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Gallery of 3-SN scales: Difference between revisions

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Line 2,959: Line 2,959:
|L - m = m - s
|L - m = m - s
|LsLALsL
|LsLALsL
|Tetracot[7] MODMOS
|[[Tetracot family#Subgroup temperament|Tetracot]][7] MODMOS
|100/99, 243/242
|100/99, 243/242
|}
|}
Line 3,129: Line 3,129:
|(6, 5, 4)
|(6, 5, 4)
|}
|}
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
 
===== (2/1, 3/2, 6/5: 100/99, 144/143)[7] (No-7 Ptolemismic) =====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents
!Step sizes in cents (TE)
|-
|-
|7L 1m 4s
|1L 4m 2s
|(27/25, 25/24, 250/243)
|(9/8~25/22, 10/9~11/10, 27/25~12/11~13/12)
|(133.2376c, 70.6724c, 49.1661c)
|(209.5416c, 175.8918c, 142.7754c)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode in JI
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[12]
!Meantone[7]
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!UDP
!Porcupine mode
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -3
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|~ 12/11 6/5 4/3 13/9 8/5 9/5 2/1
|sLsLLsLmLsLL
|smmsmLm
|sLsLLsLsLsLL
|sLLsLLL
|<nowiki>1|10</nowiki>
|<nowiki>0|6</nowiki>
| -0.0622
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
|
|-
|-
| -5
| -2
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|sLmLsLLsLsLL
|msmmsmL
|sLsLsLLsLsLL
|LsLLsLL
|<nowiki>0|11</nowiki>
|<nowiki>2|4</nowiki>
| -0.0587
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|
|-
|-
| -4
| -1
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|~ 12/11 6/5 15/11 3/2 13/8 9/5 2/1
|sLLsLsLLsLmL
|smLmsmm
|sLLsLsLLsLsL
|sLLLsLL
|<nowiki>4|7</nowiki>
|<nowiki>1|5</nowiki>
| -0.0338
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|
|-
|-
| -3
|0
|250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|sLLsLmLsLLsL
|msmLmsm
|sLLsLsLsLLsL
|LsLLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|3</nowiki>
| -0.0302
|Dorian
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|
|-
|-
| -2
|1
|25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|mLsLLsLsLLsL
|mmsmLms
|sLsLLsLsLLsL
|LLsLLLs
|<nowiki>2|9</nowiki>
|<nowiki>5|1</nowiki>
| -0.0267
|Ionian
|-
|ssssLss
|  -1
|<nowiki>2|4</nowiki>
|27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1
|Bright diminished
|LsLsLLsLmLsL
|
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
| -0.0018
|-
|1
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0018
|-
|-
|2
|2
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LsLLsLsLLsLm
|Lmsmmsm
|LsLLsLsLLsLs
|LLsLLsL
|<nowiki>9|2</nowiki>
|<nowiki>4|2</nowiki>
|0.0267
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|
|-
|-
|3
|3
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|LsLLsLmLsLLs
|mLmsmms
|LsLLsLsLsLLs
|LLLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>6|0</nowiki>
|0.0302
|Lydian
|-
|sLsssss
|4
|<nowiki>5|1</nowiki>
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|Dark major
|LmLsLLsLsLLs
|
|LsLsLLsLsLLs
|}
|<nowiki>7|4</nowiki>
|0.0338
|-
|5
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0587
|-
|6
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0622
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-2 temperings (mode 2)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 3,239: Line 3,237:
|-
|-
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[1L 6s|sssLsss]]
|[[Meantone family|Meantone]][12]
|[[Porcupine family#13-limit|Porcupine]][7]
|81/80
|40/39, 55/54, 66/65
|-
|-
|L = m
|L = m
|sLLsLLLsLLsL
|[[5L 2s|LsLLLsL]]
|[[Dimipent family|Diminished]][12] MODMOS
|[[Meantone family#Flattone|Flattone]][7]
|648/625
|45/44, 65/64, 81/80
|-
|L = s
|[[11L 1s|LLLLLsLLLLLL]]
|[[Ripple family|Ripple]][12]
|6561/6250
|-
|-
|L - m = m - s
|L - m = m - s
|dLLdLsLdLLdL
|LsLALsL
|Augmented[12] MODMOS
|[[Tetracot family#Subgroup temperament|Tetracot]][7] MODMOS
|128/125
|100/99, 144/143, 243/242
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porcupine|Porcupine]][8]
|250/243
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
{| class="wikitable"
{| class="wikitable"
!Step signature
|+Rank-1 temperings
!Steps in JI
!ET
!Step sizes in cents (TE)
|8
|-
|[[12edo|12]]
|7L 1m 4s
|[[15edo|15]]
|(27/25~15/14, 25/24~21/20, 250/243~28/27)
|[[19edo|19]]
|(123.5395c, 78.929c, 64.0225c)
|22f
|[[26edo|26]]
|27e
|[[34edo|34]]
|[[41edo|41]]
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 2)
|(3, 3, 2)
|(4, 3, 3)
|(4, 4, 3)
|(5, 4, 3)
|(6, 5, 4)
|(7, 6, 5)
|}
|}
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
{| class="wikitable"
{| class="wikitable"
!Mode number
!Step signature
!Mode as simplest JI pre-image
!Steps in JI
!Step sizes in cents
|-
|7L 1m 4s
|(27/25, 25/24, 250/243)
|(133.2376c, 70.6724c, 49.1661c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!Step pattern
!Meantone[12]
!Meantone[12]
Line 3,281: Line 3,294:
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -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
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL  
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
| -0.0440
| -0.0622
|-
|-
| -5
| -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
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
| -0.0417
| -0.0587
|-
|-
| -4
| -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
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
| -0.0237
| -0.0338
|-
|-
| -3
| -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
|250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
| -0.0214
| -0.0302
|-
|-
|  -2
|  -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
|25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  -0.0191
|  -0.0267
|-
|-
|  -1
|  -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
|27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  -0.0011
|  -0.0018
|-
|-
|1
|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
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|0.0011
|0.0018
|-
|-
|2
|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
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|0.0191
|0.0267
|-
|-
|3
|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
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|0.0214
|0.0302
|-
|-
|4
|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
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|0.0237
|0.0338
|-
|-
|5
|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
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|0.0417
|0.0587
|-
|-
|6
|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
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|0.0440
|0.0622
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,375: Line 3,388:
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family|Meantone]][12]
|[[Meantone family|Meantone]][12]
|81/80, 126/125
|81/80
|-
|-
|L = m
|L = m
|sLLsLLLsLLsL
|sLLsLLLsLLsL
|[[Diminished]][12] MODMOS
|[[Dimipent family|Diminished]][12] MODMOS
|36/35, 50/49
|648/625
|-
|-
|L - m = m - s
|L = s
|dLLdLsLdLLdL
|[[11L 1s|LLLLLsLLLLLL]]
|Augene[12] MODMOS
|[[Ripple family|Ripple]][12]
|64/63, 126/125  
|6561/6250
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augmented[12] MODMOS
|128/125
|-
|-
|s = 0
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|[[Porcupine family#Porcupine|Porcupine]][8]
|28/27, 126/125
|250/243
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
!Step signature
!ET
!Steps in JI
|[[15edo|15]]
!Step sizes in cents (TE)
|[[16edo|16]]
|-
|[[19edo|19]]
|7L 1m 4s
|[[27edo|27]]
|(27/25~15/14, 25/24~21/20, 250/243~28/27)
|[[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]]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|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)
|(123.5395c, 78.929c, 64.0225c)
|}
|}
Line 3,435: Line 3,429:
|-
|-
|  -6
|  -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
|~ 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
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
|  -0.0465
|  -0.0440
|-
|-
|  -5
|  -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
|~ 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
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
|  -0.0433
|  -0.0417
|-
|-
|  -4
|  -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
|~ 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
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
|  -0.0256
|  -0.0237
|-
|-
|  -3
