Gallery of 3-SN scales: Difference between revisions

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m →((2/1, 5/4)[3], 16/15): added some 12e and 53e
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Line 1: Line 1:
See [[SN scale]] and [[Rank-3 scale]].
See [[SN scale]] and [[Rank-3 scale]].


Line 66: Line 64:
|Antitonic[4]
|Antitonic[4]
|9/8
|9/8
|-
|L - M = M - s
|LsLd
|Bug[4] MODMOS
|27/25
|-
|-
|s = 0
|s = 0
Line 145: Line 148:
|[[Enipucrop]][7]
|[[Enipucrop]][7]
|1125/1024
|1125/1024
|-
|L - M = M - s
|sAsLsAs
|[[Meantone]][7] MODMOS
|81/80
|-
|-
| s = 0
| s = 0
Line 224: Line 232:
|[[Enipucrop]][7]
|[[Enipucrop]][7]
| 35/32, 49/45
| 35/32, 49/45
|-
|L - M = M - s
|sAsLsAs
|[[Meantone]][7] MODMOS
|81/80, 126/125
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 269: Line 282:
!Mode in JI
!Mode in JI
!Step pattern
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Negri[10]
!UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 274: Line 293:
|16/15 256/225 6/5 32/25 512/375 3/2 8/5 128/75 2048/1125 2/1
|16/15 256/225 6/5 32/25 512/375 3/2 8/5 128/75 2048/1125 2/1
|mmsmmLmmmL
|mmsmmLmmmL
|sssssLsssL
|Dark minor
|LLsLLLLLLL
|<nowiki>2|7</nowiki>
| -.0564
| -.0564
|-
|-
Line 279: Line 302:
|16/15 9/8 6/5 32/25 45/32 3/2 8/5 128/75 15/8 2/1
|16/15 9/8 6/5 32/25 45/32 3/2 8/5 128/75 15/8 2/1
|msmmLmmmLm
|msmmLmmmLm
|ssssLsssLs
|Alternate minor
|LsLLLLLLLL
|<nowiki>1|8</nowiki>
| -.0411
| -.0411
|-
|-
Line 284: Line 311:
|135/128 9/8 6/5 675/512 45/32 3/2 8/5 225/128 15/8 2/1
|135/128 9/8 6/5 675/512 45/32 3/2 8/5 225/128 15/8 2/1
|smmLmmmLmm
|smmLmmmLmm
|sssLsssLss
|Bright minor
|sLLLLLLLLL
|<nowiki>0|9</nowiki>
| -.0258
| -.0258
|-
|-
Line 289: Line 320:
|16/15 256/225 4096/3375 4/3 64/45 1024/675 8/5 128/75 2048/1125 2/1
|16/15 256/225 4096/3375 4/3 64/45 1024/675 8/5 128/75 2048/1125 2/1
|mmmLmmsmmL
|mmmLmmsmmL
|sssLsssssL
|Standard minor
|LLLLLLsLLL
|<nowiki>6|3</nowiki>
| -.0230
| -.0230
|-
|-
Line 294: Line 329:
|16/15 256/225 5/4 4/3 64/45 3/2 8/5 128/75 15/8 2/1
|16/15 256/225 5/4 4/3 64/45 3/2 8/5 128/75 15/8 2/1
|mmLmmsmmLm
|mmLmmsmmLm
|ssLsssssLs
|Dark major
|LLLLLsLLLL
|<nowiki>5|4</nowiki>
| -.0077
| -.0077
|-
|-
Line 299: Line 338:
|16/15 75/64 5/4 4/3 45/32 3/2 8/5 225/128 15/8 2/1
|16/15 75/64 5/4 4/3 45/32 3/2 8/5 225/128 15/8 2/1
|mLmmsmmLmm
|mLmmsmmLmm
|sLsssssLss
|Alternate major
|LLLLsLLLLL
|<nowiki>4|5</nowiki>
|.0077
|.0077
|-
|-
Line 304: Line 347:
|1125/1024 75/64 5/4 675/512 45/32 3/2 3375/2048 225/128 15/8 2/1
|1125/1024 75/64 5/4 675/512 45/32 3/2 3375/2048 225/128 15/8 2/1
|LmmsmmLmmm
|LmmsmmLmmm
|LsssssLsss
|Bright major
|LLLsLLLLLL
|<nowiki>3|6</nowiki>
|.0239
|.0239
|-
|-
Line 309: Line 356:
|16/15 256/225 5/4 4/3 64/45 1024/675 5/3 16/9 256/135 2/1
|16/15 256/225 5/4 4/3 64/45 1024/675 5/3 16/9 256/135 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|Standard major
|LLLLLLLLLs
|<nowiki>9|0</nowiki>
|.0258
|.0258
|-
|-
Line 314: Line 365:
|16/15 75/64 5/4 4/3 64/45 25/16 5/3 16/9 15/8 2/1
|16/15 75/64 5/4 4/3 64/45 25/16 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|mLmmmLmmsm
|sLsssLssss
|Dark Augmented
|LLLLLLLLsL
|<nowiki>8|1</nowiki>
|.0411
|.0411
|-
|-
Line 319: Line 374:
|1125/1024 75/64 5/4 4/3 375/256 25/16 5/3 225/128 15/8 2/1
|1125/1024 75/64 5/4 4/3 375/256 25/16 5/3 225/128 15/8 2/1
|LmmmLmmsmm
|LmmmLmmsmm
|LsssLsssss
|Bright Augmented
|LLLLLLLsLL
|<nowiki>7|2</nowiki>
|.0564
|.0564
|}
|}
Line 329: Line 388:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|2048/2025
Line 338: Line 397:
|16875/16384  
|16875/16384  
|-
|-
|L= s
|L = s
|[[7L 3s|LsLLsLLsLL]]
|[[7L 3s|LsLLsLLsLL]]
|[[Dicot]][10]
|[[Dicot]][10]
|25/24
|25/24
|-
|L - m = m - s
|sLssdssLss
|[[Ampersand]][10] MODMOS
|34171875/33554432
|-
|-
|s = 0
|s = 0
Line 372: Line 436:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Negri[10]
!UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 377: Line 447:
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|mmsmmLmmmL
|mmsmmLmmmL
|sssssLsssL
|Dark minor
|LLsLLLLLLL
|<nowiki>2|7</nowiki>
| -.0475
| -.0475
|-
|-
Line 382: Line 456:
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
|msmmLmmmLm
|ssssLsssLs
|Alternate minor
|LsLLLLLLLL
|<nowiki>1|8</nowiki>
| -.0400
| -.0400
|-
|-
Line 387: Line 465:
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
|smmLmmmLmm
|sssLsssLss
|Bright minor
|sLLLLLLLLL
|<nowiki>0|9</nowiki>
| -.0325
| -.0325
|-
|-
Line 392: Line 474:
|~ 16/15 8/7 60/49 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|~ 16/15 8/7 60/49 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|mmmLmmsmmL
|mmmLmmsmmL
|sssLsssssL
|Standard minor
|LLLLLLsLLL
|<nowiki>6|3</nowiki>
| -.0112
| -.0112
|-
|-
Line 397: Line 483:
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
|mmLmmsmmLm
|ssLsssssLs
|Dark major
|LLLLLsLLLL
|<nowiki>5|4</nowiki>
| -.0037
| -.0037
|-
|-
Line 402: Line 492:
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|mLmmsmmLmm
|sLsssssLss
|Alternate major
|LLLLsLLLLL
|<nowiki>4|5</nowiki>
|.0037
|.0037
|-
|-
Line 407: Line 501:
|~ 35/32 7/6 5/4 21/16 7/5 3/2 49/30 7/4 15/8 2/1
|~ 35/32 7/6 5/4 21/16 7/5 3/2 49/30 7/4 15/8 2/1
|LmmsmmLmmm
|LmmsmmLmmm
|LsssssLsss
|Bright major
|LLLsLLLLLL
|<nowiki>3|6</nowiki>
|.0112
|.0112
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|Standard major
|LLLLLLLLLs
|<nowiki>9|0</nowiki>
|.0325
|.0325
|-
|-
Line 417: Line 519:
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|mLmmmLmmsm
|sLsssLssss
|Dark Augmented
|LLLLLLLLsL
|<nowiki>8|1</nowiki>
|.0400
|.0400
|-
|-
Line 422: Line 528:
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|LmmmLmmsmm
|LsssLsssss
|Bright Augmented
|LLLLLLLsLL
|<nowiki>7|2</nowiki>
|.0475
|.0475
|}
|}
Line 432: Line 542:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajara]][10] 4M (pentachordal decatonic)
|[[Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|50/49, 64/63
Line 445: Line 555:
|[[Sharp]][10]
|[[Sharp]][10]
|25/24, 28/27
|25/24, 28/27
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 1029/1024
|-
|-
|s = 0
|s = 0
Line 489: Line 604:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Negri[10]
!UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 494: Line 615:
|~ 16/15 8/7 6/5 9/7 11/8 3/2 8/5 12/7 11/6 2/1
|~ 16/15 8/7 6/5 9/7 11/8 3/2 8/5 12/7 11/6 2/1
|mmsmmLmmmL
|mmsmmLmmmL
|sssssLsssL
|Dark minor
|LLsLLLLLLL
|<nowiki>2|7</nowiki>
| -.0472
| -.0472
|-
|-
Line 499: Line 624:
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
|msmmLmmmLm
|ssssLsssLs
|Alternate minor
|LsLLLLLLLL
|<nowiki>1|8</nowiki>
| -.0400
| -.0400
|-
|-
Line 504: Line 633:
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
|smmLmmmLmm
|sssLsssLss
|Bright minor
|sLLLLLLLLL
|<nowiki>0|9</nowiki>
| -.0327
| -.0327
|-
|-
Line 509: Line 642:
|~ 16/15 8/7 11/9 4/3 10/7 32/21 8/5 12/7 11/6 2/1
|~ 16/15 8/7 11/9 4/3 10/7 32/21 8/5 12/7 11/6 2/1
|mmmLmmsmmL
|mmmLmmsmmL
|sssLsssssL
|Standard minor
|LLLLLLsLLL
|<nowiki>6|3</nowiki>
| -.0109
| -.0109
|-
|-
Line 514: Line 651:
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
|mmLmmsmmLm
|ssLsssssLs
|Dark major
|LLLLLsLLLL
|<nowiki>5|4</nowiki>
| -.0036
| -.0036
|-
|-
Line 519: Line 660:
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|mLmmsmmLmm
|sLsssssLss
|Alternate major
|LLLLsLLLLL
|<nowiki>4|5</nowiki>
|.0036
|.0036
|-
|-
Line 524: Line 669:
|~ 12/11 7/6 5/4 21/16 7/5 3/2 18/11 7/4 15/8 2/1
|~ 12/11 7/6 5/4 21/16 7/5 3/2 18/11 7/4 15/8 2/1
|LmmsmmLmmm
|LmmsmmLmmm
|LsssssLsss
|Bright major
|LLLsLLLLLL
|<nowiki>3|6</nowiki>
|.0109
|.0109
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|Standard major
|LLLLLLLLLs
|<nowiki>9|0</nowiki>
|.0327
|.0327
|-
|-
Line 534: Line 687:
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|mLmmmLmmsm
|sLsssLssss
|Dark Augmented
|LLLLLLLLsL
|<nowiki>8|1</nowiki>
|.0400
|.0400
|-
|-
Line 539: Line 696:
|~ 12/11 7/6 5/4 4/3 16/11 14/9 5/3 7/4 15/8 2/1
|~ 12/11 7/6 5/4 4/3 16/11 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|LmmmLmmsmm
|LsssLsssss
|Bright Augmented
|LLLLLLLsLL
|<nowiki>7|2</nowiki>
|.0472
|.0472
|}
|}
Line 549: Line 710:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajarous]][10] 4M (pentachordal decatonic)
|[[Pajarous]][10] 4M (pentachordal decatonic)
|50/49, 55/54, 64/63
|50/49, 55/54, 64/63
Line 557: Line 718:
|[[Marvel temperaments#Negri|Negri]][10]
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55  
|45/44, 49/48, 56/55  
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 594: Line 760:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Negroni[10]
!UDP
![[Mode height]]
![[Mode height]]
|-
|-
Line 599: Line 771:
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1
|mmsmmLmmmL
|mmsmmLmmmL
|sssssLsssL
|Dark minor
|LLsLLLLLLL
|<nowiki>2|7</nowiki>
| -.0466
| -.0466
|-
|-
Line 604: Line 780:
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1
|msmmLmmmLm
|msmmLmmmLm
|ssssLsssLs
|Alternate minor
|LsLLLLLLLL
|<nowiki>1|8</nowiki>
| -.0404
| -.0404
|-
|-
Line 609: Line 789:
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1
|smmLmmmLmm
|smmLmmmLmm
|sssLsssLss
|Bright minor
|sLLLLLLLLL
|<nowiki>0|9</nowiki>
| -.0343
| -.0343
|-
|-
Line 614: Line 798:
|~ 16/15 8/7 27/22 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|~ 16/15 8/7 27/22 4/3 10/7 32/21 8/5 12/7 64/35 2/1
|mmmLmmsmmL
|mmmLmmsmmL
|sssLsssssL
|Standard minor
|LLLLLLsLLL
|<nowiki>6|3</nowiki>
| -.0092
| -.0092
|-
|-
Line 619: Line 807:
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1
|mmLmmsmmLm
|mmLmmsmmLm
|ssLsssssLs
|Dark major
|LLLLLsLLLL
|<nowiki>5|4</nowiki>
| -.0031
| -.0031
|-
|-
Line 624: Line 816:
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1
|mLmmsmmLmm
|mLmmsmmLmm
|sLsssssLss
|Alternate major
|LLLLsLLLLL
|<nowiki>4|5</nowiki>
|.0031
|.0031
|-
|-
Line 629: Line 825:
|~ 35/32 7/6 5/4 21/16 7/5 3/2 44/27 7/4 15/8 2/1
|~ 35/32 7/6 5/4 21/16 7/5 3/2 44/27 7/4 15/8 2/1
|LmmsmmLmmm
|LmmsmmLmmm
|LsssssLsss
|Bright major
|LLLsLLLLLL
|<nowiki>3|6</nowiki>
|.0092
|.0092
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|Standard major
|LLLLLLLLLs
|<nowiki>9|0</nowiki>
|.0343
|.0343
|-
|-
Line 639: Line 843:
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1
|mLmmmLmmsm
|mLmmmLmmsm
|sLsssLssss
|Dark Augmented
|LLLLLLLLsL
|<nowiki>8|1</nowiki>
|.0404
|.0404
|-
|-
Line 644: Line 852:
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1
|LmmmLmmsmm
|LmmmLmmsmm
|LsssLsssss
|Bright Augmented
|LLLLLLLsLL
|<nowiki>7|2</nowiki>
|.0466
|.0466
|}
|}
Line 654: Line 866:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajaric]][10] 4M (pentachordal decatonic)
|[[Pajaric]][10] 4M (pentachordal decatonic)
|45/44, 50/49, 56/55
|45/44, 50/49, 56/55
Line 662: Line 874:
|[[Negroni]][10]
|[[Negroni]][10]
|49/48, 55/54, 225/224  
|49/48, 55/54, 225/224  
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 705: Line 922:
|-
|-
|0
|0
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 15/8 40/21 2/1
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1
|LsLsLMLsLsLsLMLsLsL
|LsLsLMLsLsLsLMLsLsL
|0
|0
Line 730: Line 947:
|[[Marvel temperaments#Negri|Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|49/48, 225/224  
|49/48, 225/224  
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Magic]][19] MODMOS
|225/224, 245/243
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajara]][12] 4M (hexachordal dodecatonic)
|[[Pajara]][12] 4M (hexachordal dodecatonic)
|50/49, 64/63
|50/49, 64/63
Line 784: Line 1,006:
|-
|-
|0
|0
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 15/8 40/21 2/1
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1
|LsLsLMLsLsLsLMLsLsL
|LsLsLMLsLsLsLMLsLsL
|0
|0
Line 809: Line 1,031:
|[[Marvel temperaments#Negri|Negri]][19]
|[[Marvel temperaments#Negri|Negri]][19]
|45/44, 49/48, 56/55
|45/44, 49/48, 56/55
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Magic]][19] MODMOS
|100/99, 225/224, 245/243
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajarous]][12] 4M (hexachordal dodecatonic)
|[[Pajarous]][12] 4M (hexachordal dodecatonic)
|50/49, 55/54, 64/63
|50/49, 55/54, 64/63
Line 856: Line 1,083:
|-
|-
|0
|0
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 15/8 40/21 2/1
|~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1
|LsLsLMLsLsLsLMLsLsL
|LsLsLMLsLsLsLMLsLsL
|0
|0
Line 881: Line 1,108:
|[[Marvel temperaments#Negroni|Negroni]][19]
|[[Marvel temperaments#Negroni|Negroni]][19]
|49/48, 55/54, 225/224  
|49/48, 55/54, 225/224  
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Witchcraft]][19] MODMOS
|225/224, 245/243, 441/440
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|45/44, 50/49, 56/55
|45/44, 50/49, 56/55
Line 969: Line 1,201:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|2L 1M 4s
|1L 2M 4s
|(6/5, 75/64, 16/15)
|(6/5, 75/64, 16/15)
| (315.6413c, 267.8165c, 111.7313c)
| (315.6413c, 267.8165c, 111.7313c)
Line 1,013: Line 1,245:
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
|+Rank-2 temperings (mode 2)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
|-
|L = M
| L = M
|LsLsLs
| LsLsLs
|[[Augmented family|Augmented]][6]
| [[Augmented (temperament)|Augmented]][6]
|128/125
| 128/125
|-
|-
|M = s
| M = s
|ssLsss
| ssLsss
|[[Enipucrop]][6]
| [[Enipucrop]][6]
|1125/1024
| 1125/1024
|-
|-
|L = s
| L = s
|LsssLs
| LsssLs
|Antitonic[6] 4M
| Antitonic[6] 4M
| 9/8
| 9/8
|-
|-
|s = 0
| s = 0
|LsL
| LsL
|[[Trienstonic clan#Father|Father]][3]
| [[Father]][3]
|16/15
| 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)]]=====
Line 1,044: Line 1,276:
!Step sizes in cents (TE tuning)
!Step sizes in cents (TE tuning)
|-
|-
|2L 1M 4s
|1L 2M 4s
|6/5, 75/64~7/6, 16/15~15/14
|6/5, 75/64~7/6, 16/15~15/14
| (316.9276c, 267.8165c, 116.0124c)
| (316.9276c, 267.8165c, 116.0124c)
Line 1,086: Line 1,318:
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
|+Rank-2 temperings (mode 2)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
|-
|L = M
| L = M
|LsLsLs
| LsLsLs
|[[Augmented family|August]][6]
| [[August]][6]
|128/125
| 128/125
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,131: Line 1,363:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|2L 1M 6s
|1L 2M 6s
|(9/8, 1125/1024, 16/15)
|(9/8, 1125/1024, 16/15)
| (203.9100c, 162.8511c, 111.7313c)
| (203.9100c, 162.8511c, 111.7313c)
Line 1,190: Line 1,422:
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 0)
|+Rank-2 temperings (mode 0)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
|-
|L = M
| L = M
|[[3L 6s|sLssLssLs]]
| [[3L 6s|sLssLssLs]]
|[[Augmented family|Augmented]][9]
| [[Augmented (temperament)|Augmented]][9]
|128/125
| 128/125
|-
|-
|M = s
| M = s
|[[1L 8s|ssssLssss]]
| [[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
| [[Negri]][9]
|16875/16384
| 16875/16384
|-
|-
|L = s
| L = s
|sLsssssLs
| [[OTC 2L ns|sLsssssLs]]
|[[Mavila]][9] MODMOS
| [[Mavila]][9] MODMOS
| 135/128
| 135/128
|-
|-
|s = 0
| L - M = M - s
|LsL
| sLssAssLs
|[[Father]][3]
| [[Orson]][9] MODMOS
|16/15
| 2109375/2097152
|-
| s = 0
| LsL
| [[Father]][3]
| 16/15
|-
|-
|m = 0
| m = 0
|[[1L 6s|sssLsss]]
| [[1L 6s|sssLsss]]
|[[Enipucrop]][7]
| [[Enipucrop]][7]
|1125/1024
| 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)]]=====
Line 1,226: Line 1,463:
!Step sizes in cents (TE tuning)
!Step sizes in cents (TE tuning)
|-
|-
|2L 1M 6s
|1L 2M 6s
|(9/8~28/25, 35/32~49/45, 16/15~15/14)
|(9/8~28/25, 35/32~49/45, 16/15~15/14)
| (203.9100c, 162.8511c, 111.7313c)
| (203.9100c, 162.8511c, 111.7313c)
Line 1,232: Line 1,469:
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode in JI
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
![[Mode height]]
![[Mode height]]
Line 1,299: Line 1,536:
|-
|-
|L = s
|L = s
|sLsssssLs
|[[OTC 2L ns|sLsssssLs]]
|[[Pelogic]][9] MODMOS
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
| 21/20, 135/128
|-
|L - M = M - s
|sLssAssLs
|[[Orwell]][9] MODMOS
|225/224, 1728/1715
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,337: Line 1,579:
!Step sizes in cents (TE tuning)
!Step sizes in cents (TE tuning)
|-
|-
|2L 1M 6s
|1L 2M 6s
|(9/8~28/25, 35/32~49/45~12/11, 16/15~15/14)
|(9/8~28/25, 35/32~49/45~12/11, 16/15~15/14)
| (200.8846c, 151.4797c, 116.1327c)
| (200.8846c, 151.4797c, 116.1327c)
Line 1,343: Line 1,585:
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode in JI
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
![[Mode height]]
![[Mode height]]
Line 1,408: Line 1,650:
|[[Marvel temperaments#Negri|Negri]][9]
|[[Marvel temperaments#Negri|Negri]][9]
|45/44, 49/48, 56/55
|45/44, 49/48, 56/55
|-
|L - M = M - s
|sLssAssLs
|[[Orwell]][9] MODMOS
|99/88, 121/120, 176/175
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,436: Line 1,683:


====[[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
{| class="wikitable"
 
! Step signature
~ 16/15 35/32 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as LsLLLMLLLsLL
! Steps in JI
 
!Step sizes in cents (TE tuning)
L = M -> LsLLLLLLLsLL Pajara[12] MODMOS; M = s -> LsLLLsLLLsLLs August[12]; L = s -> sssssLssssss Passion[12];
|-
 
|9L 1M 2s
s = 0 -> LLLLsLLLLL Negri[10]; M = 0 -> LsLLLLLLsLL Pelogic[11] MODMOS
|(16/15~15/14, 135/128~21/20, ~49/48)
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-12|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12] (Marvel)]]=====
| (116.0124c, 84.9028c, 35.7917c)
9L 1M 2s = (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55) = (116.1327c, 84.7519c, 35.347c) TE
|}
 
{| class="wikitable"
~ 16/15 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as LsLLLMLLLsLL
!Mode number
 
!Mode as simplest JI pre-image
L = M -> LsLLLLLLLsLL Pajarous[12] MODMOS; M = s -> LsLLLsLLLsLLs August[12]; L = s -> sssssLssssss Passion[12]; s = 0 -> LLLLsLLLLL Negri[10]
!Step pattern
====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-22|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[22] (Marvel)]]====
![[Mode height]]
9L 1m 12s = (~22/21, 36/35~33/32, 49/48~45/44~56/55) = (80.7857c, 49.4049c, 35.347c) TE
|-
 
| -6
~ 49/48 16/15 12/11 49/44 7/6 105/88 5/4 14/11 4/3 15/11 7/5 63/44 3/2 49/32 8/5 18/11 12/7 7/4 98/55 15/8 21/11 2/1 as sLssLsLsLsmsLsLsLssLsL
|~ 49/48 35/32 7/6 5/4 245/192 49/36 35/24 14/9 49/30 7/4 15/8 2/1
 
|sLLLsLLLMLLL
m = s -> sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS; L = m -> sLssLsLsLsLsLsLsLssLsL Pajarous[22]; L = s -> MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22];
| -0.0733
 
|-
s = 0 -> LLLLsLLLLL Negri[10]
| -5
=== ((2/1, 3/2)[5], 16/15)===
|~ 15/14 35/32 7/6 5/4 4/3 49/36 35/24 14/9 5/3 7/4 15/8 2/1
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
|LsLLLsLLLMLL
2L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)
| -0.0433
 
|-
135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
|  -4
 
|~ 49/48 35/32 7/6 5/4 12/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1
m = s -> ssLsssLsss Srutal[10] MODMOS; L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10]; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
|sLLLMLLLsLLL
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
|  -0.0435
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE
|-
 
|  -3
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
|~ 15/14 8/7 7/6 5/4 4/3 10/7 35/24 14/9 5/3 16/9 15/8 2/1
 
|LLsLLLsLLLML
m = s -> ssLsssLsss Pajara[10] MODMOS; L = m -> sLLLsLLLsL Dicot[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
|  -0.0152
=====[[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
|  -2
 
|~ 15/14 35/32 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
|LsLLLMLLLsLL
 
|  -0.0145
m = s -> ssLsssLsss Pajaric[10] MODMOS
|-
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
|  -1
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c,
|~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1
 
|MLLLsLLLsLLL
135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL
|  -0.0138
 
|-
L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
|1
 
|~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1
s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
|LLLsLLLsLLLM
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
|0.0138
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
|-
 
|2
~ 21/20 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 40/21 2/1 as MsMLMsMMsMMsMLMsM
|~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 64/35 15/8 2/1
 
|LLsLLLMLLLsL
L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
|0.0145
 
|-
s = 0 -> LLsLLLLLLsLL Pajara[12] 4M (Hexachordal Dodecatonic)
|3
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-17|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[17] (Prodigy)]]=====
|~ 15/14 9/8 6/5 9/7 48/35 7/5 3/2 8/5 12/7 7/4 15/8 2/1
2L 10M 5s = (256/243~35/33, 135/128~21/20~22/21, 2048/2025~50/49~64/63~45/44~56/55) = (101.0757c, 82.9601c, 33.8068c) TE
|LMLLLsLLLsLL
 
|0.0152
~ 22/21 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 21/11 2/1 as LsLmLsLLsLLsLmLsL
|-
 
|4
L = M -> LsLLLsLLsLLsLLLsL Andromeda[17]; s = 0 -> s = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)
|~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 8/5 12/7 64/35 96/49 2/1
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-29|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] (Prodigy)]]====
|LLLsLLLMLLLs
2L 10m 17s = (25/24~28/27, ~33/32, 2048/2025~50/49~64/63~45/44~56/55) = (67.2689c, 49.1533c, 33.8068c) TE
|0.0435
 
|-
~ 50/49 22/21 16/15 11/10 9/8 8/7 33/28 6/5 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 5/3 56/33 7/4 16/9 20/11 15/8 21/11 49/25 2/1 as smsmssmsLsmssmsmssmsLsmssmsms
|5
 
|~ 15/14 8/7 6/5 9/7 48/35 72/49 3/2 8/5 12/7 64/35 15/8 2/1
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];
|LLMLLLsLLLsL
 
|0.0443
L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
|-
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-41|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)]]====
|6
29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE
|~ 15/14 8/7 60/49 9/7 48/35 72/49 384/245 8/5 12/7 64/35 96/49 2/1
 
|LLLMLLLsLLLs
~ 50/49 33/32 22/21 16/15 12/11 11/10 9/8 8/7 7/6 32/27 40/33 11/9 5/4 14/11 128/99 21/16 4/3 15/11 11/8 7/5 10/7 16/11 22/15 3/2 32/16 99/64 11/7 8/5 18/11 33/20 27/16 12/7 7/4 16/9 20/11 11/6 15/8 21/11 64/33 49/25 2/1 as LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL
|0.0733
 
|}
L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];
{| class="wikitable"
 
|+Rank-2 temperings (mode -2)
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS
!Equivalence
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-72|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] (Prodigy)]]====
!Step pattern
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE
!Scale
 
