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Gallery of 3-SN scales: Difference between revisions

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See [[SN scale]] and [[Rank-3 scales]].
See [[SN scale]] and [[Rank-3 scale]].


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


Commas tempered out are shown in their simplest basis set, as per SN labeling conventions.
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 scale|MOS]] (2-SN) scales is ([[Octave|2/1]], [[3/2]]). Germinations are grouped by their [[subgroup]], and within that, by the first [[comma]] [[Tempering out|tempered out]] in scales evolved from the germination.


Tempered scales are shown in JI as their simplest symmetric pre-image.
Commas tempered out are shown in their simplest basis set, as per [[SN scale#Labeling|SN labeling conventions]].


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 (scales of even cardinality)
Tempered scales are shown in [[Just intonation|JI]] as their simplest symmetric pre-image.


== 2.3.5, Marvel ==
Scales are written in [[Just intonation|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 [[Octave|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) ===
====[[SNS (2/1, 3/2, 5/4)-4|(2/1, 3/2, 5/4)[4]]]====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 1M 1s
|(5/4, 6/5, 16/15)
|(386.3137c, 315.6413c, 111.7313c)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 1s|LLLs]]
|[[Dicot]][4]
|25/24
|-
|M = s
|[[2L 2s|LsLs]]
|Antitonic[4]
|9/8
|-
|L - M = M - s
|LsLd
|Bug[4] MODMOS
|27/25
|-
|s = 0
|LsL
|[[Trienstonic clan#Father|Father]][3]
|16/15
|}


=== (2/1, 3/2, 5/4) ===
====[[SNS (2/1, 3/2, 5/4)-7|(2/1, 3/2, 5/4)[7]]]====
{| class="wikitable"
! Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 1M 4s
|(75/64, 9/8, 16/15)
|(274.5824c, 203.9100c, 111.7313c)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 4s|sLsLsLs]]
|[[Dicot]][7]
|25/24
|-
|M = s
|[[2L 5s|sLsssLs]]
|[[Mavila]][7]
|135/128
|-
|L = s
| [[6L 1s|LLLsLLL]]
|[[Enipucrop]][7]
|1125/1024
|-
|L - M = M - s
|sAsLsAs
|[[Meantone]][7] MODMOS
|81/80
|-
| s = 0
|LsL
|[[Trienstonic clan#Father|Father]][3]
|16/15
|}


==== [[SNS (2/1, 3/2, 5/4)-4|(2/1, 3/2, 5/4)[4]]] ====
=====[[SNS (2/1, 3/2, 5/4: 225/224)-7|(2/1, 3/2, 5/4: 225/224)[7]]] ([[Marvel]])=====
2L 1M 1s = (5/4, 6/5, 16/15)
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 4s|sLsLsLs]]
|[[Sharp]][7]
|25/24, 28/27
|-
|M = s
|[[2L 5s|sLsssLs]]
|[[Pelogic]][7]
|135/128, 21/20
|-
|L= s
|[[6L 1s|LLLsLLL]]
|[[Enipucrop]][7]
| 35/32, 49/45
|-
|L - M = M - s
|sAsLsAs
|[[Meantone]][7] MODMOS
|81/80, 126/125
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[9edo|9]]
|[[10edo|10]]
|[[12edo|12]]
|[[19edo|19]]
| [[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}