|  -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
|~ 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
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
|  -0.0225
|  -0.0214
|-
|-
|  -2
|  -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
|~ 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
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  -0.0193
|  -0.0191
|-
|-
|  -1
|  -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
|~ 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
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  -0.0016
|  -0.0011
|-
|-
|1
|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
|~ 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
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|0.0016
|0.0011
|-
|-
|2
|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
|~ 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
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|0.0193
|0.0191
|-
|-
|3
|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
|~ 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
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|0.0225
|0.0214
|-
|-
|4
|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
|~ 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
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|0.0256
|0.0237
|-
|-
|5
|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
|~ 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
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|0.0433
|0.0417
|-
|-
|6
|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
|~ 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
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|0.0465
|0.0440
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,527: Line 3,521:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanpop]][12]
|[[Meantone family|Meantone]][12]
|81/80, 105/104, 126/125
|81/80, 126/125
|-
|L = m
|sLLsLLLsLLsL
|[[Diminished]][12] MODMOS
|36/35, 50/49
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|64/63, 126/125
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 126/125
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|15f
|[[15edo|15]]
|[[16edo|16]]
|[[19edo|19]]
|[[19edo|19]]
|[[27edo|27]]
|[[27edo|27]]
Line 3,544: Line 3,554:
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(1, 1, 2)
|(2, 1, 1)
|(2, 1, 1)
|(3, 2, 1)
|(3, 2, 1)
Line 3,552: Line 3,563:
|(8, 5, 4)
|(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: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]]=====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
Line 3,559: Line 3,570:
|-
|-
|7L 1m 4s
|7L 1m 4s
|(27/25~12/11, 25/24~33/32, 250/243~55/54~121/120)
|(27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63)
|(146.6352c, 63.1434c, 27.4197c)
|(123.5395c, 78.929c, 64.0225c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,570: Line 3,581:
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|~ 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
|sLsLLsLmLsLL
|sLsLLsLsLsLL  
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
| -0.0899
| -0.0465
|-
|-
| -5
| -5
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|~ 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
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
| -0.0819
| -0.0433
|-
|-
| -4
| -4
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|~ 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
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
| -0.0510
| -0.0256
|-
|-
| -3
| -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|~ 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
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
| -0.0430
| -0.0225
|-
|-
|  -2
|  -2
|~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|~ 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
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  -0.0349
|  -0.0193
|-
|-
|  -1
|  -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
|~ 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
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  -0.0040
|  -0.0016
|-
|-
|1
|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
|~ 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
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|0.0040
|0.0016
|-
|-
|2
|2
|~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1
|~ 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
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|0.0349
|0.0193
|-
|-
|3
|3
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 18/11 5/3 9/5 108/55 2/1
|~ 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
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|0.0430
|0.0225
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 108/55 2/1
|~ 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
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|0.0510
|0.0256
|-
|-
|5
|5
|~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1
|~ 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
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|0.0819
|0.0433
|-
|-
|6
|6
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 18/11 216/121 9/5 108/55 2/1
|~ 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
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|0.0899
|0.0465
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,663: Line 3,674:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanenneadecal]][12] or [[Meantone family#Flattone|Flattone]][12]
|[[Meanpop]][12]
|45/44, 81/80
|81/80, 105/104, 126/125
|-
|L = m
|sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
|100/99, 128/121
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|100/99, 128/125
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porkypine|Porkypine]][8]
|55/54, 100/99
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|[[15edo|15]]
|15f
|[[19edo|19]]
|[[19edo|19]]
|[[22edo|22]]
|[[27edo|27]]
|[[26edo|26]]
|[[31edo|31]]
|27e
|[[46edo|46]]
|[[29edo|29]]
|[[50edo|50]]
|[[34edo|34]]
|[[58edo|58]]
|[[37edo|37]]
|[[77edo|77]]
|[[41edo|41]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(3, 2, 1)
|(3, 2, 1)
|(4, 1, 0)
|(3, 2, 2)
|(4, 2, 1)
|(5, 3, 2)
|(5, 2, 0)
|(5, 3, 3)
|(5, 2, 1)
|(6, 4, 3)
|(8, 5, 4)
|}
|}
=====(2/1, 3/2, 6/5: 100/99, 385/384)[12] ([[Keemic family#Supermagic|Supermagic]])=====
=====[[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"
!Step signature
!Step signature
Line 3,713: Line 3,706:
|-
|-
|7L 1m 4s
|7L 1m 4s
|(27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120)
|(27/25~12/11, 25/24~33/32, 250/243~55/54~121/120)
|(149.51592c, 58.8799c, 23.6254c)
|(146.6352c, 63.1434c, 27.4197c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,724: Line 3,717:
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL  
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
|  
| -0.0899
|-
|-
| -5
| -5
|~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
|  
| -0.0819
|-
|-
| -4
| -4
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
|  
| -0.0510
|-
|-
| -3
| -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
|  
| -0.0430
|-
|  -2
|~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0349
|-
|  -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>
|  -0.0040
|-
|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
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|0.0040
|-
|2
|~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0349
|-
|3
|~ 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
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0430
|-
|4
|~ 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
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0510
|-
|5
|~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0819
|-
|6
|~ 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
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0899
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meanenneadecal]][12] or [[Meantone family#Flattone|Flattone]][12]
|45/44, 81/80
|-
|L = m
|sLLsLLLsLLsL
|[[Dimipent family|Diminished]][12] MODMOS
|100/99, 128/121
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|100/99, 128/125
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porkypine|Porkypine]][8]
|55/54, 100/99
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|27e
|[[29edo|29]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(3, 2, 1)
|(4, 1, 0)
|(4, 2, 1)
|(5, 2, 0)
|(5, 2, 1)
|}
 
