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Gallery of 3-SN scales: Difference between revisions

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See [[SN scale]].
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).
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 in the mode symmetric without 2/1 (scales of even cardinality).
Tempered scales are shown in [[Just intonation|JI]] as their simplest symmetric pre-image.


== (2/1, 3/2, 5/4) ==
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)[4] ===
====[[SNS (2/1, 3/2, 5/4)-7|(2/1, 3/2, 5/4)[7]]]====
2L 1M 1s = (5/4, 6/5, 16/15)
{| 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
|}


5/4 3/2 15/8 2/1 as LMLs
=====[[SNS (2/1, 3/2, 5/4: 225/224)-7|(2/1, 3/2, 5/4: 225/224)[7]]] ([[Marvel]])=====
{| 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)
|}


tempers to LLLs Dicot[4], Antitonic[4] LsLs
====[[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)
|}


=== (2/1, 3/2, 5/4)[7] ===
=====[[SNS (2/1, 3/2, 5/4: 225/224, 385/384)-19|(2/1, 3/2, 5/4: 225/224, 385/384)[19]]] (Marvel)=====
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, 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)
|}


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)-19|(2/1, 3/2, 5/4: 225/224, 441/440)[19]]] ([[Prodigy]])=====
{| 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)
|}


tempers to sLsLsLs Dicot[7], sLsssLs Mavila[7], LLLsLLL Enipucrop[7]
====[[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)
|}


==== '''(2/1, 3/2, 5/4: 225/224)[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
2L 1M 4s = (75/64~7/6, ~9/8, 16/15~15/14)


~ 16/15 5/4 4/3 3/2 8/5 15/8 as sLsMsLs
as mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm
 
{| 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


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


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


16/15 75/64 5/4 4/3 10/7 3/2 8/5 128/75 15/8 as mLmmsmmLmm
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;


tempers to sLsssssLss Srutal[10] MODMOS, LsLLsLLsLL Dicot[10],
L - m = m - s -> Unidec[20] MODMOS


==== '''(2/1, 3/2, 5/4: 225/224)[10]''' ====
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
2L 7M 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20)


~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as mLmmsmmLmm
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)


tempers to sLsssssLss Pajara[10] MODMOS, LsLLsLLsLL Dicot[10]      
===== [[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


==== '''(2/1, 3/2, 5/4: 225/224, 385/384)[10]''' ====
~ 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
2L 1M 7s = (35/32~49/45~12/11, 16/15~15/14, 135/128~21/20)


~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as sLssMssLss
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;


==== '''(2/1, 3/2, 5/4: 225/224, 441/440)[10]''' ====
s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL
2L 7m 1s = (35/32~49/45, 16/15~15/14, 135/128~21/20~22/21) = (150.229c, 116.7669c, 82.9601c)


~ 16/15 7/6 5/4 4/3 10/7 3/2 8/5 7/4 15/8 as sLssMssLss
19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)


=== (2/1, 3/2, 5/4: 225/224)[19] ===
==== [[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-39|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)]] ====
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49)
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) 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
~ 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


tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs


==== '''(2/1, 3/2, 5/4: 225/224, 385/384)[19]''' ====
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)
10L 2M 7s = (135/128~21/20, 25/24~28/27, 64/63~50/49~55/54)


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


tempers to LsLsLLLsLsLsLLLsLsL Meanpop[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negri[19]
==== ((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>
|}


==== '''(2/1, 3/2, 5/4: 225/224, 441/440)[19]''' ====
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) TOP


~ 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
{| 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
|}


tempers to LsLsLLLsLsLsLLLsLsL Meantone[19] MODMOS, LsLsLsLsLsLsLsLsLsL Negroni[19]
{| 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, 3/2, 5/4: 225/224, 441/440)[31] ===
===== ((2/1, 6/5)[4], 10/9: 875/864)[8] Supermagic =====
10L+19m+2s = (~33/32, 64/63~50/49~45/44~56/55, 49/48~55/54) = (49.1533c, 33.8068c, 33.4621c) TOP
{| 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>
|}


~ 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
{| 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
|}


