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Gallery of 3-SN scales: Difference between revisions

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Line 1: Line 1:
See [[SN scale]] and [[Rank-3 scale]].
See [[SN scale]] and [[Rank-3 scale]].


Line 153: Line 151:
|L - M = M - s
|L - M = M - s
|sAsLsAs
|sAsLsAs
|Meantone[7] MODMOS
|[[Meantone]][7] MODMOS
|81/80
|81/80
|-
|-
Line 237: Line 235:
|L - M = M - s
|L - M = M - s
|sAsLsAs
|sAsLsAs
|Meantone[7] MODMOS
|[[Meantone]][7] MODMOS
|81/80, 126/125
|81/80, 126/125
|}
|}
Line 390: Line 388:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Srutal]][10] 4M (pentachordal decatonic)
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|2048/2025
Line 406: Line 404:
|L - m = m - s
|L - m = m - s
|sLssdssLss
|sLssdssLss
|Ampersand[10] MODMOS
|[[Ampersand]][10] MODMOS
|34171875/33554432
|34171875/33554432
|-
|-
Line 510: Line 508:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 544: Line 542:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajara]][10] 4M (pentachordal decatonic)
|[[Pajara]][10] 4M (pentachordal decatonic)
|50/49, 64/63
|50/49, 64/63
Line 560: Line 558:
|L - m = m - s
|L - m = m - s
|sLssdssLss
|sLssdssLss
|Miracle[10] MODMOS
|[[Miracle]][10] MODMOS
|225/224, 1029/1024
|225/224, 1029/1024
|-
|-
Line 678: Line 676:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 712: Line 710:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajarous]][10] 4M (pentachordal decatonic)
|[[Pajarous]][10] 4M (pentachordal decatonic)
|50/49, 55/54, 64/63
|50/49, 55/54, 64/63
Line 723: Line 721:
|L - m = m - s
|L - m = m - s
|sLssdssLss
|sLssdssLss
|Miracle[10] MODMOS
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|225/224, 243/242, 385/384
|}
|}
Line 834: Line 832:
|-
|-
|3
|3
|~ 16/15 8/7 5/4 4/3 10/7 32/16 5/3 16/9 40/21 2/1
|~ 16/15 8/7 5/4 4/3 10/7 32/21 5/3 16/9 40/21 2/1
|mmLmmmLmms
|mmLmmmLmms
|ssLsssLsss
|ssLsssLsss
Line 868: Line 866:
|-
|-
|m = s
|m = s
|sLsssssLss
|[[OTC 2L 8s|sLsssssLss]]
|[[Pajaric]][10] 4M (pentachordal decatonic)
|[[Pajaric]][10] 4M (pentachordal decatonic)
|45/44, 50/49, 56/55
|45/44, 50/49, 56/55
Line 879: Line 877:
|L - m = m - s
|L - m = m - s
|sLssdssLss
|sLssdssLss
|Miracle[10] MODMOS
|[[Miracle]][10] MODMOS
|225/224, 243/242, 385/384
|225/224, 243/242, 385/384
|}
|}
Line 952: Line 950:
|L - M = M - s
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|LdLdLsLdLdLdLsLdLdL
|Magic[19] MODMOS
|[[Magic]][19] MODMOS
|225/224, 245/243
|225/224, 245/243
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajara]][12] 4M (hexachordal dodecatonic)
|[[Pajara]][12] 4M (hexachordal dodecatonic)
|50/49, 64/63
|50/49, 64/63
Line 1,036: Line 1,034:
|L - M = M - s
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|LdLdLsLdLdLdLsLdLdL
|Magic[19] MODMOS
|[[Magic]][19] MODMOS
|100/99, 225/224, 245/243
|100/99, 225/224, 245/243
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajarous]][12] 4M (hexachordal dodecatonic)
|[[Pajarous]][12] 4M (hexachordal dodecatonic)
|50/49, 55/54, 64/63
|50/49, 55/54, 64/63
Line 1,113: Line 1,111:
|L - M = M - s
|L - M = M - s
|LdLdLsLdLdLdLsLdLdL
|LdLdLsLdLdLdLsLdLdL
|Witchcraft[19] MODMOS
|[[Witchcraft]][19] MODMOS
|225/224, 245/243, 441/440
|225/224, 245/243, 441/440
|-
|-
|s = 0
|s = 0
|LLLsLLLLsLLL
|[[OTC 10L 2s|LLLsLLLLsLLL]]
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|[[Pajaric]][12] 4M (hexachordal dodecatonic)
|45/44, 50/49, 56/55
|45/44, 50/49, 56/55
Line 1,203: Line 1,201:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|1L 2M 4s
|1L 2M 4s
Line 1,365: Line 1,363:
! Step signature
! Step signature
! Steps in JI
! Steps in JI
!Step sizes in cents (TE tuning)
!Step sizes in cents
|-
|-
|1L 2M 6s
|1L 2M 6s
Line 1,440: Line 1,438:
|-
|-
|L = s
|L = s
|sLsssssLs
|[[OTC 2L ns|sLsssssLs]]
|[[Mavila]][9] MODMOS
|[[Mavila]][9] MODMOS
| 135/128
| 135/128
Line 1,446: Line 1,444:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orson[9] MODMOS
|[[Orson]][9] MODMOS
|2109375/2097152
|2109375/2097152
|-
|-
Line 1,538: Line 1,536:
|-
|-
|L = s
|L = s
|sLsssssLs
|[[OTC 2L ns|sLsssssLs]]
|[[Pelogic]][9] MODMOS
|[[Pelogic]][9] MODMOS
| 21/20, 135/128
| 21/20, 135/128
Line 1,544: Line 1,542:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orwell[9] MODMOS
|[[Orwell]][9] MODMOS
|225/224, 1728/1715
|225/224, 1728/1715
|}
|}
Line 1,655: Line 1,653:
|L - M = M - s
|L - M = M - s
|sLssAssLs
|sLssAssLs
|Orwell[9] MODMOS
|[[Orwell]][9] MODMOS
|99/88, 121/120, 176/175
|99/88, 121/120, 176/175
|}
|}
Line 1,784: Line 1,782:
|L - M = M - s
|L - M = M - s
|LdLLLsLLLdLL
|LdLLLsLLLdLL
|Meantone[12] MODMOS
|[[Meantone]][12] MODMOS
|81/80, 126/125
|81/80, 126/125
|-
|-
Line 1,795: Line 1,793:
|LsLLLLLLsLL
|LsLLLLLLsLL
|[[Pelogic]][11] MODMOS
|[[Pelogic]][11] MODMOS
|21/20, 135/
|21/20, 135/128
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,919: Line 1,917:
|L - M = M - s
|L - M = M - s
|LdLLLsLLLdLL
|LdLLLsLLLdLL
|Meanpop[12] MODMOS
|[[Meanpop]][12] MODMOS
|81/80, 126/125, 385/384
|81/80, 126/125, 385/384
|-
|-
Line 1,947: Line 1,945:
|(7, 5, 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)]]
 
===== [[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"
{| class="wikitable"
!Step signature
!Step signature
Line 1,997: Line 1,996:
|L - m = m - s
|L - m = m - s
|sAssAsAsAsLsAsAsAssAsA
|sAssAsAsAsLsAsAsAssAsA
|Magic[22] MODMOS
|[[Magic]][22] MODMOS
|100/99, 225/224, 245/243
|100/99, 225/224, 245/243
|-
|-
Line 2,024: Line 2,023:
=== ((2/1, 3/2)[5], 16/15)===
=== ((2/1, 3/2)[5], 16/15)===
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
====[[SNS ((2/1, 3/2)-5, 16/15)-10|((2/1, 3/2)[5], 16/15)[10]]]====
2L 5m 3s = (10/9, 16/15, 135/128) = (182.4037c, 111.7313c, 92.1787c)
{| class="wikitable"
 
!Step signature
135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
!Steps in JI
 
!Step sizes in cents
m = s -> ssLsssLsss Srutal[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L = s -> LsLsLsLsLs Blackwood[10];
|-
 
|2L 5m 3s
L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Mavila[9]; m =0 -> sLsLs Father[5]
|(10/9, 16/15, 135/128)
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
| (182.4037c, 111.7313c, 92.1787c)
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20) = (182.9137c, 116.0124c, 84.9028c) TE
|}
 
{| class="wikitable"
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
!Mode number
 
!Mode in JI
m = s -> ssLsssLsss Pajara[10] 4M (Pentachordal decatonic); L = m -> sLLLsLLLsL Dicot[10] MODMOS; L - m = m - s -> sLALsLALsL Negri[10] MODMOS; s = 0 -> sLssLss Pelogic[9]
!Step pattern
=====[[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)]]=====
!Pentachordal  
2L 5m 3s = (10/9, 16/15~15/14, 135/128~21/20~22/21) = (184.0358c, 116.7669c, 82.9601c) TE
Decatonic
 
!Pent. Dec.
~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1 as smLmsmLmsm
Mode name
 