===== (2/1, 3/2, 6/5: 100/99, 144/143)[12] (No-7 Ptolemismic) =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~13/12, 25/24~33/32~27/26, 250/243~55/54~121/120~40/39)
|[http://x31eq.com/cgi-bin/rt.cgi?ets=7%261ce%264f&limit=2.3.5.11.13 (142.77537c, 66.76626c, 33.11646c)]
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 40/39 10/9 44/39 11/9 4/3 110/81 22/15 20/13 5/3 22/13 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|
|-
|  -5
|~ 40/39 10/9 15/13 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|
|-
|  -4
|~ 40/39 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>
|
|-
|  -3
|~ 40/39 10/9 6/5 11/9 4/3 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|
|-
|  -2
|~ 25/24 9/8 15/13 5/4 15/11 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|
|-
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 13/9 22/15 8/5 5/3 9/5 11/6 2/1
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|
|-
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 13/8 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|-
|2
|~ 12/11 10/9 6/5 13/10 4/3 13/9 22/15 8/5 26/15 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|
|-
|3
|~ 12/11 10/9 6/5 13/10 4/3 13/9 3/2 13/8 5/3 9/5 39/20 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|
|-
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 13/8 5/3 9/5 39/20 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|
|-
|5
|~ 12/11 13/11 6/5 13/10 4/3 13/9 52/33 8/5 26/15 9/5 39/20 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|
|-
|6
|~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 13/8 39/22 9/5 39/20 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 65/64, 81/80
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#13-limit|Porcupine]][8]
|40/39, 55/54, 66/65
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|22f
|[[26edo|26]]
|27e
|[[34edo|34]]
|[[41edo|41]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(3, 2, 1)
|(4, 2, 1)
|(5, 2, 1)
|}
 