!Comma list
as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs
|-
 
|L = M
L = M -> LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS;
|LsLLLLLLLsLL
 
|[[Pajara]][12] MODMOS
M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;
|50/49, 64/63
 
|-
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;
|M = s
 
|LsLLLsLLLsLLs
m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
|[[August]][12]
==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], and [[Ragismic family#Ragismic|Ragismic]]==
|36/35, 128/125
===(2/1, 3/2, 6/5)===
|-
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
|L = s
1L 2M 1s = (5/4, 6/5, 10/9)
|sssssLssssss
 
|[[Passion family#Septimal passion|Passion]][12]
6/5 3/2 9/5 2/1 as MLMs
| 64/63, 3125/3087
 
|-
L = M -> LLLs Dicot[4]; M = s -> sLss Bug[4]; L = s -> LsLs Antitonic[4]
|L - M = M - s
====[[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]]====
|LdLLLsLLLdLL
1L 4M 2S = (9/8, 10/9, 27/25)
|[[Meantone]][12] MODMOS
 
|81/80, 126/125
10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
|-
 
|s = 0
L = M -> LsLLLsL Meantone[7], M = s -> sssLsss Porcupine[7]; L = s -> LsLsLsL Dicot[7]; s = 0 -> ssLss Bug[5]
|LLLLsLLLLL
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
|[[Marvel temperaments#Negri|Negri]][10]
1L 4M 2S = (~9/8, ~10/9, 27/25~15/14) = (202.4685c, 187.562c, 123.5395c) TE
|49/48, 225/224
 
|-
~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
|M = 0
 
|LsLLLLLLsLL
L = M -> LsLLLsL Meantone[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]
|[[Pelogic]][11] MODMOS
 
|21/20, 135/128
8d-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 16-ET: (2, 3, 1); 19-ET: (3, 3, 2); 27-ET: (5, 4, 3); 31-ET: (5, 5, 3); 46-ET: (8, 7, 5); 50-ET: (8, 8, 5); 58-ET: (10, 9, 6); 77-ET: (13, 12, 8)
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====
{| class="wikitable"
1L 4M 2S = (~9/8, 10/9~11/10, 27/25~12/11) = (209.7786c, 174.0549c, 146.6352c) TE
|+Rank-1 temperings
 
!ET
~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as msmLmsm
|[[19edo|19]]
 
|[[22edo|22]]
m = s -> sssLsss Porcupine[7], L = m -> LsLLLsL Meanenneadecal[7], L = s -> LsLsLsL Flat[7]
|[[29edo|29]]
 
|[[31edo|31]]
8-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 19-ET: (3, 3, 2); 22-ET: (4, 3, 3); 27e-ET: (5, 4, 3); 29-ET: (5, 4, 4); 34-ET: (6, 5, 4); 41-ET: (7, 6, 5)
|[[41edo|41]]
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-7|(2/1, 3/2, 6/5: 56/55, 100/99)[7] (Thrasher)]]=====
|[[50edo|50]]
1L 4M 2S = (~9/8, 10/9~11/10, 27/25~15/14~12/11) = (215.4452c, 179.0856c, 132.5782c) TE
|[[53edo|53]]
 
|[[72edo|72]]
~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
|-
 
!Step sizes in ET
L = M -> LsLLLsL Meanenneadecal[7]; M = s -> sssLsss Opossum[7]; L = s -> LsLsLsL Flat[7]
|(2, 1, 0)
 
|(2, 2, 1)
8d-ET: (2, 1, 1); 12-ET: (2, 2, 1); 15-ET: (3, 2, 2); 19-ET: (3, 3, 2); 27e-ET: (5, 4, 3); 34-ET: (6, 5, 4)
|(3, 2, 0)
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
|(3, 2, 1)
7L 1m 4s = (27/25, 25/24, 250/243)
|(4, 3, 1)
 
|(5, 3, 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 as sLLsLmLsLLsL
|(5, 4, 2)
 
|(7, 5, 2)
m = s -> sLLsLsLsLLsL Meantone[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; L = s -> LLLLLsLLLLLL Ripple[12]; s = 0 -> LLLsLLLL Porcupine[8]
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-12|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12] (Marvel)]]=====
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 tuning)
m = s -> sLLsLsLsLLsL Meantone[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]
|-
 
|9L 1M 2s
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)
|(16/15~15/14, 135/128~21/20, 49/48~45/44~56/55)
=====[[SNS (2/1, 3/2, 6/5: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]]=====
| (116.1327c, 84.7519c, 35.347c)
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"
~ 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
!Mode number
 
!Mode as simplest JI pre-image
m = s -> sLLsLsLsLLsL Meanpop[12]; L = m -> sLLsLLLsLLsL MODMOS; s = 0 -> LLLsLLLL
!Step pattern
 
![[Mode height]]
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)
|-
=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
| -6
7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54) = (146.6352c, 63.1434c, 27.4197c) TE
|~ 45/44 12/11 7/6 5/4 14/11 15/11 16/11 14/9 18/11 7/4 15/8 2/1
 
|sLLLsLLLMLLL
~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1 as sLLsLmLsLLsL
| -0.0738
 
|-
m = s -> sLLsLsLsLLsL Meanenneadecal[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Porkypine[8]
| -5
 
|~ 15/14 12/11 7/6 5/4 4/3 15/11 16/11 14/9 5/3 7/4 15/8 2/1
12-ET: (1, 1, 1); 15-ET: (2, 1, 0); 19-ET: (2, 1, 1); 22-ET: (3, 1, 0); 27e-ET: (3, 2, 1); 29-ET: (4, 1, 0); 34-ET: (4, 2, 1); 41-ET: (5, 2, 1)
|LsLLLsLLLMLL
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)]]=====
| -0.0445
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
|-
 
|  -4
~ 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
|~ 45/44 12/11 7/6 5/4 12/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1
 
|sLLLMLLLsLLL
m = s -> sLLsLsLsLLsL Meanenneadecal[12]; L = m -> sLLsLLLsLLsL Diminished[12] MODMOS; s = 0 -> LLLsLLLL Opossum[8]
|  -0.0438
 
|-
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)
|  -3
=====[[SNS (2/1, 3/2, 6/5: 4375/4374)-12|(2/1, 3/2, 6/5: 4375/4374)[12] (Ragismic)]]=====
|~ 15/14 8/7 7/6 5/4 4/3 10/7 16/11 14/9 5/3 16/9 15/8 2/1
7L 1m 4s = (~27/25, ~25/24, 250/243~36/35) = (133.4115c, 70.5569c, 48.8911c) TE
|LLsLLLsLLLML
 
|  -0.0153
~ 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
|-
 
|  -2
m = s -> LsLLsLsLsLLs Falttone[12]; L = m -> LsLLsLLLsLLs MODMOS; L = s -> LLLLLLsLLLLL; s = 0 -> LLLLsLLL Hystrix[8]
|~ 15/14 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1
 
|LsLLLMLLLsLL
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)
|  -0.0146
====[[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
|  -1
 
|~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
|MLLLsLLLsLLL
 
|  -0.0139
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
|-
 
|1
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
|~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1
|LLLsLLLsLLLM
|0.0139
|-
|2
|~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 11/6 15/8 2/1
|LLsLLLMLLLsL
|0.0146
|-
|3
|~ 15/14 9/8 6/5 9/7 11/8 7/5 3/2 8/5 12/7 7/4 15/8 2/1
|LMLLLsLLLsLL
|0.0153
|-
|4
|~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 8/5 12/7 11/6 55/28 2/1
|LLLsLLLMLLLs
|0.0438
|-
|5
|~ 15/14 8/7 6/5 9/7 11/8 22/15 3/2 8/5 12/7 11/6 15/8 2/1
|LLMLLLsLLLsL
|0.0445
|-
|6
|~ 15/14 8/7 11/9 9/7 11/8 22/15 11/7 8/5 12/7 11/6 55/28 2/1
|LLLMLLLsLLLs
|0.0738
|}
{| class="wikitable"
|+Rank-2 temperings (mode -2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LsLLLLLLLsLL
|[[Pajarous]][12] MODMOS
|50/49, 55/54, 64/63
|-
|M = s
|LsLLLsLLLsLL
|[[August]][12]
|36/35, 45/44, 56/55
|-
|L = s
|sssssLssssss
|[[Passion family#Septimal passion|Passion]][12]
| 64/63, 100/99, 1375/1372
|-
|L - M = M - s
|LdLLLsLLLdLL
|[[Meanpop]][12] MODMOS
|81/80, 126/125, 385/384
|-
|s = 0
|LLLLsLLLLL
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[19edo|19]]
|[[22edo|22]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|72]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 2, 1)
|(3, 2, 1)
|(4, 3, 1)
|(5, 3, 1)
|(5, 4, 2)
|(7, 5, 2)
|}


19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
===== [[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-22|(2/1, 5/4)[3], 16/15: 225/224, 385/384)[22] (Marvel)]] =====
=====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-20|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)]]=====
{| class="wikitable"
7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE
!Step signature
 
!Steps in JI
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
!Step sizes in cents (TE tuning)
 
|-
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
|9L 1m 12s
 
|(~22/21, 36/35~33/32, 49/48~45/44~56/55)
s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL
| (80.7857c, 49.4049c, 35.347c)
 
|}
19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
{| class="wikitable"
====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-39|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)]]====
!Mode number
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE
!Mode as simplest JI pre-image
 
!Step pattern
~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms
![[Mode height]]
 
|-
m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs
|  -7
 
|~ 45/44 16/15 12/11 49/44 7/6 105/88 5/4 14/11 4/3 15/11 7/5 63/44 3/2 49/32 8/5 18/11 12/7 7/4 98/55 15/8 21/11 2/1
46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)
|sLssLsLsLsmsLsLsLssLsL
==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
|  -.0229
===((2/1, 3/2)[5], 10/9)===
|-
====[[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]]====
|7
5L 2M 3s = (10/9, 16/15, 81/80)
|~ 22/21 16/15 55/49 8/7 7/6 11/9 5/4 64/49 4/3 88/63 10/7 22/11 3/2 11/7 8/5 176/105 12/7 88/49 11/6 15/8 55/28 2/1
 
|LsLssLsLsLsmsLsLsLssLs
81/80 9/8 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1 as sLMLsLMLsL
|.0229
|}
{| class="wikitable"
|+Rank-2 temperings (mode -7)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|sLssLsLsLsssLsLsLssLsL
|[[Semicomma family#Orwell|Orwell]][22] MODMOS
|99/98, 121/120, 176/175
|-
|L = m
|sLssLsLsLsLsLsLsLssLsL
|[[Pajarous]][22] MODMOS
|50/49, 55/54, 64/63
|-
|L = s
|LLLLLLLLLLsLLLLLLLLLLL
|[[Escapade family#Septimal escapade|Escapade]][22]
| 99/98, 176/175, 2560/2541
|-
|L - m = m - s
|sAssAsAsAsLsAsAsAssAsA
|[[Magic]][22] MODMOS
|100/99, 225/224, 245/243
|-
|s = 0
|LLLLsLLLLL
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|72]]
|-
!Step sizes in ET
|(2, 1, 1)
|(3, 2, 1)
|(4, 2, 1)
|(3, 2, 2)
|(5, 3, 2)
|}


L = M -> sLLLsLLLsL Dicot[10] MOSMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;
=== ((2/1, 3/2)[5], 16/15)===
 
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
{| class="wikitable"
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)]]====
!Step signature
5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE
!Steps in JI
 
!Step sizes in cents
~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs
|-
 
|2L 5m 3s
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs
|(10/9, 16/15, 135/128)
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)]]=====
| (182.4037c, 111.7313c, 92.1787c)
5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE
|}
{| 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
|LsssssLsss
|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
|}


~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs
{| class="wikitable"
 
|+Rank-2 temperings (mode 1)
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Arnold[7]; m = 0 -> sLssLssLssLssLs
! Equivalence
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-24|((2/1, 3/2)[5], 10/9: 5120/5103)[24] (Hemifamity)]]====
! Step pattern
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63) = (132.1305c, 61.3411c, 24.4931c) TE
! Scale
! Comma list
|-
| m = s
| [[OTC 2L 8s|ssLsssLsss]]
| [[Diaschismic]][10] 4M (pentachordal decatonic)
| 2048/2025
|-
| L = m
| [[7L 3s|sLLLsLLLsL]]
| [[Dicot]][10] modmos
| 25/24
|-
| L = s
| [[5L 5s|LsLsLsLsLs]]
| [[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]]
| [[Father]][5]
| 16/15
|}


~ 64/63 35/32 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 35/24 40/27 3/2 32/21 105/64 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
 
{| class="wikitable"
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]
!Step signature
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-24|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24] (Akea)]]=====
!Steps in JI
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE
!Step sizes in cents (TE tuning)
 
|-
~ 64/63 12/11 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 16/11 40/27 3/2 32/21 18/11 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss
|2L 5m 3s
 
|(10/9, 16/15~15/14, 135/128~21/20)
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Arnold[7]
| (182.9137c, 116.0124c, 84.9028c)
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-31|((2/1, 3/2)[5], 10/9: 5120/5103)[31] (Hemifamity)]]====
|}
5L 2m 24s = (~1225/1152, ~49/48, 81/80~64/63) = (107.6374c, 36.848c, 24.4931c) TE
{| class="wikitable"
 
!Mode number
~ 64/63 36/35 35/32 10/9 9/8 8/7 7/6 32/27 6/5 128/105 35/27 21/16 4/3 27/20 48/35 35/24 40/27 3/2 32/21 54/35 105/64 5/3 27/16 12/7 7/4 16/9 9/5 64/35 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss
!Mode as simplest JI pre-image
 
!Step pattern
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
!Pentachordal
 
Decatonic
s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS
!Pent. Dec.
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-31|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31] (Akea)]]=====
Mode name
5L 2m 24s = (~35/33, 49/48~56/55, 81/80~64/63~55/54) = (100.7664c, 33.3269c, 26.2356c) TE
!Blackwood[10]
 
!UDP
~ 64/63 36/35 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 35/27 21/16 4/3 27/20 11/8 16/11 40/27 3/2 32/21 54/35 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss
![[Mode height]]
 
|-
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
|  -5
 
|~ 15/14 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss
|msmsmLmsmL
===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) ===
|sssssLsssL
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)]]====
|Dark minor
5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE
|sLsLsLsLsL
 
|<nowiki>0|1 (5)</nowiki>
~ 64/63 15/14 243/224 9/8 8/7 32/27 6/5 81/64 9/7 4/3 27/20 10/7 81/56 3/2 32/21 45/28 80/49 27/16 12/7 16/9 9/5 243/128 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM
|  -.0763
 
|-
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]
|  -4
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-24|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24] (Pele)]]=====
|~ 21/20 9/8 189/160 81/64 7/5 3/2 63/40 27/16 15/8 2/1
5L 7M 12s = (135/128~35/33, 28/27~33/32, 81/80~64/63~99/98) = (97.5911c, 58.2557c, 25.3165c) TE
|smsmLmsmLm
 
|ssssLsssLs
~ 64/63 15/14 12/11 9/8 8/7 32/27 6/5 14/11 9/7 4/3 27/20 10/7 16/11 3/2 32/21 45/28 18/11 27/16 12/7 16/9 9/5 12/11 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM
|Alternate minor
 
|LsLsLsLsLs
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]
|<nowiki>1|0 (5)</nowiki>
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5013)-36|((2/1, 3/2)[12], 64/63: 5120/5013)[36] (Hemifamity)]]====
|  -.0688
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE
|-
 
|  -3
~ 64/63 36/35 15/14 243/224 54/49 9/8 8/7 81/70 32/27 6/5 128/105 81/64 9/7 64/49 4/3 27/20 48/35 10/7 81/56 72/49 3/2 32/21 54/35 45/28 80/49 81/49 27/16 12/7 243/140 16/9 9/5 64/35 243/128 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1
 
|msmLmsmsmL
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
|sssLsssssL
 
|Standard minor
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
|sLsLsLsLsL
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36] (Pele)]]=====
|<nowiki>0|1 (5)</nowiki>
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63~99/98) = (72.2746c, 32.9392c, 25.3165c) TE
|  -.0400
 
|-
~ 64/63 36/35 15/14 12/11 54/49 9/8 8/7 64/55 32/27 6/5 128/105 14/11 9/7 64/49 4/3 27/20 48/35 10/7 16/11 72/49 3/2 32/21 54/35 45/28 18/11 81/49 27/16 12/7 96/55 16/9 9/5 64/35 22/21 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM
|  -2
 
|~ 21/20 9/8 5/4 4/3 7/5 3/2 63/40 27/16 15/8 2/1
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
|smLmsmsmLm
 
|ssLsssssLs
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
|Dark major
==2.5.9; Marvel ==
|LsLsLsLsLs
=== ((2/1, 5/4)[3], 9/8)===
|<nowiki>1|0 (5)</nowiki>
====[[SNS ((2/1, 5/4)-3, 9/8)-6|((2/1, 5/4)[3], 9/8)[6]]]====
|  -.0326
1L 3M 2s = (256/225, 9/8, 10/9)
|-
 
|  -1
9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 40/21 2/1
 
|msmLmsmLms
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
|sssLsssLss
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-6|((2/1, 5/4)[3], 9/8: 225/224)[6] (Marvel)]]=====
|Bright minor
1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c) TE
|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
|LsssssLsss
|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
|[[OTC 2L 8s|ssLsssLsss]]
|[[Diaschismic family#Pajara|Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|-
|L = m
|[[OTC 7L 3s|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)]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE tuning)
|-
|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
|LsssssLsss
|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
|[[OTC 2L 8s|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]]]====
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)


~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL


L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-6|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6] (Apollo)]]=====
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c) TE
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE


~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
~ 21/20 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 40/21 2/1 as MsMLMsMMsMMsMLMsM


L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
====[[SNS ((2/1, 5/4)-3, 9/8)-10|((2/1, 5/4)[3], 9/8)[10]]]====
6L 1M 3s = (10/9, 128/125, 81/80)


10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,
s = 0 -> LLsLLLLLLsLL Pajara[12] 4M (Hexachordal Dodecatonic)
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-17|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[17] (Prodigy)]]=====
2L 10M 5s = (256/243~35/33, 135/128~21/20~22/21, 2048/2025~50/49~64/63~45/44~56/55) = (101.0757c, 82.9601c, 33.8068c) TE


m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL
~ 22/21 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 21/11 2/1 as LsLmLsLLsLLsLmLsL
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-10|((2/1, 5/4)[3], 9/8: 225/224)[10] (Marvel)]]=====
6L 1M 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE


~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
L = M -> LsLLLsLLsLLsLLLsL Andromeda[17]; s = 0 -> s = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-29|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] (Prodigy)]]====
2L 10m 17s = (25/24~28/27, ~33/32, 2048/2025~50/49~64/63~45/44~56/55) = (67.2689c, 49.1533c, 33.8068c) TE


m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL
~ 50/49 22/21 16/15 11/10 9/8 8/7 33/28 6/5 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 5/3 56/33 7/4 16/9 20/11 15/8 21/11 49/25 2/1 as smsmssmsLsmssmsmssmsLsmssmsms
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-10|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10] (Apollo)]]=====
6L 1M 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE


~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];


m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL
L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;
====[[SNS ((2/1, 5/4)-3, 9/8)-17|((2/1, 5/4)[3], 9/8)[17]]]====
6L 10m 1s = (800/729, 81/80, 2048/2025)


81/80 10/9 9/8 100/81 5/4 81/64 25/18 45/32 64/45 36/18 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as mLmLmmLmsmLmmLmLm
s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-41|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)]]====
29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE


m = s -> sLsLssLsssLssLsLs MODMOS;  L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL
~ 50/49 33/32 22/21 16/15 12/11 11/10 9/8 8/7 7/6 32/27 40/33 11/9 5/4 14/11 128/99 21/16 4/3 15/11 11/8 7/5 10/7 16/11 22/15 3/2 32/16 99/64 11/7 8/5 18/11 33/20 27/16 12/7 7/4 16/9 20/11 11/6 15/8 21/11 64/33 49/25 2/1 as LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-17|((2/1, 5/4)[3], 9/8: 225/224)[17] (Marvel)]]=====
6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE


~ 81/80 10/9 9/8 100/81 5/4 81/64 25/18 7/5 10/7 36/25 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as sLsLssLsmsLssLsLs
L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];


m = s -> sLsLssLsssLssLsLs MODMOS;  L = m ->  sLsLssLsLsLssLsLs; L = s -> LLLLLLLLsLLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLsLssLssLssLsLs MODMOS
L - M = M - s -> Witchcraft[41] MODMOS
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-17|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17] (Apollo)]]=====
6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE


~ 56/55 10/9 9/8 11/9 5/4 14/11 11/8 7/5 10/7 16/11 11/7 8/5 11/9 16/9 9/5 55/28 2/1 as mLmLmmLmsmLmmLmLm
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS
====[[SNS ((2/1, 3/2)-5, 16/15: 225/224, 441/440)-72|((2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] (Prodigy)]]====
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE


m = s -> sLsLssLsssLssLsLs Machine[17] MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL
as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs
==2.5.9; Starling==
===((2/1, 5/4)[3], 10/9)===
====[[SNS ((2/1, 5/4)-3, 10/9)-6|((2/1, 5/4)[3], 10/9)[6]]]====
1L 2m 3s = (144/125, 9/8, 10/9)


9/8 5/4 36/25 8/5 9/5 2/1 as msLsms
L = M -> LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS;


m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;
=====[[SNS ((2/1, 5/4)-3, 10/9: 126/125)-6|((2/1, 5/4)[3], 10/9: 126/125)[6]]]=====
1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c) TE


~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms
L - M = M - s -> Compton MODMOS


m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;
====[[SNS ((2/1, 5/4)-3, 10/9)-9|((2/1, 5/4)[3], 10/9)[9]]]====
6L 1m 2s = (10/9, 648/625, 81/80)


10/9 9/8 5/4 25/18 36/25 8/5 16/9 9/5 2/1 as LsLLmLLsL
m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
 
==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], [[Supermagic]], and [[Ragismic family#Ragismic|Ragismic]]==
m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS
===(2/1, 3/2, 6/5)===
=====[[SNS ((2/1, 5/4)-3, 10/9: 126/125)-9|((2/1, 5/4)[3], 10/9: 126/125)[9]]]=====
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c) TE
{| class="wikitable"
 
!Step signature
~ 10/9 9/8 5/4 7/5 10/7 8/5 16/9 9/5 2/1 as LsLLmLLsL
!Steps in JI
 
!Step sizes in cents
m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS
|-
====[[SNS ((2/1, 5/4)-3, 10/9: 126/126, 896/891)-16|((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16]]]====
|1L 2M 1s
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55) = (163.6623c, 24.4284c, 21.4103c) TE
|(5/4, 6/5, 10/9)
 
|(386.3137c, 315.6413c, 182.4037c)
~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 81/50 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL
|}
 
{| class="wikitable"
m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
!Mode number
=====[[SNS ((2/1, 5/4)-3, 10/9: 91/90, 126/126, 896/891)-16|((2/1, 5/4)[3], 10/9: 91/90, 126/125, 896/891)[16]]]=====
!Mode in JI
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143) = (160.4106c, 30.0969c, 23.0825c) TE
!Step pattern
 
![[Mode height]]
~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 13/8 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL
|-
 
|  -2
m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
|10/9 4/3 5/3 2/1
==2.3.7; [[Orwellismic family#Orwellismic|Orwellismic]]==
|sMLM
===(2/1, 3/2, 7/6)===
|  -0.1307
====[[SNS (2/1, 3/2, 7/6)-4|(2/1, 3/2, 7/6)[4]]]====
|-
1L 2m 1s = (9/7, 7/6, 8/7)
|  -1
|6/5 4/3 8/5 2/1
|MsML
|  -0.0959
|-
|1
|5/4 3/2 5/3 2/1
|LMsM
|0.0959
|-
|2
|6/5 3/2 9/5 2/1
|MLMs
|0.1307
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 1s|LLLs]]
|[[Dicot]][4]
|25/24
|-
|M = s
|[[1L 3s|sLss]]
|[[Bug family|Bug]][4]
|27/25
|-
|L = s
|[[2L 2s|LsLs]]
|Antitonic[4]
|9/8
|}