!Blackwood[10]
m = s -> ssLsssLsss Pajaric[10] 4M (Pentachordal decatonic); L - m = m - s -> sLALsLALsL Negroni[10] MODMOS
!UDP
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
![[Mode height]]
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)
|-
 
|  -5
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
|16/15 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
 
|msmsmLmsmL
L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
|sssssLsssL
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
|Dark minor
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
|sLsLsLsLsL
 
|<nowiki>0|1 (5)</nowiki>
~ 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
|  -.0745
 
|-
L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
|  -4
 
|135/128 9/8 1215/1024 81/64 45/32 3/2 405/256 27/16 15/8 2/1
s = 0 -> LLsLLLLLLsLL Pajara[12] 4M (Hexachordal Dodecatonic)
|smsmLmsmLm
=====[[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)]]=====
|ssssLsssLs
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
|Alternate minor
 
|LsLsLsLsLs
~ 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
|<nowiki>1|0 (5)</nowiki>
 
|  -.0592
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)]]====
| -3
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
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 27/16 9/5 2/1
 
|msmLmsmsmL
~ 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
|sssLsssssL
 
|Standard minor
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];
|sLsLsLsLsL
 
|<nowiki>0|1 (5)</nowiki>
L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;
|  -.0411
 
|-
s = 0 -> LLLsLLLLsLLL Pajaric[12] 4M (Hexachordal Dodecatonic)
| -2
====[[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)]]====
|135/128 9/8 5/4 4/3 45/32 3/2 405/256 27/16 15/8 2/1
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
|smLmsmsmLm
 
|ssLsssssLs
~ 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
|Dark major
 
|LsLsLsLsLs
L = M -> LsLLLsLLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Miracle[31] MODMOS; M = s -> LsLLLsLLsLLsLLLsLLsLLLsLLsLLLsLLsLLsLLLsL Andromeda[31];
|<nowiki>1|0 (5)</nowiki>
 
|  -.0258
L - M = M - s -> Witchcraft[41] MODMOS
|-
 
|  -1
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS; m = 0 -> LsLLLsLLLLsLLLsLLsLLLsLLsLLLsLLLLLsLLLsL Negroni[39] MODMOS
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 16/9 256/135 2/1
====[[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)]]====
|msmLmsmLms
29L 2M 41s = (1344/1331~1350/1331, 100/99~245/242~896/891, ~121/120) = (18.4603c, 18.1156c, 15.3465c) TE
|sssLsssLss
 
|Bright minor
as LssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssLs
|sLsLsLsLsL
 
|<nowiki>0|1 (5)</nowiki>
L = M -> LssLsLsLssLsLsLsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsLsLsLssLsLsLssLs Marvolo[72] MODMOS;
|  -.0077
 
|-
M = s -> LssLsLsLssLsLsssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Miracle[72] MODMOS;
|1
 
|135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
L - M = M - s -> Compton MODMOS
|smLmsmLmsm
 
|ssLsssLsss
s = 0 -> LLLLLLsLLLLLLLLLLLLLLLLLsLLLLLL Tritonic[31] MODMOS;
|Standard major
 
|LsLsLsLsLs
m = 0 -> LssLsLsLssLsLssLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsssLsLssLsLsLssLs Andromeda[70] MODMOS
|<nowiki>1|0 (5)</nowiki>
==2.3.5; [[Starling]], [[Ptolemismic temperaments|No-7 Ptolemismic]], and [[Ragismic family#Ragismic|Ragismic]]==
|.0077
===(2/1, 3/2, 6/5)===
|-
====[[SNS (2/1, 3/2, 6/5)-4|(2/1, 3/2, 6/5)[4]]]====
|2
{| class="wikitable"
|16/15 32/27 512/405 4/3 64/45 3/2 8/5 16/9 256/135 2/1
!Step signature
|mLmsmsmLms
!Steps in JI
|sLsssssLss
!Step sizes in cents
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0258
|-
|-
|1L 2M 1s
|3
|(5/4, 6/5, 10/9)
|10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|(386.3137c, 315.6413c, 182.4037c)
|LmsmsmLmsm
|}
|LsssssLsss
{| class="wikitable"
|Bright major
!Mode number
|LsLsLsLsLs
!Mode in JI
|<nowiki>1|0 (5)</nowiki>
!Step pattern
|.0411
![[Mode height]]
|-
|-
| -2
|4
|10/9 4/3 5/3 2/1
|16/15 32/27 512/405 4/3 64/45 128/81 2048/1215 16/9 256/135 2/1
|sMLM
|mLmsmLmsms
| -0.1307
|sLsssLssss
|Dark Augmented
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0592
|-
|-
| -1
|5
|6/5 4/3 8/5 2/1
|10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1
|MsML
|LmsmLmsmsm
|  -0.0959
|LsssLsssss
|-
|Bright Augmented
|1
|LsLsLsLsLs
|5/4 3/2 5/3 2/1
|<nowiki>1|0 (5)</nowiki>
|LMsM
|.0745
|0.0959
|-
|2
|6/5 3/2 9/5 2/1
|MLMs
|0.1307
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
|+Rank-2 temperings (mode 1)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 2,142: Line 2,141:
!Comma list
!Comma list
|-
|-
|L = M
|m = s
|[[3L 1s|LLLs]]
|[[OTC 2L 8s|ssLsssLsss]]
|[[Dicot]][4]
|[[Srutal]][10] 4M (pentachordal decatonic)
|2048/2025
|-
|L = m
|[[7L 3s|sLLLsLLLsL]]
|[[Dicot family|Dicot]][10] MODMOS
|25/24
|25/24
|-
|-
|M = s
|L = s
|[[1L 3s|sLss]]
|[[5L 5s|LsLsLsLsLs]]
|[[Bug family|Bug]][4]
|[[Limmic temperaments#5-limit .28blackwood.29|Blackwood]][10]
|27/25
|256/243
|-
|L - m = m - s
|sLALsLALsL
|[[Marvel temperaments#Negri|Negri]][10] MODMOS
|16875/16384
|-
|s = 0
|[[2L 5s|sLssLss]]
|[[Mavila]][7]
|135/128
|-
|-
|L = s
|m = 0
|[[2L 2s|LsLs]]
|[[2L 3s|sLsLs]]
|Antitonic[4]
|[[Trienstonic clan#Father|Father]][5]
|9/8
|16/15
|}
|}
 
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-10|((2/1, 3/2)[5], 16/15: 225/224)[10] (Marvel)]]=====
====[[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]]====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents
!Step sizes in cents (TE tuning)
|-
|-
|1L 4M 2s
|2L 5m 3s
|(9/8, 10/9, 27/25)
|(10/9, 16/15~15/14, 135/128~21/20)
|(203.9100c, 182.4037c, 133.2376c)
| (182.9137c, 116.0124c, 84.9028c)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode in JI
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[7]
!Pentachordal
!UDP
Decatonic
!Diatonic mode
!Pent. Dec.
!Porcupine[7]
Mode name
!Blackwood[10]
!UDP
!UDP
!Porcupine mode
![[Mode height]]
![[Mode height]]
|-
|-
| -3
| -5
|27/25 6/5 4/3 36/25 8/5 9/5 2/1
|~ 15/14 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|sMMsMLM
|msmsmLmsmL
|sLLsLLL
|sssssLsssL
|<nowiki>0|6</nowiki>
|Dark minor
|Lochrian
|sLsLsLsLsL
|sssssLs
|<nowiki>0|1 (5)</nowiki>
|<nowiki>1|5</nowiki>
| -.0763
|Dark diminished
|-
| -0.0529
| -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
|  -2
|10/9 6/5 4/3 40/27 8/5 16/9 2/1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 63/40 27/16 15/8 2/1
|MsMMsML
|smLmsmsmLm
|LsLLsLL
|ssLsssssLs
|<nowiki>2|4</nowiki>
|Dark major
|Aeolian
|LsLsLsLsLs
|ssssssL
|<nowiki>1|0 (5)</nowiki>
|<nowiki>0|6</nowiki>
|  -.0326
|Magical seventh
|  -0.0316
|-
|-
|  -1
|  -1
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
|~ 15/14 9/8 6/5 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|sMLMsMM
|msmLmsmLms
|sLLLsLL
|sssLsssLss
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|Bright minor
| -0.0213
|sLsLsLsLsL
|-
|<nowiki>0|1 (5)</nowiki>
|0
| -.0037
|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
|1
|10/9 100/81 4/3 40/27 5/3 50/27 2/1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|MMsMLMs
|smLmsmLmsm
|LLsLLLs
|ssLsssLsss
|<nowiki>5|1</nowiki>
|Standard major
|Ionian
|LsLsLsLsLs
|ssssLss
|<nowiki>1|0 (5)</nowiki>
|<nowiki>2|4</nowiki>
|.0037
|Bright diminished
|0.0213
|-
|-
|2
|2
|9/8 5/4 27/20 3/2 5/3 9/5 2/1
|~ 15/14 32/27 80/63 4/3 10/7 3/2 8/5 16/9 40/21 2/1
|LMsMMsM
|mLmsmsmLms
|LLsLLsL
|sLsssssLss
|<nowiki>4|2</nowiki>
|Alternate major
|Mixolydian
|sLsLsLsLsL
|Lssssss
|<nowiki>0|1 (5)</nowiki>
|<nowiki>6|0</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
|Bright major
|0.0316
|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
|-
|-
|3
|5
|10/9 5/4 25/18 3/2 5/3 50/27 2/1
|~ 10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1
|MLMsMMs
|LmsmLmsmsm
|LLLsLLs
|LsssLsssss
|<nowiki>6|0</nowiki>
|Bright Augmented
|Lydian
|LsLsLsLsLs
|sLsssss
|<nowiki>1|0 (5)</nowiki>
|<nowiki>5|1</nowiki>
|.0763
|Dark major
|0.0529
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
|+Rank-2 temperings (mode 1)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 2,264: Line 2,290:
!Comma list
!Comma list
|-
|-
|L = M
|m = s
|[[5L 2s|LsLLLsL]]
|[[OTC 2L 8s|ssLsssLsss]]
|[[Meantone family|Meantone]][7]
|[[Diaschismic family#Pajara|Pajara]][10] 4M (pentachordal decatonic)
|81/80
|50/49, 64/63
|-
|-
|M = s
|L = m
|[[1L 6s|sssLsss]]
|[[OTC 7L 3s|sLLLsLLLsL]]
|[[Porcupine family#Porcupine|Porcupine]][7]
|[[Dicot family|Sharp]][10] MODMOS
|250/243
|25/24, 28/27
|-
|-
|L = s
|L - m = m - s
|[[4L 3s|LsLsLsL]]
|sLALsLALsL
|[[Dicot family|Dicot]][7]
|[[Marvel temperaments#Negri|Negri]][10] MODMOS
|25/24
|49/48, 225/224
|-
|L - M = M - s
|LsLALsL
|Tetracot[7] MODMOS
|20000/19683
|-
|-
|s = 0
|s = 0
|[[1L 4s|ssLss]]
|[[2L 5s|sLssLss]]
|[[Bug family|Bug]][5]
|[[Pelogic family#Pelogic|Pelogic]][7]
|27/25
|21/20, 135/128
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 126/125)-7|(2/1, 3/2, 6/5: 126/125)[7] (Starling)]]=====
=====[[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"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents (TE)
!Step sizes in cents (TE tuning)
|-
|-
|1L 4M 2s
|2L 5m 3s
|(~9/8, ~10/9, 27/25~15/14)
|(10/9, 16/15~15/14, 135/128~21/20~22/21)
|(202.4685c, 187.562c, 123.5395c)
| (184.0358c, 116.7669c, 82.9601c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 2,303: Line 2,324:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[7]
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!Porcupine mode
![[Mode height]]
![[Mode height]]
|-
|-
| -3
| -5
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
|~ 15/14 9/8 6/5 44/35 27/20 3/2 8/5 27/16 9/5 2/1
|sMMsMLM
|msmsmLmsmL
|sLLsLLL
|sssssLsssL
|<nowiki>0|6</nowiki>
|Dark minor
|Lochrian
|sLsLsLsLsL
|sssssLs
|<nowiki>0|1 (5)</nowiki>
|<nowiki>1|5</nowiki>
| -.0779
|Dark diminished
|-
| -0.0616
|  -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
|  -2
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
|~ 21/20 9/8 5/4 4/3 7/5 3/2 11/7 27/16 15/8 2/1
|sMLMsMM
|smLmsmsmLm
|sLLLsLL
|ssLsssssLs
|<nowiki>1|5</nowiki>
|Dark major
|Phrygian
|LsLsLsLsLs
|ssLssss
|<nowiki>1|0 (5)</nowiki>
|<nowiki>4|2</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
|Bright minor
| -0.0314
|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
|-
|-
| -1
|2
|~ 10/9 6/5 4/3 40/27 8/5 16/9 2/1
|~ 15/14 32/27 15/11 4/3 10/7 3/2 8/5 16/9 21/11 2/1
|MsMMsML
|mLmsmsmLms
|LsLLsLL
|sLsssssLss
|<nowiki>2|4</nowiki>
|Alternate major
|Aeolian
|sLsLsLsLsL
|ssssssL
|<nowiki>0|1 (5)</nowiki>
|<nowiki>0|6</nowiki>
|.0343
|Magical seventh
| -0.0302
|-
|-
|0
|3
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|~ 10/9 32/27 5/4 4/3 7/5 3/2 5/3 16/9 15/8 2/1
|MsMLMsM
|LmsmsmLmsm
|LsLLLsL
|LsssssLsss
|<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
|Bright major
|0.0302
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0405
|-
|-
|2
|4
|~ 10/9 56/45 4/3 40/27 5/3 28/15 2/1
|~ 15/14 32/27 14/11 4/3 10/7 35/22 56/33 16/9 40/21 2/1
|MMsMLMs
|mLmsmLmsms
|LLsLLLs
|sLsssLssss
|<nowiki>5|1</nowiki>
|Dark Augmented
|Ionian
|sLsLsLsLsL
|ssssLss
|<nowiki>0|1 (5)</nowiki>
|<nowiki>2|4</nowiki>
|.0718
|Bright diminished
|0.0314
|-
|-
|3
|5
|~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1
|~ 10/9 32/27 5/4 4/3 40/27 35/22 5/3 16/9 15/8 2/1
|MLMsMMs
|LmsmLmsmsm
|LLLsLLs
|LsssLsssss
|<nowiki>6|0</nowiki>
|Bright Augmented
|Lydian
|LsLsLsLsLs
|sLsssss
|<nowiki>1|0 (5)</nowiki>
|<nowiki>5|1</nowiki>
|.0779
|Dark major
|0.0616
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 0)
|+Rank-2 temperings (mode 1)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 2,395: Line 2,429:
!Comma list
!Comma list
|-
|-
|L = M
|m = s
|[[5L 2s|LsLLLsL]]
|[[OTC 2L 8s|ssLsssLsss]]
|[[Meantone family#Septimal meantone|Meantone]][7]
|[[Diaschismic family#Pajaric|Pajaric]][10] 4M (pentachordal decatonic)
|81/80, 126/125
|45/44, 50/49, 56/55
|-
|-
|M = s
|L - m = m - s
|[[1L 6s|sssLsss]]
|sLALsLALsL
|[[Trienstonic clan#Opossum|Opossum]][7]
|[[Marvel temperaments#Negroni|Negroni]][10] MODMOS
|28/27, 126/125
|49/48, 55/54, 225/224
|-
|L = s
|[[4L 3s|LsLsLsL]]
|[[Dicot family#Flat|Flat]][7]
|21/20, 25/24
|}
|}
{| class="wikitable"
====[[SNS ((2/1, 3/2)-5, 16/15)-17|((2/1, 3/2)[5], 16/15)[17]]]====
|+Rank-1 temperings
10L 2M 5s = (135/128, 256/243, 2048/2025) = (92.1787c, 90.2250c, 19.5526c)
!ET
 