5/4 3/2 15/8 2/1 as LMLs
====[[SNS (2/1, 3/2, 5/4)-10|(2/1, 3/2, 5/4)[10]]]====
{| class="wikitable"
! Step signature
! Steps in JI
!Step sizes in cents
|-
|2L 7m 1s
|(1125/1024, 16/15, 135/128)
| (162.8511c, 111.7313c, 92.1787c)
|}
{| class="wikitable"
|+
!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
|<nowiki>2|7</nowiki>
| -.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
|<nowiki>1|8</nowiki>
| -.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
|<nowiki>0|9</nowiki>
| -.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
|<nowiki>6|3</nowiki>
| -.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
|<nowiki>5|4</nowiki>
| -.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
|<nowiki>4|5</nowiki>
|.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
|<nowiki>3|6</nowiki>
|.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
|<nowiki>9|0</nowiki>
|.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
|<nowiki>8|1</nowiki>
|.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
|<nowiki>7|2</nowiki>
|.0564
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[OTC 2L 8s|sLsssssLss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|-
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[Marvel temperaments#Negri|Negri]][10]
|16875/16384
|-
|L = s
|[[7L 3s|LsLLsLLsLL]]
|[[Dicot]][10]
|25/24
|-
|L - m = m - s
|sLssdssLss
|[[Ampersand]][10] MODMOS
|34171875/33554432
|-
|s = 0
|[[2L 7s|sLssssLss]]
|[[Mavila]][9]
|135/128
|-
|m = 0
|LsL
|[[Trienstonic clan#Father|Father]][3]
|16/15
|-
|L = 0
|[[7L 1s|LLLsLLLL]]
|[[Enipucrop]][8]
|1125/1024
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224)-10|(2/1, 3/2, 5/4: 225/224)[10]]] ([[Marvel]])=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|<nowiki>2|7</nowiki>
| -.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
|<nowiki>1|8</nowiki>
| -.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
|<nowiki>0|9</nowiki>
| -.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
|<nowiki>6|3</nowiki>
| -.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
|<nowiki>5|4</nowiki>
| -.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
|<nowiki>4|5</nowiki>
|.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
|<nowiki>3|6</nowiki>
|.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
|<nowiki>9|0</nowiki>
|.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
|<nowiki>8|1</nowiki>
|.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
|<nowiki>7|2</nowiki>
|.0475
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|-
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[Marvel temperaments#Negri|Negri]][10]
|49/48, 225/224
|-
|L = s
|[[7L 3s|LsLLsLLsLL]]
|[[Sharp]][10]
|25/24, 28/27
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 1029/1024
|-
|s = 0
|[[2L 7s|sLssssLss]]
|[[Pelogic]][9]
|21/20, 135/128
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[12edo|12]]
|[[19edo|19]]
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-10|(2/1, 3/2, 5/4: 225/224, 385/384)[10]]] ([[Marvel]])=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|<nowiki>2|7</nowiki>
| -.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
|<nowiki>1|8</nowiki>
| -.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
|<nowiki>0|9</nowiki>
| -.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
|<nowiki>6|3</nowiki>
| -.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
|<nowiki>5|4</nowiki>
| -.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
|<nowiki>4|5</nowiki>
|.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
|<nowiki>3|6</nowiki>
|.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
|<nowiki>9|0</nowiki>
|.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
|<nowiki>8|1</nowiki>
|.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
|<nowiki>7|2</nowiki>
|.0472
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajarous]][10] 4M (pentachordal decatonic)
|50/49, 55/54, 64/63
|-
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[Marvel temperaments#Negri|Negri]][10]
|45/44, 49/48, 56/55
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|12e
|[[19edo|19]]
|[[22edo|22]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-10|(2/1, 3/2, 5/4: 225/224, 441/440)[10]]] ([[Prodigy]])=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|<nowiki>2|7</nowiki>
| -.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
|<nowiki>1|8</nowiki>
| -.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
|<nowiki>0|9</nowiki>
| -.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
|<nowiki>6|3</nowiki>
| -.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
|<nowiki>5|4</nowiki>
| -.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
|<nowiki>4|5</nowiki>
|.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
|<nowiki>3|6</nowiki>
|.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
|<nowiki>9|0</nowiki>
|.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
|<nowiki>8|1</nowiki>
|.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
|<nowiki>7|2</nowiki>
|.0466
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajaric]][10] 4M (pentachordal decatonic)
|45/44, 50/49, 56/55
|-
|L = m
|[[9L 1s|LLLLsLLLLL]]
|[[Negroni]][10]
|49/48, 55/54, 225/224
|-
|L - m = m - s
|sLssdssLss
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[12edo|12]]
|19e
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|53e
|[[72edo|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)
|}
====[[SNS (2/1, 3/2, 5/4: 225/224)-19|(2/1, 3/2, 5/4: 225/224)[19]]] (Marvel)====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LsLsLLLsLsLsLLLsLsL
|[[Septimal meantone|Meantone]][19] MODMOS
|81/80, 126/125
|-
|M = s
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[Marvel temperaments#Negri|Negri]][19]
|49/48, 225/224
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Magic]][19] MODMOS
|225/224, 245/243
|-
|s = 0
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajara]][12] 4M (hexachordal dodecatonic)
|50/49, 64/63
|-
|m = 0
|[[10L 7s|LsLsLLsLsLsLLsLsL]]
|[[Sharp]][17]
|25/24, 28/27
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}


tempers to LLLs Dicot[4], LsLs Antitonic[4]
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-19|(2/1, 3/2, 5/4: 225/224, 385/384)[19]]] (Marvel)=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+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
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[Marvel temperaments#Negri|Negri]][19]
|45/44, 49/48, 56/55
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Magic]][19] MODMOS
|100/99, 225/224, 245/243
|-
|s = 0
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajarous]][12] 4M (hexachordal dodecatonic)
|50/49, 55/54, 64/63
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[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)
|(3, 3, 2)
|(4, 3, 1)
|(5, 4, 2)
|}


==== [[SNS (2/1, 3/2, 5/4)-7|(2/1, 3/2, 5/4)[7]]] ====
=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-19|(2/1, 3/2, 5/4: 225/224, 441/440)[19]]] ([[Prodigy]])=====
2L 1M 4s = (75/64, 9/8, 16/15)
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|LsLsLLLsLsLsLLLsLsL
|[[Septimal meantone|Meantone]][19] MODMOS
|81/80, 99/98, 126/125
|-
|M = s
|[[10L 9s|LsLsLsLsLsLsLsLsLsL]]
|[[Marvel temperaments#Negroni|Negroni]][19]
|49/48, 55/54, 225/224
|-
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|[[Witchcraft]][19] MODMOS
|225/224, 245/243, 441/440
|-
|s = 0
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|45/44, 50/49, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|53e
|[[72edo|72]]
|-
!Step sizes in ET
|(2, 1, 1)
|(2, 2, 1)
|(3, 2, 1)
|(4, 3, 1)
|(5, 4, 2)
|}


16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31]]] ([[Prodigy]])====
{| class="wikitable"
! 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)
|}


tempers to sLsLsLs Dicot[7], sLsssLs Mavila[7], LLLsLLL Enipucrop[7]
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


=====[[SNS (2/1, 3/2, 5/4: 225/224)-7|(2/1, 3/2, 5/4: 225/224)[7]]]=====
as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm
2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14) = (267.8165c, 200.9152c, 116.0124c) TE  
 