7/6 3/2 7/4 2/1 as mLms
====[[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]]====
 
{| class="wikitable"
m = s -> sLss Sempahore[4]
!Step signature
====[[SNS (2/1, 3/2, 7/6)-7|(2/1, 3/2, 7/6)[7]]]====
!Steps in JI
4L 1M 2s = (8/7, 9/8, 49/48)
!Step sizes in cents
 
|-
8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL
|1L 4M 2s
 
|(9/8, 10/9, 27/25)
L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]
|(203.9100c, 182.4037c, 133.2376c)
=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)]]=====
|}
4L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE
{| class="wikitable"
 
!Mode number
~ 8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL
!Mode in JI
 
!Step pattern
L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]
!Meantone[7]
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)]]====
!UDP
4L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE
!Diatonic mode
 
!Porcupine[7]
~ 36/35 8/7 7/6 6/5 4/3 48/35 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
!UDP
 
!Porcupine mode
L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Beep[5]
![[Mode height]]
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-12|(2/1, 3/2, 7/6: 99/98, 385/384)[12] (Orwellian)]]=====
|-
4L 1M 7s = (~10/9, 54/49~35/32~12/11, 49/48~36/35~33/32) = (185.7619, 155.4288c, 155.4288c) TE
| -3
 
|27/25 6/5 4/3 36/25 8/5 9/5 2/1
~ 33/32 8/7 7/6 6/5 4/3 11/8 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
|sMMsMLM
 
|sLLsLLL
L = M -> sLssLsLsLssL Suprapyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Pentoid[5]
|<nowiki>0|6</nowiki>
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-12|(2/1, 3/2, 7/6: 176/175, 540/539)[12] (Guanyin)]]=====
|Lochrian
4L 1M 7s = (~10/9, 54/49~35/32~11/10, 49/48~36/35~45/44) = (183.8734c, 162.5743c, 43.0239c) TE
|sssssLs
 
|<nowiki>1|5</nowiki>
~ 36/35 8/7 7/6 6/5 4/3 15/11 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
|Dark diminished
 
| -0.0529
L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS
|-
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)]]====
|  -2
4L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE
|10/9 6/5 4/3 40/27 8/5 16/9 2/1
 
|MsMMsML
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 48/35 35/24 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
|LsLLsLL
 
|<nowiki>2|4</nowiki>
L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Beep[5]
|Aeolian
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-17|(2/1, 3/2, 7/6: 99/98, 385/384)[17] (Orwellian)]]=====
|ssssssL
4L 1M 12s = (~160/147, 15/14~35/33, 49/48~36/35~33/32) = (142.5744c, 112.2413c, 43.1875c) TE
|<nowiki>0|6</nowiki>
 
|Magical seventh
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 11/8 16/11 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
|  -0.0316
 
|-
L = M -> sLsssLssLssLsssLs Suprapyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Pentoid[5]
|  -1
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-17|(2/1, 3/2, 7/6: 176/175, 540/539)[17] (Guanyin)]]=====
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
4L 1M 12s = (~88/81, 15/14~77/72, 49/48~36/35~45/44) = (140.8495c, 119.5504c, 43.0239c) TE
|sMLMsMM
 
|sLLLsLL
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 15/11 22/15 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
|<nowiki>1|5</nowiki>
 
|Phrygian
L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs
|ssLssss
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)]]====
|<nowiki>4|2</nowiki>
4L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE
|Bright minor
 
|  -0.0213
~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 48/35 7/5 35/24 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs
|-
 
|0
m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]; s = 0 -> LLsLL Beep[5]
|10/9 6/5 4/3 3/2 5/3 9/5 2/1
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-22|(2/1, 3/2, 7/6: 99/98, 385/384)[22] (Orwellian)]]=====
|MsMLMsM
4L 1m 17s = (~200/189, 25/24~80/77, 49/48~36/35~33/32) = (99.3869c, 69.0538c, 43.1875c) TE
|LsLLLsL
 
|<nowiki>3|3</nowiki>
~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 11/8 7/5 16/11 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs
|Dorian
 
|sssLsss
m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Suprapyth[17]; s = 0 -> LLsLL Pentoid[5]
|<nowiki>3|3</nowiki>
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-22|(2/1, 3/2, 7/6: 176/175, 540/539)[22] (Guanyin)]]=====
|Dark minor
4L 1m 17s = (~200/189, 25/24~22/21, 49/48~36/35~45/44) = (97.8256c, 76.5265c, 43.0239c) TE
|0
 
|-
~ 36/35 21/20 10/9 8/7 7/6 6/5 27/22 35/27 4/3 15/11 7/5 22/15 3/2 54/27 63/40 5/3 12/7 7/4 9/5 81/44 35/18 2/1 as ssLssssLsssmsssLssssLs
|1
 
|10/9 100/81 4/3 40/27 5/3 50/27 2/1
m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]
|MMsMLMs
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)]]====
|LLsLLLs
4L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE
|<nowiki>5|1</nowiki>
 
|Ionian
~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 48/35 7/5 10/7 35/24 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM
|ssssLss
 
|<nowiki>2|4</nowiki>
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; M = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
|Bright diminished
 
|0.0213
s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Beep[5]
|-
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-27|(2/1, 3/2, 7/6: 99/98, 385/384)[27] (Orwellian)]]=====
|2
4L 22M 1s = (~250/243, 49/48~36/35~33/32, 50/49~100/99) = (56.1994c, 43.1875c, 25.8663c) TE
|9/8 5/4 27/20 3/2 5/3 9/5 2/1
 
|LMsMMsM
~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 11/8 7/5 10/7 16/11 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM
|LLsLLsL
 
|<nowiki>4|2</nowiki>
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartz[27]; M = s -> ssLsssssLsssssssssLsssssLss Myno[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Suprapyth[27];
|Mixolydian
 
|Lssssss
s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Pentoid[5]
|<nowiki>6|0</nowiki>
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-27|(2/1, 3/2, 7/6: 176/175, 540/539)[27] (Guanyin)]]=====
|Bright major
4L 22M 1s = (~250/243, 49/48~36/35~45/44, 50/49~55/54) = (54.8017c, 43.0239c, 33.5026c) TE
|0.0316
 
|-
~ 36/35 21/20 88/81 10/9 8/7 7/6 6/5 27/22 80/63 35/27 4/3 15/11 7/5 10/7 22/15 3/2 54/27 63/40 44/27 5/3 12/7 7/4 9/5 81/44 40/21 35/18 2/1 as mmLmmmmmLmmmmsmmmmLmmmmmLmm
|3
 
|10/9 5/4 25/18 3/2 5/3 50/27 2/1
m = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = m -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
|MLMsMMs
 
|LLLsLLs
s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS
|<nowiki>6|0</nowiki>
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)]]====
|Lydian
27L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE
|sLsssss
 
|<nowiki>5|1</nowiki>
~ 50/49 36/35 360/343 21/20 15/14 27/25 54/49 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 48/35 480/343 7/5 10/7 343/240 35/24 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 49/27 50/27 28/15 40/21 343/180 35/18 49/25 2/1 as LsLsLsLsLMLsLsLsLsLsLMLsLsLsLsLMLsLsLsLsLsLMLsLsLsLsL
|Dark major
 
|0.0529
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
|}
 
{| class="wikitable"
M = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53]; L = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss
|+Rank-2 temperings (mode 2)
 
!Equivalence
s = 0 -> LLLLLsLLLLLLsLLLLLsLLLLLLsLLLLL Myna[31] MODMOS; M = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49];
!Step pattern
 
!Scale
L = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS
!Comma list
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-53|(2/1, 3/2, 7/6: 99/98, 385/384)[53] (Orwellian)]]=====
|-
4L 27M 22s = (64/63~245/243~55/54, 50/49~100/99, 126/125~2401/2400) = (30.3331c, 25.8663c, 17.3212c) TE
|L = M
 
|[[5L 2s|LsLLLsL]]
~ 50/49 36/35 80/77 21/20 15/14 27/25 12/11 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 11/8 480/343 7/5 10/7 343/240 16/11 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 11/6 50/27 28/15 40/21 77/40 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM
|[[Meantone family|Meantone]][7]
 
|81/80
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
|-
 
|M = s
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartz[53];
|[[1L 6s|sssLsss]]
 
|[[Porcupine family#Porcupine|Porcupine]][7]
s = 0 -> sssssLssssssLsssssLssssssLsssss Myno[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS;
|250/243
 
|-
L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Suprapyth[49]
|L = s
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-53|(2/1, 3/2, 7/6: 176/175, 540/539)[53] (Guanyin)]]=====
|[[4L 3s|LsLsLsL]]
4L 27M 22s = (64/63~245/243~100/99, 50/49~55/54, 126/125~2401/2400~441/440) = (33.5026c, 21.2991c, 9.5213c) TE
|[[Dicot family|Dicot]][7]
 
|25/24
~ 50/49 36/35 22/21 21/20 15/14 27/25 11/10 243/220 9/8 8/7 125/108 7/6 25/21 6/5 11/9 27/22 5/4 63/50 9/7 162/125 21/16 4/3 110/81 15/11 88/63 7/5 10/7 63/44 22/15 81/55 3/2 32/16 125/81 14/9 100/63 8/5 44/27 18/11 5/3 42/25 12/7 216/125 7/4 16/9 440/243 20/11 50/27 40/21 21/11 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM
|-
 
|L - M = M - s
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
|LsLALsL
 
|[[Tetracot]][7] MODMOS
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss Kleiboh[53] MODMOS; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53];
|20000/19683
 
|-
s = 0 -> sssssLssssssLsssssLssssssLsssss Myna[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Fleetwood[22] MODMOS;
|s = 0
 
|[[1L 4s|ssLss]]
L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49]
|[[Bug family|Bug]][5]
===((2/1, 3/2)[12], 49/48) or ((2/1, 3/2)[12], 36/35)===
|27/25
====((2/1, 3/2)[12], 36/35: 1728/1715)[24] (Orwellian)====
|}
 
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
== 2.3.7 Sensamagic ==
{| class="wikitable"
 
!Step signature
=== (2/1, 3/2, 9/7) ===
!Steps in JI
 
!Step sizes in cents (TE)
==== (2/1, 3/2, 9/7)[4] ====
|-
2L 1M 1s = (9/7, 7/6, 28/27) = (435.0841c, 266.8709c, 62.9609c)
|1L 4M 2s
 
|(~9/8, ~10/9, 27/25~15/14)
9/7 3/2 27/14 2/1 as LMLs
|(202.4685c, 187.562c, 123.5395c)
 
|}
L = M -> LLLs; M = s -> LsLs; s = 0 -> LsL
{| class="wikitable"
==== (2/1, 3/2, 9/7: 245/243)[7] Sensamagic ====
!Mode number
2L 1m 4s = (~5/4, ~9/8, 28/27~36/35)
!Mode as simplest JI pre-image
 
!Step pattern
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 as sLsmsLs
!Meantone[7]
 
!UDP
m = s -> sLsssLs; s = 0 -> LsL
!Diatonic mode
 
!Porcupine[7]
5-ET: (2, 1, 0); 14c-ET: (4, 2, 1); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22-ET: (7, 4, 1) 24-ET: (8, 4, 1); 27-ET: (9, 5, 1); 41-ET: (13, 7, 2); 46-ET: (15, 8, 2); 68-ET: (22, 12, 3); 87-ET: (28, 15, 4)
!UDP
 
!Porcupine mode
==== (2/1, 3/2, 9/7: 245/243)[10] Sensamagic ====
![[Mode height]]
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35)
|-
 
| -3
~ 28/27 5/4 9/7 4/3 35/24 3/2 14/9 15/8 27/14 2/1 as sLssmssLss
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
 
|sMMsMLM
m  = s -> sLsssssLss; s = 0 -> LsL
|sLLsLLL
 
|<nowiki>0|6</nowiki>
14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)
|Lochrian
 
|sssssLs
==== (2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic ====
|<nowiki>1|5</nowiki>
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)
|Dark diminished
 
| -0.0616
~ 28/27 5/4 9/7 4/3 16/11 3/2 14/9 15/8 27/14 2/1 as sLssmssLss
|-
 
|  -2
m  = s -> sLsssssLss; s = 0 -> LsL
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
 
|sMLMsMM
17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 63-ET: (18, 8, 3); 68-ET: (19, 9, 3); 87-ET: (24, 11, 4)
|sLLLsLL
 
|<nowiki>1|5</nowiki>
==== (2/1, 3/2, 9/7: 245/243)[13] Sensamagic ====
|Phrygian
2L 1m 10s = (~75/64, ~135/128, 28/27~36/35)
|ssLssss
 
|<nowiki>4|2</nowiki>
~ 28/27 16/15 5/4 9/7 4/3 48/35 35/24 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss
|Bright minor
 
|  -0.0314
m = s -> ssLsssssssLss Pycnic[13] MODMOS; s = 0 -> LsL
|-
| -1
|~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1
|MsMMsML
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
| -0.0302
|-
|0
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|MsMLMsM
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|0
|-
|1
|~ 9/8 5/4 27/20 3/2 5/3 9/5 2/1
|LMsMMsM
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|0.0302
|-
|2
|~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|0.0314
|-
|3
|~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|0.0616
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[5L 2s|LsLLLsL]]
|[[Meantone family#Septimal meantone|Meantone]][7]
|81/80, 126/125
|-
|M = s
|[[1L 6s|sssLsss]]
|[[Trienstonic clan#Opossum|Opossum]][7]
|28/27, 126/125
|-
|L = s
|[[4L 3s|LsLsLsL]]
|[[Dicot family#Flat|Flat]][7]
|21/20, 25/24
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|8d
|[[12edo|12]]
|[[15edo|15]]
|[[16edo|16]]
|[[19edo|19]]
|[[27edo|27]]
|[[31edo|31]]
|[[46edo|46]]
|[[50edo|50]]
|[[58edo|58]]
|[[77edo|77]]
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 2)
|(2, 3, 1)
|(3, 3, 2)
|(5, 4, 3)
|(5, 5, 3)
|(8, 7, 5)
|(8, 8, 5)
|(10, 9, 6)
|(13, 12, 8)
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|1L 4m 2s
|(9/8~25/22, 10/9~11/10, 27/25~12/11)
|(209.7786c, 174.0549c, 146.6352c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[7]
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!Porcupine mode
![[Mode height]]
|-
| -3
|~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
|smmsmLm
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0427
|-
|  -2
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|msmmsmL
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|  -0.0374
|-
|  -1
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|smLmsmm
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|  -0.0053
|-
|0
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|msmLmsm
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|0
|-
|1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|mmsmLms
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|0.0053
|-
|2
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|Lmsmmsm
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|0.0374
|-
|3
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|mLmsmms
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|0.0427
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[1L 6s|sssLsss]]
|[[Porcupine family#Porkypine|Porkypine]][7]
|55/54, 100/99
|-
|L = m
|[[5L 2s|LsLLLsL]]
|[[Meanenneadecal]][7] or [[Meantone family#Flattone|Flattone]][7]
|45/44, 81/80
|-
|L = s
|[[4L 3s|LsLsLsL]]
|[[Dicot family|Flat]][7]
|25/24, 33/32
|-
|L - m = m - s
|LsLALsL
|[[Tetracot family#Subgroup temperament|Tetracot]][7] MODMOS
|100/99, 243/242
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|8
|[[12edo|12]]
|[[15edo|15]]
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|27e
|[[29edo|29]]
|[[34edo|34]]
|[[37edo|37]]
|[[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)
|(5, 4, 4)
|(6, 5, 4)
|(7, 5, 5)
|(7, 6, 5)
|}
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-7|(2/1, 3/2, 6/5: 56/55, 100/99)[7] (Thrasher)]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|1L 4M 2s
|(9/8~25/22, 10/9~11/10, 27/25~15/14~12/11)
|(215.4452c, 179.0856c, 132.5782c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[7]
!UDP
!Porcupine[7]
!UDP
!Porcupine mode
!Diatonic mode
![[Mode height]]
|-
| -3
|~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1
|sMMsMLM
|sLLsLLL
|<nowiki>0|6</nowiki>
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
|Lochrian
| -0.0591
|-
|  -2
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|MsMMsML
|LsLLsLL
|<nowiki>2|4</nowiki>
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|Aeolian
|  -0.0433
|-
|  -1
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|Phrygian
|  -0.0158
|-
|0
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|MsMLMsM
|LsLLLsL
|<nowiki>3|3</nowiki>
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|Dorian
|0
|-
|1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|Ionian
|0.0158
|-
|2
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LMsMMsM
|LLsLLsL
|<nowiki>4|2</nowiki>
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|Mixolydian
|0.0433
|-
|3
|~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|Lydian
|0.0591
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[5L 2s|LsLLLsL]]
|[[Meanenneadecal]][7]
|45/44, 56/55, 81/80
|-
|M = s
|[[1L 6s|sssLsss]]
|[[Trienstonic clan#Opossum|Opossum]][7]
|28/27, 55/54, 77/75
|-
|L = s
|[[4L 3s|LsLsLsL]]
|[[Dicot family#Flat|Flat]][7]
|21/20, 25/24, 33/32
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|8d
|[[12edo|12]]
|[[15edo|15]]
|[[19edo|19]]
|27e
|[[34edo|34]]
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 2)
|(3, 3, 2)
|(5, 4, 3)
|(6, 5, 4)
|}


14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)
===== (2/1, 3/2, 6/5: 100/99, 144/143)[7] (No-7 Ptolemismic) =====
 
{| class="wikitable"
==== (2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic ====
!Step signature
2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)
!Steps in JI
 
!Step sizes in cents (TE)
~ 28/27 16/15 5/4 9/7 4/3 11/8 16/11 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss
|-
 
|1L 4m 2s
m = s -> ssLsssssssLss; s = 0 -> LsL
|(9/8~25/22, 10/9~11/10, 27/25~12/11~13/12)
 
|(209.5416c, 175.8918c, 142.7754c)
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 63-ET: (15, 5, 3); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)
|}
 
{| class="wikitable"
==== (2/1, 3/2, 9/7: 245/243, 385/384)[16] Sensamagic ====
!Mode number
2L 13m 1s = (~25/22, 28/27~36/35~33/32, ~45/44)
!Mode as simplest JI pre-image
!Step pattern
!Meantone[7]
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!Porcupine mode
![[Mode height]]
|-
|  -3
|~ 12/11 6/5 4/3 13/9 8/5 9/5 2/1
|smmsmLm
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
|
|-
|  -2
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|msmmsmL
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|
|-
|  -1
|~ 12/11 6/5 15/11 3/2 13/8 9/5 2/1
|smLmsmm
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|
|-
|0
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|msmLmsm
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|
|-
|1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|mmsmLms
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|
|-
|2
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|Lmsmmsm
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|
|-
|3
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|mLmsmms
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[1L 6s|sssLsss]]
|[[Porcupine family#13-limit|Porcupine]][7]
|40/39, 55/54, 66/65
|-
|L = m
|[[5L 2s|LsLLLsL]]
|[[Meantone family#Flattone|Flattone]][7]
|45/44, 65/64, 81/80
|-
|L - m = m - s
|LsLALsL
|[[Tetracot family#Subgroup temperament|Tetracot]][7] MODMOS
|100/99, 144/143, 243/242
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|8
|[[12edo|12]]
|[[15edo|15]]
|[[19edo|19]]
|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)
|}


~ 28/27 16/15 40/33 5/4 9/7 4/3 11/8 45/32 16/11 3/2 14/9 8/5 20/11 15/8 27/14 2/1 as mmLmmmmsmmmmLmmm
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
 
{| class="wikitable"
m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss
!Step signature
 
!Steps in JI
17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 22-ET: (4, 1, 1) 24-ET: (5, 1, 1); 27-ET: (6, 1, 2); 41-ET: (7, 2, 1); 46-ET: (9, 2, 2); 63-ET: (12, 3, 2); 68-ET: (13, 3, 3); 87-ET: (16, 4, 3)
!Step sizes in cents
 
|-
==== (2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic ====
|7L 1m 4s
2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)
|(27/25, 25/24, 250/243)
|(133.2376c, 70.6724c, 49.1661c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
| -6
|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
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
| -0.0622
|-
| -5
|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
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
| -0.0587
|-
| -4
|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
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
| -0.0338
|-
| -3
|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
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
| -0.0302
|-
|  -2
|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
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|  -0.0267
|-
|  -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
|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
|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
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|0.0267
|-
|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
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|0.0302
|-
|4
|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
|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"
|+Rank-2 temperings (mode -3)
! Equivalence
! Step pattern
! Scale
! Comma list
|-
| m = s
| [[7L 5s|sLLsLsLsLLsL]]
| [[Meantone]][12]
| 81/80
|-
| L = m
| sLLsLLLsLLsL
| [[Diminished (temperament)|Diminished]][12] MODMOS
| 648/625
|-
| L = s
| [[11L 1s|LLLLLsLLLLLL]]
| [[Ripple]][12]
| 6561/6250
|-
| L - m = m - s
| dLLdLsLdLLdL
| [[Augmented (temperament)|Augmented]][12] modmos
| 128/125
|-
| s = 0
| [[7L 1s|LLLsLLLL]]
| [[Porcupine]][8]
| 250/243
|}


~ 45/44 28/27 35/33 16/15 12/11 11/10 9/8 154/135 7/6 9/7 405/308 4/3 15/11 11/8 45/32 64/45 16/11 22/15 3/2 616/405 14/9 12/7 135/77 16/9 20/11 11/6 15/8 66/35 27/14 88/45 2/1 as msmsmsmsmLmsmsmsmsmsmLmsmsmsmsm
=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(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]][12]
| 81/80, 126/125
|-
| L = m
| sLLsLLLsLLsL
| [[Diminished (temperament)|Diminished]][12] MODMOS
| 36/35, 50/49
|-
| L - m = m - s
| dLLdLsLdLLdL
| [[Augene]][12] MODMOS
| 64/63, 126/125
|-
| s = 0
| [[7L 1s|LLLsLLLL]]
| [[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]]]=====
{| 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)
|}
{| 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)]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11, 25/24~33/32, 250/243~55/54~121/120)
|(146.6352c, 63.1434c, 27.4197c)
|}
{| 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 55/36 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
| -0.0899
|-
| -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
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
| -0.0819
|-
| -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>
| -0.0510
|-
| -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
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<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 [[Flattone]][12]
| 45/44, 81/80
|-
| L = m
| sLLsLLLsLLsL
| [[Diminished (temperament)|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]][8]
| 55/54, 100/99
|}


m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS
{| 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]]) =====
{| 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>
|
|-
|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"
|+Rank-2 temperings (mode -3)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 81/80, 385/384
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#11-limit|Porcupine]][8]
|55/54, 64/63, 100/99
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|[[34edo|34]]
|[[41edo|41]]
|[[104edo|104]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(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]]) =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~13/12~35/32, 25/24~27/26~33/32, 250/243~40/39~55/54~64/63~121/120)
|(145.47082c, 58.39270c, 30.85183c)
|}
{| 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 8/7 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 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 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 7/4 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 7/4 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, 78/77, 81/80
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#13-limit|Porcupine]][8]
|40/39, 55/54, 64/63, 66/65
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|22f
|[[26edo|26]]
|[[34edo|34]]
|[[41edo|41]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(4, 2, 1)
|(5, 2, 1)
|}
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)]]=====
{| 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
| [[Diminished (temperament)|Diminished]][12] MODMOS
| 36/35, 50/49, 56/55
|-
| s = 0
| [[7L 1s|LLLsLLLL]]
| [[Opossum]][8]
| 28/27, 55/54, 77/75
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[19edo|19]]
|27e
|[[34edo|34]]
|-
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(3, 2, 1)
|(4, 2, 1)
|}
=====(2/1, 3/2, 6/5: 56/55, 91/90, 100/99)[12] (Thrasher)=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~15/14~12/11~13/12, 25/24~21/20~33/32~27/26, 250/243~28/27~55/54~40/39)
|
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 28/27 10/9 44/39 11/9 4/3 110/81 22/15 14/9 5/3 22/13 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|
|-
|  -5
|~ 28/27 10/9 7/6 5/4 33/26 11/8 3/2 14/9 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|
|-
|  -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>
|
|-
|  -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>
|
|-
|  -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>
|
|-
|  -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 81/50 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|-
|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>
|
|-
|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>
|
|-
|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>
|
|-
|5
|~ 12/11 13/11 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>
|
|-
|6
|~ 12/11 13/11 6/5 9/7 15/11 81/55 3/2 81/50 39/22 9/5 27/14 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#Vincenzo|Vincenzo]][12]
|45/44, 56/55, 65/64, 81/80
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 40/39, 55/54, 66/65
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[15edo|15]]
|[[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)]] =====
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
 
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)
 
==== (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] (Keemic) ====
7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE
 
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
==== [[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
 
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
 
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
 
L - m = m - s -> Unidec[20] MODMOS
 
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
 
19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
 
===== [[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-20|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)]] =====
7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE
 
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
 
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
 
s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL
 
19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
 
==== [[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-39|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)]] ====
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE
 
~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms
 
m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs
 
46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)
 
=== ((2/1, 6/5)[4], 10/9) ===
 
==== ((2/1, 6/5)[4], 10/9)[8] ====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9, 27/25, 25/24
|(182.4037c, 133.2376c, 70.6724c)
|}
{| class="wikitable"
|+
!Mode number
!Mode in JI (height order)
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|10/9 6/5 4/3 36/25 8/5 216/125 48/25 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|10/9 6/5 4/3 36/25 8/5 5/3 50/27 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|27/25 6/5 162/125 36/25 972/625 216/125 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|10/9 6/5 4/3 25/18 125/81 5/3 50/27 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|27/25 6/5 162/125 36/25 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|10/9 125/108 625/486 25/18 125/81 5/3 50/27 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -4
|25/24 125/108 5/4 25/18 3/2 5/3 9/5 2/1
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
 