=====(2/1, 3/2, 6/5: 100/99, 385/384)[12] ([[Keemic family#Supermagic|Supermagic]])=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120)
|(149.51592c, 58.8799c, 23.6254c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|
|-
|  -5
|~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|
|-
|  -4
|~ 55/54 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>
|
|-
|  -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|
|-
|  -2
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|
|-
|  -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>
|
|-
|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
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|-
|2
|~ 12/11 10/9 6/5 21/16 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|
|-
|3
|~ 12/11 10/9 6/5 21/16 4/3 16/11 3/2 18/11 5/3 9/5 63/32 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|
|-
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|
|-
|5
|~ 12/11 144/121 6/5 21/16 4/3 16/11 192/121 8/5 7/4 9/5 63/32 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|
|-
|-
| -2
|6
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1
|mLsLLsLsLLsL
|LLsLmLsLLsLs
|sLsLLsLsLLsL
|LLsLsLsLLsLs
|<nowiki>2|9</nowiki>
|<nowiki>10|1</nowiki>
|  
|
|}
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|-
| -1
|m = s
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|[[7L 5s|sLLsLsLsLLsL]]
|LsLsLLsLmLsL
|[[Meantone family#Flattone|Flattone]][12]
|LsLsLLsLsLsL
|45/44, 81/80, 385/384
|<nowiki>6|5</nowiki>
|
|-
|-
|1
|s = 0
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|[[7L 1s|LLLsLLLL]]
|LsLmLsLLsLsL
|[[Porcupine family#11-limit|Porcupine]][8]
|LsLsLsLLsLsL
|55/54, 64/63, 100/99
|<nowiki>5|6</nowiki>
|}
|
 