{| class="wikitable"
|+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
|[[Septimal meantone|Meantone[]]31] MODMOS
|81/80, 99/98, 126/125
|-
|s = 0
|mLmmLmmLmmLmmLmLmmLmmLmmLmmLm
|[[Marvel temperaments#Negroni|Negroni]][29]
|49/48, 55/54, 225/224
|-
|m = 0
|LLsLLLLLLsLL
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|45/44, 50/49, 56/55
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[41edo|41]]
|53e
|[[72edo|72]]
|-
!Step sizes in ET
|(2, 1, 1)
|(3, 1, 2)
|(3, 2, 2)
|}
 
===((2/1, 5/4)[3], 16/15)===
====[[SNS ((2/1, 5/4)-3, 16/15)-6|((2/1, 5/4)[3], 16/15)[6]]]====
{| class="wikitable"
! Step signature
! Steps in JI
!Step sizes in cents
|-
|1L 2M 4s
|(6/5, 75/64, 16/15)
| (315.6413c, 267.8165c, 111.7313c)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
! Equivalence
! Step pattern
! Scale
! Comma list
|-
| L = M
| LsLsLs
| [[Augmented (temperament)|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
|}
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-6|((2/1, 5/4)[3], 16/15: 225/224)[6] (Marvel)]]=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
! Equivalence
! Step pattern
! Scale
! Comma list
|-
| L = M
| LsLsLs
| [[August]][6]
| 128/125
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[7edo|7]]
|[[9edo|9]]
|[[10edo|10]]
|[[12edo|12]]
|[[19edo|19]]
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
====[[SNS ((2/1, 5/4)-3, 16/15)-9|((2/1, 5/4)[3], 16/15)[9]]]====
 
{| class="wikitable"
! Step signature
! Steps in JI
!Step sizes in cents
|-
|1L 2M 6s
|(9/8, 1125/1024, 16/15)
| (203.9100c, 162.8511c, 111.7313c)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
! Equivalence
! Step pattern
! Scale
! Comma list
|-
| L = M
| [[3L 6s|sLssLssLs]]
| [[Augmented (temperament)|Augmented]][9]
| 128/125
|-
| M = s
| [[1L 8s|ssssLssss]]
| [[Negri]][9]
| 16875/16384
|-
| L = s
| [[OTC 2L ns|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
| [[1L 6s|sssLsss]]
| [[Enipucrop]][7]
| 1125/1024
|}
=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-9|((2/1, 5/4)[3], 16/15: 225/224)[9] (Marvel)]]=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 6s|sLssLssLs]]
|[[August]][9]
|36/35, 128/125
|-
|M = s
|[[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
|49/48, 225/224
|-
|L = s
|[[OTC 2L ns|sLsssssLs]]
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
|-
|L - M = M - s
|sLssAssLs
|[[Orwell]][9] MODMOS
|225/224, 1728/1715
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[10edo|10]]
|[[12edo|12]]
|[[19edo|19]]
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
 
====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-9|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9] (Marvel)]]====
 
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 0)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[3L 6s|sLssLssLs]]
|[[August]][9]
|36/35, 45/44, 56/55
|-
|M = s
|[[1L 8s|ssssLssss]]
|[[Marvel temperaments#Negri|Negri]][9]
|45/44, 49/48, 56/55
|-
|L - M = M - s
|sLssAssLs
|[[Orwell]][9] MODMOS
|99/88, 121/120, 176/175
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[10edo|10]]
|12e
|[[19edo|19]]
|[[22edo|22]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
 
 
====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-12|((2/1, 5/4)[3], 16/15: 225/224)[12] (Marvel)]]====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| class="wikitable"
|+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 family#Septimal passion|Passion]][12]
| 64/63, 3125/3087
|-
|L - M = M - s
|LdLLLsLLLdLL
|[[Meantone]][12] MODMOS
|81/80, 126/125
|-
|s = 0
|LLLLsLLLLL
|[[Marvel temperaments#Negri|Negri]][10]
|49/48, 225/224
|-
|M = 0
|LsLLLLLLsLL
|[[Pelogic]][11] MODMOS
|21/20, 135/128
|}
{| class="wikitable"
|+Rank-1 temperings
!ET
|[[19edo|19]]
|[[22edo|22]]
|[[29edo|29]]
|[[31edo|31]]
|[[41edo|41]]
|[[50edo|50]]
|[[53edo|53]]
|[[72edo|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)
|}
=====[[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)]]=====
{| class="wikitable"
! 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)
|}
{| class="wikitable"
!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
|}
{| 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)
|}
 
===== [[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)]] =====
{| class="wikitable"
!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)
|}
{| class="wikitable"
!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
|}
{| 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)
|}
 