 
{| class="wikitable"
|+Rank-2 temperings (mode 4)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|M = 0
|LLLLs
|Bug[5]
|27/25
|-
|s = 0
|LsLsLsL
|Dicot[7]
|25/24
|-
|L = M
|LLLLLLLs
|Porcupine[8]
|250/243
|-
|M = s
|LsLsLsLs
|Diminished[8]
|648/625
|-
|L - M = M - s
|LsLsLsLd
|Sensipent[8] MODMOS
|78732/78125
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|12
|15
|19
|22
|26
|27
|29
|31
|34
|41
|46
|53
|65
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(4, 3, 2)
|(4, 4, 1)
|(5, 3, 2)
|(5, 4, 2)
|(6, 5, 2)
|(7, 5, 3)
|(8, 6, 3)
|(10, 7, 4)
|}
 
===== ((2/1, 6/5)[4], 10/9: 875/864)[8] Supermagic =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9, 27/25~35/32, 25/24~36/35
|176.8769, 144.8100, 59.11533
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|~ 10/9 6/5 4/3 35/24 8/5 7/4 35/18 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|~ 10/9 6/5 4/3 35/24 8/5 5/3 50/27 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|~ 27/25 6/5 21/16 35/24 63/40 7/4 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|~ 10/9 6/5 4/3 25/18 32/21 5/3 50/27 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|~ 27/25 6/5 21/16 35/24 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|~ 10/9 8/7 80/63 25/18 32/21 5/3 50/27 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|~ 27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -4
|~ 25/24 8/7 5/4 25/18 3/2 5/3 9/5 2/1
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
 
{| class="wikitable"
|+Rank-2 temperings (mode 4)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|s = 0
|LsLsLsL
|Dicot[7]
|25/24, 15/14
|-
|L = M
|LLLLLLLs
|Porcupine[8]
|250/243, 64/63
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|15
|19
|22
|26
|34
|37
|41
|60
|-
!Step sizes in ET
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(9, 7, 3)
|}
 
===== ((2/1, 6/5)[4], 10/9: 100/99, 385/384)[8] Supermagic =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9~11/10, 27/25~35/32~12/11, 25/24~36/35~33/32
|173.1413, 149.5159, 58.8799
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|~ 10/9 6/5 4/3 16/11 8/5 7/4 35/18 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|~ 10/9 6/5 4/3 16/11 8/5 5/3 11/6 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|~ 12/11 6/5 21/16 16/11 63/40 7/4 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|~ 10/9 6/5 4/3 11/8 32/21 5/3 11/6 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|~ 12/11 6/5 21/16 16/11 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|~ 10/9 8/7 44/35 11/8 32/21 5/3 11/6 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -4
|~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
 
{| class="wikitable"
|+Rank-2 temperings (mode 4)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LLLLLLLs
|Porcupine[8]
|55/54, 64/63, 100/99
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|15
|19
|22
|26
|34
|37
|41
|63
|-
!Step sizes in ET
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(5, 4, 2)
|(5, 5, 2)
|(6, 5, 2)
|(9, 8, 3)
|}
 
===== ((2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[8] Supermagic =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9~11/10, 27/25~35/32~12/11~13/12, 25/24~36/35~33/32~27/26
|176.3227, 145.4708, 58.3927
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Porcupine[8]
step pattern and UDP
!Diminished[8]
step pattern and UDP
|-
|4
|~ 10/9 6/5 4/3 13/9 8/5 7/4 35/18 2/1
|LMLMLMLs
|<nowiki>LLLLLLLs 7|0</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|3
|~ 10/9 6/5 4/3 13/9 8/5 5/3 11/6 2/1
|LMLMLsLM
|<nowiki>LLLLLsLL 5|2</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
|2
|~ 12/11 6/5 13/10 13/9 39/25 7/4 9/5 2/1
|MLMLMLsL
|<nowiki>LLLLLLsL 6|1</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
|1
|~ 10/9 6/5 4/3 11/8 20/13 5/3 11/6 2/1
|LMLsLMLM
|<nowiki>LLLsLLLL 3|4</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -1
|~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|MLMLsLML
|<nowiki>LLLLsLLL 4|3</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -2
|~ 10/9 8/7 44/35 11/8 20/13 5/3 11/6 2/1
|LsLMLMLM
|<nowiki>LsLLLLLL 1|6</nowiki>
|<nowiki>LsLsLsLs 1|0 (4)</nowiki>
|-
| -3
|~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1
|MLsLMLML
|<nowiki>LLsLLLLL 2|5</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|-
| -4
|~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1
|sLMLMLML
|<nowiki>sLLLLLLL 0|7</nowiki>
|<nowiki>sLsLsLsL 0|1 (4)</nowiki>
|}
 
{| class="wikitable"
|+Rank-2 temperings (mode 4)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LLLLLLLs
|Porcupine[8]
|40/39, 55/54, 64/63, 66/65
|}
 
{| class="wikitable"
|+Rank-1 temperings
!ET
|15
|19
|22f
|26
|34
|41
|60
|-
!Step sizes in ET
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(5, 4, 2)
|(6, 5, 2)
|(9, 7, 3)
|}
 
===== ((2/1, 6/5)[4], 10/9: 325/324)[8] (2.3.5.13 Marveltwin) =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9, 27/25~13/12, 25/24~27/26
|180.4645c, 136.7099c, 68.1467c
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
|-
|4
|~ 10/9 6/5 4/3 13/9 8/5 26/15 48/25 2/1
|LMLMLMLs
|-
|3
|~ 10/9 6/5 4/3 13/9 8/5 5/3 24/13 2/1
|LMLMLsLM
|-
|2
|~ 13/12 6/5 13/10 13/9 39/25 26/15 9/5 2/1
|MLMLMLsL
|-
|1
|~ 10/9 6/5 4/3 13/9 20/13 5/3 24/13 2/1
|LMLsLMLM
|-
| -1
|~ 13/12 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|MLMLsLML
|-
| -2
|~ 10/9 15/13 50/39 18/13 20/13 5/3 24/13 2/1
|LsLMLMLM
|-
| -3
|~ 13/12 6/5 5/4 18/13 3/2 5/3 9/5 2/1
|MLsLMLML
|-
| -4
|~ 25/24 15/13 5/4 18/13 3/2 5/3 9/5 2/1
|sLMLMLML
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|12
|15
|19
|22f
|26
|27e
|29
|31
|34
|41
|46
|53
|72
|87
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(4, 3, 2)
|(4, 4, 1)
|(5, 4, 1)
|(5, 4, 2)
|(6, 5, 2)
|(7, 5, 3)
|(8, 6, 3)
|(11, 8, 4)
|(13, 9, 5)
|}
 
===== ((2/1, 6/5)[4], 10/9: 100/99, 144/143)[8] (2.3.5.11.13 Ptolemismic) =====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|4L 3M 1s
|10/9~11/10, 27/25~12/11~13/12, 25/24~33/32~27/26
|175.8918c, 142.7754c, 66.7663c
|}
{| class="wikitable"
|+
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Mode in cents
|-
|4
|~ 10/9 6/5 4/3 13/9 8/5 26/15 48/25 2/1
|LMLMLMLs
|175.892 318.667 494.559 637.334 813.226 956.002 1131.893 1198.660
|-
|3
|~ 10/9 6/5 4/3 13/9 8/5 5/3 11/6 2/1
|LMLMLsLM
|175.892 318.667 494.559 637.334 813.226 879.993 1055.884 1198.660
|-
|2
|~ 12/11 6/5 13/10 13/9 39/25 26/15 9/5 2/1
|MLMLMLsL
|142.775 318.667 461.443 637.334 780.120 956.002 1022.768 1198.660
|-
|1
|~ 10/9 6/5 4/3 13/9 20/13 5/3 11/6 2/1
|LMLsLMLM
|175.892 318.667 494.559 561.325 737.218 879.993 1055.884 1198.660
|-
| -1
|~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1
|MLMLsLML
|142.775 318.667 461.443 637.334 704.101 879.993 1022.768 1198.660
|-
| -2
|~ 10/9 15/13 50/39 11/8 20/13 5/3 11/6 2/1
|LsLMLMLM
|175.892 242.658 418.550 561.325 737.218 879.993 1055.884 1198.660
|-
| -3
|~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1
|MLsLMLML
|142.775 318.667 385.433 561.325 704.101 879.993 1022.768 1198.660
|-
| -4
|~ 25/24 15/13 5/4 11/8 3/2 5/3 9/5 2/1
|sLMLMLML
|66.766 242.658 385.433 561.325 704.101 879.993 1022.768 1198.660
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|12
|15
|19
|22f
|26
|27e
|29
|34
|41
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(3, 3, 1)
|(4, 3, 1)
|(4, 3, 2)
|(4, 4, 1)
|(5, 4, 2)
|(6, 5, 2)
|}
 
==== (2/1, 6/5)[4], 10/9)[15] ====
4L 8m 3s = (16/15, 25/24, 648/625) = (111.7313, 70.6724, 62.5652)
 
25/24 10/9 125/108 6/5 5/4 4/3 25/18 36/25 3/2 8/5 5/3 216/125 9/5 48/25 2/1 as mLmsmLmsmLmsmLm
 
m = s -> sLsssLsssLsssLs Hanson[15]; L = -> LLLsLLLsLLLsLLL Augmented[15] MODMOS; L = s -> sLsLsLsLsLsLsLs Porcupine[15];
 
s = 0 -> ssLsLssLsssL Diminished[12] MODMOS; m = 0 -> sLLsLsL Dicot[7]; L = 0 -> Father[11].
 
19-ET: (2, 1, 1); 22-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27-ET: (2, 2, 1); 29-ET: (3, 1, 3); 31-ET: (3, 2, 1); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3); 46-ET: (4, 3, 2); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)
 
===== (2/1, 6/5)[4], 10/9: 875/864)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20, 25/24~36/35)
 
~ 25/24 10/9 8/7 6/5 5/4 4/3 25/18 35/24 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)
 
===== (2/1, 6/5)[4], 10/9: 100/99, 385/384)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20~128/121, 25/24~36/35~33/32)
 
~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 63-ET: (6, 5, 3)
 
===== (2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[15] Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20~128/121~26/25, 25/24~36/35~33/32~27/26)
 
~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)
 
===== (2/1, 6/5)[4], 10/9: 325/324)[15] (2.3.5.13 Marveltwin) =====
4L 3m 8s = (16/15, 648/625~26/25, 25/24~27/26) = (112.3178, 68.5631, 68.1467)
 
~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27-ET: (2, 2, 1); 29-ET: (3, 3, 1); 31-ET: (3, 1, 2); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2); 46-ET: (4, 2, 3); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)
 
===== (2/1, 6/5)[4], 10/9: 105/104, 325/324)[15] 2.3.5.7.13 Supermagic =====
4L 3m 8s = (16/15, 648/625~21/20~26/25, 25/24~36/35~27/26) = (121.6150, 81.3115, 58.8960)
 
~ 25/24 10/9 8/7 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)
===== (2/1, 6/5)[4], 10/9: 100/99, 144/143)[15] (2.3.5.11.13 Ptolemismic) =====
4L 3m 8s = (16/15, 648/625~128/121~26/25, 25/24~33/32~27/26) = (109.1256, 76.0091, 66.7663) ⟨109.12557, 76.00911, 66.76626]
 
~ 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs
 
15-ET: (1, 1, 1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27e-ET: (2, 1, 2); 29-ET: (3, 3, 1); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2)
 
==2.3.5; [[Hemifamity family#Hemifamity|Hemifamity]] ==
===((2/1, 3/2)[5], 10/9)===
====[[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]]====
5L 2M 3s = (10/9, 16/15, 81/80)
 
81/80 9/8 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1 as sLMLsLMLsL
 
L = M -> sLLLsLLLsL Dicot[10] MODMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;
 
L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS
 
s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)]]====
5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE
 
~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs
 
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss;
 
L - m = m - s -> Garibaldi[17]; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)]]=====
5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE
 
~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs
 
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Arnold[7]; m = 0 -> sLssLssLssLssLs
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-24|((2/1, 3/2)[5], 10/9: 5120/5103)[24] (Hemifamity)]]====
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63) = (132.1305c, 61.3411c, 24.4931c) TE
 
~ 64/63 35/32 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 35/24 40/27 3/2 32/21 105/64 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss
 
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-24|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24] (Akea)]]=====
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE
 
~ 64/63 12/11 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 16/11 40/27 3/2 32/21 18/11 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss
 
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Arnold[7]
====[[SNS ((2/1, 3/2)-5, 10/9: 5120/5103)-31|((2/1, 3/2)[5], 10/9: 5120/5103)[31] (Hemifamity)]]====
5L 2m 24s = (~1225/1152, ~49/48, 81/80~64/63) = (107.6374c, 36.848c, 24.4931c) TE
 
~ 64/63 36/35 35/32 10/9 9/8 8/7 7/6 32/27 6/5 128/105 35/27 21/16 4/3 27/20 48/35 35/24 40/27 3/2 32/21 54/35 105/64 5/3 27/16 12/7 7/4 16/9 9/5 64/35 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss
 
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
 
s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS
=====[[SNS ((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-31|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31] (Akea)]]=====
5L 2m 24s = (~35/33, 49/48~56/55, 81/80~64/63~55/54) = (100.7664c, 33.3269c, 26.2356c) TE
 
~ 64/63 36/35 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 35/27 21/16 4/3 27/20 11/8 16/11 40/27 3/2 32/21 54/35 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss
 
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
 
s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss
===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) ===
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)]]====
5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE
 
~ 64/63 15/14 243/224 9/8 8/7 32/27 6/5 81/64 9/7 4/3 27/20 10/7 81/56 3/2 32/21 45/28 80/49 27/16 12/7 16/9 9/5 243/128 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM
 
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-24|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24] (Pele)]]=====
5L 7M 12s = (135/128~35/33, 28/27~33/32, 81/80~64/63~99/98) = (97.5911c, 58.2557c, 25.3165c) TE
 
~ 64/63 15/14 12/11 9/8 8/7 32/27 6/5 14/11 9/7 4/3 27/20 10/7 16/11 3/2 32/21 45/28 18/11 27/16 12/7 16/9 9/5 12/11 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM
 
L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]
====[[SNS ((2/1, 3/2)-12, 64/63: 5120/5013)-36|((2/1, 3/2)[12], 64/63: 5120/5013)[36] (Hemifamity)]]====
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE
 
~ 64/63 36/35 15/14 243/224 54/49 9/8 8/7 81/70 32/27 6/5 128/105 81/64 9/7 64/49 4/3 27/20 48/35 10/7 81/56 72/49 3/2 32/21 54/35 45/28 80/49 81/49 27/16 12/7 243/140 16/9 9/5 64/35 243/128 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM
 
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
 
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
=====[[SNS ((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36] (Pele)]]=====
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63~99/98) = (72.2746c, 32.9392c, 25.3165c) TE
 
~ 64/63 36/35 15/14 12/11 54/49 9/8 8/7 64/55 32/27 6/5 128/105 14/11 9/7 64/49 4/3 27/20 48/35 10/7 16/11 72/49 3/2 32/21 54/35 45/28 18/11 81/49 27/16 12/7 96/55 16/9 9/5 64/35 22/21 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM
 
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
 
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
 
==2.3.25==
===(2/1, 3/2, 100/81)===
====(2/1, 3/2, 100/81)[7]====
=====(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 1m 4s
|(2500/2187~8/7, ~9/8, ~27/25)
|(231.1884c, 203.974c, 133.4123c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
|  -3
|~ 9/8 175/144 25/18 3/2 81/50 50/27 2/1
|msLssLs
|  0.0158
|-
|  -2
|~ 27/25 175/144 21/16 3/2 81/50 7/4 2/1
|smsLssL
|  -0.0211
|-
|  -1
|~ 8/7 100/81 25/18 3/2 12/7 50/27 2/1
|LsmsLss
|  0.037
|-
|  0
|~ 27/25 100/81 4/3 3/2 81/50 50/27 2/1
|sLsmsLs
|  0
|-
|  1
|~ 27/25 7/6 4/3 36/25 81/50 7/4 2/1
|ssLsmsL
|  -0.037
|-
|  2
|~ 8/7 100/81 4/3 32/21 288/175 50/27 2/1
|LssLsms
|  0.0211
|-
|  3
|~ 27/25 100/81 4/3 36/25 288/175 16/9 2/1
|sLssLsm
|  -0.0158
|}
 
=====[[SNS_(2/1,_3/2,_100/81:_1225/1224,_1701/1700)-7|(2/1, 3/2, 100/81: 1225/1224, 1701/1700)[7]]]=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 1m 4s
|(2500/2187~8/7, ~9/8, ~27/25)
|(231.5807c, 203.8094c, 133.2573c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
![[Mode height]]
|-
|  -3
|~ 9/8 17/14 25/18 3/2 34/21 50/27 2/1
|msLssLs
|  0.0157
|-
|  -2
|~ 27/25 17/14 21/16 3/2 34/21 7/4 2/1
|smsLssL
|  -0.0214
|-
|  -1
|~ 8/7 21/17 25/18 3/2 12/7 50/27 2/1
|LsmsLss
|  0.0371
|-
|  0
|~ 27/25 21/17 4/3 3/2 34/21 50/27 2/1
|sLsmsLs
|  0
|-
|  1
|~ 27/25 7/6 4/3 36/25 34/21 7/4 2/1
|ssLsmsL
|  -0.0371
|-
|  2
|~ 8/7 21/17 4/3 32/21 28/17 50/27 2/1
|LssLsms
|  0.0214
|-
|  3
|~ 27/25 21/17 4/3 36/25 28/17 16/9 2/1
|sLssLsm
|  -0.0157
|}
 
==2.5.9; Marvel ==
=== ((2/1, 5/4)[3], 9/8)===
====[[SNS ((2/1, 5/4)-3, 9/8)-6|((2/1, 5/4)[3], 9/8)[6]]]====
1L 3M 2s = (256/225, 9/8, 10/9)
 
9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs
 
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-6|((2/1, 5/4)[3], 9/8: 225/224)[6] (Marvel)]]=====
1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c) TE
 
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
 
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-6|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6] (Apollo)]]=====
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c) TE
 
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
 
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
====[[SNS ((2/1, 5/4)-3, 9/8)-10|((2/1, 5/4)[3], 9/8)[10]]]====
6L 1m 3s = (10/9, 128/125, 81/80)
 
10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,
 
m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-10|((2/1, 5/4)[3], 9/8: 225/224)[10] (Marvel)]]=====
6L 1m 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE
 
~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
 
m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-10|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10] (Apollo)]]=====
6L 1m 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE
 
~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL
 
m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL
====[[SNS ((2/1, 5/4)-3, 9/8)-17|((2/1, 5/4)[3], 9/8)[17]]]====
6L 10m 1s = (800/729, 81/80, 2048/2025)
 
81/80 10/9 9/8 100/81 5/4 81/64 25/18 45/32 64/45 36/18 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as mLmLmmLmsmLmmLmLm
 
m = s -> sLsLssLsssLssLsLs MODMOS;  L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL
=====[[SNS ((2/1, 5/4)-3, 9/8: 225/224)-17|((2/1, 5/4)[3], 9/8: 225/224)[17] (Marvel)]]=====
6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE
 
~ 81/80 10/9 9/8 100/81 5/4 81/64 25/18 7/5 10/7 36/25 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as sLsLssLsmsLssLsLs
 
m = s -> sLsLssLsssLssLsLs MODMOS;  L = m ->  sLsLssLsLsLssLsLs; L = s -> LLLLLLLLsLLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLsLssLssLssLsLs MODMOS
=====[[SNS ((2/1, 5/4)-3, 9/8: 100/99, 225/224)-17|((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17] (Apollo)]]=====
6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE
 
~ 56/55 10/9 9/8 11/9 5/4 14/11 11/8 7/5 10/7 16/11 11/7 8/5 11/9 16/9 9/5 55/28 2/1 as mLmLmmLmsmLmmLmLm
 
m = s -> sLsLssLsssLssLsLs Machine[17] MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL
==2.5.9; Starling==
===((2/1, 5/4)[3], 10/9)===
====[[SNS ((2/1, 5/4)-3, 10/9)-6|((2/1, 5/4)[3], 10/9)[6]]]====
1L 2m 3s = (144/125, 9/8, 10/9)
 
9/8 5/4 36/25 8/5 9/5 2/1 as msLsms
 
m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
=====[[SNS ((2/1, 5/4)-3, 10/9: 126/125)-6|((2/1, 5/4)[3], 10/9: 126/125)[6]]]=====
1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c) TE
 
~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms
 
m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
====[[SNS ((2/1, 5/4)-3, 10/9)-9|((2/1, 5/4)[3], 10/9)[9]]]====
6L 1m 2s = (10/9, 648/625, 81/80)
 
10/9 9/8 5/4 25/18 36/25 8/5 16/9 9/5 2/1 as LsLLmLLsL
 
m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS
=====[[SNS ((2/1, 5/4)-3, 10/9: 126/125)-9|((2/1, 5/4)[3], 10/9: 126/125)[9]]]=====
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c) TE
 
~ 10/9 9/8 5/4 7/5 10/7 8/5 16/9 9/5 2/1 as LsLLmLLsL
 
m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS
====[[SNS ((2/1, 5/4)-3, 10/9: 126/126, 896/891)-16|((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16]]]====
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55) = (163.6623c, 24.4284c, 21.4103c) TE
 
~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 81/50 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL
 
m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
=====[[SNS ((2/1, 5/4)-3, 10/9: 91/90, 126/126, 896/891)-16|((2/1, 5/4)[3], 10/9: 91/90, 126/125, 896/891)[16]]]=====
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143) = (160.4106c, 30.0969c, 23.0825c) TE
 
~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 13/8 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL
 
m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
==2.3.7; [[Orwellismic family#Orwellismic|Orwellismic]]==
===(2/1, 3/2, 7/6)===
====[[SNS (2/1, 3/2, 7/6)-4|(2/1, 3/2, 7/6)[4]]]====
1L 2m 1s = (9/7, 7/6, 8/7)
 
7/6 3/2 7/4 2/1 as mLms
 
m = s -> sLss Sempahore[4]
====[[SNS (2/1, 3/2, 7/6)-7|(2/1, 3/2, 7/6)[7]]]====
4L 1M 2s = (8/7, 9/8, 49/48)
 
8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL
 
L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]
=====[[SNS (2/1, 3/2, 7/6: 1728/1715)-7|(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)]]=====
4L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE
 
~ 8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL
 
L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-12|(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)]]====
4L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE
 
~ 36/35 8/7 7/6 6/5 4/3 48/35 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
 
L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Beep[5]
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-12|(2/1, 3/2, 7/6: 99/98, 385/384)[12] (Orwellian)]]=====
4L 1M 7s = (~10/9, 54/49~35/32~12/11, 49/48~36/35~33/32) = (185.7619, 155.4288c, 155.4288c) TE
 
~ 33/32 8/7 7/6 6/5 4/3 11/8 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
 
L = M -> sLssLsLsLssL Suprapyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Pentoid[5]
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-12|(2/1, 3/2, 7/6: 176/175, 540/539)[12] (Guanyin)]]=====
4L 1M 7s = (~10/9, 54/49~35/32~11/10, 49/48~36/35~45/44) = (183.8734c, 162.5743c, 43.0239c) TE
 
~ 36/35 8/7 7/6 6/5 4/3 15/11 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL
 
L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-17|(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)]]====
4L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE
 
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 48/35 35/24 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
 
L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Beep[5]
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-17|(2/1, 3/2, 7/6: 99/98, 385/384)[17] (Orwellian)]]=====
4L 1M 12s = (~160/147, 15/14~35/33, 49/48~36/35~33/32) = (142.5744c, 112.2413c, 43.1875c) TE
 
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 11/8 16/11 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
 
L = M -> sLsssLssLssLsssLs Suprapyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Pentoid[5]
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-17|(2/1, 3/2, 7/6: 176/175, 540/539)[17] (Guanyin)]]=====
4L 1M 12s = (~88/81, 15/14~77/72, 49/48~36/35~45/44) = (140.8495c, 119.5504c, 43.0239c) TE
 
~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 15/11 22/15 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs
 
L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-22|(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)]]====
4L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE
 
~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 48/35 7/5 35/24 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs
 
m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]; s = 0 -> LLsLL Beep[5]
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-22|(2/1, 3/2, 7/6: 99/98, 385/384)[22] (Orwellian)]]=====
4L 1m 17s = (~200/189, 25/24~80/77, 49/48~36/35~33/32) = (99.3869c, 69.0538c, 43.1875c) TE
 
~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 11/8 7/5 16/11 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs
 
m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Suprapyth[17]; s = 0 -> LLsLL Pentoid[5]
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-22|(2/1, 3/2, 7/6: 176/175, 540/539)[22] (Guanyin)]]=====
4L 1m 17s = (~200/189, 25/24~22/21, 49/48~36/35~45/44) = (97.8256c, 76.5265c, 43.0239c) TE
 
~ 36/35 21/20 10/9 8/7 7/6 6/5 27/22 35/27 4/3 15/11 7/5 22/15 3/2 54/27 63/40 5/3 12/7 7/4 9/5 81/44 35/18 2/1 as ssLssssLsssmsssLssssLs
 
m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-27|(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)]]====
4L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE
 
~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 48/35 7/5 10/7 35/24 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM
 
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; M = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
 
s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Beep[5]
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-27|(2/1, 3/2, 7/6: 99/98, 385/384)[27] (Orwellian)]]=====
4L 22M 1s = (~250/243, 49/48~36/35~33/32, 50/49~100/99) = (56.1994c, 43.1875c, 25.8663c) TE
 