|-
{| class="wikitable"
|2
|+Rank-1 temperings
|~ 12/11 10/9 6/5 21/16 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
!ET
|LsLLsLsLLsLm
|[[15edo|15]]
|LsLLsLsLLsLs
|[[19edo|19]]
|<nowiki>9|2</nowiki>
|[[22edo|22]]
|
|[[26edo|26]]
|[[34edo|34]]
|[[41edo|41]]
|[[104edo|104]]
|-
|-
|3
!Step sizes in ET
|~ 12/11 10/9 6/5 21/16 4/3 16/11 3/2 18/11 5/3 9/5 63/32 2/1
|(2, 1, 0)
|LsLLsLmLsLLs
|(2, 1, 1)
|LsLLsLsLsLLs
|(3, 1, 0)
|<nowiki>8|3</nowiki>
|(3, 1, 1)
|
|(4, 2, 1)
|-
|(5, 2, 1)
|4
|(13, 5, 2)
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1
|}
|LmLsLLsLsLLs
=====[[SNS (2/1, 3/2, 6/5: 100/99, 105/104, 144/143)-12|(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12]]] ([[Keemic family#Supermagic|Supermagic]])=====
|LsLsLLsLsLLs
{| class="wikitable"
|<nowiki>7|4</nowiki>
!Step signature
|
!Steps in JI
!Step sizes in cents (TE)
|-
|-
|5
|7L 1m 4s
|~ 12/11 144/121 6/5 21/16 4/3 16/11 192/121 8/5 7/4 9/5 63/32 2/1
|(27/25~12/11~13/12~35/32, 25/24~27/26~33/32, 250/243~40/39~55/54~64/63~121/120)
|LLsLsLLsLmLs
|(145.47082c, 58.39270c, 30.85183c)
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|
|-
|6
|~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
!Mode number
!Equivalence
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Scale
!Meantone[12]
!Comma list
!UDP
![[Mode height]]
|-
|-
|m = s
| -6
|[[7L 5s|sLLsLsLsLLsL]]
|~ 40/39 10/9 44/39 11/9 4/3 110/81 22/15 20/13 5/3 22/13 11/6 2/1
|[[Meantone family#Flattone|Flattone]][12]
|sLsLLsLmLsLL
|45/44, 81/80, 385/384
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|  
|-
|-
|s = 0
| -5
|[[7L 1s|LLLsLLLL]]
|~ 40/39 10/9 8/7 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1
|[[Porcupine family#Septimal porcupine|Porcupine]][8]
|sLmLsLLsLsLL
|55/54, 64/63, 100/99
|sLsLsLLsLsLL
|}
|<nowiki>0|11</nowiki>
 