|8d
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
|[[12edo|12]]
 
|[[15edo|15]]
L = M -> LsLLLsLLsLLsLLLsL Helmholtz[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS; s = 0 -> LLsLLLLLLsLL Srutal[12] 4M (Hexachordal Dodecatonic); M = 0 -> LsLLsLLsLLsLLsL Blackwood[15]
|[[16edo|16]]
=====[[SNS ((2/1, 3/2)-5, 16/15: 225/224)-17|((2/1, 3/2)[5], 16/15: 225/224)[17] (Marvel)]]=====
|[[19edo|19]]
2L 10M 5s = (256/243, 135/128~21/20, 2048/2025~50/49~64/63) = (98.0109c, 84.9028c, 31.1096)  TE
|[[27edo|27]]
 
|[[31edo|31]]
~ 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
|[[46edo|46]]
 
|[[50edo|50]]
L = M -> LsLLLsLLsLLsLLLsL Garibaldi[17]; M = s -> LsLsLsLLsLLsLsLsL Dicot[17] MODMOS;
|[[58edo|58]]
 
|[[77edo|77]]
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)]]=====
!Step sizes in ET
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
|(2, 1, 1)
 
|(2, 2, 1)
~ 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
|(3, 2, 2)
 
|(2, 3, 1)
L = M -> LsLLLsLLsLLsLLLsL Andromeda[17]; s = 0 -> s = 0 -> LLsLLLLLLsLL Pajaric[12] 4M (Hexachordal Dodecatonic)
|(3, 3, 2)
====[[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)]]====
|(5, 4, 3)
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
|(5, 5, 3)
 
|(8, 7, 5)
~ 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
|(8, 8, 5)
 
|(10, 9, 6)
m = s -> ssssssssLsssssssssssLssssssss Tritonic[29] MODMOS; L = m -> sLsLssLsLsLssLsLssLsLsLssLsLs Andromeda[29];
|(13, 12, 8)
 
|}
L = s -> LsLsLLsLLLsLLsLsLLsLLLsLLsLsL Negroni[29] MODMOS; L - m = m - s -> Marvolo[29] MODMOS;
=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====
 
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]], 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"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents (TE)
!Step sizes in cents
|-
|-
|1L 4m 2s
|1L 2M 1s
|(9/8~25/22, 10/9~11/10, 27/25~12/11)
|(5/4, 6/5, 10/9)
|(209.7786c, 174.0549c, 146.6352c)
|(386.3137c, 315.6413c, 182.4037c)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode as simplest JI pre-image
!Mode in JI
!Step pattern
!Step pattern
!Meantone[7]
![[Mode height]]
!UDP
|-
!Diatonic mode
|  -2
!Porcupine[7]
|10/9 4/3 5/3 2/1
!UDP
|sMLM
!Porcupine mode
|  -0.1307
![[Mode height]]
|-
|-
| -3
| -1
|~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
|6/5 4/3 8/5 2/1
|smmsmLm
|MsML
|sLLsLLL
| -0.0959
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0427
|-
|-
| -2
|1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|5/4 3/2 5/3 2/1
|msmmsmL
|LMsM
|LsLLsLL
|0.0959
|<nowiki>2|4</nowiki>
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
| -0.0374
|-
|-
| -1
|2
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|6/5 3/2 9/5 2/1
|smLmsmm
|MLMs
|sLLLsLL
|0.1307
|<nowiki>1|5</nowiki>
|}
|Phrygian
{| class="wikitable"
|ssLssss
|+Rank-2 temperings (mode 2)
|<nowiki>4|2</nowiki>
!Equivalence
|Bright minor
!Step pattern
|  -0.0053
!Scale
!Comma list
|-
|-
|0
|L = M
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|[[3L 1s|LLLs]]
|msmLmsm
|[[Dicot]][4]
|LsLLLsL
|25/24
|<nowiki>3|3</nowiki>
|Dorian
|sssLsss
|<nowiki>3|3</nowiki>
|Dark minor
|0
|-
|-
|1
|M = s
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|[[1L 3s|sLss]]
|mmsmLms
|[[Bug family|Bug]][4]
|LLsLLLs
|27/25
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|0.0053
|-
|-
|2
|L = s
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|[[2L 2s|LsLs]]
|Lmsmmsm
|Antitonic[4]
|LLsLLsL
|9/8
|<nowiki>4|2</nowiki>
|}
|Mixolydian
 