=== ((2/1, 3/2)[5], 16/15)===
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|2L 5m 3s
|(10/9, 16/15, 135/128)
| (182.4037c, 111.7313c, 92.1787c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
|  -5
|16/15 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0745
|-
|  -4
|135/128 9/8 1215/1024 81/64 45/32 3/2 405/256 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0592
|-
|  -3
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0411
|-
|  -2
|135/128 9/8 5/4 4/3 45/32 3/2 405/256 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0258
|-
|  -1
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0077
|-
|1
|135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0077
|-
|2
|16/15 32/27 512/405 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0258
|-
|3
|10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|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
|}
{| class="wikitable"
|+Rank-2 temperings (mode 1)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|m = s
|[[OTC 2L 8s|ssLsssLsss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|-
|L = m
|[[7L 3s|sLLLsLLLsL]]
|[[Dicot family|Dicot]][10] MODMOS
|25/24
|-
|L = s
|[[5L 5s|LsLsLsLsLs]]
|[[Limmic temperaments#5-limit .28blackwood.29|Blackwood]][10]
|256/243
|-
|L - m = m - s
|sLALsLALsL
|[[Marvel temperaments#Negri|Negri]][10] MODMOS
|16875/16384
|-
|s = 0
|[[2L 5s|sLssLss]]
|[[Mavila]][7]
|135/128
|-
|m = 0
|[[2L 3s|sLsLs]]
|[[Trienstonic clan#Father|Father]][5]
|16/15
|}
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
{| 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)
| (182.9137c, 116.0124c, 84.9028c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
|  -5
|~ 15/14 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0763
|-
|  -4
|~ 21/20 9/8 189/160 81/64 7/5 3/2 63/40 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0688
|-
|  -3
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0400
|-
|  -2
|~ 21/20 9/8 5/4 4/3 7/5 3/2 63/40 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|  -.0326
|-
|  -1
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|  -.0037
|-
|1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0037
|-
|2
|~ 15/14 32/27 80/63 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0326
|-
|3
|~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|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)
 
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]
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((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)
=====[[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
 
~ 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)
====[[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
 
~ 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)
====[[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
 
~ 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
====[[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
 
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]], [[Ptolemismic temperaments|No-7 Ptolemismic]], [[Supermagic]], and [[Ragismic family#Ragismic|Ragismic]]==
===(2/1, 3/2, 6/5)===
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|1L 2M 1s
|(5/4, 6/5, 10/9)
|(386.3137c, 315.6413c, 182.4037c)
|}
{| class="wikitable"
!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
|}
{| 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
|}
 
====[[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]]====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|1L 4M 2s
|(9/8, 10/9, 27/25)
|(203.9100c, 182.4037c, 133.2376c)
|}
{| class="wikitable"
!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
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0529
|-
|  -2
|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
|  -0.0316
|-
|  -1
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|  -0.0213
|-
|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
|10/9 100/81 4/3 40/27 5/3 50/27 2/1
|MMsMLMs
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|0.0213
|-
|2
|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
|0.0316
|-
|3
|10/9 5/4 25/18 3/2 5/3 50/27 2/1
|MLMsMMs
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|0.0529
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|L = M
|[[5L 2s|LsLLLsL]]
|[[Meantone family|Meantone]][7]
|81/80
|-
|M = s
|[[1L 6s|sssLsss]]
|[[Porcupine family#Porcupine|Porcupine]][7]
|250/243
|-
|L = s
|[[4L 3s|LsLsLsL]]
|[[Dicot family|Dicot]][7]
|25/24
|-
|L - M = M - s
|LsLALsL
|[[Tetracot]][7] MODMOS
|20000/19683
|-
|s = 0
|[[1L 4s|ssLss]]
|[[Bug family|Bug]][5]
|27/25
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
{| class="wikitable"
!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)
|}
{| 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
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
|sMMsMLM
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0616
|-
|  -2
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
|sMLMsMM
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|  -0.0314
|-
| -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)
|}
 
===== (2/1, 3/2, 6/5: 100/99, 144/143)[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, 27/25~12/11~13/12)
|(209.5416c, 175.8918c, 142.7754c)
|}
{| 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 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)
|}
 
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents
|-
|7L 1m 4s
|(27/25, 25/24, 250/243)
|(133.2376c, 70.6724c, 49.1661c)
|}
{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!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
|}
 
=====[[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
|}
 
{| 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


~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
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)


tempers to sLsLsLs Dicot[7], sLsssLs Pelogic[7], LLLsLLL Enipucrop[7]
===== (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)


==== [[SNS (2/1, 3/2, 5/4)-10|(2/1, 3/2, 5/4)[10]]] ====
~ 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
2L 7m 1s = (1125/1024, 16/15, 135/128)


16/15 75/64 5/4 4/3 45/32 3/2 8/5 128/75 15/8 as mLmmsmmLmm
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)


tempers to sLsssssLss Srutal[10] MODMOS, LsLLsLLsLL Dicot[10],  
===== (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)


=====[[SNS (2/1, 3/2, 5/4: 225/224)-10|(2/1, 3/2, 5/4: 225/224)[10]]]=====
~ 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
2L 7M 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20) = (151.8041c, 116.0124c, 84.9028c) TE
 
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


~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
L = M -> sLLLsLLLsL Dicot[10] MODMOS; M = s -> sLsLsLsLsL Blackwood[10]; L = s -> ssLsssLsss Supersharp[10] MODMOS;


tempers to sLsssssLss Pajara[10] MODMOS, LsLLsLLsLL Dicot[10]       
L - M = M - s -> dLsLdLsLdL Srutal[10] MODMOS


=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-10|(2/1, 3/2, 5/4: 225/224, 385/384)[10]]]=====
s = 0 -> LsLLsLL Meantone[7]; M = 0 -> sLLsLLsL Father[8]
2L 1M 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20) = (151.4797c, 116.1327c, 84.7519c) TE
====[[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


~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
~ 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


=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-10|(2/1, 3/2, 5/4: 225/224, 441/440)[10]]]=====
m = s -> sLsssLssLssLsssLs; L = m -> sLsLsLssLssLsLsLs; L = s -> sssLsssssssssLsss;
2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) = (150.229c, 116.7669c, 82.9601c) TE


~ 16/15 7/6 5/4 4/3 7/5 3/2 8/5 7/4 15/8 as mLmmsmmLmm
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