|  
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|[[34edo|34]]
|[[41edo|41]]
|[[104edo|104]]
|-
|-
!Step sizes in ET
| -4
|(2, 1, 0)
|~ 40/39 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|(2, 1, 1)
|sLLsLsLLsLmL
|(3, 1, 0)
|sLLsLsLLsLsL
|(3, 1, 1)
|<nowiki>4|7</nowiki>
|(4, 2, 1)
|
|(5, 2, 1)
|(13, 5, 2)
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99, 105/104, 144/143)-12|(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12]]] ([[Keemic family#Supermagic|Supermagic]])=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|-
|7L 1m 4s
| -3
|(27/25~12/11~13/12~35/32, 25/24~27/26~33/32, 250/243~40/39~55/54~64/63~121/120)
|~ 40/39 10/9 6/5 11/9 4/3 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|(145.47082c, 58.39270c, 30.85183c)
|sLLsLmLsLLsL
|}
|sLLsLsLsLLsL
{| class="wikitable"
|<nowiki>3|8</nowiki>
!Mode number
|
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|-
|  -6
|  -2
|~ 40/39 10/9 44/39 11/9 4/3 110/81 22/15 20/13 5/3 22/13 11/6 2/1
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|sLsLLsLmLsLL
|mLsLLsLsLLsL
|sLsLLsLsLsLL
|sLsLLsLsLLsL
|<nowiki>1|10</nowiki>
|<nowiki>2|9</nowiki>
|  
|  
|-
|-
|  -5
|  -1
|~ 40/39 10/9 8/7 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1
|~ 12/11 10/9 6/5 11/9 4/3 13/9 22/15 8/5 5/3 9/5 11/6 2/1
|sLmLsLLsLsLL
|LsLsLLsLmLsL
|sLsLsLLsLsLL
|LsLsLLsLsLsL
|<nowiki>0|11</nowiki>
|<nowiki>6|5</nowiki>
|  
|  
|-
|-
| -4
|1
|~ 40/39 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 13/8 5/3 9/5 11/6 2/1
|sLLsLsLLsLmL
|LsLmLsLLsLsL
|sLLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>5|6</nowiki>
|
|-
|  -3
|~ 40/39 10/9 6/5 11/9 4/3 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|
|-
|  -2
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 20/13 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|
|-
|  -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>
|
|-
|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
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|
|-
|-
|2
|2
|~ 12/11 10/9 6/5 13/10 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
|~ 12/11 10/9 6/5 13/10 4/3 13/9 22/15 8/5 7/4 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
Line 3,921: Line 4,210:
|-
|-
|3
|3
|~ 12/11 10/9 6/5 13/10 4/3 16/11 3/2 18/11 5/3 9/5 39/20 2/1
|~ 12/11 10/9 6/5 13/10 4/3 13/9 3/2 13/8 5/3 9/5 39/20 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
Line 3,928: Line 4,217:
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 39/20 2/1
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 13/8 5/3 9/5 39/20 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
Line 3,935: Line 4,224:
|-
|-
|5
|5
|~ 12/11 13/11 6/5 13/10 4/3 16/11 52/33 8/5 7/4 9/5 39/20 2/1
|~ 12/11 13/11 6/5 13/10 4/3 13/9 52/33 8/5 7/4 9/5 39/20 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
Line 3,942: Line 4,231:
|-
|-
|6
|6
|~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 18/11 39/22 9/5 39/20 2/1
|~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 13/8 39/22 9/5 39/20 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
Line 3,962: Line 4,251:
|s = 0
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Septimal porcupine|Porcupine]][8]
|[[Porcupine family#13-limit|Porcupine]][8]
|40/39, 55/54, 64/63, 66/65
|40/39, 55/54, 64/63, 66/65
|}
|}
Line 4,243: Line 4,532:
|}
|}