|Lssssss
====[[SNS (2/1, 3/2, 6/5)-7|(2/1, 3/2, 6/5)[7]]]====
|<nowiki>6|0</nowiki>
{| class="wikitable"
|Bright major
!Step signature
|0.0374
!Steps in JI
!Step sizes in cents
|-
|-
|3
|1L 4M 2s
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|(9/8, 10/9, 27/25)
|mLmsmms
|(203.9100c, 182.4037c, 133.2376c)
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|0.0427
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Mode number
!Equivalence
!Mode in JI
!Step pattern
!Step pattern
!Scale
!Meantone[7]
!Comma list
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!Porcupine mode
![[Mode height]]
|-
|-
|m = s
| -3
|[[1L 6s|sssLsss]]
|27/25 6/5 4/3 36/25 8/5 9/5 2/1
|[[Porcupine family#Porkypine|Porkypine]][7]
|sMMsMLM
|55/54, 100/99
|sLLsLLL
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0529
|-
|-
|L = m
| -2
|[[5L 2s|LsLLLsL]]
|10/9 6/5 4/3 40/27 8/5 16/9 2/1
|[[Meanenneadecal]][7] or [[Meantone family#Flattone|Flattone]][7]
|MsMMsML
|45/44, 81/80
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|  -0.0316
|-
|-
|L = s
| -1
|[[4L 3s|LsLsLsL]]
|27/25 6/5 27/20 3/2 81/50 9/5 2/1
|[[Dicot family|Flat]][7]
|sMLMsMM
|25/24, 33/32
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|  -0.0213
|-
|-
|L - m = m - s
|0
|LsLALsL
|10/9 6/5 4/3 3/2 5/3 9/5 2/1
|Tetracot[7] MODMOS
|MsMLMsM
|100/99, 243/242
|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"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-2 temperings (mode 2)
!ET
!Equivalence
|8
!Step pattern
|[[12edo|12]]
!Scale
|[[15edo|15]]
!Comma list
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|27e
|[[29edo|29]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|-
|-
!Step sizes in ET
|L = M
|(2, 1, 1)
|[[5L 2s|LsLLLsL]]
|(2, 2, 1)
|[[Meantone family|Meantone]][7]
|(3, 2, 2)
|81/80
|(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
|M = s
|(9/8~25/22, 10/9~11/10, 27/25~15/14~12/11)
|[[1L 6s|sssLsss]]
|(215.4452c, 179.0856c, 132.5782c)
|[[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"
{| class="wikitable"
Line 2,608: Line 2,701:
!Meantone[7]
!Meantone[7]
!UDP
!UDP
!Diatonic mode
!Porcupine[7]
!Porcupine[7]
!UDP
!UDP
!Porcupine mode
!Porcupine mode
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
| -3
| -3
|~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1
|~ 15/14 6/5 4/3 10/7 8/5 9/5 2/1
|sMMsMLM
|sMMsMLM
|sLLsLLL
|sLLsLLL
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|Lochrian
|sssssLs
|sssssLs
|<nowiki>1|5</nowiki>
|<nowiki>1|5</nowiki>
|Dark diminished
|Dark diminished
|Lochrian
| -0.0616
| -0.0591
|-
|-
|  -2
|  -2
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|~ 15/14 6/5 27/20 3/2 45/28 9/5 2/1
|MsMMsML
|sMLMsMM
|LsLLsLL
|sLLLsLL
|<nowiki>2|4</nowiki>
|<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
|ssssssL
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|Magical seventh
|Magical seventh
|Aeolian
| -0.0302
|  -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
|0
Line 2,652: Line 2,745:
|LsLLLsL
|LsLLLsL
|<nowiki>3|3</nowiki>
|<nowiki>3|3</nowiki>
|Dorian
|sssLsss
|sssLsss
|<nowiki>3|3</nowiki>
|<nowiki>3|3</nowiki>
|Dark minor
|Dark minor
|Dorian
|0
|0
|-
|-
|1
|1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|~ 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
|MMsMLMs
|LLsLLLs
|LLsLLLs
|<nowiki>5|1</nowiki>
|<nowiki>5|1</nowiki>
|Ionian
|ssssLss
|ssssLss
|<nowiki>2|4</nowiki>
|<nowiki>2|4</nowiki>
|Bright diminished
|Bright diminished
|Ionian
|0.0314
|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
|3
|~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1
|~ 10/9 5/4 7/5 3/2 5/3 28/15 2/1
|MLMsMMs
|MLMsMMs
|LLLsLLs
|LLLsLLs
|<nowiki>6|0</nowiki>
|<nowiki>6|0</nowiki>
|Lydian
|sLsssss
|sLsssss
|<nowiki>5|1</nowiki>
|<nowiki>5|1</nowiki>
|Dark major
|Dark major
|Lydian
|0.0616
|0.0591
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode 2)
|+Rank-2 temperings (mode 0)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 2,700: Line 2,793:
|L = M
|L = M
|[[5L 2s|LsLLLsL]]
|[[5L 2s|LsLLLsL]]
|[[Meanenneadecal]][7]
|[[Meantone family#Septimal meantone|Meantone]][7]
|45/44, 56/55, 81/80
|81/80, 126/125
|-
|-
|M = s
|M = s
|[[1L 6s|sssLsss]]
|[[1L 6s|sssLsss]]
|[[Trienstonic clan#Opossum|Opossum]][7]
|[[Trienstonic clan#Opossum|Opossum]][7]
|28/27, 55/54, 77/75
|28/27, 126/125
|-
|-
|L = s
|L = s
|[[4L 3s|LsLsLsL]]
|[[4L 3s|LsLsLsL]]
|[[Dicot family#Flat|Flat]][7]
|[[Dicot family#Flat|Flat]][7]
|21/20, 25/24, 33/32
|21/20, 25/24
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 2,719: Line 2,812:
|[[12edo|12]]
|[[12edo|12]]
|[[15edo|15]]
|[[15edo|15]]
|[[16edo|16]]
|[[19edo|19]]
|[[19edo|19]]
|27e
|[[27edo|27]]
|[[34edo|34]]
|[[31edo|31]]
|[[46edo|46]]
|[[50edo|50]]
|[[58edo|58]]
|[[77edo|77]]
|-
|-
!Step sizes in ET
!Step sizes in ET
Line 2,727: Line 2,825:
|(2, 2, 1)
|(2, 2, 1)
|(3, 2, 2)
|(3, 2, 2)
|(2, 3, 1)
|(3, 3, 2)
|(3, 3, 2)
|(5, 4, 3)
|(5, 4, 3)
|(6, 5, 4)
|(5, 5, 3)
|(8, 7, 5)
|(8, 8, 5)
|(10, 9, 6)
|(13, 12, 8)
|}
|}
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
=====[[SNS (2/1, 3/2, 6/5: 100/99)-7|(2/1, 3/2, 6/5: 100/99)[7] (No-7 Ptolemismic)]]=====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents
!Step sizes in cents (TE)
|-
|-
|7L 1m 4s
|1L 4m 2s
|(27/25, 25/24, 250/243)
|(9/8~25/22, 10/9~11/10, 27/25~12/11)
|(133.2376c, 70.6724c, 49.1661c)
|(209.7786c, 174.0549c, 146.6352c)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode in JI
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[12]
!Meantone[7]
!UDP
!Diatonic mode
!Porcupine[7]
!UDP
!UDP
!Porcupine mode
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -3
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
|sLsLLsLmLsLL
|smmsmLm
|sLsLLsLsLsLL
|sLLsLLL
|<nowiki>1|10</nowiki>
|<nowiki>0|6</nowiki>
| -0.0622
|Lochrian
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
| -0.0427
|-
|-
| -5
| -2
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|sLmLsLLsLsLL
|msmmsmL
|sLsLsLLsLsLL
|LsLLsLL
|<nowiki>0|11</nowiki>
|<nowiki>2|4</nowiki>
| -0.0587
|Aeolian
|-
|ssssssL
| -4
|<nowiki>0|6</nowiki>
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|Magical seventh
|sLLsLsLLsLmL
|  -0.0374
|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
|  -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
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|LsLsLLsLmLsL
|smLmsmm
|LsLsLLsLsLsL
|sLLLsLL
|<nowiki>6|5</nowiki>
|<nowiki>1|5</nowiki>
|  -0.0018
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|  -0.0053
|-
|-
|1
|0
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|LsLmLsLLsLsL
|msmLmsm
|LsLsLsLLsLsL
|LsLLLsL
|<nowiki>5|6</nowiki>
|<nowiki>3|3</nowiki>
|0.0018
|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
|2
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LsLLsLsLLsLm
|Lmsmmsm
|LsLLsLsLLsLs
|LLsLLsL
|<nowiki>9|2</nowiki>
|<nowiki>4|2</nowiki>
|0.0267
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|0.0374
|-
|-
|3
|3
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|LsLLsLmLsLLs
|mLmsmms
|LsLLsLsLsLLs
|LLLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>6|0</nowiki>
|0.0302
|Lydian
|-
|sLsssss
|4
|<nowiki>5|1</nowiki>
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|Dark major
|LmLsLLsLsLLs
|0.0427
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|0.0338
|-
|5
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|0.0587
|-
|6
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|0.0622
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-2 temperings (mode 2)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 2,841: Line 2,941:
|-
|-
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[1L 6s|sssLsss]]
|[[Meantone family|Meantone]][12]
|[[Porcupine family#Porkypine|Porkypine]][7]
|81/80
|55/54, 100/99
|-
|-
|L = m
|L = m
|sLLsLLLsLLsL
|[[5L 2s|LsLLLsL]]
|[[Dimipent family|Diminished]][12] MODMOS
|[[Meanenneadecal]][7] or [[Meantone family#Flattone|Flattone]][7]
|648/625
|45/44, 81/80
|-
|-
|L = s
|L = s
|[[11L 1s|LLLLLsLLLLLL]]
|[[4L 3s|LsLsLsL]]
|[[Ripple family|Ripple]][12]
|[[Dicot family|Flat]][7]
|6561/6250
|25/24, 33/32
|-
|-
|L - m = m - s
|L - m = m - s
|dLLdLsLdLLdL
|LsLALsL
|Augmented[12] MODMOS
|[[Tetracot family#Subgroup temperament|Tetracot]][7] MODMOS
|128/125
|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]]
|-
|-
|s = 0
!Step sizes in ET
|[[7L 1s|LLLsLLLL]]
|(2, 1, 1)
|[[Porcupine family#Porcupine|Porcupine]][8]
|(2, 2, 1)
|250/243
|(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: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
=====[[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"
{| class="wikitable"
!Step signature
!Step signature
Line 2,871: Line 2,994:
!Step sizes in cents (TE)
!Step sizes in cents (TE)
|-
|-
|7L 1m 4s
|1L 4M 2s
|(27/25~15/14, 25/24~21/20, 250/243~28/27)
|(9/8~25/22, 10/9~11/10, 27/25~15/14~12/11)
|(123.5395c, 78.929c, 64.0225c)
|(215.4452c, 179.0856c, 132.5782c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 2,879: Line 3,002:
!Mode as simplest JI pre-image
!Mode as simplest JI pre-image
!Step pattern
!Step pattern
!Meantone[12]
!Meantone[7]
!UDP
!UDP
!Porcupine[7]
!UDP
!Porcupine mode
!Diatonic mode
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -3
|~ 28/27 10/9 280/243 56/45 4/3 112/81 40/27 14/9 5/3 140/81 28/15 2/1
|~ 12/11 6/5 4/3 10/7 8/5 9/5 2/1
|sLsLLsLmLsLL
|sMMsMLM
|sLsLLsLsLsLL
|sLLsLLL
|<nowiki>1|10</nowiki>
|<nowiki>0|6</nowiki>
| -0.0440
|sssssLs
|<nowiki>1|5</nowiki>
|Dark diminished
|Lochrian
| -0.0591
|-
|-
|  -5
|  -2
|~ 28/27 10/9 7/6 5/4 35/27 7/5 3/2 14/9 5/3 140/81 28/15 2/1
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|sLmLsLLsLsLL
|MsMMsML
|sLsLsLLsLsLL
|LsLLsLL
|<nowiki>0|11</nowiki>
|<nowiki>2|4</nowiki>
|  -0.0417
|ssssssL
|<nowiki>0|6</nowiki>
|Magical seventh
|Aeolian
|  -0.0433
|-
|-
|  -4
|  -1
|~ 28/27 10/9 6/5 56/45 4/3 112/81 40/27 8/5 224/135 16/9 28/15 2/1
|~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1
|sLLsLsLLsLmL
|sMLMsMM
|sLLsLsLLsLsL
|sLLLsLL
|<nowiki>4|7</nowiki>
|<nowiki>1|5</nowiki>
| -0.0237
|ssLssss
|-
|<nowiki>4|2</nowiki>
|  -3
|Bright minor
|~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|Phrygian
|sLLsLmLsLLsL
|  -0.0158
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|  -0.0214
|-
|-
| -2
|0
|~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|mLsLLsLsLLsL
|MsMLMsM
|sLsLLsLsLLsL
|LsLLLsL
|<nowiki>2|9</nowiki>
|<nowiki>3|3</nowiki>
| -0.0191
|sssLsss
|-
|<nowiki>3|3</nowiki>
|  -1
|Dark minor
|~ 15/14 10/9 6/5 56/45 4/3 10/7 40/27 8/5 5/3 9/5 28/15 2/1
|Dorian
|LsLsLLsLmLsL
|0
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
| -0.0011
|-
|-
|1
|1
|~ 15/14 10/9 6/5 5/4 27/20 7/5 3/2 45/28 5/3 9/5 28/15 2/1
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|LsLmLsLLsLsL
|MMsMLMs
|LsLsLsLLsLsL
|LLsLLLs
|<nowiki>5|6</nowiki>
|<nowiki>5|1</nowiki>
|0.0011
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|Ionian
|0.0158
|-
|-
|2
|2
|~ 15/14 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LsLLsLsLLsLm
|LMsMMsM
|LsLLsLsLLsLs
|LLsLLsL
|<nowiki>9|2</nowiki>
|<nowiki>4|2</nowiki>
|0.0191
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|Mixolydian
|0.0433
|-
|-
|3
|3
|~ 15/14 10/9 6/5 9/7 4/3 10/7 3/2 45/28 5/3 9/5 27/14 2/1
|~ 10/9 5/4 7/5 3/2 5/3 11/6 2/1
|LsLLsLmLsLLs
|MLMsMMs
|LsLLsLsLsLLs
|LLLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>6|0</nowiki>
|0.0214
|sLsssss
|<nowiki>5|1</nowiki>
|Dark major
|Lydian
|0.0591
|}
{| class="wikitable"
|+Rank-2 temperings (mode 2)
!Equivalence
!Step pattern
!Scale
!Comma list
|-
|-
|4
|L = M
|~ 15/14 9/8 135/112 5/4 27/20 81/56 3/2 45/28 5/3 9/5 27/14 2/1
|[[5L 2s|LsLLLsL]]
|LmLsLLsLsLLs
|[[Meanenneadecal]][7]
|LsLsLLsLsLLs
|45/44, 56/55, 81/80
|<nowiki>7|4</nowiki>
|0.0237
|-
|-
|5
|M = s
|~ 15/14 81/70 6/5 9/7 4/3 10/7 54/35 8/5 12/7 9/5 27/14 2/1
|[[1L 6s|sssLsss]]
|LLsLsLLsLmLs
|[[Trienstonic clan#Opossum|Opossum]][7]
|LLsLsLLsLsLs
|28/27, 55/54, 77/75
|<nowiki>11|0</nowiki>
|0.0417
|-
|-
|6
|L = s
|~ 15/14 81/70 6/5 9/7 27/20 81/56 3/2 45/28 243/140 9/5 27/14 2/1
|[[4L 3s|LsLsLsL]]
|LLsLmLsLLsLs
|[[Dicot family#Flat|Flat]][7]
|LLsLsLsLLsLs
|21/20, 25/24, 33/32
|<nowiki>10|1</nowiki>
|0.0440
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-1 temperings
!Equivalence
!ET
!Step pattern
|8d
!Scale
|[[12edo|12]]
!Comma list
|[[15edo|15]]
|[[19edo|19]]
|27e
|[[34edo|34]]
|-
|-
|m = s
!Step sizes in ET
|[[7L 5s|sLLsLsLsLLsL]]
|(2, 1, 1)
|[[Meantone family|Meantone]][12]
|(2, 2, 1)
|81/80, 126/125
|(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)
|-
|-
|L = m
|1L 4m 2s
|sLLsLLLsLLsL
|(9/8~25/22, 10/9~11/10, 27/25~12/11~13/12)
|[[Diminished]][12] MODMOS
|(209.5416c, 175.8918c, 142.7754c)
|36/35, 50/49
|-
|L - m = m - s
|dLLdLsLdLLdL
|Augene[12] MODMOS
|64/63, 126/125
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 126/125
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
!Mode number
!ET
!Mode as simplest JI pre-image
|[[15edo|15]]
!Step pattern
|[[16edo|16]]
!Meantone[7]
|[[19edo|19]]
!UDP
|[[27edo|27]]
!Diatonic mode
|[[31edo|31]]
!Porcupine[7]
|[[46edo|46]]
!UDP
|[[50edo|50]]
!Porcupine mode
|[[58edo|58]]
![[Mode height]]
|[[77edo|77]]
|-
|-
!Step sizes in ET
| -3
|(2, 1, 0)
|~ 12/11 6/5 4/3 13/9 8/5 9/5 2/1
|(1, 1, 2)
|smmsmLm
|(2, 1, 1)
|sLLsLLL
|(3, 2, 1)
|<nowiki>0|6</nowiki>
|(3, 2, 2)
|Lochrian
|(5, 3, 2)
|sssssLs
|(5, 3, 3)
|<nowiki>1|5</nowiki>
|(6, 4, 3)
|Dark diminished
|(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
|  -2
|(27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63)
|~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1
|(123.5395c, 78.929c, 64.0225c)
|msmmsmL
|}
|LsLLsLL
{| class="wikitable"
|<nowiki>2|4</nowiki>
!Mode number
|Aeolian
!Mode as simplest JI pre-image
|ssssssL
!Step pattern
|<nowiki>0|6</nowiki>
!Meantone[12]
|Magical seventh
!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
|  -1
|~ 28/27 10/9 7/6 5/4 13/10 7/5 3/2 14/9 5/3 26/15 13/7 2/1
|~ 12/11 6/5 15/11 3/2 13/8 9/5 2/1
|sLmLsLLsLsLL
|smLmsmm
|sLsLsLLsLsLL
|sLLLsLL
|<nowiki>0|11</nowiki>
|<nowiki>1|5</nowiki>
| -0.0433
|Phrygian
|ssLssss
|<nowiki>4|2</nowiki>
|Bright minor
|
|-
|-
| -4
|0
|~ 28/27 10/9 6/5 26/21 4/3 104/75 40/27 8/5 104/63 16/9 13/7 2/1
|~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1
|sLLsLsLLsLmL
|msmLmsm
|sLLsLsLLsLsL
|LsLLLsL
|<nowiki>4|7</nowiki>
|<nowiki>3|3</nowiki>
|  -0.0256
|Dorian
|-
|sssLsss
|  -3
|<nowiki>3|3</nowiki>
|~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 13/7 2/1
|Dark minor
|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
|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
|~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1
|LsLmLsLLsLsL
|mmsmLms
|LsLsLsLLsLsL
|LLsLLLs
|<nowiki>5|6</nowiki>
|<nowiki>5|1</nowiki>
|0.0016
|Ionian
|ssssLss
|<nowiki>2|4</nowiki>
|Bright diminished
|
|-
|-
|2
|2
|~ 14/13 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1
|LsLLsLsLLsLm
|Lmsmmsm
|LsLLsLsLLsLs
|LLsLLsL
|<nowiki>9|2</nowiki>
|<nowiki>4|2</nowiki>
|0.0193
|Mixolydian
|Lssssss
|<nowiki>6|0</nowiki>
|Bright major
|
|-
|-
|3
|3
|~ 14/13 10/9 6/5 9/7 4/3 10/7 3/2 21/13 5/3 9/5 27/14 2/1
|~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1
|LsLLsLmLsLLs
|mLmsmms
|LsLLsLsLsLLs
|LLLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>6|0</nowiki>
|0.0225
|Lydian
|-
|sLsssss
|4
|<nowiki>5|1</nowiki>
|~ 14/13 9/8 63/52 5/4 27/20 75/52 3/2 21/13 5/3 9/5 27/14 2/1
|Dark major
|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"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-2 temperings (mode 2)
!Equivalence
!Equivalence
!Step pattern
!Step pattern
Line 3,128: Line 3,235:
|-
|-
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[1L 6s|sssLsss]]
|[[Meanpop]][12]
|[[Porcupine family#13-limit|Porcupine]][7]
|81/80, 105/104, 126/125
|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"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|15f
|8
|[[12edo|12]]
|[[15edo|15]]
|[[19edo|19]]
|[[19edo|19]]
|[[27edo|27]]
|22f
|[[31edo|31]]
|[[26edo|26]]
|[[46edo|46]]
|27e
|[[50edo|50]]
|[[34edo|34]]
|[[58edo|58]]
|[[41edo|41]]
|[[77edo|77]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 2, 1)
|(2, 2, 1)
|(3, 2, 2)
|(3, 2, 2)
|(5, 3, 2)
|(3, 3, 2)
|(5, 3, 3)
|(4, 3, 3)
|(6, 4, 3)
|(4, 4, 3)
|(8, 5, 4)
|(5, 4, 3)
|(6, 5, 4)
|(7, 6, 5)
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
 