~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 11/8 7/5 10/7 16/11 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM
 
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartz[27]; M = s -> ssLsssssLsssssssssLsssssLss Myno[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Suprapyth[27];
 
s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Pentoid[5]
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-27|(2/1, 3/2, 7/6: 176/175, 540/539)[27] (Guanyin)]]=====
4L 22M 1s = (~250/243, 49/48~36/35~45/44, 50/49~55/54) = (54.8017c, 43.0239c, 33.5026c) TE
 
~ 36/35 21/20 88/81 10/9 8/7 7/6 6/5 27/22 80/63 35/27 4/3 15/11 7/5 10/7 22/15 3/2 54/27 63/40 44/27 5/3 12/7 7/4 9/5 81/44 40/21 35/18 2/1 as mmLmmmmmLmmmmsmmmmLmmmmmLmm
 
m = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = m -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
 
s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS
====[[SNS (2/1, 3/2, 7/6: 1728/1715)-53|(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)]]====
27L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE
 
~ 50/49 36/35 360/343 21/20 15/14 27/25 54/49 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 48/35 480/343 7/5 10/7 343/240 35/24 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 49/27 50/27 28/15 40/21 343/180 35/18 49/25 2/1 as LsLsLsLsLMLsLsLsLsLsLMLsLsLsLsLMLsLsLsLsLsLMLsLsLsLsL
 
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
 
M = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53]; L = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss
 
s = 0 -> LLLLLsLLLLLLsLLLLLsLLLLLLsLLLLL Myna[31] MODMOS; M = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49];
 
L = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS
=====[[SNS (2/1, 3/2, 7/6: 99/98, 385/384)-53|(2/1, 3/2, 7/6: 99/98, 385/384)[53] (Orwellian)]]=====
4L 27M 22s = (64/63~245/243~55/54, 50/49~100/99, 126/125~2401/2400) = (30.3331c, 25.8663c, 17.3212c) TE
 
~ 50/49 36/35 80/77 21/20 15/14 27/25 12/11 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 11/8 480/343 7/5 10/7 343/240 16/11 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 11/6 50/27 28/15 40/21 77/40 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM
 
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
 
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartz[53];
 
s = 0 -> sssssLssssssLsssssLssssssLsssss Myno[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS;
 
L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Suprapyth[49]
=====[[SNS (2/1, 3/2, 7/6: 176/175, 540/539)-53|(2/1, 3/2, 7/6: 176/175, 540/539)[53] (Guanyin)]]=====
4L 27M 22s = (64/63~245/243~100/99, 50/49~55/54, 126/125~2401/2400~441/440) = (33.5026c, 21.2991c, 9.5213c) TE
 
~ 50/49 36/35 22/21 21/20 15/14 27/25 11/10 243/220 9/8 8/7 125/108 7/6 25/21 6/5 11/9 27/22 5/4 63/50 9/7 162/125 21/16 4/3 110/81 15/11 88/63 7/5 10/7 63/44 22/15 81/55 3/2 32/16 125/81 14/9 100/63 8/5 44/27 18/11 5/3 42/25 12/7 216/125 7/4 16/9 440/243 20/11 50/27 40/21 21/11 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM
 
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
 
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss Kleiboh[53] MODMOS; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53];
 
s = 0 -> sssssLssssssLsssssLssssssLsssss Myna[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Fleetwood[22] MODMOS;
 
L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49]
===((2/1, 3/2)[12], 49/48) or ((2/1, 3/2)[12], 36/35)===
====((2/1, 3/2)[12], 36/35: 1728/1715)[24] (Orwellian)====
 
== 2.3.7 Sensamagic ==
 
=== (2/1, 3/2, 9/7) ===
 
==== (2/1, 3/2, 9/7)[4] ====
2L 1M 1s = (9/7, 7/6, 28/27) = (435.0841c, 266.8709c, 62.9609c)
 
9/7 3/2 27/14 2/1 as LMLs
 
L = M -> LLLs; M = s -> LsLs; s = 0 -> LsL
==== (2/1, 3/2, 9/7: 245/243)[7] Sensamagic ====
2L 1m 4s = (~5/4, ~9/8, 28/27~36/35)
 
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 as sLsmsLs
 
m = s -> sLsssLs; s = 0 -> LsL
 
5-ET: (2, 1, 0); 14c-ET: (4, 2, 1); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22-ET: (7, 4, 1) 24-ET: (8, 4, 1); 27-ET: (9, 5, 1); 41-ET: (13, 7, 2); 46-ET: (15, 8, 2); 68-ET: (22, 12, 3); 87-ET: (28, 15, 4)
 
==== (2/1, 3/2, 9/7: 245/243)[10] Sensamagic ====
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35)
 
~ 28/27 5/4 9/7 4/3 35/24 3/2 14/9 15/8 27/14 2/1 as sLssmssLss
 
m  = s -> sLsssssLss; s = 0 -> LsL
 
14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)
 
===== (2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic =====
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)
 
~ 28/27 5/4 9/7 4/3 16/11 3/2 14/9 15/8 27/14 2/1 as sLssmssLss
 
m  = s -> sLsssssLss; s = 0 -> LsL
 
17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 63-ET: (18, 8, 3); 68-ET: (19, 9, 3); 87-ET: (24, 11, 4)
 
==== (2/1, 3/2, 9/7: 245/243)[13] Sensamagic ====
2L 1m 10s = (~75/64, ~135/128, 28/27~36/35)
 
~ 28/27 16/15 5/4 9/7 4/3 48/35 35/24 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss
 
m = s -> ssLsssssssLss Pycnic[13] MODMOS; s = 0 -> LsL
 
14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)
 
===== (2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic =====
2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)
 
~ 28/27 16/15 5/4 9/7 4/3 11/8 16/11 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss
 
m = s -> ssLsssssssLss; s = 0 -> LsL
 
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 63-ET: (15, 5, 3); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)
 
==== (2/1, 3/2, 9/7: 245/243, 385/384)[16] Sensamagic ====
2L 13m 1s = (~25/22, 28/27~36/35~33/32, ~45/44)
 
~ 28/27 16/15 40/33 5/4 9/7 4/3 11/8 45/32 16/11 3/2 14/9 8/5 20/11 15/8 27/14 2/1 as mmLmmmmsmmmmLmmm
 
m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss
 
17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 22-ET: (4, 1, 1) 24-ET: (5, 1, 1); 27-ET: (6, 1, 2); 41-ET: (7, 2, 1); 46-ET: (9, 2, 2); 63-ET: (12, 3, 2); 68-ET: (13, 3, 3); 87-ET: (16, 4, 3)
 
==== (2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic ====
2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)
 
~ 45/44 28/27 35/33 16/15 12/11 11/10 9/8 154/135 7/6 9/7 405/308 4/3 15/11 11/8 45/32 64/45 16/11 22/15 3/2 616/405 14/9 12/7 135/77 16/9 20/11 11/6 15/8 66/35 27/14 88/45 2/1 as msmsmsmsmLmsmsmsmsmsmLmsmsmsmsm
 
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS
 
41-ET: (6, 1, 1); 46-ET: (7, 2, 0); 63-ET: (10, 2, 1); 68-ET: (10, 3, 0); 87-ET: (13, 3, 1)
 
==== (2/1, 3/2, 9/7: 729/728)[7] ====
2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)
 
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs
 
m = s -> sLsssLs; s = 0 -> LsL
 
5-ET: (2, 1, 0); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22f-ET: (7, 4, 1) 24-ET: (8, 4, 1); 36-ET: (11, 6, 2); 41-ET: (13, 7, 2); 53-ET: (16, 9, 3); 58-ET: (18, 10, 3); 77-ET: (24, 13, 4); 94-ET: (29, 16, 5)
 
==== (2/1, 3/2, 9/7: 729/728)[10] ====
2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)
 
~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss
 
m  = s -> sLsssssLss; s = 0 -> LsL
 
17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22f-ET: (6, 3, 1) 24-ET: (7, 3, 1); 36-ET: (9, 4, 2); 41-ET: (11, 5, 2); 53-ET: (13, 6, 3); 58-ET: (15, 7, 3); 77-ET: (20, 9, 4); 94-ET: (24, 11, 5)
 
==== (2/1, 3/2, 9/7: 729/728)[13] ====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26)
 
~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss
 
m = s -> ssLsssssssLss; s = 0 -> LsL
 
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)
 
===== (2/1, 3/2, 9/7: 351/350, 676/675)[13] =====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)
 
~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss
 
m = s -> ssLsssssssLss; s = 0 -> LsL
 
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 24-ET: (6, 2, 1); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 111-ET: (22, 7, 6); 130-ET: (26, 8, 7)
 
==== (2/1, 3/2, 9/7: 351/350, 676/675)[16] ====
2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)
 
~ 26/25 14/13 25/21 26/21 9/7 4/3 18/13 39/28 13/9 3/2 14/9 21/13 25/14 13/7 23/13 2/1 as mmLmmmmsmmmmLmmm
 
m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss
 
17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 24-ET: (5, 1, 1); 53-ET: (7, 3, 0); 58-ET: (9, 3, 1); 77-ET: (12, 4, 1); 111-ET: (16, 6, 1); 130-ET: (19, 7, 1)
 
==== (2/1, 3/2, 9/7: 351/350, 676/675)[31] ====
2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)
 
~169/168 26/25 117/112 14/13 13/12 28/25 9/8 378/325 7/6 9/7 325/252 4/3 75/56 18/13 39/28 56/39 13/9 112/75 3/2 14/9 12/7 325/189 16/9 25/14 24/13 13/7 224/117 25/13 336/169 2/1 as smsmsmsmsLsmsmsmsmsmsLsmsmsmsms
 
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS
 
53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)


41-ET: (6, 1, 1); 46-ET: (7, 2, 0); 63-ET: (10, 2, 1); 68-ET: (10, 3, 0); 87-ET: (13, 3, 1)
== 2.3.11 Pentacircle ==


==== (2/1, 3/2, 9/7: 729/728)[7] ====
=== ((2/1, 3/2)[5], 12/11) ===
2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)


~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs
==== ((2/1, 3/2)[5], 12/11)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32)


m = s -> sLsssLs; s = 0 -> LsL
12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM


5-ET: (2, 1, 0); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22f-ET: (7, 4, 1) 24-ET: (8, 4, 1); 36-ET: (11, 6, 2); 41-ET: (13, 7, 2); 53-ET: (16, 9, 3); 58-ET: (18, 10, 3); 77-ET: (24, 13, 4); 94-ET: (29, 16, 5)
==== ((2/1, 3/2)[5], 12/11: 896/891)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32~28/27)


==== (2/1, 3/2, 9/7: 729/728)[10] ====
~  12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM
2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)


~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss
==== ((2/1, 3/2)[5], 12/11: 896/891)[17] ====
5L 2M 10s = (128/121~81/77, 256/243~22/21, 33/32~28/27)


m  = s -> sLsssssLss; s = 0 -> LsL
~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 16/11 3/2 14/9 18/11 27/16 16/9 11/6 27/14 2/1 as sLsMsLssLssLsMsLs


17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22f-ET: (6, 3, 1) 24-ET: (7, 3, 1); 36-ET: (9, 4, 2); 41-ET: (11, 5, 2); 53-ET: (13, 6, 3); 58-ET: (15, 7, 3); 77-ET: (20, 9, 4); 94-ET: (24, 11, 5)
== 2.3.13 Squbema ==


==== (2/1, 3/2, 9/7: 729/728)[13] ====
=== ((2/1, 3/2)[5], 13/12) ===
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26)


~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss
==== ((2/1, 3/2)[5], 13/12)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26)


m = s -> ssLsssssssLss; s = 0 -> LsL
13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM


17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)
==== ((2/1, 3/2)[5], 13/12: 729/728)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26~28/27)


==== (2/1, 3/2, 9/7: 351/350, 676/675)[13] ====
~ 13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)


~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss
===== ((2/1, 3/2)[5], 13/12: 729/728)[17] =====
5L 2M 10s = (91/81, 256/243~96/91, 27/26~28/27)


m = s -> ssLsssssssLss; s = 0 -> LsL
~ 28/27 13/12 9/8 32/27 16/13 9/7 4/3 18/13 13/9 3/2 14/9 13/8 27/16 16/9 24/13 27/14 2/1 as sLsMsLssLssLsMsLs


17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 24-ET: (6, 2, 1); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 111-ET: (22, 7, 6); 130-ET: (26, 8, 7)
===== ((2/1, 3/2)[5], 12/11~13/12: 144/143, 729/728)[17] =====
5L 2M 10s = (91/81~81/77, 256/243~96/91~22/21, 27/26~28/27~33/32)


==== (2/1, 3/2, 9/7: 351/350, 676/675)[16] ====
~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 13/9 3/2 14/9 13/8 27/16 16/9 12/11 27/14 2/1 as sLsMsLssLssLsMsLs
2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)


~ 26/25 14/13 25/21 26/21 9/7 4/3 18/13 39/28 13/9 3/2 14/9 21/13 25/14 13/7 23/13 2/1 as mmLmmmmsmmmmLmmm
m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss


17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 24-ET: (5, 1, 1); 53-ET: (7, 3, 0); 58-ET: (9, 3, 1); 77-ET: (12, 4, 1); 111-ET: (16, 6, 1); 130-ET: (19, 7, 1)


==== (2/1, 3/2, 9/7: 351/350, 676/675)[31] ====
{{Navbox scale gallery}}
2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)
 
~169/168 26/25 117/112 14/13 13/12 28/25 9/8 378/325 7/6 9/7 325/252 4/3 75/56 18/13 39/28 56/39 13/9 112/75 3/2 14/9 12/7 325/189 16/9 25/14 24/13 13/7 224/117 25/13 336/169 2/1 as smsmsmsmsLsmsmsmsmsmsLsmsmsmsms
 
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS
 
53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
[[Category:Gallery]]
[[Category:Scales]]
[[Category:Step-nested scales]]
[[Category:Step-nested scales]]
[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:Rank 3]]
[[Category:Rank 3]]
{{Todo| cleanup }}

Latest revision as of 12:10, 28 June 2026

See SN scale and Rank-3 scale.

For more concise summary that's better for viewing on mobile devices, see Gallery of 3-SN scales mobile.

Scales are grouped by their germinations, the sequence of introduction of generators until 3 are reached, at which point the primitive 3-SN scale is developed (the first listed under each germination), from which all others of that germination evolve. The germination of Pythagorean, Meantone, Superpyth, Mavila, and Father MOS (2-SN) scales is (2/1, 3/2). Germinations are grouped by their subgroup, and within that, by the first comma tempered out in scales evolved from the germination.

Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.

Tempered scales are shown in JI as their simplest symmetric pre-image.

Scales are written in JI and as step patterns in their symmetric mode (scales of odd cardinality) or, for scales of even cardinality, mostly in the even-symmetric mode: the mode symmetric without 2/1, otherwise in the inverse of the even-symmetric mode (the mode symmetric without 1/1).

2.3.5; Marvel

(2/1, 3/2, 5/4)

(2/1, 3/2, 5/4)[4]

Step signature Steps in JI Step sizes in cents
2L 1M 1s (5/4, 6/5, 16/15) (386.3137c, 315.6413c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-2 16/15 4/3 8/5 2/1 sLML -.2092
-1 5/4 4/3 5/3 2/1 LsLM -.0174
1 6/5 3/2 8/5 2/1 MLsL .0174
2 5/4 3/2 15/8 2/1 LMLs .2092
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LLLs Dicot[4] 25/24
M = s LsLs Antitonic[4] 9/8
L - M = M - s LsLd Bug[4] MODMOS 27/25
s = 0 LsL Father[3] 16/15

(2/1, 3/2, 5/4)[7]

Step signature Steps in JI Step sizes in cents
2L 1M 4s (75/64, 9/8, 16/15) (274.5824c, 203.9100c, 111.7313c)
Mode number Mode in JI Step pattern Mode height
-3 16/15 256/225 4/3 64/45 8/5 128/75 2/1 ssLsMsL -.1161
-2 16/15 6/5 32/25 3/2 8/5 128/75 2/1 sMsLssL -.0845
-1 16/15 5/4 4/3 64/45 5/3 16/9 2/1 sLssLsM -.0316
0 16/15 5/4 4/3 3/2 8/5 15/8 2/1 sLsMsLs 0
1 9/8 6/5 45/32 3/2 8/5 15/8 2/1 MsLssLs .0316
2 75/64 5/4 4/3 25/16 5/3 15/8 2/1 LssLsMs .0845
3 75/64 5/4 45/32 3/2 225/128 15/8 2/1 LsMsLss .1161
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLsLsLs Dicot[7] 25/24
M = s sLsssLs Mavila[7] 135/128
L = s LLLsLLL Enipucrop[7] 1125/1024
L - M = M - s sAsLsAs Meantone[7] MODMOS 81/80
s = 0 LsL Father[3] 16/15
(2/1, 3/2, 5/4: 225/224)[7] (Marvel)
Step signature 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)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-3 ~ 16/15 8/7 4/3 10/7 8/5 12/7 2/1 ssLsMsL -.1079
-2 ~ 16/15 6/5 9/7 3/2 8/5 12/7 2/1 sMsLssL -.0793
-1 ~ 16/15 5/4 4/3 10/7 5/3 16/9 2/1 sLssLsM -.0286
0 ~ 16/15 5/4 4/3 3/2 8/5 15/8 2/1 sLsMsLs 0
1 ~ 9/8 6/5 7/5 3/2 8/5 15/8 2/1 MsLssLs .0286
2 ~ 7/6 5/4 4/3 14/9 5/3 15/8 2/1 LssLsMs .0793
3 ~ 7/6 5/4 7/5 3/2 7/4 15/8 2/1 LsMsLss .1079
Rank-2 temperings (mode 0)
Equivalence Step pattern 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
L - M = M - s sAsLsAs Meantone[7] MODMOS 81/80, 126/125
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)

(2/1, 3/2, 5/4)[10]

Step signature Steps in JI Step sizes in cents
2L 7m 1s (1125/1024, 16/15, 135/128) (162.8511c, 111.7313c, 92.1787c)
Mode number Mode in JI Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 16/15 256/225 6/5 32/25 512/375 3/2 8/5 128/75 2048/1125 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0564
-4 16/15 9/8 6/5 32/25 45/32 3/2 8/5 128/75 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0411
-3 135/128 9/8 6/5 675/512 45/32 3/2 8/5 225/128 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0258
-2 16/15 256/225 4096/3375 4/3 64/45 1024/675 8/5 128/75 2048/1125 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0230
-1 16/15 256/225 5/4 4/3 64/45 3/2 8/5 128/75 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0077
1 16/15 75/64 5/4 4/3 45/32 3/2 8/5 225/128 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0077
2 1125/1024 75/64 5/4 675/512 45/32 3/2 3375/2048 225/128 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0239
3 16/15 256/225 5/4 4/3 64/45 1024/675 5/3 16/9 256/135 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0258
4 16/15 75/64 5/4 4/3 64/45 25/16 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0411
5 1125/1024 75/64 5/4 4/3 375/256 25/16 5/3 225/128 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0564
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Srutal[10] 4M (pentachordal decatonic) 2048/2025
L = m LLLLsLLLLL Negri[10] 16875/16384
L = s LsLLsLLsLL Dicot[10] 25/24
L - m = m - s sLssdssLss Ampersand[10] MODMOS 34171875/33554432
s = 0 sLssssLss Mavila[9] 135/128
m = 0 LsL Father[3] 16/15
L = 0 LLLsLLLL Enipucrop[8] 1125/1024
(2/1, 3/2, 5/4: 225/224)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45, 16/15~15/14, 135/128~21/20) (151.8041c, 116.0124c, 84.9028c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0475
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0400
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0325
-2 ~ 16/15 8/7 60/49 4/3 10/7 32/21 8/5 12/7 64/35 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0112
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0037
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0037
2 ~ 35/32 7/6 5/4 21/16 7/5 3/2 49/30 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0112
3 ~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0325
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0400
5 ~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0475
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajara[10] 4M (pentachordal decatonic) 50/49, 64/63
L = m LLLLsLLLLL Negri[10] 49/48, 225/224
L = s LsLLsLLsLL Sharp[10] 25/24, 28/27
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 1029/1024
s = 0 sLssssLss Pelogic[9] 21/20, 135/128
Rank-1 temperings
ET 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (4, 3, 2) (5, 4, 3) (6, 5, 3) (7, 5, 4) (9, 7, 5)
(2/1, 3/2, 5/4: 225/224, 385/384)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) (151.4797c, 116.1327c, 84.7519c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negri[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 11/8 3/2 8/5 12/7 11/6 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0472
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0400
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0327
-2 ~ 16/15 8/7 11/9 4/3 10/7 32/21 8/5 12/7 11/6 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0109
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0036
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0036
2 ~ 12/11 7/6 5/4 21/16 7/5 3/2 18/11 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0109
3 ~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0327
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0400
5 ~ 12/11 7/6 5/4 4/3 16/11 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0472
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajarous[10] 4M (pentachordal decatonic) 50/49, 55/54, 64/63
L = m LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 243/242, 385/384
Rank-1 temperings
ET 12e 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 4, 3) (6, 5, 3) (7, 5, 4) (9, 7, 5)
(2/1, 3/2, 5/4: 225/224, 441/440)[10] (Prodigy)
Step signature Steps in JI Step sizes in cents (TE)
2L 7m 1s (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) (150.229c, 116.7669c, 82.9601c)
Mode number Mode as simplest JI pre-image Step pattern Pentachordal

Decatonic

Pent. Dec.

Mode name

Negroni[10] UDP Mode height
-5 ~ 16/15 8/7 6/5 9/7 48/35 3/2 8/5 12/7 64/35 2/1 mmsmmLmmmL sssssLsssL Dark minor LLsLLLLLLL 2|7 -.0466
-4 ~ 16/15 9/8 6/5 9/7 7/5 3/2 8/5 12/7 15/8 2/1 msmmLmmmLm ssssLsssLs Alternate minor LsLLLLLLLL 1|8 -.0404
-3 ~ 21/20 9/8 6/5 21/16 7/5 3/2 8/5 7/4 15/8 2/1 smmLmmmLmm sssLsssLss Bright minor sLLLLLLLLL 0|9 -.0343
-2 ~ 16/15 8/7 27/22 4/3 10/7 32/21 8/5 12/7 64/35 2/1 mmmLmmsmmL sssLsssssL Standard minor LLLLLLsLLL 6|3 -.0092
-1 ~ 16/15 8/7 5/4 4/3 10/7 3/2 8/5 12/7 15/8 2/1 mmLmmsmmLm ssLsssssLs Dark major LLLLLsLLLL 5|4 -.0031
1 ~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 2/1 mLmmsmmLmm sLsssssLss Alternate major LLLLsLLLLL 4|5 .0031
2 ~ 35/32 7/6 5/4 21/16 7/5 3/2 44/27 7/4 15/8 2/1 LmmsmmLmmm LsssssLsss Bright major LLLsLLLLLL 3|6 .0092
3 ~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1 mmLmmmLmms ssLsssLsss Standard major LLLLLLLLLs 9|0 .0343
4 ~ 16/15 7/6 5/4 4/3 10/7 14/9 5/3 16/9 15/8 2/1 mLmmmLmmsm sLsssLssss Dark Augmented LLLLLLLLsL 8|1 .0404
5 ~ 35/32 7/6 5/4 4/3 35/24 14/9 5/3 7/4 15/8 2/1 LmmmLmmsmm LsssLsssss Bright Augmented LLLLLLLsLL 7|2 .0466
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s sLsssssLss Pajaric[10] 4M (pentachordal decatonic) 45/44, 50/49, 56/55
L = m LLLLsLLLLL Negroni[10] 49/48, 55/54, 225/224
L - m = m - s sLssdssLss Miracle[10] MODMOS 225/224, 243/242, 385/384
Rank-1 temperings
ET 12 19e 29 31 41 53e 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 3, 2) (4, 3, 2) (5, 4, 3) (7, 5, 4) (9, 7, 5)

(2/1, 3/2, 5/4: 225/224)[19] (Marvel)