==== [[SNS (2/1, 3/2, 5/4: 225/224)-19|(2/1, 3/2, 5/4: 225/224)[19]]] ====
~ 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
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49) = (84.9028c, 66.9013c, 31.1096c) TE


~ 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 as LsLsLMLsLsLsLMLsLsL
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


tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
~ 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, 5/4: 225/224, 385/384)-19|(2/1, 3/2, 5/4: 225/224, 385/384)[19]]]=====
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54) = (84.7519c, 66.7278c, 31.3808c) TE
=====[[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


~ 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 as LsLsLMLsLsLsLMLsLsL
~ 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


tempers to LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
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


=====[[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-19|(2/1, 3/2, 5/4: 225/224, 441/440)[19]]]=====
~ 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
10L 2M 7s = (135/128~21/20~22/21, 25/24~28/27, 64/63~50/49~45/44~56/55) = (82.9601c, 67.2689c, 33.8068c) TE


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


tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negroni[19]
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


==== [[SNS (2/1, 3/2, 5/4: 225/224, 441/440)-31|(2/1, 3/2, 5/4: 225/224, 441/440)[31]]] ====
~ 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
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TE


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


as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm
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


tempers to sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS, LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS, sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS
~ 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


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


==== [[SNS ((2/1, 5/4)-3, 16/15)-6|((2/1, 5/4)[3], 16/15)[6]]] ====
~ 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
1L 2M 3s = (6/5, 75/64, 16/15)


75/64 5/4 3/2 8/5 15/8 2/1 as MsLsMs
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


tempers to LsLsLs Augmented[6], ssLsss Enipucrop[6], LsssLs Antitonic[6] MODMOS
~ 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


=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-6|((2/1, 5/4)[3], 16/15: 225/224)[6]]]=====
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
1L 2M 3s = (6/5, 75/64~7/6, 16/15~15/14) = (316.9276c, 267.8165c, 116.0124c) TE


~ 7/6 5/4 3/2 8/5 15/8 2/1 as MsLsMs
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


==== [[SNS ((2/1, 5/4)-3, 16/15)-9|((2/1, 5/4)[3], 16/15)[9]]] ====
~ 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
1L 2M 6s = (9/8, 1125/1024, 16/15)


16/15 75/64 5/4 4/3 3/2 8/5 128/75 15/8 2/1 as sMssLssMs
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;


tempers to sLssLssLs Augmented[9], ssssLssss Negri[9], sLsssssLs Mavila[9] MODMOS
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS


=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224)-9|((2/1, 5/4)[3], 16/15: 225/224)[9]]]=====
==2.3.25==
1L 2M 6s = (~9/8, 35/32~49/45, 16/15~15/14) = (200.9152c, 151.8041c, 116.0124c) TE
===(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
|}


~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
=====[[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
|}


tempers to sLssLssLs August[9], ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
==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)


=====[[SNS ((2/1, 5/4)-3, 16/15: 225/224, 385/384)-9|((2/1, 5/4)[3], 16/15: 225/224, 385/384)[9]]]=====
9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs
1L 2M 6s = (~9/8, 35/32~49/45~12/11, 16/15~15/14) = (200.8846c, 151.4797c, 116.1327c) TE


~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
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


tempers to sLssLssLs August[9] , ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs


==== [[SNS ((2/1, 5/4)-3, 16/15: 225/224)-12|((2/1, 5/4)[3], 16/15: 225/224)[12]]] ====
L = M -> LsLLLs; M = s -> sssLss; L = s -> LsLsLs
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48) = (116.0124c, 84.9028c, 35.7917c) TE
=====[[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


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


tempers to LsLLLLLLLsLL Pajara[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]
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)


=====[[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]]]=====
10/9 9/8 5/4 25/18 45/32 25/16 8/5 16/9 9/5 2/1 as LsLLsLmLsL,
9L 1M 2s = (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55) = (116.1327c, 84.7519c, 35.347c) TE


~ 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
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


tempers to LsLLLLLLLsLL Pajarous[12] MODMOS, LsLLLsLLLsLLs August[12], sssssLssssss Passion[12]
~ 10/9 9/8 5/4 25/18 7/5 14/9 8/5 16/9 9/5 2/1 as LsLmLsLLsL


==== [[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]]] ====
m = s -> LsLsLsLLsL MODMOS; L = m -> LsLLLsLLsL; L = s -> LLLsLLLLLL; s = 0 -> LLsLLLL; m = 0 -> LsLLsLLsL
9L 1m 12s = (~22/21, 36/35~33/32, 49/48~45/44~56/55) = (80.7857c, 49.4049c, 35.347c) TE
=====[[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


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


tempers to sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, sLssLsLsLsLsLsLsLssLsL Pajarous[22], MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]
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)


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


==== [[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]] ====
m = s -> sLsLssLsssLssLsLs MODMOS;  L = m -> LLLLLLLLsLLLLLLLL; L = s -> sLsLssLsLsLssLsLs; s = 0 -> sLsLssLssLssLsLs MODMOS; m = 0 -> LLLsLLL
2L 5m 3s = (10/9, 16/15, 135/128)
=====[[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


135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
~ 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


tempers to ssLsssLsss Srutal[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS, LsLsLsLsLs Blackwood[10]
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


=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10]]]=====
~ 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
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE


~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
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)


tempers to ssLsssLsss Pajara[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS
9/8 5/4 36/25 8/5 9/5 2/1 as msLsms