====[[SNS (2/1, 3/2, 6/5)-12|(2/1, 3/2, 6/5)[12]]]====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
!Steps in JI
!Steps in JI
!Step sizes in cents (TE)
!Step sizes in cents
|-
|-
|7L 1m 4s
|7L 1m 4s
|(27/25~12/11, 25/24~33/32, 250/243~55/54~121/120)
|(27/25, 25/24, 250/243)
|(146.6352c, 63.1434c, 27.4197c)
|(133.2376c, 70.6724c, 49.1661c)
|}
|}
{| class="wikitable"
{| class="wikitable"
!Mode number
!Mode number
!Mode as simplest JI pre-image
!Mode in JI
!Step pattern
!Step pattern
!Meantone[12]
!Meantone[12]
Line 3,173: Line 3,293:
|-
|-
| -6
| -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|250/243 10/9 2500/2187 100/81 4/3 1000/729 40/27 125/81 5/3 1250/729 50/27 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL  
|sLsLLsLsLsLL  
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
| -0.0899
| -0.0622
|-
|-
| -5
| -5
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|250/243 10/9 125/108 5/4 625/486 25/18 3/2 125/81 5/3 1250/729 50/27 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
| -0.0819
| -0.0587
|-
|-
| -4
| -4
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|250/243 10/9 6/5 100/81 4/3 1000/729 40/27 8/5 400/243 16/9 50/27 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
| -0.0510
| -0.0338
|-
|-
| -3
| -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|250/243 10/9 6/5 100/81 4/3 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
| -0.0430
| -0.0302
|-
|-
|  -2
|  -2
|~ 25/24 9/8 55/48 5/4 15/11 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|25/24 9/8 125/108 5/4 27/20 25/18 3/2 125/81 5/3 9/5 50/27 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  -0.0349
|  -0.0267
|-
|-
|  -1
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|27/25 10/9 6/5 100/81 4/3 36/25 40/27 8/5 5/3 9/5 50/27 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  -0.0040
|  -0.0018
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|27/25 10/9 6/5 5/4 27/20 25/18 3/2 81/50 5/3 9/5 50/27 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|0.0040
|0.0018
|-
|-
|2
|2
|~ 12/11 10/9 6/5 72/55 4/3 16/11 22/15 8/5 96/55 16/9 48/25 2/1
|27/25 10/9 6/5 162/125 4/3 36/25 40/27 8/5 216/125 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|0.0349
|0.0267
|-
|-
|3
|3
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 18/11 5/3 9/5 108/55 2/1
|27/25 10/9 6/5 162/125 4/3 36/25 3/2 81/50 5/3 9/5 243/125 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|0.0430
|0.0302
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 108/55 2/1
|27/25 9/8 243/200 5/4 27/20 729/500 3/2 81/50 5/3 9/5 243/125 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|0.0510
|0.0338
|-
|-
|5
|5
|~ 12/11 144/121 6/5 72/55 4/3 16/11 192/121 8/5 96/55 9/5 108/55 2/1
|27/25 729/625 6/5 162/125 4/3 36/25 972/625 8/5 216/125 9/5 243/125 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|0.0819
|0.0587
|-
|-
|6
|6
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 18/11 216/121 9/5 108/55 2/1
|27/25 729/625 6/5 162/125 27/20 729/500 3/2 81/50 2187/1250 9/5 243/125 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|0.0899
|0.0622
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-2 temperings (mode -3)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
| m = s
| [[7L 5s|sLLsLsLsLLsL]]
| [[Meantone]][12]
| 81/80
|-
|-
|m = s
| L = m
|[[7L 5s|sLLsLsLsLLsL]]
| sLLsLLLsLLsL
|[[Meanenneadecal]][12] or [[Meantone family#Flattone|Flattone]][12]
| [[Diminished]][12] MODMOS
|45/44, 81/80
| 648/625
|-
|-
|L = m
| L = s
|sLLsLLLsLLsL
| [[11L 1s|LLLLLsLLLLLL]]
|[[Dimipent family|Diminished]][12] MODMOS
| [[Ripple]][12]
|100/99, 128/121
| 6561/6250
|-
|-
|L - m = m - s
| L - m = m - s
|dLLdLsLdLLdL
| dLLdLsLdLLdL
|Augene[12] MODMOS
| [[Augmented]][12] modmos
|100/99, 128/125
| 128/125
|-
|-
|s = 0
| s = 0
|[[7L 1s|LLLsLLLL]]
| [[7L 1s|LLLsLLLL]]
|[[Porcupine family#Porkypine|Porkypine]][8]
| [[Porcupine]][8]
|55/54, 100/99
| 250/243
|}
|}