Step signature Steps in JI Step sizes in cents (TE)
10L 2M 7s (135/128~21/20, 25/24~28/27, 64/63~50/49) (84.9028c, 66.9013c, 31.1096c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 160/147 8/7 512/441 60/49 80/63 4/3 256/189 10/7 640/441 32/21 8/5 80/49 12/7 256/147 64/35 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0464
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 35/32 147/128 7/6 49/40 5/4 21/16 441/320 7/5 189/128 3/2 63/40 49/30 441/256 7/4 147/80 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0464
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS 81/80, 126/125
M = s LsLsLsLsLsLsLsLsLsL Negri[19] 49/48, 225/224
L - M = M - s LdLdLsLdLdLdLsLdLdL Magic[19] MODMOS 225/224, 245/243
s = 0 LLLsLLLLsLLL Pajara[12] 4M (hexachordal dodecatonic) 50/49, 64/63
m = 0 LsLsLLsLsLsLLsLsL Sharp[17] 25/24, 28/27
Rank-1 temperings
ET 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 2) (4, 3, 1) (5, 4, 2)
(2/1, 3/2, 5/4: 225/224, 385/384)[19] (Marvel)
Step signature Steps in JI Step sizes in cents (TE)
10L 2M 7s (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) (84.7519c, 66.7278c, 31.3808c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 88/81 8/7 220/189 11/9 80/63 4/3 110/81 10/7 352/243 32/21 8/5 44/27 12/7 110/63 11/6 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0460
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 12/11 63/55 7/6 27/22 5/4 21/16 243/176 7/5 81/55 3/2 63/40 18/11 189/110 7/4 81/44 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0460
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS 81/80, 126/125, 385/384
M = s LsLsLsLsLsLsLsLsLsL Negri[19] 45/44, 49/48, 56/55
L - M = M - s LdLdLsLdLdLdLsLdLdL Magic[19] MODMOS 100/99, 225/224, 245/243
s = 0 LLLsLLLLsLLL Pajarous[12] 4M (hexachordal dodecatonic) 50/49, 55/54, 64/63
Rank-1 temperings
ET 22 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 1) (3, 3, 2) (4, 3, 1) (5, 4, 2)
(2/1, 3/2, 5/4: 225/224, 441/440)[19] (Prodigy)
Step signature Steps in JI Step sizes in cents (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)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-9 ~ 50/49 16/15 12/11 8/7 64/55 27/22 14/11 4/3 15/11 10/7 16/11 32/21 8/5 18/11 12/7 96/55 64/35 40/21 2/1 sLsLsLMLsLsLLsLsLML -.0428
0 ~ 21/20 16/15 9/8 8/7 6/5 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 5/3 7/4 16/9 15/8 40/21 2/1 LsLsLMLsLsLsLMLsLsL 0
9 ~ 21/20 35/32 55/48 7/6 11/9 5/4 21/16 11/8 7/5 22/15 3/2 11/7 44/27 55/32 7/4 11/6 15/8 49/25 2/1 LMLsLsLLsLsLMLsLsLs .0428
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS 81/80, 99/98, 126/125
M = s LsLsLsLsLsLsLsLsLsL Negroni[19] 49/48, 55/54, 225/224
L - M = M - s LdLdLsLdLdLdLsLdLdL Witchcraft[19] MODMOS 225/224, 245/243, 441/440
s = 0 LLLsLLLLsLLL Pajaric[12] 4M (hexachordal dodecatonic) 45/44, 50/49, 56/55
Rank-1 temperings
ET 29 31 41 53e 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (4, 3, 1) (5, 4, 2)

(2/1, 3/2, 5/4: 225/224, 441/440)[31] (Prodigy)

Step signature Steps in JI Step sizes in cents (TE)
10L 19M 2s (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) (49.1533c, 33.8068c, 33.4621c)

Mode 0: ~ 50/49 22/21 16/15 12/11 9/8 8/7 7/6 6/5 27/22 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 44/27 5/3 12/7 7/4 16/9 11/6 15/8 21/11 49/25 2/1

as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm

Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
m = s sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS 225/224, 243/242, 385/384
L = m LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS 121/120, 225/224, 441/440
L = s sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS 81/80, 99/98, 126/125
s = 0 mLmmLmmLmmLmmLmLmmLmmLmmLmmLm Negroni[29] 49/48, 55/54, 225/224
m = 0 LLsLLLLLLsLL Pajaric[12] 4M (hexachordal dodecatonic) 45/44, 50/49, 56/55
Rank-1 temperings
ET 41 53e 72
Step sizes in ET (2, 1, 1) (3, 1, 2) (3, 2, 2)

((2/1, 5/4)[3], 16/15)

((2/1, 5/4)[3], 16/15)[6]

Step signature Steps in JI Step sizes in cents
1L 2M 4s (6/5, 75/64, 16/15) (315.6413c, 267.8165c, 111.7313c)
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
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLsLs Augmented[6] 128/125
M = s ssLsss Enipucrop[6] 1125/1024
L = s LsssLs Antitonic[6] 4M 9/8
s = 0 LsL Father[3] 16/15
((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 4s 6/5, 75/64~7/6, 16/15~15/14 (316.9276c, 267.8165c, 116.0124c)
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 -0.1168
-2 ~ 15/14 5/4 4/3 8/5 12/7 2/1 sMsLsM -0.0840
-1 ~ 15/14 9/7 48/35 8/5 12/7 2/1 sLsMsM -0.0513
1 ~ 7/6 5/4 35/28 14/9 15/8 2/1 MsMsLs 0.0513
2 ~ 7/6 5/4 3/2 8/5 15/8 2/1 MsLsMs 0.0840
3 ~ 6/5 9/7 3/2 8/5 15/8 2/1 LsMsMs 0.1168
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLsLs August[6] 128/125
Rank-1 temperings
ET 7 9 10 12 19 22 29 31 41 50 53 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)

((2/1, 5/4)[3], 16/15)[9]

Step signature Steps in JI Step sizes in cents
1L 2M 6s (9/8, 1125/1024, 16/15) (203.9100c, 162.8511c, 111.7313c)
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
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs Augmented[9] 128/125
M = s ssssLssss Negri[9] 16875/16384
L = s sLsssssLs Mavila[9] MODMOS 135/128
L - M = M - s sLssAssLs Orson[9] MODMOS 2109375/2097152
s = 0 LsL Father[3] 16/15
m = 0 sssLsss Enipucrop[7] 1125/1024
((2/1, 5/4)[3], 16/15: 225/224)[9] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 6s (9/8~28/25, 35/32~49/45, 16/15~15/14) (203.9100c, 162.8511c, 111.7313c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-4 ~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1 ssMssMssL -0.0633
-3 ~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 64/35 2/1 ssMssLssM -0.0326
-2 ~ 15/14 7/6 5/4 4/3 35/24 14/9 5/3 15/8 2/1 sMssMssLs -0.0307
-1 ~ 15/14 8/7 9/7 48/35 72/49 8/5 12/7 64/35 2/1 ssLssMssM -0.0019
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 0.0019
2 ~ 15/14 6/5 9/7 48/35 3/2 8/5 12/7 15/8 2/1 sLssMssMs 0.0307
3 ~ 35/32 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1 MssLssMss 0.0326
4 ~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1 LssMssMss 0.0633
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs August[9] 36/35, 128/125
M = s ssssLssss Negri[9] 49/48, 225/224
L = s sLsssssLs Pelogic[9] MODMOS 21/20, 135/128
L - M = M - s sLssAssLs Orwell[9] MODMOS 225/224, 1728/1715
Rank-1 temperings
ET 10 12 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 3, 3) (5, 4, 3) (7, 5, 4) (8, 6, 5) (9, 8, 5) (12, 9, 7)

((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9] (Marvel)

Step signature Steps in JI Step sizes in cents (TE tuning)
1L 2M 6s (9/8~28/25, 35/32~49/45~12/11, 16/15~15/14) (200.8846c, 151.4797c, 116.1327c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-4 ~ 15/14 8/7 5/4 4/3 10/7 14/9 5/3 16/9 2/1 ssMssMssL -0.0632
-3 ~ 15/14 8/7 5/4 4/3 10/7 8/5 12/7 11/6 2/1 ssMssLssM -0.0324
-2 ~ 15/14 7/6 5/4 4/3 16/11 14/9 5/3 15/8 2/1 sMssMssLs -0.0309
-1 ~ 15/14 8/7 9/7 11/8 22/15 8/5 12/7 11/6 2/1 ssLssMssM -0.0015
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 0.0015
2 ~ 15/14 6/5 9/7 11/8 3/2 8/5 12/7 15/8 2/1 sLssMssMs 0.0309
3 ~ 12/11 7/6 5/4 7/5 3/2 8/5 7/4 15/8 2/1 MssLssMss 0.0324
4 ~ 9/8 6/5 9/7 7/5 3/2 8/5 7/4 15/8 2/1 LssMssMss 0.0632
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M sLssLssLs August[9] 36/35, 45/44, 56/55
M = s ssssLssss Negri[9] 45/44, 49/48, 56/55
L - M = M - s sLssAssLs Orwell[9] MODMOS 99/88, 121/120, 176/175
Rank-1 temperings
ET 10 12e 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (4, 3, 2) (5, 4, 3) (7, 5, 4) (8, 6, 5) (9, 8, 5) (12, 9, 7)


((2/1, 5/4)[3], 16/15: 225/224)[12] (Marvel)

Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1M 2s (16/15~15/14, 135/128~21/20, ~49/48) (116.0124c, 84.9028c, 35.7917c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-6 ~ 49/48 35/32 7/6 5/4 245/192 49/36 35/24 14/9 49/30 7/4 15/8 2/1 sLLLsLLLMLLL -0.0733
-5 ~ 15/14 35/32 7/6 5/4 4/3 49/36 35/24 14/9 5/3 7/4 15/8 2/1 LsLLLsLLLMLL -0.0433
-4 ~ 49/48 35/32 7/6 5/4 12/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1 sLLLMLLLsLLL -0.0435
-3 ~ 15/14 8/7 7/6 5/4 4/3 10/7 35/24 14/9 5/3 16/9 15/8 2/1 LLsLLLsLLLML -0.0152
-2 ~ 15/14 35/32 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LsLLLMLLLsLL -0.0145
-1 ~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 49/30 7/4 15/8 2/1 MLLLsLLLsLLL -0.0138
1 ~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1 LLLsLLLsLLLM 0.0138
2 ~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 64/35 15/8 2/1 LLsLLLMLLLsL 0.0145
3 ~ 15/14 9/8 6/5 9/7 48/35 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LMLLLsLLLsLL 0.0152
4 ~ 15/14 8/7 60/49 5/4 4/3 10/7 32/21 8/5 12/7 64/35 96/49 2/1 LLLsLLLMLLLs 0.0435
5 ~ 15/14 8/7 6/5 9/7 48/35 72/49 3/2 8/5 12/7 64/35 15/8 2/1 LLMLLLsLLLsL 0.0443
6 ~ 15/14 8/7 60/49 9/7 48/35 72/49 384/245 8/5 12/7 64/35 96/49 2/1 LLLMLLLsLLLs 0.0733
Rank-2 temperings (mode -2)
Equivalence Step pattern Scale Comma list
L = M LsLLLLLLLsLL Pajara[12] MODMOS 50/49, 64/63
M = s LsLLLsLLLsLLs August[12] 36/35, 128/125
L = s sssssLssssss Passion[12] 64/63, 3125/3087
L - M = M - s LdLLLsLLLdLL Meantone[12] MODMOS 81/80, 126/125
s = 0 LLLLsLLLLL Negri[10] 49/48, 225/224
M = 0 LsLLLLLLsLL Pelogic[11] MODMOS 21/20, 135/128
Rank-1 temperings
ET 19 22 29 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 0) (3, 2, 1) (4, 3, 1) (5, 3, 1) (5, 4, 2) (7, 5, 2)
((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1M 2s (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55) (116.1327c, 84.7519c, 35.347c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-6 ~ 45/44 12/11 7/6 5/4 14/11 15/11 16/11 14/9 18/11 7/4 15/8 2/1 sLLLsLLLMLLL -0.0738
-5 ~ 15/14 12/11 7/6 5/4 4/3 15/11 16/11 14/9 5/3 7/4 15/8 2/1 LsLLLsLLLMLL -0.0445
-4 ~ 45/44 12/11 7/6 5/4 12/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1 sLLLMLLLsLLL -0.0438
-3 ~ 15/14 8/7 7/6 5/4 4/3 10/7 16/11 14/9 5/3 16/9 15/8 2/1 LLsLLLsLLLML -0.0153
-2 ~ 15/14 12/11 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LsLLLMLLLsLL -0.0146
-1 ~ 21/20 9/8 6/5 9/7 21/16 7/5 3/2 8/5 18/11 7/4 15/8 2/1 MLLLsLLLsLLL -0.0139
1 ~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 14/9 5/3 16/9 40/21 2/1 LLLsLLLsLLLM 0.0139
2 ~ 15/14 8/7 7/6 5/4 4/3 10/7 3/2 8/5 12/7 11/6 15/8 2/1 LLsLLLMLLLsL 0.0146
3 ~ 15/14 9/8 6/5 9/7 11/8 7/5 3/2 8/5 12/7 7/4 15/8 2/1 LMLLLsLLLsLL 0.0153
4 ~ 15/14 8/7 11/9 5/4 4/3 10/7 32/21 8/5 12/7 11/6 55/28 2/1 LLLsLLLMLLLs 0.0438
5 ~ 15/14 8/7 6/5 9/7 11/8 22/15 3/2 8/5 12/7 11/6 15/8 2/1 LLMLLLsLLLsL 0.0445
6 ~ 15/14 8/7 11/9 9/7 11/8 22/15 11/7 8/5 12/7 11/6 55/28 2/1 LLLMLLLsLLLs 0.0738
Rank-2 temperings (mode -2)
Equivalence Step pattern Scale Comma list
L = M LsLLLLLLLsLL Pajarous[12] MODMOS 50/49, 55/54, 64/63
M = s LsLLLsLLLsLL August[12] 36/35, 45/44, 56/55
L = s sssssLssssss Passion[12] 64/63, 100/99, 1375/1372
L - M = M - s LdLLLsLLLdLL Meanpop[12] MODMOS 81/80, 126/125, 385/384
s = 0 LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
Rank-1 temperings
ET 19 22 31 41 50 53 72
Step sizes in ET (2, 1, 0) (2, 2, 1) (3, 2, 1) (4, 3, 1) (5, 3, 1) (5, 4, 2) (7, 5, 2)
(2/1, 5/4)[3], 16/15: 225/224, 385/384)[22] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
9L 1m 12s (~22/21, 36/35~33/32, 49/48~45/44~56/55) (80.7857c, 49.4049c, 35.347c)
Mode number Mode as simplest JI pre-image Step pattern Mode height
-7 ~ 45/44 16/15 12/11 49/44 7/6 105/88 5/4 14/11 4/3 15/11 7/5 63/44 3/2 49/32 8/5 18/11 12/7 7/4 98/55 15/8 21/11 2/1 sLssLsLsLsmsLsLsLssLsL -.0229
7 ~ 22/21 16/15 55/49 8/7 7/6 11/9 5/4 64/49 4/3 88/63 10/7 22/11 3/2 11/7 8/5 176/105 12/7 88/49 11/6 15/8 55/28 2/1 LsLssLsLsLsmsLsLsLssLs .0229
Rank-2 temperings (mode -7)
Equivalence Step pattern Scale Comma list
m = s sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS 99/98, 121/120, 176/175
L = m sLssLsLsLsLsLsLsLssLsL Pajarous[22] MODMOS 50/49, 55/54, 64/63
L = s LLLLLLLLLLsLLLLLLLLLLL Escapade[22] 99/98, 176/175, 2560/2541
L - m = m - s sAssAsAsAsLsAsAsAssAsA Magic[22] MODMOS 100/99, 225/224, 245/243
s = 0 LLLLsLLLLL Negri[10] 45/44, 49/48, 56/55
Rank-1 temperings
ET 31 41 50 53 72
Step sizes in ET (2, 1, 1) (3, 2, 1) (4, 2, 1) (3, 2, 2) (5, 3, 2)

((2/1, 3/2)[5], 16/15)

((2/1, 3/2)[5], 16/15)[10]

Step signature Steps in JI Step sizes in cents
2L 5m 3s (10/9, 16/15, 135/128) (182.4037c, 111.7313c, 92.1787c)
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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) -.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 1|0 (5) .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 0|1 (5) .0258
3 10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .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 0|1 (5) .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 1|0 (5) .0745
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Diaschismic[10] 4M (pentachordal decatonic) 2048/2025
L = m sLLLsLLLsL Dicot[10] modmos 25/24
L = s LsLsLsLsLs Blackwood[10] 256/243
L - m = m - s sLALsLALsL Negri[10] modmos 16875/16384
s = 0 sLssLss Mavila[7] 135/128
m = 0 sLsLs Father[5] 16/15
((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)
Step signature Steps in JI Step sizes in cents (TE tuning)
2L 5m 3s (10/9, 16/15~15/14, 135/128~21/20) (182.9137c, 116.0124c, 84.9028c)
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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) -.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 1|0 (5) .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 0|1 (5) .0326
3 ~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .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 0|1 (5) .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 1|0 (5) .0763
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Pajara[10] 4M (pentachordal decatonic) 50/49, 64/63
L = m sLLLsLLLsL Sharp[10] MODMOS 25/24, 28/27
L - m = m - s sLALsLALsL Negri[10] MODMOS 49/48, 225/224
s = 0 sLssLss Pelogic[7] 21/20, 135/128
((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10] (Prodigy)
Step signature Steps in JI Step sizes in cents (TE tuning)
2L 5m 3s (10/9, 16/15~15/14, 135/128~21/20~22/21) (184.0358c, 116.7669c, 82.9601c)
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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) -.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 1|0 (5) -.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 0|1 (5) .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 1|0 (5) .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 0|1 (5) .0343
3 ~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 LmsmsmLmsm LsssssLsss Bright major LsLsLsLsLs 1|0 (5) .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 0|1 (5) .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 1|0 (5) .0779
Rank-2 temperings (mode 1)
Equivalence Step pattern Scale Comma list
m = s ssLsssLsss Pajaric[10] 4M (pentachordal decatonic) 45/44, 50/49, 56/55
L - m = m - s sLALsLALsL Negroni[10] MODMOS 49/48, 55/54, 225/224

((2/1, 3/2)[5], 16/15)[17]

10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)

135/128 16/15 9/8 32/27 5/4 81/64 4/3 45/32 64/45 3/2 128/81 8/5 27/16 16/9 15/8 256/135 2/1 as LsLMLsLLsLLsLMLsL

L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]

((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)

2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE

~ 21/20 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 40/21 2/1 as MsMLMsMMsMMsMLMsM

L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;

s = 0 -> LLsLLLLLLsLL Pajara[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[17] (Prodigy)

2L 10M 5s = (256/243~35/33, 135/128~21/20~22/21, 2048/2025~50/49~64/63~45/44~56/55) = (101.0757c, 82.9601c, 33.8068c) TE

~ 22/21 16/15 9/8 32/27 5/4 81/64 4/3 7/5 10/7 3/2 128/81 8/5 27/16 16/9 15/8 21/11 2/1 as LsLmLsLLsLLsLmLsL

L = M -> LsLLLsLLsLLsLLLsL Andromeda[17]; s = 0 -> s = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] (Prodigy)

2L 10m 17s = (25/24~28/27, ~33/32, 2048/2025~50/49~64/63~45/44~56/55) = (67.2689c, 49.1533c, 33.8068c) TE

~ 50/49 22/21 16/15 11/10 9/8 8/7 33/28 6/5 5/4 14/11 21/16 4/3 15/11 7/5 10/7 22/15 3/2 32/21 11/7 8/5 5/3 56/33 7/4 16/9 20/11 15/8 21/11 49/25 2/1 as smsmssmsLsmssmsmssmsLsmssmsms

m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];

L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;

s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] (Prodigy)

29L 2M 10s = (2048/2025~50/49~64/63~45/44~56/55, 49/48~55/54, ~121/120) = (33.8068c, 33.4621c, 15.3465c) TE

~ 50/49 33/32 22/21 16/15 12/11 11/10 9/8 8/7 7/6 32/27 40/33 11/9 5/4 14/11 128/99 21/16 4/3 15/11 11/8 7/5 10/7 16/11 22/15 3/2 32/16 99/64 11/7 8/5 18/11 33/20 27/16 12/7 7/4 16/9 20/11 11/6 15/8 21/11 64/33 49/25 2/1 as LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL

L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];

L - M = M - s -> Witchcraft[41] MODMOS

s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS

((2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] (Prodigy)

29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE

as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs

L = M -> LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS;

M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;

L - M = M - s -> Compton MODMOS

s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;

m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS

2.3.5; Starling, No-7 Ptolemismic, Supermagic, and Ragismic

(2/1, 3/2, 6/5)

(2/1, 3/2, 6/5)[4]

Step signature Steps in JI Step sizes in cents
1L 2M 1s (5/4, 6/5, 10/9) (386.3137c, 315.6413c, 182.4037c)
Mode number Mode in JI Step pattern Mode height
-2 10/9 4/3 5/3 2/1 sMLM -0.1307
-1 6/5 4/3 8/5 2/1 MsML -0.0959
1 5/4 3/2 5/3 2/1 LMsM 0.0959
2 6/5 3/2 9/5 2/1 MLMs 0.1307
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LLLs Dicot[4] 25/24
M = s sLss Bug[4] 27/25
L = s LsLs Antitonic[4] 9/8

(2/1, 3/2, 6/5)[7]

Step signature Steps in JI Step sizes in cents
1L 4M 2s (9/8, 10/9, 27/25) (203.9100c, 182.4037c, 133.2376c)
Mode number Mode in JI Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 27/25 6/5 4/3 36/25 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0529
-2 10/9 6/5 4/3 40/27 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0316
-1 27/25 6/5 27/20 3/2 81/50 9/5 2/1 sMLMsMM sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0213
0 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 10/9 100/81 4/3 40/27 5/3 50/27 2/1 MMsMLMs LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0213
2 9/8 5/4 27/20 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0316
3 10/9 5/4 25/18 3/2 5/3 50/27 2/1 MLMsMMs LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0529
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meantone[7] 81/80
M = s sssLsss Porcupine[7] 250/243
L = s LsLsLsL Dicot[7] 25/24
L - M = M - s LsLALsL Tetracot[7] MODMOS 20000/19683
s = 0 ssLss Bug[5] 27/25
(2/1, 3/2, 6/5: 126/125)[7] (Starling)
Step signature Steps in JI Step sizes in cents (TE)
1L 4M 2s (~9/8, ~10/9, 27/25~15/14) (202.4685c, 187.562c, 123.5395c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0616
-2 ~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1 sMLMsMM sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0314
-1 ~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0302
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 ~ 9/8 5/4 27/20 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0302
2 ~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1 MMsMLMs LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0314
3 ~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1 MLMsMMs LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0616
Rank-2 temperings (mode 0)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meantone[7] 81/80, 126/125
M = s sssLsss Opossum[7] 28/27, 126/125
L = s LsLsLsL Flat[7] 21/20, 25/24
Rank-1 temperings
ET 8d 12 15 16 19 27 31 46 50 58 77
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (2, 3, 1) (3, 3, 2) (5, 4, 3) (5, 5, 3) (8, 7, 5) (8, 8, 5) (10, 9, 6) (13, 12, 8)
(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
1L 4m 2s (9/8~25/22, 10/9~11/10, 27/25~12/11) (209.7786c, 174.0549c, 146.6352c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 smmsmLm sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished -0.0427
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 msmmsmL LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh -0.0374
-1 ~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1 smLmsmm sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor -0.0053
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 msmLmsm LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor 0
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 mmsmLms LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished 0.0053
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 Lmsmmsm LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major 0.0374
3 ~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1 mLmsmms LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major 0.0427
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
m = s sssLsss Porkypine[7] 55/54, 100/99
L = m LsLLLsL Meanenneadecal[7] or Flattone[7] 45/44, 81/80
L = s LsLsLsL Flat[7] 25/24, 33/32
L - m = m - s LsLALsL Tetracot[7] MODMOS 100/99, 243/242
Rank-1 temperings
ET 8 12 15 19 22 26 27e 29 34 37 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) (5, 4, 4) (6, 5, 4) (7, 5, 5) (7, 6, 5)
(2/1, 3/2, 6/5: 56/55, 100/99)[7] (Thrasher)
Step signature Steps in JI Step sizes in cents (TE)
1L 4M 2s (9/8~25/22, 10/9~11/10, 27/25~15/14~12/11) (215.4452c, 179.0856c, 132.5782c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Porcupine[7] UDP Porcupine mode Diatonic mode Mode height
-3 ~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1 sMMsMLM sLLsLLL 0|6 sssssLs 1|5 Dark diminished Lochrian -0.0591
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 MsMMsML LsLLsLL 2|4 ssssssL 0|6 Magical seventh Aeolian -0.0433
-1 ~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1 sMLMsMM sLLLsLL 1|5 ssLssss 4|2 Bright minor Phrygian -0.0158
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 MsMLMsM LsLLLsL 3|3 sssLsss 3|3 Dark minor Dorian 0
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 MMsMLMs LLsLLLs 5|1 ssssLss 2|4 Bright diminished Ionian 0.0158
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 LMsMMsM LLsLLsL 4|2 Lssssss 6|0 Bright major Mixolydian 0.0433
3 ~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1 MLMsMMs LLLsLLs 6|0 sLsssss 5|1 Dark major Lydian 0.0591
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
L = M LsLLLsL Meanenneadecal[7] 45/44, 56/55, 81/80
M = s sssLsss Opossum[7] 28/27, 55/54, 77/75
L = s LsLsLsL Flat[7] 21/20, 25/24, 33/32
Rank-1 temperings
ET 8d 12 15 19 27e 34
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 2) (3, 3, 2) (5, 4, 3) (6, 5, 4)
(2/1, 3/2, 6/5: 100/99, 144/143)[7] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
1L 4m 2s (9/8~25/22, 10/9~11/10, 27/25~12/11~13/12) (209.5416c, 175.8918c, 142.7754c)
Mode number Mode as simplest JI pre-image Step pattern Meantone[7] UDP Diatonic mode Porcupine[7] UDP Porcupine mode Mode height
-3 ~ 12/11 6/5 4/3 13/9 8/5 9/5 2/1 smmsmLm sLLsLLL 0|6 Lochrian sssssLs 1|5 Dark diminished
-2 ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 msmmsmL LsLLsLL 2|4 Aeolian ssssssL 0|6 Magical seventh
-1 ~ 12/11 6/5 15/11 3/2 13/8 9/5 2/1 smLmsmm sLLLsLL 1|5 Phrygian ssLssss 4|2 Bright minor
0 ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 msmLmsm LsLLLsL 3|3 Dorian sssLsss 3|3 Dark minor
1 ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 mmsmLms LLsLLLs 5|1 Ionian ssssLss 2|4 Bright diminished
2 ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 Lmsmmsm LLsLLsL 4|2 Mixolydian Lssssss 6|0 Bright major
3 ~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1 mLmsmms LLLsLLs 6|0 Lydian sLsssss 5|1 Dark major
Rank-2 temperings (mode 2)
Equivalence Step pattern Scale Comma list
m = s sssLsss Porcupine[7] 40/39, 55/54, 66/65
L = m LsLLLsL Flattone[7] 45/44, 65/64, 81/80
L - m = m - s LsLALsL Tetracot[7] MODMOS 100/99, 144/143, 243/242
Rank-1 temperings
ET 8 12 15 19 22f 26 27e 34 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)