{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|[[15edo|15]]
|[[15edo|15]]
|[[19edo|19]]
|[[19edo|19]]
|27e
|27e
|[[34edo|34]]
|[[34edo|34]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 2, 1)
|(3, 2, 1)
|(4, 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
 
 
~ 27/25 10/9 6/5 35/27 4/3 36/25 3/2 81/50 5/3 9/5 35/18 2/1 as LsLLsLmLsLLs
~ 27/25 10/9 6/5 35/27 4/3 36/25 3/2 81/50 5/3 9/5 35/18 2/1 as LsLLsLmLsLLs
 
 
m = s -> LsLLsLsLsLLs Falttone[12]; L = m -> LsLLsLLLsLLs MODMOS; L = s -> LLLLLLsLLLLL; s = 0 -> LLLLsLLL Hystrix[8]
m = s -> LsLLsLsLsLLs Falttone[12]; L = m -> LsLLsLLLsLLs MODMOS; L = s -> LLLLLLsLLLLL; s = 0 -> LLLLsLLL Hystrix[8]
 
 
19-ET: (2, 1, 1); 53-ET: (6, 3, 2); 72-ET: (8, 4, 3); 99-ET: (11, 6, 4); 118-ET: (13, 7, 5); 152-ET: (17, 9, 6); 171-ET: (19, 10, 7); 224-ET: (25, 13, 9); 270-ET: (30, 16, 11); 441-ET: (49, 26, 18); 494-ET: (55, 29, 20); 612-ET: (68, 36, 25)
19-ET: (2, 1, 1); 53-ET: (6, 3, 2); 72-ET: (8, 4, 3); 99-ET: (11, 6, 4); 118-ET: (13, 7, 5); 152-ET: (17, 9, 6); 171-ET: (19, 10, 7); 224-ET: (25, 13, 9); 270-ET: (30, 16, 11); 441-ET: (49, 26, 18); 494-ET: (55, 29, 20); 612-ET: (68, 36, 25)
====(2/1, 3/2, 6/5: 100/99, 144/143)[20] (No-7 Ptolemismic)====
7L 12m 1s = (~189/176, 250/243~55/54~121/120~40/39, 81/80~45/44~65/64) =
 
====(2/1, 3/2, 6/5: 100/99, 385/384)[20] (Supermagic)====
====(2/1, 3/2, 6/5: 100/99, 385/384)[20] (Supermagic)====
7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE
7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE


~ 189/176 12/11 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
40/39 12/11 10/9 32/27 6/5 11/9 13/10 4/3 11/8 22/15 3/2 20/13 13/8 5/3 16/9 9/5 11/6 39/20 2/1
 
~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1 as LmmLmLmmLmsmLmmLmLmm
 
m = s -> LssLsLssLsssLssLsLss Tetracot[20] MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL Camahueto[20]; L = s -> LssLsLssLsLsLssLsLss Diminished[20] MODMOS;
 
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Porcupine[8]
 
19-ET: (1, 1, 0); 22-ET: (3, 0, 1); 26-ET: ( 34-ET; 41-ET; 104-ET:
====[[SNS (2/1, 3/2, 6/5: 4375/4374)-20|(2/1, 3/2, 6/5: 4375/4374)[20] (Ragismic)]]====
====[[SNS (2/1, 3/2, 6/5: 4375/4374)-20|(2/1, 3/2, 6/5: 4375/4374)[20] (Ragismic)]]====
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c) TE
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c) TE
Retrieved from "https://en.xen.wiki/w/Gallery_of_3-SN_scales"