=====[[SNS (2/1, 3/2, 6/5: 126/125)-12|(2/1, 3/2, 6/5: 126/125)[12] (Starling)]]=====
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
!Step signature
!ET
!Steps in JI
|[[15edo|15]]
!Step sizes in cents (TE)
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|27e
|[[29edo|29]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|-
|-
!Step sizes in ET
|7L 1m 4s
|(2, 1, 0)
|(27/25~15/14, 25/24~21/20, 250/243~28/27)
|(2, 1, 1)
|(123.5395c, 78.929c, 64.0225c)
|(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, 385/384)[12] ([[Keemic family#Supermagic|Supermagic]])=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120)
|(149.51592c, 58.8799c, 23.6254c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,327: Line 3,428:
|-
|-
|  -6
|  -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
|~ 28/27 10/9 280/243 56/45 4/3 112/81 40/27 14/9 5/3 140/81 28/15 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
|  
| -0.0440
|-
|-
|  -5
|  -5
|~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1
|~ 28/27 10/9 7/6 5/4 35/27 7/5 3/2 14/9 5/3 140/81 28/15 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
|  
| -0.0417
|-
|-
|  -4
|  -4
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|~ 28/27 10/9 6/5 56/45 4/3 112/81 40/27 8/5 224/135 16/9 28/15 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
|  
| -0.0237
|-
|-
|  -3
|  -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|~ 28/27 10/9 6/5 56/45 4/3 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
|  
| -0.0214
|-
|-
|  -2
|  -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
|~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 28/15 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  
| -0.0191
|-
|-
|  -1
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|~ 15/14 10/9 6/5 56/45 4/3 10/7 40/27 8/5 5/3 9/5 28/15 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  
| -0.0011
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|~ 15/14 10/9 6/5 5/4 27/20 7/5 3/2 45/28 5/3 9/5 28/15 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|
|0.0011
|-
|-
|2
|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
|~ 15/14 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|
|0.0191
|-
|-
|3
|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
|~ 15/14 10/9 6/5 9/7 4/3 10/7 3/2 45/28 5/3 9/5 27/14 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|
|0.0214
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1
|~ 15/14 9/8 135/112 5/4 27/20 81/56 3/2 45/28 5/3 9/5 27/14 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|
|0.0237
|-
|-
|5
|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
|~ 15/14 81/70 6/5 9/7 4/3 10/7 54/35 8/5 12/7 9/5 27/14 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|
|0.0417
|-
|-
|6
|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
|~ 15/14 81/70 6/5 9/7 27/20 81/56 3/2 45/28 243/140 9/5 27/14 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|
|0.0440
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,419: Line 3,520:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Flattone|Flattone]][12]
|[[Meantone family|Meantone]][12]
|45/44, 81/80, 385/384
|81/80, 126/125
|-
|L = m
|sLLsLLLsLLsL
|[[Diminished]][12] MODMOS
|36/35, 50/49
|-
|L - m = m - s
|dLLdLsLdLLdL
|[[Augmented family#Augene|Augene]][12] MODMOS
|64/63, 126/125
|-
|-
|s = 0
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Septimal porcupine|Porcupine]][8]
|[[Trienstonic clan#Opossum|Opossum]][8]
|55/54, 64/63, 100/99
|28/27, 126/125
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|[[15edo|15]]
|[[15edo|15]]
|[[16edo|16]]
|[[19edo|19]]
|[[19edo|19]]
|[[22edo|22]]
|[[27edo|27]]
|[[26edo|26]]
|[[31edo|31]]
|[[34edo|34]]
|[[46edo|46]]
|[[41edo|41]]
|[[50edo|50]]
|[[104edo|104]]
|[[58edo|58]]
|[[77edo|77]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(1, 1, 2)
|(2, 1, 1)
|(2, 1, 1)
|(3, 1, 0)
|(3, 2, 1)
|(3, 1, 1)
|(3, 2, 2)
|(4, 2, 1)
|(5, 3, 2)
|(5, 2, 1)
|(5, 3, 3)
|(13, 5, 2)
|(6, 4, 3)
|(8, 5, 4)
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 100/99, 105/104, 144/143)-12|(2/1, 3/2, 6/5: 100/99, 105/104, 144/143)[12]]] ([[Keemic family#Supermagic|Supermagic]])=====
=====[[SNS (2/1, 3/2, 6/5: 126/125, 196/195)-12|(2/1, 3/2, 6/5: 126/125, 196/195)[12]]]=====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
Line 3,455: Line 3,569:
|-
|-
|7L 1m 4s
|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)
|(27/25~15/14~14/13, 25/24~21/20, 250/243~28/27~65/63)
|(145.47082c, 58.39270c, 30.85183c)
|(123.5395c, 78.929c, 64.0225c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,467: Line 3,581:
|-
|-
|  -6
|  -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
|~ 28/27 10/9 52/45 26/21 4/3 104/75 40/27 14/9 5/3 26/15 13/7 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
|  
| -0.0465
|-
|-
|  -5
|  -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
|~ 28/27 10/9 7/6 5/4 13/10 7/5 3/2 14/9 5/3 26/15 13/7 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
|  
| -0.0433
|-
|-
|  -4
|  -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
|~ 28/27 10/9 6/5 26/21 4/3 104/75 40/27 8/5 104/63 16/9 13/7 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
|  
| -0.0256
|-
|-
|  -3
|  -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
|~ 28/27 10/9 6/5 26/21 4/3 7/5 3/2 14/9 5/3 9/5 13/7 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
|  
| -0.0225
|-
|-
|  -2
|  -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
|~ 21/20 9/8 7/6 5/4 27/20 7/5 3/2 14/9 5/3 9/5 13/7 2/1
|mLsLLsLsLLsL
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  
| -0.0193
|-
|-
|  -1
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|~ 14/13 10/9 6/5 26/21 4/3 10/7 40/27 8/5 5/3 9/5 13/7 2/1
|LsLsLLsLmLsL
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  
| -0.0016
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|~ 14/13 10/9 6/5 5/4 27/20 7/5 3/2 21/13 5/3 9/5 13/7 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|
|0.0016
|-
|-
|2
|2
|~ 12/11 10/9 6/5 13/10 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
|~ 14/13 10/9 6/5 9/7 4/3 10/7 40/27 8/5 12/7 16/9 40/21 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|
|0.0193
|-
|-
|3
|3
|~ 12/11 10/9 6/5 13/10 4/3 16/11 3/2 18/11 5/3 9/5 39/20 2/1
|~ 14/13 10/9 6/5 9/7 4/3 10/7 3/2 21/13 5/3 9/5 27/14 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|
|0.0225
|-
|-
|4
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 39/20 2/1
|~ 14/13 9/8 63/52 5/4 27/20 75/52 3/2 21/13 5/3 9/5 27/14 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|
|0.0256
|-
|-
|5
|5
|~ 12/11 13/11 6/5 13/10 4/3 16/11 52/33 8/5 7/4 9/5 39/20 2/1
|~ 14/13 15/13 6/5 9/7 4/3 10/7 20/13 8/5 12/7 9/5 27/14 2/1
|LLsLsLLsLmLs
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|
|0.0433
|-
|-
|6
|6
|~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 18/11 39/22 9/5 39/20 2/1
|~ 14/13 15/13 6/5 9/7 27/20 75/52 3/2 21/13 45/26 9/5 27/14 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|
|0.0465
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,559: Line 3,673:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Flattone|Flattone]][12]
|[[Meanpop]][12]
|45/44, 65/64, 78/77, 81/80
|81/80, 105/104, 126/125
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Porcupine family#Septimal porcupine|Porcupine]][8]
|40/39, 55/54, 64/63, 66/65
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-1 temperings
|+Rank-1 temperings
!ET
!ET
|[[15edo|15]]
|15f
|[[19edo|19]]
|[[19edo|19]]
|22f
|[[27edo|27]]
|[[26edo|26]]
|[[31edo|31]]
|[[34edo|34]]
|[[46edo|46]]
|[[41edo|41]]
|[[50edo|50]]
|[[58edo|58]]
|[[77edo|77]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 1, 0)
|(3, 2, 1)
|(3, 1, 1)
|(3, 2, 2)
|(4, 2, 1)
|(5, 3, 2)
|(5, 2, 1)
|(5, 3, 3)
|(6, 4, 3)
|(8, 5, 4)
|}
|}
=====[[SNS (2/1, 3/2, 6/5: 56/55, 100/99)-12|(2/1, 3/2, 6/5: 56/55, 100/99)[12] (Thrasher)]]=====
=====[[SNS (2/1, 3/2, 6/5: 100/99)-12|(2/1, 3/2, 6/5: 100/99)[12] (No-7 Ptolemismic)]]=====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
Line 3,593: Line 3,705:
|-
|-
|7L 1m 4s
|7L 1m 4s
|(27/25~15/14~12/11, 25/24~21/20~33/32, 250/243~28/27~55/54)
|(27/25~12/11, 25/24~33/32, 250/243~55/54~121/120)
|(132.5782c, 82.867c, 46.5074c)
|(146.6352c, 63.1434c, 27.4197c)
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 3,604: Line 3,716:
![[Mode height]]
![[Mode height]]
|-
|-
| -6
| -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
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 55/36 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL  
|<nowiki>1|10</nowiki>
|<nowiki>1|10</nowiki>
| -0.0671
| -0.0899
|-
|-
| -5
| -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
|~ 55/54 10/9 55/48 5/4 121/96 11/8 3/2 55/36 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|<nowiki>0|11</nowiki>
| -0.0526
| -0.0819
|-
|-
| -4
| -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
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|<nowiki>4|7</nowiki>
| -0.0445
| -0.0510
|-
|-
| -3
| -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
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 55/36 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|<nowiki>3|8</nowiki>
| -0.0299
| -0.0430
|-
|-
|  -2
|  -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
|~ 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
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|<nowiki>2|9</nowiki>
|  -0.0154
|  -0.0349
|-
|-
|  -1
|  -1
Line 3,644: Line 3,756:
|LsLsLLsLsLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|<nowiki>6|5</nowiki>
|  -0.0073
|  -0.0040
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|<nowiki>5|6</nowiki>
|0.0073
|0.0040
|-
|-
|2
|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
|~ 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
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|<nowiki>9|2</nowiki>
|0.0154
|0.0349
|-
|-
|3
|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
|~ 12/11 10/9 6/5 72/55 4/3 16/11 3/2 18/11 5/3 9/5 108/55 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|<nowiki>8|3</nowiki>
|0.0299
|0.0430
|-
|-
|4
|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
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 108/55 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|<nowiki>7|4</nowiki>
|0.0445
|0.0510
|-
|-
|5
|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
|~ 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
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|<nowiki>11|0</nowiki>
|0.0526
|0.0819
|-
|-
|6
|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
|~ 12/11 144/121 6/5 72/55 15/11 81/55 3/2 18/11 216/121 9/5 108/55 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
|<nowiki>10|1</nowiki>
|<nowiki>10|1</nowiki>
|0.0671
|0.0899
|}
|}
{| class="wikitable"
{| class="wikitable"
|+Rank-2 temperings (mode -3)
|+Rank-2 temperings (mode -3)
!Equivalence
! Equivalence
!Step pattern
! Step pattern
!Scale
! Scale
!Comma list
! Comma list
|-
| m = s
| [[7L 5s|sLLsLsLsLLsL]]
| [[Meanenneadecal]][12] or [[Flattone]][12]
| 45/44, 81/80
|-
|-
|m = s
| L = m
|[[7L 5s|sLLsLsLsLLsL]]
| sLLsLLLsLLsL
|[[Meanenneadecal]][12]
| [[Diminished]][12] modmos
|45/44, 56/55, 81/80
| 100/99, 128/121
|-
|-
|L = m
| L - m = m - s
|sLLsLLLsLLsL
| dLLdLsLdLLdL
|[[Jubilismic clan#Diminished|Diminished]][12] MODMOS
| [[Augene]][12] modmos
|36/35, 50/49, 56/55
| 100/99, 128/125
|-
|-
|s = 0
| s = 0
|[[7L 1s|LLLsLLLL]]
| [[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
| [[Porcupine]][8]
|28/27, 55/54, 77/75
| 55/54, 100/99
|}
|}