(2/1, 3/2, 6/5)[12]

Step signature Steps in JI Step sizes in cents
7L 1m 4s (27/25, 25/24, 250/243) (133.2376c, 70.6724c, 49.1661c)
Mode number Mode in JI Step pattern Meantone[12] UDP Mode height
-6 250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0622
-5 250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0587
-4 250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1 sLLsLsLLsLmL sLLsLsLLsLsL 4|7 -0.0338
-3 250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -0.0302
-2 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 sLsLLsLsLLsL 2|9 -0.0267
-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 LsLsLLsLsLsL 6|5 -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 5|6 0.0018
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 LsLLsLsLLsLm LsLLsLsLLsLs 9|2 0.0267
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 LsLLsLmLsLLs LsLLsLsLsLLs 8|3 0.0302
4 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 LsLsLLsLsLLs 7|4 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 11|0 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 10|1 0.0622
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meantone[12] 81/80
L = m sLLsLLLsLLsL Diminished[12] MODMOS 648/625
L = s LLLLLsLLLLLL Ripple[12] 6561/6250
L - m = m - s dLLdLsLdLLdL Augmented[12] modmos 128/125
s = 0 LLLsLLLL Porcupine[8] 250/243
(2/1, 3/2, 6/5: 126/125)[12] (Starling)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14, 25/24~21/20, 250/243~28/27) (123.5395c, 78.929c, 64.0225c)
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 1|10 -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 0|11 -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 4|7 -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 3|8 -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 2|9 -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 6|5 -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 5|6 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 9|2 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 8|3 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 7|4 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 11|0 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 10|1 0.0440
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meantone[12] 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 LLLsLLLL Opossum[8] 28/27, 126/125
Rank-1 temperings
ET 15 16 19 27 31 46 50 58 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)
(2/1, 3/2, 6/5: 126/125, 196/195)[12]
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)
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 1|10 -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 0|11 -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 4|7 -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 3|8 -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 2|9 -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 6|5 -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 5|6 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 9|2 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 8|3 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 7|4 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 11|0 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 10|1 0.0465
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanpop[12] 81/80, 105/104, 126/125
Rank-1 temperings
ET 15f 19 27 31 46 50 58 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)
(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11, 25/24~33/32, 250/243~55/54~121/120) (146.6352c, 63.1434c, 27.4197c)
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 55/36 5/3 121/72 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10 -0.0899
-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 sLmLsLLsLsLL sLsLsLLsLsLL 0|11 -0.0819
-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 4|7 -0.0510
-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 sLLsLmLsLLsL sLLsLsLsLLsL 3|8 -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 2|9 -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 6|5 -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 5|6 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 9|2 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 8|3 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 7|4 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 11|0 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 10|1 0.0899
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanenneadecal[12] or Flattone[12] 45/44, 81/80
L = m sLLsLLLsLLsL Diminished[12] modmos 100/99, 128/121
L - m = m - s dLLdLsLdLLdL Augene[12] modmos 100/99, 128/125
s = 0 LLLsLLLL Porcupine[8] 55/54, 100/99
Rank-1 temperings
ET 15 19 22 26 27e 29 34 37 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)
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) (142.77537c, 66.76626c, 33.11646c)
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 1|10
-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 0|11
-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 4|7
-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 3|8
-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 2|9
-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 6|5
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 5|6
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 9|2
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 8|3
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 7|4
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 11|0
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 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 65/64, 81/80
s = 0 LLLsLLLL Porcupine[8] 40/39, 55/54, 66/65
Rank-1 temperings
ET 15 19 22f 26 27e 34 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)
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)
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 1|10
-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 0|11
-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 4|7
-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 3|8
-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 2|9
-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 6|5
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 5|6
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 9|2
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 8|3
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 7|4
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 11|0
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 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 81/80, 385/384
s = 0 LLLsLLLL Porcupine[8] 55/54, 64/63, 100/99
Rank-1 temperings
ET 15 19 22 26 34 41 104
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (4, 2, 1) (5, 2, 1) (13, 5, 2)
(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12] (Keemic)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~12/11~13/12~35/32, 25/24~27/26~33/32, 250/243~40/39~55/54~64/63~121/120) (145.47082c, 58.39270c, 30.85183c)
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 1|10
-5 ~ 40/39 10/9 8/7 5/4 33/26 11/8 3/2 20/13 5/3 22/13 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-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 4|7
-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 3|8
-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 2|9
-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 6|5
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 5|6
2 ~ 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 LsLLsLsLLsLs 9|2
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 8|3
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 7|4
5 ~ 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 LLsLsLLsLsLs 11|0
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 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Flattone[12] 45/44, 65/64, 78/77, 81/80
s = 0 LLLsLLLL Porcupine[8] 40/39, 55/54, 64/63, 66/65
Rank-1 temperings
ET 15 19 22f 26 34 41
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 1, 0) (3, 1, 1) (4, 2, 1) (5, 2, 1)
(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)
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)
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 1|10 -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 0|11 -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 4|7 -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 3|8 -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 2|9 -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 6|5 -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 5|6 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 9|2 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 8|3 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 7|4 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 11|0 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 10|1 0.0671
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Meanenneadecal[12] 45/44, 56/55, 81/80
L = m sLLsLLLsLLsL Diminished[12] MODMOS 36/35, 50/49, 56/55
s = 0 LLLsLLLL Opossum[8] 28/27, 55/54, 77/75
Rank-1 temperings
ET 15 19 27e 34
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 2, 1) (4, 2, 1)
(2/1, 3/2, 6/5: 56/55, 91/90, 100/99)[12] (Thrasher)
Step signature Steps in JI Step sizes in cents (TE)
7L 1m 4s (27/25~15/14~12/11~13/12, 25/24~21/20~33/32~27/26, 250/243~28/27~55/54~40/39)
Mode number Mode as simplest JI pre-image Step pattern Meantone[12] UDP Mode height
-6 ~ 28/27 10/9 44/39 11/9 4/3 110/81 22/15 14/9 5/3 22/13 11/6 2/1 sLsLLsLmLsLL sLsLLsLsLsLL 1|10
-5 ~ 28/27 10/9 7/6 5/4 33/26 11/8 3/2 14/9 5/3 121/72 11/6 2/1 sLmLsLLsLsLL sLsLsLLsLsLL 0|11
-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 4|7
-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 3|8
-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 2|9
-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 6|5
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 5|6
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 9|2
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 8|3
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 7|4
5 ~ 12/11 13/11 6/5 9/7 4/3 16/11 192/121 8/5 12/7 9/5 27/14 2/1 LLsLsLLsLmLs LLsLsLLsLsLs 11|0
6 ~ 12/11 13/11 6/5 9/7 15/11 81/55 3/2 81/50 39/22 9/5 27/14 2/1 LLsLmLsLLsLs LLsLsLsLLsLs 10|1
Rank-2 temperings (mode -3)
Equivalence Step pattern Scale Comma list
m = s sLLsLsLsLLsL Vincenzo[12] 45/44, 56/55, 65/64, 81/80
s = 0 LLLsLLLL Opossum[8] 28/27, 40/39, 55/54, 66/65
Rank-1 temperings
ET 15 19 27e 34
Step sizes in ET (2, 1, 0) (2, 1, 1) (3, 2, 1) (4, 2, 1)
(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

~ 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]

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] (Keemic)

7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE

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

(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

~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm

m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;

L - m = m - s -> Unidec[20] MODMOS

s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]

19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)

(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)

7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE

~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm

m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;

s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL

19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)

(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)

7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE

~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms

m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs

46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)

((2/1, 6/5)[4], 10/9)

((2/1, 6/5)[4], 10/9)[8]

Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9, 27/25, 25/24 (182.4037c, 133.2376c, 70.6724c)
Mode number Mode in JI (height order) Step pattern Porcupine[8]

step pattern and UDP

Diminished[8]

step pattern and UDP

4 10/9 6/5 4/3 36/25 8/5 216/125 48/25 2/1 LMLMLMLs LLLLLLLs 7|0 LsLsLsLs 1|0 (4)
3 10/9 6/5 4/3 36/25 8/5 5/3 50/27 2/1 LMLMLsLM LLLLLsLL 5|2 LsLsLsLs 1|0 (4)
2 27/25 6/5 162/125 36/25 972/625 216/125 9/5 2/1 MLMLMLsL LLLLLLsL 6|1 sLsLsLsL 0|1 (4)
1 10/9 6/5 4/3 25/18 125/81 5/3 50/27 2/1 LMLsLMLM LLLsLLLL 3|4 LsLsLsLs 1|0 (4)
-1 27/25 6/5 162/125 36/25 3/2 5/3 9/5 2/1 MLMLsLML LLLLsLLL 4|3 sLsLsLsL 0|1 (4)
-2 10/9 125/108 625/486 25/18 125/81 5/3 50/27 2/1 LsLMLMLM LsLLLLLL 1|6 LsLsLsLs 1|0 (4)
-3 27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1 MLsLMLML LLsLLLLL 2|5 sLsLsLsL 0|1 (4)
-4 25/24 125/108 5/4 25/18 3/2 5/3 9/5 2/1 sLMLMLML sLLLLLLL 0|7 sLsLsLsL 0|1 (4)


Rank-2 temperings (mode 4)
Equivalence Step pattern Scale Comma list
M = 0 LLLLs Bug[5] 27/25
s = 0 LsLsLsL Dicot[7] 25/24
L = M LLLLLLLs Porcupine[8] 250/243
M = s LsLsLsLs Diminished[8] 648/625
L - M = M - s LsLsLsLd Sensipent[8] MODMOS 78732/78125
Rank-1 temperings
ET 12 15 19 22 26 27 29 31 34 41 46 53 65
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (4, 3, 2) (4, 4, 1) (5, 3, 2) (5, 4, 2) (6, 5, 2) (7, 5, 3) (8, 6, 3) (10, 7, 4)
((2/1, 6/5)[4], 10/9: 875/864)[8] Supermagic
Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9, 27/25~35/32, 25/24~36/35 176.8769, 144.8100, 59.11533
Mode number Mode as simplest JI pre-image Step pattern Porcupine[8]

step pattern and UDP

Diminished[8]

step pattern and UDP

4 ~ 10/9 6/5 4/3 35/24 8/5 7/4 35/18 2/1 LMLMLMLs LLLLLLLs 7|0 LsLsLsLs 1|0 (4)
3 ~ 10/9 6/5 4/3 35/24 8/5 5/3 50/27 2/1 LMLMLsLM LLLLLsLL 5|2 LsLsLsLs 1|0 (4)
2 ~ 27/25 6/5 21/16 35/24 63/40 7/4 9/5 2/1 MLMLMLsL LLLLLLsL 6|1 sLsLsLsL 0|1 (4)
1 ~ 10/9 6/5 4/3 25/18 32/21 5/3 50/27 2/1 LMLsLMLM LLLsLLLL 3|4 LsLsLsLs 1|0 (4)
-1 ~ 27/25 6/5 21/16 35/24 3/2 5/3 9/5 2/1 MLMLsLML LLLLsLLL 4|3 sLsLsLsL 0|1 (4)
-2 ~ 10/9 8/7 80/63 25/18 32/21 5/3 50/27 2/1 LsLMLMLM LsLLLLLL 1|6 LsLsLsLs 1|0 (4)
-3 ~ 27/25 6/5 5/4 25/18 3/2 5/3 9/5 2/1 MLsLMLML LLsLLLLL 2|5 sLsLsLsL 0|1 (4)
-4 ~ 25/24 8/7 5/4 25/18 3/2 5/3 9/5 2/1 sLMLMLML sLLLLLLL 0|7 sLsLsLsL 0|1 (4)
Rank-2 temperings (mode 4)
Equivalence Step pattern Scale Comma list
s = 0 LsLsLsL Dicot[7] 25/24, 15/14
L = M LLLLLLLs Porcupine[8] 250/243, 64/63
Rank-1 temperings
ET 15 19 22 26 34 37 41 60
Step sizes in ET (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (5, 4, 2) (5, 5, 2) (6, 5, 2) (9, 7, 3)
((2/1, 6/5)[4], 10/9: 100/99, 385/384)[8] Supermagic
Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9~11/10, 27/25~35/32~12/11, 25/24~36/35~33/32 173.1413, 149.5159, 58.8799
Mode number Mode as simplest JI pre-image Step pattern Porcupine[8]

step pattern and UDP

Diminished[8]

step pattern and UDP

4 ~ 10/9 6/5 4/3 16/11 8/5 7/4 35/18 2/1 LMLMLMLs LLLLLLLs 7|0 LsLsLsLs 1|0 (4)
3 ~ 10/9 6/5 4/3 16/11 8/5 5/3 11/6 2/1 LMLMLsLM LLLLLsLL 5|2 LsLsLsLs 1|0 (4)
2 ~ 12/11 6/5 21/16 16/11 63/40 7/4 9/5 2/1 MLMLMLsL LLLLLLsL 6|1 sLsLsLsL 0|1 (4)
1 ~ 10/9 6/5 4/3 11/8 32/21 5/3 11/6 2/1 LMLsLMLM LLLsLLLL 3|4 LsLsLsLs 1|0 (4)
-1 ~ 12/11 6/5 21/16 16/11 3/2 5/3 9/5 2/1 MLMLsLML LLLLsLLL 4|3 sLsLsLsL 0|1 (4)
-2 ~ 10/9 8/7 44/35 11/8 32/21 5/3 11/6 2/1 LsLMLMLM LsLLLLLL 1|6 LsLsLsLs 1|0 (4)
-3 ~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1 MLsLMLML LLsLLLLL 2|5 sLsLsLsL 0|1 (4)
-4 ~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1 sLMLMLML sLLLLLLL 0|7 sLsLsLsL 0|1 (4)
Rank-2 temperings (mode 4)
Equivalence Step pattern Scale Comma list
L = M LLLLLLLs Porcupine[8] 55/54, 64/63, 100/99
Rank-1 temperings
ET 15 19 22 26 34 37 41 63
Step sizes in ET (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (5, 4, 2) (5, 5, 2) (6, 5, 2) (9, 8, 3)
((2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[8] Supermagic
Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9~11/10, 27/25~35/32~12/11~13/12, 25/24~36/35~33/32~27/26 176.3227, 145.4708, 58.3927
Mode number Mode as simplest JI pre-image Step pattern Porcupine[8]

step pattern and UDP

Diminished[8]

step pattern and UDP

4 ~ 10/9 6/5 4/3 13/9 8/5 7/4 35/18 2/1 LMLMLMLs LLLLLLLs 7|0 LsLsLsLs 1|0 (4)
3 ~ 10/9 6/5 4/3 13/9 8/5 5/3 11/6 2/1 LMLMLsLM LLLLLsLL 5|2 LsLsLsLs 1|0 (4)
2 ~ 12/11 6/5 13/10 13/9 39/25 7/4 9/5 2/1 MLMLMLsL LLLLLLsL 6|1 sLsLsLsL 0|1 (4)
1 ~ 10/9 6/5 4/3 11/8 20/13 5/3 11/6 2/1 LMLsLMLM LLLsLLLL 3|4 LsLsLsLs 1|0 (4)
-1 ~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1 MLMLsLML LLLLsLLL 4|3 sLsLsLsL 0|1 (4)
-2 ~ 10/9 8/7 44/35 11/8 20/13 5/3 11/6 2/1 LsLMLMLM LsLLLLLL 1|6 LsLsLsLs 1|0 (4)
-3 ~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1 MLsLMLML LLsLLLLL 2|5 sLsLsLsL 0|1 (4)
-4 ~ 25/24 8/7 5/4 11/8 3/2 5/3 9/5 2/1 sLMLMLML sLLLLLLL 0|7 sLsLsLsL 0|1 (4)
Rank-2 temperings (mode 4)
Equivalence Step pattern Scale Comma list
L = M LLLLLLLs Porcupine[8] 40/39, 55/54, 64/63, 66/65
Rank-1 temperings
ET 15 19 22f 26 34 41 60
Step sizes in ET (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (5, 4, 2) (6, 5, 2) (9, 7, 3)
((2/1, 6/5)[4], 10/9: 325/324)[8] (2.3.5.13 Marveltwin)
Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9, 27/25~13/12, 25/24~27/26 180.4645c, 136.7099c, 68.1467c
Mode number Mode as simplest JI pre-image Step pattern
4 ~ 10/9 6/5 4/3 13/9 8/5 26/15 48/25 2/1 LMLMLMLs
3 ~ 10/9 6/5 4/3 13/9 8/5 5/3 24/13 2/1 LMLMLsLM
2 ~ 13/12 6/5 13/10 13/9 39/25 26/15 9/5 2/1 MLMLMLsL
1 ~ 10/9 6/5 4/3 13/9 20/13 5/3 24/13 2/1 LMLsLMLM
-1 ~ 13/12 6/5 13/10 13/9 3/2 5/3 9/5 2/1 MLMLsLML
-2 ~ 10/9 15/13 50/39 18/13 20/13 5/3 24/13 2/1 LsLMLMLM
-3 ~ 13/12 6/5 5/4 18/13 3/2 5/3 9/5 2/1 MLsLMLML
-4 ~ 25/24 15/13 5/4 18/13 3/2 5/3 9/5 2/1 sLMLMLML
Rank-1 temperings
ET 12 15 19 22f 26 27e 29 31 34 41 46 53 72 87
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (4, 3, 2) (4, 4, 1) (5, 4, 1) (5, 4, 2) (6, 5, 2) (7, 5, 3) (8, 6, 3) (11, 8, 4) (13, 9, 5)
((2/1, 6/5)[4], 10/9: 100/99, 144/143)[8] (2.3.5.11.13 Ptolemismic)
Step signature Steps in JI Step sizes in cents
4L 3M 1s 10/9~11/10, 27/25~12/11~13/12, 25/24~33/32~27/26 175.8918c, 142.7754c, 66.7663c
Mode number Mode as simplest JI pre-image Step pattern Mode in cents
4 ~ 10/9 6/5 4/3 13/9 8/5 26/15 48/25 2/1 LMLMLMLs 175.892 318.667 494.559 637.334 813.226 956.002 1131.893 1198.660
3 ~ 10/9 6/5 4/3 13/9 8/5 5/3 11/6 2/1 LMLMLsLM 175.892 318.667 494.559 637.334 813.226 879.993 1055.884 1198.660
2 ~ 12/11 6/5 13/10 13/9 39/25 26/15 9/5 2/1 MLMLMLsL 142.775 318.667 461.443 637.334 780.120 956.002 1022.768 1198.660
1 ~ 10/9 6/5 4/3 13/9 20/13 5/3 11/6 2/1 LMLsLMLM 175.892 318.667 494.559 561.325 737.218 879.993 1055.884 1198.660
-1 ~ 12/11 6/5 13/10 13/9 3/2 5/3 9/5 2/1 MLMLsLML 142.775 318.667 461.443 637.334 704.101 879.993 1022.768 1198.660
-2 ~ 10/9 15/13 50/39 11/8 20/13 5/3 11/6 2/1 LsLMLMLM 175.892 242.658 418.550 561.325 737.218 879.993 1055.884 1198.660
-3 ~ 12/11 6/5 5/4 11/8 3/2 5/3 9/5 2/1 MLsLMLML 142.775 318.667 385.433 561.325 704.101 879.993 1022.768 1198.660
-4 ~ 25/24 15/13 5/4 11/8 3/2 5/3 9/5 2/1 sLMLMLML 66.766 242.658 385.433 561.325 704.101 879.993 1022.768 1198.660
Rank-1 temperings
ET 12 15 19 22f 26 27e 29 34 41
Step sizes in ET (2, 1, 1) (2, 2, 1) (3, 2, 1) (3, 3, 1) (4, 3, 1) (4, 3, 2) (4, 4, 1) (5, 4, 2) (6, 5, 2)

(2/1, 6/5)[4], 10/9)[15]

4L 8m 3s = (16/15, 25/24, 648/625) = (111.7313, 70.6724, 62.5652)

25/24 10/9 125/108 6/5 5/4 4/3 25/18 36/25 3/2 8/5 5/3 216/125 9/5 48/25 2/1 as mLmsmLmsmLmsmLm

m = s -> sLsssLsssLsssLs Hanson[15]; L = -> LLLsLLLsLLLsLLL Augmented[15] MODMOS; L = s -> sLsLsLsLsLsLsLs Porcupine[15];

s = 0 -> ssLsLssLsssL Diminished[12] MODMOS; m = 0 -> sLLsLsL Dicot[7]; L = 0 -> Father[11].

19-ET: (2, 1, 1); 22-ET: (2, 1, 2); 26-ET: (3, 1, 2); 27-ET: (2, 2, 1); 29-ET: (3, 1, 3); 31-ET: (3, 2, 1); 34-ET: (3, 2, 2); 41-ET: (4, 2, 3); 46-ET: (4, 3, 2); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)

(2/1, 6/5)[4], 10/9: 875/864)[15] Supermagic

4L 3m 8s = (16/15, 648/625~21/20, 25/24~36/35)

~ 25/24 10/9 8/7 6/5 5/4 4/3 25/18 35/24 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)

(2/1, 6/5)[4], 10/9: 100/99, 385/384)[15] Supermagic

4L 3m 8s = (16/15, 648/625~21/20~128/121, 25/24~36/35~33/32)

~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15-ET: (1,1,1); 19-ET: (2, 1, 1); 22-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 63-ET: (6, 5, 3)

(2/1, 6/5)[4], 10/9: 100/99, 105/104, 144/143)[15] Supermagic

4L 3m 8s = (16/15, 648/625~21/20~128/121~26/25, 25/24~36/35~33/32~27/26)

~ 25/24 10/9 8/7 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)

(2/1, 6/5)[4], 10/9: 325/324)[15] (2.3.5.13 Marveltwin)

4L 3m 8s = (16/15, 648/625~26/25, 25/24~27/26) = (112.3178, 68.5631, 68.1467)

~ 25/24 10/9 15/13 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15d-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27-ET: (2, 2, 1); 29-ET: (3, 3, 1); 31-ET: (3, 1, 2); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2); 46-ET: (4, 2, 3); 53-ET: (5, 3, 3); 72-ET: (7, 4, 4); 87-ET: (8, 5, 5)

(2/1, 6/5)[4], 10/9: 105/104, 325/324)[15] 2.3.5.7.13 Supermagic

4L 3m 8s = (16/15, 648/625~21/20~26/25, 25/24~36/35~27/26) = (121.6150, 81.3115, 58.8960)

~ 25/24 10/9 8/7 6/5 5/4 4/3 18/13 13/9 3/2 8/5 5/3 7/4 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15-ET: (1,1,1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 34-ET: (3, 2, 2); 37-ET: (3, 3, 2); 41-ET: (4, 3, 2); 60-ET: (6, 4, 3)

(2/1, 6/5)[4], 10/9: 100/99, 144/143)[15] (2.3.5.11.13 Ptolemismic)

4L 3m 8s = (16/15, 648/625~128/121~26/25, 25/24~33/32~27/26) = (109.1256, 76.0091, 66.7663) ⟨109.12557, 76.00911, 66.76626]

~ 25/24 10/9 15/13 6/5 5/4 4/3 11/8 13/9 3/2 8/5 5/3 26/15 9/5 48/25 2/1 as sLsmsLsmsLsmsLs

15-ET: (1, 1, 1); 19-ET: (2, 1, 1); 22f-ET: (2, 2, 1); 26-ET: (3, 2, 1); 27e-ET: (2, 1, 2); 29-ET: (3, 3, 1); 34-ET: (3, 2, 2); 41-ET: (4, 3, 2)

2.3.5; Hemifamity

((2/1, 3/2)[5], 10/9)

((2/1, 3/2)[5], 10/9)[10]

5L 2M 3s = (10/9, 16/15, 81/80)

81/80 9/8 6/5 4/3 27/20 3/2 8/5 16/9 9/5 2/1 as sLMLsLMLsL

L = M -> sLLLsLLLsL Dicot[10] MODMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;

L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS

s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]

((2/1, 3/2)[5], 10/9: 5120/5103)[17] (Hemifamity)

5L 2m 10s = (~35/32, 256/243~21/20, 81/80~64/63) = (153.2376c, 85.8342c, 24.4931c) TE

~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs

m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss;

L - m = m - s -> Garibaldi[17]; s = 0 -> LsLLLsL Dominant[7]; m = 0 -> sLssLssLssLssLs

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17] (Akea)

5L 2m 10s = (35/32~12/11, 256/243~21/20, 81/80~64/63~55/54) = (156.6236c, 85.7981c, 26.2356c) TE

~ 64/63 10/9 9/8 32/27 6/5 21/16 4/3 27/20 40/27 3/2 32/21 5/3 27/16 16/9 9/5 63/32 2/1 as sLsmsLssLssLsmsLs

m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss; s = 0 -> LsLLLsL Arnold[7]; m = 0 -> sLssLssLssLssLs

((2/1, 3/2)[5], 10/9: 5120/5103)[24] (Hemifamity)

5L 2m 17s = (~175/162, ~28/27, 81/80~64/63) = (132.1305c, 61.3411c, 24.4931c) TE

~ 64/63 35/32 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 35/24 40/27 3/2 32/21 105/64 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss

m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24] (Akea)

5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE

~ 64/63 12/11 10/9 9/8 7/6 32/27 6/5 35/27 21/16 4/3 27/20 16/11 40/27 3/2 32/21 18/11 5/3 27/16 7/4 16/9 9/5 35/18 63/32 2/1 as sLssmssLsssLsssLssmssLss

m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Arnold[7]

((2/1, 3/2)[5], 10/9: 5120/5103)[31] (Hemifamity)

5L 2m 24s = (~1225/1152, ~49/48, 81/80~64/63) = (107.6374c, 36.848c, 24.4931c) TE

~ 64/63 36/35 35/32 10/9 9/8 8/7 7/6 32/27 6/5 128/105 35/27 21/16 4/3 27/20 48/35 35/24 40/27 3/2 32/21 54/35 105/64 5/3 27/16 12/7 7/4 16/9 9/5 64/35 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss

m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;

s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS

((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31] (Akea)