=====[[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]]]=====
m = s -> ssLsss; L = m -> LsLsLs; L = s -> sLLLsL
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE
=====[[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


~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
~ 9/8 5/4 10/7 8/5 9/5 2/1 as msLsms


tempers to ssLsssLsss Pajaric[10] MODMOS
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)


==== [[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]] ====
10/9 9/8 5/4 25/18 36/25 8/5 16/9 9/5 2/1 as LsLLmLLsL
10L 2M 5s = (135/128, 256/243, 2048/2025)


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
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


tempers to LsLLLsLLsLLsLLLsL Helmholtz[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
~ 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


=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17]]]=====
m = s -> sLssLsLsssLsLssL; L = m -> sLssLsLsLsLsLssL; L = s -> LLLLLLLLsLLLLLLL; s = 0 -> LLLsLLL; m = 0 -> sLssLsLssLsLssL
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
==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)


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


tempers to LsLLLsLLsLLsLLLsL Garibaldi[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
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)


=====[[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]]]=====
8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL
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 -> 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


tempers to LsLLLsLLsLLsLLLsL Andromeda[17]
~ 8/7 7/6 4/3 3/2 12/7 7/4 2/1 as LsLMLsL


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


~ 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
~ 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


tempers to  ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS, sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29], LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS
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


==== [[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]]] ====
~ 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
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 -> 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


tempers to LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS, LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31]
~ 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


==== [[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]]] ====
L = M -> sLssLsLsLssL Superpyth[12]; M = s -> sLssLsssLssL MODMOS
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE
====[[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


as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs
~ 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


tempers to LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS, LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS
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


== 2.3.5, Starling and Luyoyo ==
~ 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


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


==== [[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]] ====
~ 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
1L 2M 1s = (5/4, 6/5, 10/9)


6/5 3/2 9/5 2/1 as MLMs
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


tempers to LLLs Dicot[4], sLss Bug[4], LsLs Antitonic[4]
~ 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


==== [[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]] ====
m = s -> ssLssssLsssssssLssssLs Doublewide[22] MODMOS; L = m -> ssLssssLsssLsssLssssLs Superpyth[17]; s = 0 -> LLsLL Beep[5]
1L 4M 2S = (9/8, 10/9, 27/25)
=====[[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


10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
~ 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


tempers to LsLLLsL Meantone[7], sssLsss Porcupine[7], LsLsLsL Dicot[7]
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


===== [[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7]]] =====
~ 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
1L 4M 2S = (~9/8, ~10/9, 27/25~15/14) = (202.4685c, 187.562c, 123.5395c) TE


~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
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


tempers to LsLLLsL Meantone[7], sssLsss Opossum[7], LsLsLsL Flat[7]
~ 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


===== [[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7]]] =====
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; M = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
1L 4M 2S = (~9/8, 10/9~11/10, 27/25~12/11) = (209.7786c, 174.0549c, 146.6352c) TE


~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as msmLmsm
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


tempers to sssLsss Porcupine[7], LsLLLsL Meanenneadecal[7], LsLsLsL Flat[7]
~ 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


===== [[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-7|(2/1, 3/2, 6/5: 56/55, 100/99)[7]]] =====
L = M -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartz[27]; M = s -> ssLsssssLsssssssssLsssssLss Myno[27] MODMOS; L = s -> ssLsssssLssssLssssLsssssLss Suprapyth[27];
1L 4M 2S = (~9/8, 10/9~11/10, 27/25~15/14~12/11) = (215.4452c, 179.0856c, 132.5782c) TE


~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 as MsMLMsM
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


tempers to LsLLLsL Meanenneadecal[7], sssLsss Opossum[7], LsLsLsL Flat[7]
~ 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


==== [[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]] ====
m = s -> ssLsssssLsssssssssLsssssLss Myna[27] MODMOS; L = m -> LLLLLLLLLLLLLsLLLLLLLLLLLLL Quartonic[27]; L = s -> ssLsssssLssssLssssLsssssLss Superpyth[27];
7L 1m 4s = (27/25, 25/24, 250/243)


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
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


tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS, LLLLLsLLLLLL Ripple[12]
~ 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


===== [[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12]]] =====
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;
7L 1m 4s = (27/25~15/14, 25/24~21/20, 250/243~28/27) = (123.5395c, 78.929c, 64.0225c) TE


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


tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS
s = 0 -> LLLLLsLLLLLLsLLLLLsLLLLLLsLLLLL Myna[31] MODMOS; M = 0 -> LsLsLsLsLLsLsLsLsLsLLsLsLsLsLLsLsLsLsLsLLsLsLsLsL Superpyth[49];


===== [[SNS (2/1, 3/2, 6/5: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]] =====
L = 0 -> ssssLsssssLssssLsssssLssss Doublewide[22] MODMOS
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
=====[[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


~ 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
~ 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


tempers to sLLsLsLsLLsL Meantone[12], sLLsLLLsLLsL Diminished[12] MODMOS
L = M -> LsLsLsLsLLLsLsLsLsLsLLLsLsLsLsLLLsLsLsLsLsLLLsLsLsLsL Orwell[53] MODMOS;


===== [[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12]]] =====
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartz[53];
7L 1m 4s = (27/25~12/11, 25/24~33/32, 250/243~55/54) = (146.6352c, 63.1434c, 27.4197c) TE


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


tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] 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


===== [[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12]]] =====
~ 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
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