Line 3,716: Line 3,833:
|[[15edo|15]]
|[[15edo|15]]
|[[19edo|19]]
|[[19edo|19]]
|[[22edo|22]]
|[[26edo|26]]
|27e
|27e
|[[29edo|29]]
|[[34edo|34]]
|[[34edo|34]]
|[[37edo|37]]
|[[41edo|41]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(3, 2, 1)
|(3, 2, 1)
|(4, 1, 0)
|(4, 2, 1)
|(4, 2, 1)
|(5, 2, 0)
|(5, 2, 1)
|}
|}
=====(2/1, 3/2, 6/5: 56/55, 91/90, 100/99)[12] (Thrasher)=====
 
===== (2/1, 3/2, 6/5: 100/99, 144/143)[12] (No-7 Ptolemismic) =====
{| class="wikitable"
{| class="wikitable"
!Step signature
!Step signature
Line 3,732: Line 3,860:
|-
|-
|7L 1m 4s
|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)
|(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"
{| class="wikitable"
Line 3,744: Line 3,872:
|-
|-
|  -6
|  -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
|~ 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
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|sLsLLsLsLsLL
Line 3,751: Line 3,879:
|-
|-
|  -5
|  -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
|~ 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
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|sLsLsLLsLsLL
Line 3,758: Line 3,886:
|-
|-
|  -4
|  -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
|~ 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
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|sLLsLsLLsLsL
Line 3,765: Line 3,893:
|-
|-
|  -3
|  -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
|~ 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
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|sLLsLsLsLLsL
Line 3,772: Line 3,900:
|-
|-
|  -2
|  -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
|~ 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
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|sLsLLsLsLLsL
Line 3,779: Line 3,907:
|-
|-
|  -1
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|~ 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
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|LsLsLLsLsLsL
Line 3,786: Line 3,914:
|-
|-
|1
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 81/50 5/3 9/5 11/6 2/1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 13/8 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|LsLsLsLLsLsL
Line 3,793: Line 3,921:
|-
|-
|2
|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
|~ 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
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|LsLLsLsLLsLs
Line 3,800: Line 3,928:
|-
|-
|3
|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
|~ 12/11 10/9 6/5 13/10 4/3 13/9 3/2 13/8 5/3 9/5 39/20 2/1
|LsLLsLmLsLLs
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|LsLLsLsLsLLs
Line 3,807: Line 3,935:
|-
|-
|4
|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
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 13/8 5/3 9/5 39/20 2/1
|LmLsLLsLsLLs
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|LsLsLLsLsLLs
Line 3,814: Line 3,942:
|-
|-
|5
|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
|~ 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
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|LLsLsLLsLsLs
Line 3,821: Line 3,949:
|-
|-
|6
|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
|~ 12/11 13/11 6/5 13/10 15/11 81/55 3/2 13/8 39/22 9/5 39/20 2/1
|LLsLmLsLLsLs
|LLsLmLsLLsLs
|LLsLsLsLLsLs
|LLsLsLsLLsLs
Line 3,836: Line 3,964:
|m = s
|m = s
|[[7L 5s|sLLsLsLsLLsL]]
|[[7L 5s|sLLsLsLsLLsL]]
|[[Meantone family#Vincenzo|Vincenzo]][12]
|[[Meantone family#Flattone|Flattone]][12]
|45/44, 56/55, 65/64, 81/80
|45/44, 65/64, 81/80
|-
|-
|s = 0
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|[[Porcupine family#13-limit|Porcupine]][8]
|28/27, 40/39, 55/54, 66/65
|40/39, 55/54, 66/65
|}
|}