5L 2m 24s = (~35/33, 49/48~56/55, 81/80~64/63~55/54) = (100.7664c, 33.3269c, 26.2356c) TE

~ 64/63 36/35 12/11 10/9 9/8 8/7 7/6 32/27 6/5 11/9 35/27 21/16 4/3 27/20 11/8 16/11 40/27 3/2 32/21 54/35 18/11 5/3 27/16 12/7 7/4 16/9 9/5 11/6 35/18 63/32 2/1 as ssLsssmsssLssssLssssLsssmsssLss

m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;

s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss

((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63)

((2/1, 3/2)[12], 64/63: 5120/5013)[24] (Hemifamity)

5L 7M 12s = (~135/128, ~28/27, 81/80~64/63) = (95.2825c, 61.3411c, 24.4931c) TE

~ 64/63 15/14 243/224 9/8 8/7 32/27 6/5 81/64 9/7 4/3 27/20 10/7 81/56 3/2 32/21 45/28 80/49 27/16 12/7 16/9 9/5 243/128 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM

L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]

((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24] (Pele)

5L 7M 12s = (135/128~35/33, 28/27~33/32, 81/80~64/63~99/98) = (97.5911c, 58.2557c, 25.3165c) TE

~ 64/63 15/14 12/11 9/8 8/7 32/27 6/5 14/11 9/7 4/3 27/20 10/7 16/11 3/2 32/21 45/28 18/11 27/16 12/7 16/9 9/5 12/11 27/14 2/1 as sLsMsMsLsMsLsMsLsMsMsLsM

L = M -> sLsLsLsLsLsLsLsLsLsLsLsLsL; M = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = s -> sssLsLsssLsssLsssLsLsssL; s = 0 -> LssLsLsLssLs Dominant[12]

((2/1, 3/2)[12], 64/63: 5120/5013)[36] (Hemifamity)

5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE

~ 64/63 36/35 15/14 243/224 54/49 9/8 8/7 81/70 32/27 6/5 128/105 81/64 9/7 64/49 4/3 27/20 48/35 10/7 81/56 72/49 3/2 32/21 54/35 45/28 80/49 81/49 27/16 12/7 243/140 16/9 9/5 64/35 243/128 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM

L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;

s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS

((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36] (Pele)

5L 7M 12s = (~25/24, ~49/48, 81/80~64/63~99/98) = (72.2746c, 32.9392c, 25.3165c) TE

~ 64/63 36/35 15/14 12/11 54/49 9/8 8/7 64/55 32/27 6/5 128/105 14/11 9/7 64/49 4/3 27/20 48/35 10/7 16/11 72/49 3/2 32/21 54/35 45/28 18/11 81/49 27/16 12/7 96/55 16/9 9/5 64/35 22/21 27/14 96/49 2/1 as ssLssMssMssLssMssLssMssLssMssMssLssM

L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;

s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS

2.3.25

(2/1, 3/2, 100/81)

(2/1, 3/2, 100/81)[7]

(2/1, 3/2, 100/81: 4375/4374)[7] (Ragismic)
Step signature Steps in JI Step sizes in cents
2L 1m 4s (2500/2187~8/7, ~9/8, ~27/25) (231.1884c, 203.974c, 133.4123c)
Mode number Mode in JI Step pattern Mode height
-3 ~ 9/8 175/144 25/18 3/2 81/50 50/27 2/1 msLssLs 0.0158
-2 ~ 27/25 175/144 21/16 3/2 81/50 7/4 2/1 smsLssL -0.0211
-1 ~ 8/7 100/81 25/18 3/2 12/7 50/27 2/1 LsmsLss 0.037
0 ~ 27/25 100/81 4/3 3/2 81/50 50/27 2/1 sLsmsLs 0
1 ~ 27/25 7/6 4/3 36/25 81/50 7/4 2/1 ssLsmsL -0.037
2 ~ 8/7 100/81 4/3 32/21 288/175 50/27 2/1 LssLsms 0.0211
3 ~ 27/25 100/81 4/3 36/25 288/175 16/9 2/1 sLssLsm -0.0158
(2/1, 3/2, 100/81: 1225/1224, 1701/1700)[7]
Step signature Steps in JI Step sizes in cents
2L 1m 4s (2500/2187~8/7, ~9/8, ~27/25) (231.5807c, 203.8094c, 133.2573c)
Mode number Mode in JI Step pattern Mode height
-3 ~ 9/8 17/14 25/18 3/2 34/21 50/27 2/1 msLssLs 0.0157
-2 ~ 27/25 17/14 21/16 3/2 34/21 7/4 2/1 smsLssL -0.0214
-1 ~ 8/7 21/17 25/18 3/2 12/7 50/27 2/1 LsmsLss 0.0371
0 ~ 27/25 21/17 4/3 3/2 34/21 50/27 2/1 sLsmsLs 0
1 ~ 27/25 7/6 4/3 36/25 34/21 7/4 2/1 ssLsmsL -0.0371
2 ~ 8/7 21/17 4/3 32/21 28/17 50/27 2/1 LssLsms 0.0214
3 ~ 27/25 21/17 4/3 36/25 28/17 16/9 2/1 sLssLsm -0.0157

2.5.9; Marvel

((2/1, 5/4)[3], 9/8)

((2/1, 5/4)[3], 9/8)[6]

1L 3M 2s = (256/225, 9/8, 10/9)

9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8: 225/224)[6] (Marvel)

1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c) TE

~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[6] (Apollo)

1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c) TE

~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs

L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs

((2/1, 5/4)[3], 9/8)[10]

6L 1m 3s = (10/9, 128/125, 81/80)

10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,

m = s -> LsLLsLsLsL MODMOS; L = m -> LsLLsLLLsL; L = s -> LLLLLLsLLL; s = 0 -> LLLLsLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8: 225/224)[10] (Marvel)

6L 1m 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE

~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL

m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[10] (Apollo)

6L 1m 3s = (10/9~11/10, 128/125~36/35~80/77, 81/80~126/125~45/44~56/55) = (174.6095c, 55.1825c, 32.3305c) TE

~10/9 9/8 5/4 11/8 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL

m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL

((2/1, 5/4)[3], 9/8)[17]

6L 10m 1s = (800/729, 81/80, 2048/2025)

81/80 10/9 9/8 100/81 5/4 81/64 25/18 45/32 64/45 36/18 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as mLmLmmLmsmLmmLmLm

m = s -> sLsLssLsssLssLsLs MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL

((2/1, 5/4)[3], 9/8: 225/224)[17] (Marvel)

6L 1m 10s = (~800/729, 2048/2025~64/63, 81/80~126/125) = (164.9122c, 31.1096c, 18.0015c) TE

~ 81/80 10/9 9/8 100/81 5/4 81/64 25/18 7/5 10/7 36/25 128/81 8/5 81/50 16/9 9/5 160/81 2/1 as sLsLssLsmsLssLsLs

m = s -> sLsLssLsssLssLsLs MODMOS; L = m -> sLsLssLsLsLssLsLs; L = s -> LLLLLLLLsLLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLsLssLssLssLsLs MODMOS

((2/1, 5/4)[3], 9/8: 100/99, 225/224)[17] (Apollo)

6L 10m 1s = (~88/81, 81/80~126/125~45/44~56/55, 2048/2025~64/63~176/175) = (142.279c, 32.3305c, 22.852c) TE

~ 56/55 10/9 9/8 11/9 5/4 14/11 11/8 7/5 10/7 16/11 11/7 8/5 11/9 16/9 9/5 55/28 2/1 as mLmLmmLmsmLmmLmLm

m = s -> sLsLssLsssLssLsLs Machine[17] MODMOS; L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL

2.5.9; Starling

((2/1, 5/4)[3], 10/9)

((2/1, 5/4)[3], 10/9)[6]

1L 2m 3s = (144/125, 9/8, 10/9)

9/8 5/4 36/25 8/5 9/5 2/1 as msLsms

m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL

((2/1, 5/4)[3], 10/9: 126/125)[6]

1L 2m 3s = (~8/7, ~9/8, 10/9~28/25) = (232.1725c, 202.4685c, 187.562c) TE

~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms

m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL

((2/1, 5/4)[3], 10/9)[9]

6L 1m 2s = (10/9, 648/625, 81/80)

10/9 9/8 5/4 25/18 36/25 8/5 16/9 9/5 2/1 as LsLLmLLsL

m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS

((2/1, 5/4)[3], 10/9: 126/125)[9]

6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224) = (187.562c, 44.6105c, 14.9065c) TE

~ 10/9 9/8 5/4 7/5 10/7 8/5 16/9 9/5 2/1 as LsLLmLLsL

m = s -> LsLLsLLsL; L = m -> LsLLLLLsL MODMOS; L = s -> LLLLsLLLL; s = 0 -> LLLsLLL; m = 0 -> LsLLLLsL MODMOS

((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16]

6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55) = (163.6623c, 24.4284c, 21.4103c) TE

~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 81/50 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL

m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL

((2/1, 5/4)[3], 10/9: 91/90, 126/125, 896/891)[16]

6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143) = (160.4106c, 30.0969c, 23.0825c) TE

~ 56/55 10/9 9/8 63/55 5/4 9/7 7/5 45/32 16/11 8/5 13/8 16/9 9/5 20/11 2/1 as sLssLsLsmsLsLssL

m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL

2.3.7; Orwellismic

(2/1, 3/2, 7/6)

(2/1, 3/2, 7/6)[4]

1L 2m 1s = (9/7, 7/6, 8/7)

7/6 3/2 7/4 2/1 as mLms

m = s -> sLss Sempahore[4]

(2/1, 3/2, 7/6)[7]

4L 1M 2s = (8/7, 9/8, 49/48)

8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL

L = M -> LsLLLsL Archy[5]; s = 0 -> LLsLL Semaphore[5]

(2/1, 3/2, 7/6: 1728/1715)[7] (Orwellismic)

4L 1M 2s = (~8/7, ~9/8, 49/48~36/35) = (227.1393c, 204.1935c, 43.334c) TE

~ 8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL

L = M -> LsLLLsL Superpyth[5]; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 1728/1715)[12] (Orwellismic)

4L 1M 7s = (~10/9, 54/49~35/32, 49/48~36/35) = (183.8053c, 160.8595c, 43.334c) TE

~ 36/35 8/7 7/6 6/5 4/3 48/35 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[12] (Orwellian)

4L 1M 7s = (~10/9, 54/49~35/32~12/11, 49/48~36/35~33/32) = (185.7619, 155.4288c, 155.4288c) TE

~ 33/32 8/7 7/6 6/5 4/3 11/8 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Suprapyth[12]; M = s -> sLssLsssLssL MODMOS; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[12] (Guanyin)

4L 1M 7s = (~10/9, 54/49~35/32~11/10, 49/48~36/35~45/44) = (183.8734c, 162.5743c, 43.0239c) TE

~ 36/35 8/7 7/6 6/5 4/3 15/11 3/2 54/35 12/7 7/4 9/5 2/1 as sLssLsMsLssL

L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS

(2/1, 3/2, 7/6: 1728/1715)[17] (Orwellismic)

4L 1M 12s = (~160/147, ~15/14, 49/48~36/35) = (140.4713c, 117.5255c, 43.334c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 48/35 35/24 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[17] (Orwellian)

4L 1M 12s = (~160/147, 15/14~35/33, 49/48~36/35~33/32) = (142.5744c, 112.2413c, 43.1875c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 11/8 16/11 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Suprapyth[17]; M = s -> sLsssLsssssLsssLs; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[17] (Guanyin)

4L 1M 12s = (~88/81, 15/14~77/72, 49/48~36/35~45/44) = (140.8495c, 119.5504c, 43.0239c) TE

~ 36/35 10/9 8/7 7/6 6/5 35/27 4/3 15/11 22/15 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1 as sLsssLssMssLsssLs

L = M -> sLsssLssLssLsssLs Superpyth[17]; M = s -> sLsssLsssssLsssLs

(2/1, 3/2, 7/6: 1728/1715)[22] (Orwellismic)

4L 1m 17s = (~200/189, ~25/24, 49/48~36/35) = (97.1373c, 74.1915c, 43.334c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 48/35 7/5 35/24 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs

m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]; s = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[22] (Orwellian)

4L 1m 17s = (~200/189, 25/24~80/77, 49/48~36/35~33/32) = (99.3869c, 69.0538c, 43.1875c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 49/40 35/27 4/3 11/8 7/5 16/11 3/2 54/27 63/40 5/3 12/7 7/4 9/5 147/80 35/18 2/1 as ssLssssLsssMsssLssssLs

m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Suprapyth[17]; s = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[22] (Guanyin)

4L 1m 17s = (~200/189, 25/24~22/21, 49/48~36/35~45/44) = (97.8256c, 76.5265c, 43.0239c) TE

~ 36/35 21/20 10/9 8/7 7/6 6/5 27/22 35/27 4/3 15/11 7/5 22/15 3/2 54/27 63/40 5/3 12/7 7/4 9/5 81/44 35/18 2/1 as ssLssssLsssmsssLssssLs

m = s -> ssLssssLsssssssLssssLs Fleetwood[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]

(2/1, 3/2, 7/6: 1728/1715)[27] (Orwellismic)

4L 22M 1s = (~250/243, 49/48~36/35, ~50/49) = (53.8033c, 43.334c, 30.8575c) TE

~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 48/35 7/5 10/7 35/24 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM

L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; M = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Beep[5]

(2/1, 3/2, 7/6: 99/98, 385/384)[27] (Orwellian)

4L 22M 1s = (~250/243, 49/48~36/35~33/32, 50/49~100/99) = (56.1994c, 43.1875c, 25.8663c) TE

~ 36/35 21/20 160/147 10/9 8/7 7/6 6/5 49/40 80/63 35/27 4/3 11/8 7/5 10/7 16/11 3/2 54/27 63/40 80/49 5/3 12/7 7/4 9/5 147/80 40/21 35/18 2/1 as MMLMMMMMLMMMMsMMMMLMMMMMLMM

L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartz[27]; M = s -> ssLsssssLsssssssssLsssssLss Myno[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Suprapyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Doublewide[26] MODMOS; M = 0 -> LLsLL Pentoid[5]

(2/1, 3/2, 7/6: 176/175, 540/539)[27] (Guanyin)

4L 22M 1s = (~250/243, 49/48~36/35~45/44, 50/49~55/54) = (54.8017c, 43.0239c, 33.5026c) TE

~ 36/35 21/20 88/81 10/9 8/7 7/6 6/5 27/22 80/63 35/27 4/3 15/11 7/5 10/7 22/15 3/2 54/27 63/40 44/27 5/3 12/7 7/4 9/5 81/44 40/21 35/18 2/1 as mmLmmmmmLmmmmsmmmmLmmmmmLmm

m = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = m -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];

s = 0 -> ssLsssssLssssssssLsssssLss Fleetwood[26] MODMOS

(2/1, 3/2, 7/6: 1728/1715)[53] (Orwellismic)

27L 4M 22s = (~50/49, 64/63~245/243, 126/125~2401/2400) = (30.8575c, 22.9458c, 12.4765c) TE

~ 50/49 36/35 360/343 21/20 15/14 27/25 54/49 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 48/35 480/343 7/5 10/7 343/240 35/24 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 49/27 50/27 28/15 40/21 343/180 35/18 49/25 2/1 as LsLsLsLsLMLsLsLsLsLsLMLsLsLsLsLMLsLsLsLsLsLMLsLsLsLsL

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53]; L = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss

s = 0 -> LLLLLsLLLLLLsLLLLLsLLLLLLsLLLLL Myna[31] MODMOS; M = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49];

L = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS

(2/1, 3/2, 7/6: 99/98, 385/384)[53] (Orwellian)

4L 27M 22s = (64/63~245/243~55/54, 50/49~100/99, 126/125~2401/2400) = (30.3331c, 25.8663c, 17.3212c) TE

~ 50/49 36/35 80/77 21/20 15/14 27/25 12/11 441/400 9/8 8/7 125/108 7/6 25/21 6/5 60/49 49/40 5/4 63/50 9/7 162/125 21/16 4/3 200/147 11/8 480/343 7/5 10/7 343/240 16/11 147/100 3/2 32/16 125/81 14/9 100/63 8/5 80/49 49/30 5/3 42/25 12/7 216/125 7/4 16/9 800/441 11/6 50/27 28/15 40/21 77/40 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartz[53];

s = 0 -> sssssLssssssLsssssLssssssLsssss Myno[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS;

L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Suprapyth[49]

(2/1, 3/2, 7/6: 176/175, 540/539)[53] (Guanyin)

4L 27M 22s = (64/63~245/243~100/99, 50/49~55/54, 126/125~2401/2400~441/440) = (33.5026c, 21.2991c, 9.5213c) TE

~ 50/49 36/35 22/21 21/20 15/14 27/25 11/10 243/220 9/8 8/7 125/108 7/6 25/21 6/5 11/9 27/22 5/4 63/50 9/7 162/125 21/16 4/3 110/81 15/11 88/63 7/5 10/7 63/44 22/15 81/55 3/2 32/16 125/81 14/9 100/63 8/5 44/27 18/11 5/3 42/25 12/7 216/125 7/4 16/9 440/243 20/11 50/27 40/21 21/11 35/18 49/25 2/1 as MsMsMsMsMLMsMsMsMsMsMLMsMsMsMsMLMsMsMsMsMsMLMsMsMsMsM

L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;

M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss Kleiboh[53] MODMOS; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53];

s = 0 -> sssssLssssssLsssssLssssssLsssss Myna[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Fleetwood[22] MODMOS;

L = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49]

((2/1, 3/2)[12], 49/48) or ((2/1, 3/2)[12], 36/35)

((2/1, 3/2)[12], 36/35: 1728/1715)[24] (Orwellian)

2.3.7 Sensamagic

(2/1, 3/2, 9/7)

(2/1, 3/2, 9/7)[4]

2L 1M 1s = (9/7, 7/6, 28/27) = (435.0841c, 266.8709c, 62.9609c)

9/7 3/2 27/14 2/1 as LMLs

L = M -> LLLs; M = s -> LsLs; s = 0 -> LsL

(2/1, 3/2, 9/7: 245/243)[7] Sensamagic

2L 1m 4s = (~5/4, ~9/8, 28/27~36/35)

~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 as sLsmsLs

m = s -> sLsssLs; s = 0 -> LsL

5-ET: (2, 1, 0); 14c-ET: (4, 2, 1); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22-ET: (7, 4, 1) 24-ET: (8, 4, 1); 27-ET: (9, 5, 1); 41-ET: (13, 7, 2); 46-ET: (15, 8, 2); 68-ET: (22, 12, 3); 87-ET: (28, 15, 4)

(2/1, 3/2, 9/7: 245/243)[10] Sensamagic

2L 1m 7s = (~135/112, ~35/32, 28/27~36/35)

~ 28/27 5/4 9/7 4/3 35/24 3/2 14/9 15/8 27/14 2/1 as sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

14c-ET: (3, 1, 1); 17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 68-ET: (19, 9, 3); 87-ET: (24,11,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic

2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)

~ 28/27 5/4 9/7 4/3 16/11 3/2 14/9 15/8 27/14 2/1 as sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22-ET: (6, 3, 1) 24-ET: (7, 3, 1); 27-ET: (8, 4, 1); 41-ET: (11, 5, 2); 46-ET: (13, 6, 2); 63-ET: (18, 8, 3); 68-ET: (19, 9, 3); 87-ET: (24, 11, 4)

(2/1, 3/2, 9/7: 245/243)[13] Sensamagic

2L 1m 10s = (~75/64, ~135/128, 28/27~36/35)

~ 28/27 16/15 5/4 9/7 4/3 48/35 35/24 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss

m = s -> ssLsssssssLss Pycnic[13] MODMOS; s = 0 -> LsL

14c-ET: (2, 0, 1); 17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[13] Sensamagic

2L 1m 10s = (~75/64, 135/128~35/33, 28/27~36/35~33/32)

~ 28/27 16/15 5/4 9/7 4/3 11/8 16/11 3/2 14/9 8/5 15/8 27/14 2/1 as ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 63-ET: (15, 5, 3); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)

(2/1, 3/2, 9/7: 245/243, 385/384)[16] Sensamagic

2L 13m 1s = (~25/22, 28/27~36/35~33/32, ~45/44)

~ 28/27 16/15 40/33 5/4 9/7 4/3 11/8 45/32 16/11 3/2 14/9 8/5 20/11 15/8 27/14 2/1 as mmLmmmmsmmmmLmmm

m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss

17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 22-ET: (4, 1, 1) 24-ET: (5, 1, 1); 27-ET: (6, 1, 2); 41-ET: (7, 2, 1); 46-ET: (9, 2, 2); 63-ET: (12, 3, 2); 68-ET: (13, 3, 3); 87-ET: (16, 4, 3)

(2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic

2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)

~ 45/44 28/27 35/33 16/15 12/11 11/10 9/8 154/135 7/6 9/7 405/308 4/3 15/11 11/8 45/32 64/45 16/11 22/15 3/2 616/405 14/9 12/7 135/77 16/9 20/11 11/6 15/8 66/35 27/14 88/45 2/1 as msmsmsmsmLmsmsmsmsmsmLmsmsmsmsm

m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS

41-ET: (6, 1, 1); 46-ET: (7, 2, 0); 63-ET: (10, 2, 1); 68-ET: (10, 3, 0); 87-ET: (13, 3, 1)

(2/1, 3/2, 9/7: 729/728)[7]

2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)

~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs

m = s -> sLsssLs; s = 0 -> LsL

5-ET: (2, 1, 0); 17-ET: (5, 3, 1); 19-ET: (6, 3, 1); 22f-ET: (7, 4, 1) 24-ET: (8, 4, 1); 36-ET: (11, 6, 2); 41-ET: (13, 7, 2); 53-ET: (16, 9, 3); 58-ET: (18, 10, 3); 77-ET: (24, 13, 4); 94-ET: (29, 16, 5)

(2/1, 3/2, 9/7: 729/728)[10]

2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)

~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss

m = s -> sLsssssLss; s = 0 -> LsL

17-ET: (4, 2, 1); 19-ET: (5, 2, 1); 22f-ET: (6, 3, 1) 24-ET: (7, 3, 1); 36-ET: (9, 4, 2); 41-ET: (11, 5, 2); 53-ET: (13, 6, 3); 58-ET: (15, 7, 3); 77-ET: (20, 9, 4); 94-ET: (24, 11, 5)

(2/1, 3/2, 9/7: 729/728)[13]

2L 1m 10s = (~169/147, ~117/112, 28/27~27/26)

~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22f-ET: (5, 2, 1) 24-ET: (6, 2, 1); 36-ET: (7, 2, 2); 41-ET: (9, 3, 2); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 94-ET: (19, 6, 5)

(2/1, 3/2, 9/7: 351/350, 676/675)[13]

2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)

~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss

m = s -> ssLsssssssLss; s = 0 -> LsL

17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 24-ET: (6, 2, 1); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 111-ET: (22, 7, 6); 130-ET: (26, 8, 7)

(2/1, 3/2, 9/7: 351/350, 676/675)[16]

2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)

~ 26/25 14/13 25/21 26/21 9/7 4/3 18/13 39/28 13/9 3/2 14/9 21/13 25/14 13/7 23/13 2/1 as mmLmmmmsmmmmLmmm

m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss

17-ET: (2, 1, 0); 19-ET: (3, 1, 0); 24-ET: (5, 1, 1); 53-ET: (7, 3, 0); 58-ET: (9, 3, 1); 77-ET: (12, 4, 1); 111-ET: (16, 6, 1); 130-ET: (19, 7, 1)

(2/1, 3/2, 9/7: 351/350, 676/675)[31]

2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)

~169/168 26/25 117/112 14/13 13/12 28/25 9/8 378/325 7/6 9/7 325/252 4/3 75/56 18/13 39/28 56/39 13/9 112/75 3/2 14/9 12/7 325/189 16/9 25/14 24/13 13/7 224/117 25/13 336/169 2/1 as smsmsmsmsLsmsmsmsmsmsLsmsmsmsms

m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS

53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)

2.3.11 Pentacircle

((2/1, 3/2)[5], 12/11)

((2/1, 3/2)[5], 12/11)[10]

5L 2M 3s = (12/11, 88/81, 33/32)

12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM

((2/1, 3/2)[5], 12/11: 896/891)[10]

5L 2M 3s = (12/11, 88/81, 33/32~28/27)

~ 12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM

((2/1, 3/2)[5], 12/11: 896/891)[17]

5L 2M 10s = (128/121~81/77, 256/243~22/21, 33/32~28/27)

~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 16/11 3/2 14/9 18/11 27/16 16/9 11/6 27/14 2/1 as sLsMsLssLssLsMsLs

2.3.13 Squbema

((2/1, 3/2)[5], 13/12)

((2/1, 3/2)[5], 13/12)[10]

5L 2M 3s = (13/12, 128/117, 27/26)

13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM

((2/1, 3/2)[5], 13/12: 729/728)[10]

5L 2M 3s = (13/12, 128/117, 27/26~28/27)

~ 13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM

((2/1, 3/2)[5], 13/12: 729/728)[17]

5L 2M 10s = (91/81, 256/243~96/91, 27/26~28/27)

~ 28/27 13/12 9/8 32/27 16/13 9/7 4/3 18/13 13/9 3/2 14/9 13/8 27/16 16/9 24/13 27/14 2/1 as sLsMsLssLssLsMsLs

((2/1, 3/2)[5], 12/11~13/12: 144/143, 729/728)[17]

5L 2M 10s = (91/81~81/77, 256/243~96/91~22/21, 27/26~28/27~33/32)

~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 13/9 3/2 14/9 13/8 27/16 16/9 12/11 27/14 2/1 as sLsMsLssLssLsMsLs



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