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


tempers to sLLsLsLsLLsL Meanenneadecal[12], sLLsLLLsLLsL Diminished[12] MODMOS
M = s -> sssssssssLsssssssssssLsssssssssLsssssssssssLsssssssss Kleiboh[53] MODMOS; L = s -> LsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsL Quartonic[53];


== 2.3.5, Hemifamity ==
s = 0 -> sssssLssssssLsssssLssssssLsssss Myna[31] MODMOS; M = 0 -> ssssLsssssLssssLsssssLssss Fleetwood[22] MODMOS;


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


==== [[SNS ((2/1, 3/2)-5, 10/9)-10|((2/1, 3/2)[5], 10/9)[10]]] ====
== 2.3.7 Sensamagic ==
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
=== (2/1, 3/2, 9/7) ===


tempers to sLLLsLLLsL Dicot[10] MOSMOS, sLsLsLsLsL Blackwood[10], ssLsssLsss Supersharp[10] MODMOS
==== (2/1, 3/2, 9/7)[4] ====
2L 1M 1s = (9/7, 7/6, 28/27) = (435.0841c, 266.8709c, 62.9609c)


==== [[((2/1, 3/2)-5, 10/9: 5120/5103)-17|((2/1, 3/2)[5], 10/9: 5120/5103)[17]]] ====
9/7 3/2 27/14 2/1 as LMLs
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
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)


tempers to sLsssLssLssLsssLs, sLsLsLssLssLsLsLs, sssLsssssssssLsss
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 as sLsmsLs


=====[[((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-17|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[17]]]=====
m = s -> sLsssLs; s = 0 -> LsL
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
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)


tempers to sLsssLssLssLsssLs, sLsLsLssLssLsLsLs, sssLsssssssssLsss
==== (2/1, 3/2, 9/7: 245/243)[10] Sensamagic ====
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35)


==== [[((2/1, 3/2)-5, 10/9: 5120/5103)-24|((2/1, 3/2)[5], 10/9: 5120/5103)[24]]] ====
~ 28/27 5/4 9/7 4/3 35/24 3/2 14/9 15/8 27/14 2/1 as sLssmssLss
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 -> sLsssssLss; s = 0 -> LsL


tempers to sLsssssLsssLsssLsssssLss Immunity[24] MODMOS, sLssLssLsssLsssLssLssLss, LLLLsLLLLLLLLLLLLLsLLLLL
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)-5, 10/9: 385/384, 2200/2187)-24|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[24]]] =====
===== (2/1, 3/2, 9/7: 245/243, 385/384)[10] Sensamagic =====
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE
2L 1m 7s = (~135/112, ~35/32, 28/27~36/35~33/32)


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


tempers to sLsssssLsssLsssLsssssLss Immunity[24] MODMOS, sLssLssLsssLsssLssLssLss, LLLLsLLLLLLLLLLLLLsLLLLL
m  = s -> sLsssssLss; s = 0 -> LsL


==== [[((2/1, 3/2)-5, 10/9: 5120/5103)-31|((2/1, 3/2)[5], 10/9: 5120/5103)[31]]] ====
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)
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
==== (2/1, 3/2, 9/7: 245/243)[13] Sensamagic ====
2L 1m 10s = (~75/64, ~135/128, 28/27~36/35)


tempers to ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS, ssLsssLsssLssssLssssLsssLsssLss, LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL
~ 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


===== [[((2/1, 3/2)-5, 10/9: 385/384, 2200/2187)-31|((2/1, 3/2)[5], 10/9: 385/384, 2200/2187)[31]]] =====
m = s -> ssLsssssssLss Pycnic[13] MODMOS; s = 0 -> LsL
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
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)


tempers to ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS, ssLsssLsssLssssLssssLsssLsssLss, LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL
===== (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)


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


==== [[((2/1, 3/2)-12, 64/63: 5120/5103)-24|((2/1, 3/2)[12], 64/63: 5120/5013)[24]]] ====
m = s -> ssLsssssssLss; s = 0 -> LsL
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
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)


tempers to sLsLsLsLsLsLsLsLsLsLsLsLsL, sLsssssLsssLsssLsssssLss Immunity[24] MODMOS, sssLsLsssLsssLsssLsLsssL
==== (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)


===== [[((2/1, 3/2)-12, 64/63: 441/440, 896/891)-24|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[24]]] =====
~ 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
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
m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss


tempers to sLsLsLsLsLsLsLsLsLsLsLsLsL, sLsssssLsssLsssLsssssLss Immunity[24] MODMOS, sssLsLsssLsssLsssLsLsssL
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)-12, 64/63: 5120/5013)-36|((2/1, 3/2)[12], 64/63: 5120/5013)[36]]] ====
==== (2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic ====
5L 7M 12s = (~25/24, ~49/48, 81/80~64/63) = (70.7894c, 36.848c, 24.4931c) TE
2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)


~ 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
~ 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


tempers to ssLssLssLssLssLssLssLssLssLssLssLssLssL, ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS, sssssLssLsssssLsssssLsssssLssLsssssL
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS


===== [[((2/1, 3/2)-12, 64/63: 441/440, 896/891)-36|((2/1, 3/2)[12], 64/63: 441/440, 896/891)[36]]] =====
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)
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
==== (2/1, 3/2, 9/7: 729/728)[7] ====
2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)


tempers to ssLssLssLssLssLssLssLssLssLssLssLssLssL, ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS, sssssLssLsssssLsssssLsssssLssLsssssL
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs


== 2.5.9, Marvel ==
m = s -> sLsssLs; s = 0 -> LsL


=== ((2/1, 5/4)[3], 9/8) ===
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, 5/4)-3, 9/8)-6|((2/1, 5/4)[3], 9/8)[6]]] ====
==== (2/1, 3/2, 9/7: 729/728)[10] ====
1L 3M 2s = (256/225, 9/8, 10/9)  
2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)


9/8 5/4 45/32 8/5 9/5 2/1 as MsMLMs
~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss


tempers to LsLLLs, sssLss, LsLsLs
m  = s -> sLsssssLss; s = 0 -> LsL


===== [[((2/1, 5/4)-3, 9/8: 225/224)-6|((2/1, 5/4)[3], 9/8: 225/224)[6]]] =====
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)
1L 3M 2s = (~8/7, 9/8~28/25, ~10/9) = (232.0248c, 200.9152c, 182.9137c)  


~ 9/8 5/4 7/5 8/5 9/5 2/1 as MLMsMs
==== (2/1, 3/2, 9/7: 729/728)[13] ====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26)


tempers to LsLLLs, sssLss, LsLsLs
~ 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


===== [[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]]] =====
m = s -> ssLsssssssLss; s = 0 -> LsL
1L 3M 2s = (~8/7, 9/8~28/25, 10/9~11/10) = (229.792c, 206.94c, 174.6095c)


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


tempers to LsLLLs, sssLss, LsLsLs
===== (2/1, 3/2, 9/7: 351/350, 676/675)[13] =====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)


==== [[SNS ((2/1, 5/4)-3, 9/8)-10|((2/1, 5/4)[3], 9/8)[10]]] ====
~ 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
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 -> ssLsssssssLss; s = 0 -> LsL


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
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)


===== [[SNS ((2/1, 5/4)-3, 9/8: 225/224)-10|((2/1, 5/4)[3], 9/8: 225/224)[10]]] =====
==== (2/1, 3/2, 9/7: 351/350, 676/675)[16] ====
6L 1M 3s = (~10/9, 128/125~36/35, 81/80~126/125) = (182.9137c, 49.1111c, 18.0015c) TE
2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)


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


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss


===== [[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]]] =====
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)
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
==== (2/1, 3/2, 9/7: 351/350, 676/675)[31] ====
2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)


tempers to LsLLsLsLsL, LsLLsLLLsL, LLLLLLsLLL
~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


===== [[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]]] =====
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS
6L 1M 3s = (~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
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)


tempers to sLsLssLsssLssLsLs Machine[17] MODMOS, LLLLLLLLsLLLLLLLL, sLsLssLsLsLssLsLs
== 2.3.11 Pentacircle ==


== 2.5.9, Starling ==
=== ((2/1, 3/2)[5], 12/11) ===


=== ((2/1, 5/4)[3], 10/9) ===
==== ((2/1, 3/2)[5], 12/11)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32)


==== ((2/1, 5/4)[3], 10/9)[6] ====
12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM
1L 2m 3s = (144/125, 9/8, 10/9)


9/8 5/4 36/25 8/5 9/5 2/1 as msLsms
==== ((2/1, 3/2)[5], 12/11: 896/891)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32~28/27)


tempers to ssLsss, LsLsLs, sLLLsL
~  12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM


===== ((2/1, 5/4)[3], 10/9: 126/125)[6] =====
==== ((2/1, 3/2)[5], 12/11: 896/891)[17] ====
1L 2m 3s = (~8/7, ~9/8, 10/9~28/25)  
5L 2M 10s = (128/121~81/77, 256/243~22/21, 33/32~28/27)


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


tempers to ssLsss, LsLsLs, sLLLsL
== 2.3.13 Squbema ==
==== ((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
=== ((2/1, 3/2)[5], 13/12) ===


tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL
==== ((2/1, 3/2)[5], 13/12)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26)


===== ((2/1, 5/4)[3], 10/9: 126/125)[9] =====
13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM
6L 1m 2s = (10/9~28/25, 648/625~36/35, 81/80~225/224)


~ 10/9 9/8 5/4 7/5 10/7 8/5 16/9 9/5 2/1 as LsLLmLLsL
==== ((2/1, 3/2)[5], 13/12: 729/728)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26~28/27)


tempers to LsLLsLLsL, LsLLLLLsL, LLLLsLLLL
~ 13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM


==== ((2/1, 5/4)[3], 10/9: 126/125, 896/891)[16] ====
===== ((2/1, 3/2)[5], 13/12: 729/728)[17] =====
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55)
5L 2M 10s = (91/81, 256/243~96/91, 27/26~28/27)


~ 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
~ 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


tempers to sLssLsLsssLsLssL, sLssLsLsLsLsLssL, LLLLLLLLsLLLLLLL
===== ((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, 5/4)[3], 10/9: 91/90, 126/125, 325/324)[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
6L 1m 9s = (~11/10, 128/125~64/63~99/98, 81/80~225/224~56/55~144/143)


~ 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


tempers to sLssLsLsssLsLssL, sLssLsLsLsLsLssL, LLLLLLLLsLLLLLLL


[[Category:Gallery]]
{{Navbox scale gallery}}
[[Category:Scales]]
[[Category:Step-nested scales]]
[[Category:Step-Nested Scales]]
[[Category:Rank-3 scales]]
[[Category:Lists of scales]]
[[Category:Rank 3]]
{{Todo| cleanup }}
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