Line 3,850: Line 3,978:
|[[15edo|15]]
|[[15edo|15]]
|[[19edo|19]]
|[[19edo|19]]
|22f
|[[26edo|26]]
|27e
|27e
|[[34edo|34]]
|[[34edo|34]]
|[[41edo|41]]
|-
|-
!Step sizes in ET
!Step sizes in ET
|(2, 1, 0)
|(2, 1, 0)
|(2, 1, 1)
|(2, 1, 1)
|(3, 1, 0)
|(3, 1, 1)
|(3, 2, 1)
|(3, 2, 1)
|(4, 2, 1)
|(4, 2, 1)
|(5, 2, 1)
|}
=====(2/1, 3/2, 6/5: 100/99, 385/384)[12] ([[Keemic family#Supermagic|Supermagic]])=====
{| class="wikitable"
!Step signature
!Steps in JI
!Step sizes in cents (TE)
|-
|7L 1m 4s
|(27/25~12/11~35/32, 25/24~33/32, 250/243~55/54~64/63~121/120)
|(149.51592c, 58.8799c, 23.6254c)
|}
{| class="wikitable"
!Mode number
!Mode as simplest JI pre-image
!Step pattern
!Meantone[12]
!UDP
![[Mode height]]
|-
|  -6
|~ 55/54 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
|sLsLLsLmLsLL
|sLsLLsLsLsLL
|<nowiki>1|10</nowiki>
|
|-
|  -5
|~ 55/54 10/9 8/7 5/4 121/96 11/8 3/2 32/21 5/3 121/72 11/6 2/1
|sLmLsLLsLsLL
|sLsLsLLsLsLL
|<nowiki>0|11</nowiki>
|
|-
|  -4
|~ 55/54 10/9 6/5 11/9 4/3 110/81 22/15 8/5 44/27 16/9 11/6 2/1
|sLLsLsLLsLmL
|sLLsLsLLsLsL
|<nowiki>4|7</nowiki>
|
|-
|  -3
|~ 55/54 10/9 6/5 11/9 4/3 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|sLLsLmLsLLsL
|sLLsLsLsLLsL
|<nowiki>3|8</nowiki>
|
|-
|  -2
|~ 25/24 9/8 8/7 5/4 15/11 11/8 3/2 32/21 5/3 9/5 11/6 2/1
|mLsLLsLsLLsL
|sLsLLsLsLLsL
|<nowiki>2|9</nowiki>
|
|-
|  -1
|~ 12/11 10/9 6/5 11/9 4/3 16/11 22/15 8/5 5/3 9/5 11/6 2/1
|LsLsLLsLmLsL
|LsLsLLsLsLsL
|<nowiki>6|5</nowiki>
|
|-
|1
|~ 12/11 10/9 6/5 5/4 15/11 11/8 3/2 18/11 5/3 9/5 11/6 2/1
|LsLmLsLLsLsL
|LsLsLsLLsLsL
|<nowiki>5|6</nowiki>
|
|-
|2
|~ 12/11 10/9 6/5 21/16 4/3 16/11 22/15 8/5 7/4 16/9 48/25 2/1
|LsLLsLsLLsLm
|LsLLsLsLLsLs
|<nowiki>9|2</nowiki>
|
|-
|3
|~ 12/11 10/9 6/5 21/16 4/3 16/11 3/2 18/11 5/3 9/5 63/32 2/1
|LsLLsLmLsLLs
|LsLLsLsLsLLs
|<nowiki>8|3</nowiki>
|
|-
|4
|~ 12/11 9/8 27/22 5/4 15/11 81/55 3/2 18/11 5/3 9/5 63/ 2/1
|LmLsLLsLsLLs
|LsLsLLsLsLLs
|<nowiki>7|4</nowiki>
|
|-
|5
|~ 12/11 144/121 6/5 21/16 4/3 16/11 192/121 8/5 7/4 9/5 63/32 2/1
|LLsLsLLsLmLs
|LLsLsLLsLsLs
|<nowiki>11|0</nowiki>
|
|-
|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
|}
|}
=====[[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, 385/384)[20] (Supermagic)====
7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE
~ 189/176 12/11 10/9 121/108 11/9 4/3 110/81 22/15 32/21 5/3 121/72 11/6 2/1
~ 12/11 144/121 6/5 21/16 15/11 81/55 3/2 18/11 216/121 9/5 63/32 2/1 as LmmLmLmmLmsmLmmLmLmm
m = s -> LssLsLssLsssLssLsLss Tetracot[20] MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL Camahueto[20]; L = s -> LssLsLssLsLsLssLsLss Diminished[20] MODMOS;
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Porcupine[8]
19-ET: (1, 1, 0); 22-ET: (3, 0, 1); 26-ET: ( 34-ET; 41-ET; 104-ET:
====[[SNS (2/1, 3/2, 6/5: 4375/4374)-20|(2/1, 3/2, 6/5: 4375/4374)[20] (Ragismic)]]====
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c) TE
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
L - m = m - s -> Unidec[20] MODMOS
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
=====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-20|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)]]=====
7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL
19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-39|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)]]====
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE
~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms
m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs
46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)
==2.3.5; [[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] MOSMOS; 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
{| class="wikitable"
 
|+Rank-1 temperings
m = s -> sLsssssLsssLsssLsssssLss Immunity[24] MODMOS; L = m -> sLssLssLsssLsssLssLssLss; L = s -> LLLLsLLLLLLLLLLLLLsLLLLL; s = 0 -> LsLLLsL Dominant[7]
!ET
=====[[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)]]=====
|[[15edo|15]]
5L 2m 17s = (~175/162, ~28/27, 81/80~64/63~55/54) = (127.002c, 59.5625c, 26.2356c) TE
|[[19edo|19]]
 
|[[22edo|22]]
~ 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
|[[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 family#Supermagic|Supermagic]])=====
{| 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
|[[Jubilismic clan#Diminished|Diminished]][12] MODMOS
|36/35, 50/49, 56/55
|-
|s = 0
|[[7L 1s|LLLsLLLL]]
|[[Trienstonic clan#Opossum|Opossum]][8]
|28/27, 55/54, 77/75
|}
 
{| 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] (Supermagic)====
7L 12m 1s = (~189/176, 250/243~55/54~121/120~64/63, 81/80~45/44) = (125.8905c, 35.2545c, 23.6254c) TE
 
40/39 12/11 10/9 32/27 6/5 11/9 13/10 4/3 11/8 22/15 3/2 20/13 13/8 5/3 16/9 9/5 11/6 39/20 2/1
====[[SNS (2/1, 3/2, 6/5: 4375/4374)-20|(2/1, 3/2, 6/5: 4375/4374)[20] (Ragismic)]]====
7L 12m 1s = (~21/20, 250/243~36/35, ~81/80) = (84.5204c, 48.8911c, 21.6658c) TE
 
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 189/100 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
 
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
 
L - m = m - s -> Unidec[20] MODMOS
 
s = 0 -> LmmLmLmmLmmLmmLmLmm Falttone[19]; m = 0 -> LLLLsLLL Hystrix[8]
 
19-ET: (1, 1, 0); 53-ET: (4, 2, 1); 72-ET: (5, 3, 1); 99-ET: (7, 4, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 441-ET: (31, 18, 8); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
=====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-20|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[20] (Thor)]]=====
7L 12m 1s = (~21/20, 250/243~36/35, 81/80~245/242) = (84.5509c, 48.8802c, 21.6019c) TE
 
~ 21/20 27/25 10/9 7/6 6/5 63/50 35/27 4/3 7/5 36/25 35/24 3/2 63/40 81/50 5/3 7/4 9/5 121/64 35/18 2/1 as LmmLmLmmLmsmLmmLmLmm
 
m = s -> LssLsLssLsssLssLsLss MODMOS; L = m -> LLLLLLLLLLsLLLLLLLLL; L = s -> LssLsLssLsLsLssLsLss MODMOS;
 
s = 0 -> LmmLmLmmLmmLmmLmLmm; m = 0 -> LLLLsLLL
 
19-ET: (1, 1, 0); 34d: (3, 1, 1); 46-ET: (3, 2, 1); 72-ET: (5, 3, 1); 80-ET: (6, 3, 2); 118-ET: (8, 5, 2); 152-ET: (11, 6, 3); 171-ET: (12, 7, 3); 224-ET: (16, 9, 4); 270-ET: (19, 11, 5); 494-ET: (35, 20, 9); 612-ET: (43, 25, 11)
====[[SNS (2/1, 3/2, 6/5: 3025/3024, 4375/4374)-39|(2/1, 3/2, 6/5: 3025/3024, 4375/4374)[39] (Thor)]]====
7L 12m 20s = (~28/27, ~64/63, 81/80~245/242) = (62.949c, 27.2783c, 21.6019c) TE
 
~ 81/80 36/35 126/121 27/25 35/32 10/9 9/8 8/7 81/70 6/5 147/121 216/175 5/4 35/27 21/16 4/3 27/20 48/35 25/18 36/25 35/24 40/27 3/2 32/21 54/35 8/5 175/108 242/147 5/3 140/81 7/4 16/9 9/5 64/35 121/63 35/18 160/81 2/1 as smsLsmsmsLsmsLsmsmsLsmsmsLsmsLsmsmsLsms
 
m = s -> sssLsssssLsssLsssssLsssssLsssLsssssLsss Hemiamity[39] MODMOS; L = m -> sLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLsLs; s = 0 -> sLssLsLssLssLsLssLs
 
46-ET: (2, 1, 1); 72-ET: (4, 2, 1); 80-ET: (4, 1, 2); 118-ET: (6, 3, 2); 152-ET: (8, 3, 3); 171-ET: (9, 4, 3); 224-ET: (12, 5, 4); 270-ET: (14, 6, 5); 494-ET: (26, 11, 9); 612-ET: (32, 14, 11)
 
==2.3.5; [[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]
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)]]====
====[[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
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
~ 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;
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss; L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
 
 
s = 0 -> LsLLLsL Dominant[7]; m = 0 -> ssLssssssLssssLssssLssssssLss Immunity[29] MODMOS
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)]]=====
=====[[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
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
~ 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;
m = s -> ssLsssssssLssssLssssLsssssssLss Rodan[31] MODMOS; L = m -> ssLsssLsssLssssLssssLsssLsssLss, L = s -> LLLLLLsLLLLLLLLLLLLLLLLsLLLLLLL;
 
 
s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss
s = 0 -> LsLLLsL Arnold[7]; m = 0 -> ssLssssssLssssLssssLssssssLss
===((2/1, 3/2)[12], 81/80) or ((2/1, 3/2)[12], 64/63) ===
===((2/1, 3/2)[12], 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)]]====
====[[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
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
~ 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]
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)]]=====
=====[[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
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
~ 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]
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)]]====
====[[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
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
~ 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;
L = M -> ssLssLssLssLssLssLssLssLssLssLssLssLssL; M = s -> ssLssssssssLsssssLsssssLssssssssLsss Rodan[36] MODMOS; L = s -> sssssLssLsssssLsssssLsssssLssLsssssL;
 
 
s = 0 -> LssLsLsLssLs Dominant[12]; m = 0 -> ssLssssssLssssLssssLssssssLsss Immunity[29] MODMOS
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)]]=====
=====[[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
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
|}


~ 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
==2.5.9; Marvel ==
==2.5.9; Marvel ==
=== ((2/1, 5/4)[3], 9/8)===
=== ((2/1, 5/4)[3], 9/8)===
Line 4,349: Line 5,139:


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)
53-ET: (7, 3, 0); 58-ET: (8, 2, 1); 77-ET: (11, 3, 1); 111-ET: (15, 5, 1); 130-ET: (18, 6, 1)
[[Category:Gallery]]
[[Category:Step-nested scales]]
[[Category:Step-nested scales]]
[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]
[[Category:Rank 3]]
[[Category:Rank 3]]
{{Todo| cleanup }}
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