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


tempers to sLssLsssLssLssLsLssLssLsssLssLs Miracle[31] MODMOS, LLLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS, sLssLsLsLssLssLsLssLssLsLsLssLs Meantone[31] MODMOS
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 22-ET: (5, 2, 1) 24-ET: (6, 2, 1); 27-ET: (7, 3, 1); 41-ET: (9, 3, 2); 46-ET: (11, 4, 2); 63-ET: (15, 5, 3); 68-ET: (16, 6, 3); 87-ET: (20, 7,4)


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


75/64 5/4 3/2 8/5 15/8 2/1 as MsLsMs
m = s -> ssLsssssssssLsss Shrutar[16] MODMOS; s = 0 -> ssLssssssssLsss


tempers to LsLsLs Augmented[6], ssLsss Enipucrop[6], LsssLs Antitonic[6] MODMOS
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, 5/4)[3], 16/15: 225/224)[6]''' ====
==== (2/1, 3/2, 9/7: 245/243, 385/384)[31] Sensamagic ====
1L 2M 3s = (6/5, 75/64~7/6, 16/15~14/13)  
2L 16m 13s = (10/9~54/49, ~45/44, 176/175~121/120)


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


=== ((2/1, 5/4)[3], 16/15)[9] ===
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> sssssLssssssLsssss Shrutar[18] MODMOS
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
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)


tempers to sLssLssLs Augmented[9], ssssLssss Negri[9], sLsssssLs Mavila[9] MODMOS
==== (2/1, 3/2, 9/7: 729/728)[7] ====
2L 1m 4s = (~26/21, ~9/8, 28/27~27/26)


==== '''((2/1, 5/4)[3], 16/15: 225/224)[9]''' ====
~ 28/27 9/7 4/3 3/2 14/9 27/14 2/1 sLsmsLs
1L 2M 6s = (~9/8, 35/32~49/45, 16/15~15/14)


~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
m = s -> sLsssLs; s = 0 -> LsL


tempers to sLssLssLs August[9], ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
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], 16/15: 225/224, 385/384)[9]''' ====
==== (2/1, 3/2, 9/7: 729/728)[10] ====
1L 2M 6s = (~9/8, 35/32~49/45~12/11, 16/15~15/14)
2L 1m 7s = (~117/98, ~13/12, 28/27~27/26)


~ 16/15 7/6 5/4 4/3 3/2 8/5 12/7 15/8 2/1 as sMssLssMs
~ 28/27 26/21 9/7 4/3 13/9 3/2 14/9 13/7 27/14 2/1 sLssmssLss


tempers to sLssLssLs August[9] , ssssLssss Negri[9], sLsssssLs Pelogic[9] MODMOS
m  = s -> sLsssssLss; s = 0 -> LsL


=== ((2/1, 5/4)[3], 16/15: 225/224)[12] ===
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)
9L 1M 2s = (16/15~15/14, 135/128~21/20, ~49/48)


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


tempers to LsLLLsLLLsLLs August[12], LsLLLLLLLsLL Pajara[12] MODMOS, LLLLLsLLLLLL Passion[12]
~ 28/27 14/13 26/21 9/7 4/3 18/13 13/9 3/2 14/9 21/13 13/7 27/14 2/1 ssLsssmsssLss


==== '''((2/1, 5/4)[3], 16/15: 225/224, 385/384)[12]''' ====
m = s -> ssLsssssssLss; s = 0 -> LsL
9L 1M 2s = (16/15~15/14, 135/128~21/20, 49/48~45/44~56/55)


~ 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
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 LsLLLsLLLsLLs August[12], LsLLLLLLLsLL Pajarous[12] MODMOS, LLLLLsLLLLLL Passion[12]
===== (2/1, 3/2, 9/7: 351/350, 676/675)[13] =====
2L 1m 10s = (~169/147, ~117/112, 28/27~27/26~26/25)


=== ((2/1, 3/2)[5], 16/15: 225/224, 385/384)[22] ===
~ 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
9L 1M 12s = (~22/21, 36/35~33/32, 49/48~45/44~56/55)


~ 49/48 16/15 12/11 10/9 7/6 5/4 4/3 7/5 3/2 8/5 12/7 7/4 15/8 2/1 as sLssLsLsLsmsLsLsLssLsL
m = s -> ssLsssssssLss; s = 0 -> LsL


tempers to sLssLsLsLsLsLsLsLssLsL Pajarous[22] MODMOS, sLssLsLsLsssLsLsLssLsL Orwell[22] MODMOS, LLLLLLLLLLsLLLLLLLLLLL Escapade[22]
17-ET: (3, 1, 1); 19-ET: (4, 1, 1); 24-ET: (6, 2, 1); 53-ET: (10, 3, 3); 58-ET: (12, 4, 3); 77-ET: (16, 5, 4); 111-ET: (22, 7, 6); 130-ET: (26, 8, 7)


