55 3/2 81/50 216/121 9/5 27/14 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0671
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanenneadecal]][12]
|45/44, 56/55, 81/80
|-
|L = m
|sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
|36/35, 50/49, 56/55
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 55/54, 77/75
|}


~ 28/27 10/9 6/5 11/9 4/3 7/5 3/2 14/9 5/3 9/5 11/6 2/1 as sLLsLmLsLLsL
{| class="wikitable"
 
|+Rank-1 temperings
m = s -> sLLsLsLsLLsL Meanenneadecal[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]
!ET
 
|[[15edo|15]]
12-ET: (1, 1, 1); 15-ET: (2, 1, 0); 19-ET: (2, 1, 1); 27e-ET: (3, 2, 1); 34-ET: (4, 2, 1)
|[[19edo|19]]
|27e
|[[34edo|34]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 2, 1)
|(4, 2, 1)
|}
=====[[SNS (2/1, 3/2, 6/5: 4375/4374)-12|(2/1, 3/2, 6/5: 4375/4374)[12] (Ragismic)]]=====
=====[[SNS (2/1, 3/2, 6/5: 4375/4374)-12|(2/1, 3/2, 6/5: 4375/4374)[12] (Ragismic)]]=====
7L 1m 4s = (~27/25, ~25/24, 250/243~36/35) = (133.4115c, 70.5569c, 48.8911c) TE
7L 1m 4s = (~27/25, ~25/24, 250/243~36/35) = (133.4115c, 70.5569c, 48.8911c) TE
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"