== ((2/1, 3/2)[5], 16/15) ==
==== (2/1, 3/2, 9/7: 351/350, 676/675)[16] ====
2L 13m 1s = (~845/756, 28/27~27/26~26/25, ~169/168)


=== ((2/1, 3/2)[5], 16/15)[10] ===
~ 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
2L 5m 3s = (10/9, 16/15, 135/128)


~ 135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
m = s -> ssLsssssssssLsss; s = 0 -> ssLssssssssLsss


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


==== '''((2/1, 3/2)[5], 16/15: 225/224)[10]''' ====
==== (2/1, 3/2, 9/7: 351/350, 676/675)[31] ====
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20)
2L 13m 16s = (~10/9, ~336/325, 169/168~225/224)


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


tempers to ssLsssLsss Pajara[10] MODMOS, sLLLsLLLsL Dicot[10] MODMOS
m = s -> sssssssssLsssssssssssLsssssssss; s = 0 -> ssssLsssssLssss Catakleismic[15] MODMOS


===='''((2/1, 3/2)[5], 16/15: 225/224, 441/440)[10]'''====
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)
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TOP


~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
== 2.3.11 Pentacircle ==


tempers to ssLsssLsss Pajaric[10] MODMOS
=== ((2/1, 3/2)[5], 12/11) ===


=== ((2/1, 3/2)[5], 16/15)[17] ===
==== ((2/1, 3/2)[5], 12/11)[10] ====
10L 2M 5s = (135/128, 256/243, 2048/2025)
5L 2M 3s = (12/11, 88/81, 33/32)


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


tempers to LsLLLsLLsLLsLLLsL Helmholtz[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
==== ((2/1, 3/2)[5], 12/11: 896/891)[10] ====
5L 2M 3s = (12/11, 88/81, 33/32~28/27)


==== '''((2/1, 3/2)[5], 16/15: 225/224)[17]''' ====
~  12/11 9/8 27/22 4/3 16/11 3/2 18/11 27/16 81/44 2/1 as LsLMLsLsLM
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63)


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


tempers to LsLLLsLLsLLsLLLsL Garibaldi[17], LsLsLsLLsLLsLsLsL Dicot[17] MODMOS
~ 28/27 12/11 9/8 32/27 11/9 9/7 4/3 11/8 16/11 3/2 14/9 18/11 27/16 16/9 11/6 27/14 2/1 as sLsMsLssLssLsMsLs


==== '''((2/1, 3/2)[5], 16/15: 225/224, 441/440)[17]''' ====
== 2.3.13 Squbema ==
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) TOP


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


tempers to LsLLLsLLsLLsLLLsL Andromeda[17]
==== ((2/1, 3/2)[5], 13/12)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26)


=== (2/1, 3/2)[5], 16/15: 225/224, 441/440)[29] ===
13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM
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) TOP


~ 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
==== ((2/1, 3/2)[5], 13/12: 729/728)[10] ====
5L 2M 3s = (13/12, 128/117, 27/26~28/27)


tempers to  ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS, sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29], LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS
~ 13/12 9/8 39/32 4/3 13/9 3/2 13/8 27/16 117/64 2/1 as LsLMLsLsLM


=== (2/1, 3/2)[5], 16/15: 225/224, 441/440)[41] ===
===== ((2/1, 3/2)[5], 13/12: 729/728)[17] =====
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) TOP
5L 2M 10s = (91/81, 256/243~96/91, 27/26~28/27)


~ 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
~ 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 LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS, LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31]
===== ((2/1, 3/2)[5], 12/11~13/12: 144/143, 729/728)[17] =====
5L 2M 10s = (91/81~81/77, 256/243~96/91~22/21, 27/26~28/27~33/32)


=== (2/1, 3/2)[5], 16/15: 225/224, 441/440)[72] ===
~ 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
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TOP


as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs


tempers to sLssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssL Marvolo[72] MODMOS, sLssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssL Miracle[72] MODMOS


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