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== 7-Limit Intervals ==
 
7-limit, 81-odd-limit intervals.
{{Flat}}{{natural}}{{sharp}}
{| class="wikitable"
 
! colspan="2" |Interval Class
♭♮♯
! colspan="2" |Wa Intervals
 
! colspan="2" |Yo/Gu Intervals
<span class="bravura">&#xE260;</span>
! colspan="2" |Zo/Ru Intervals
<span class="bravura">&#xE261;</span>
! colspan="2" |Ruyo/Zogu Intervals
<span class="bravura">&#xE262;</span>
! colspan="2" |Yoyo/Gugu Intervals
 
! colspan="2" |Zozo/Ruru Intervals
<span class="heji">n</span>
! colspan="2" |Zoyo/Rugu Intervals
 
! colspan="2" |Biruyo/Bizogu Intervals
== Template: Temperament data ==
{{User:FloraC/Temperament data
| Subgroup = 2.3.5.7
| Comma list = 81/80, 126/125
| Mapping = {{mapping| 1 0 -4 -13 | 0 1 4 10 }}
| Mapping generators = ~2, ~3
| CTE = ~3/2 = 696.9521
| Wedgie = 1 4 10 4 13 12
| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
| Badness = 0.0137
}}
 
== 5-limit rank-2 temperaments by TE simple badness ==
Breed's simple badness.
 
=== Junk temperaments ===
 
 
=== High-badness temperaments ===
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
!Traditional Name
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
!Fifth steps
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
!Ratio
!Cent
|-
|-
| Negative diminshed 2nd
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
| +12
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|50/49
|34.976
|-
|-
|Perfect 1sn
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|0
|1/1
|0
|81/80
|21.506
|64/63
|27.264
|
|
|
|
|
|
|36/35
|48.770
|
|
|-
|-
|Augmented 1sn
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| +7
|
|
|
|
|
|
|15/14
|119.443
|25/24
|70.672
|54/49
|168.213
|
|
|
|
|-
|-
|Minor 2nd
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
| -5
|
|
|16/15
|111.731
|28/27
|62.961
|21/20
|84.467
|27/25
|133.238
|49/48
|35.697
|
|
|
|
|-
|-
|Major 2nd
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
| +2
|9/8
|203.910
|10/9
|182.404
|8/7
|231.174
|
|
|
|
|
|
|81/70
|252.680
|
|
|-
|-
|Augmented 2nd
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
| +9
|
|
|
|
|
|
|
|
|75/64
|274.582
|
|
|
|
|
|
|-
|-
|Minor 3rd
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
| -3
|32/27
|294.135
|6/5
|315.641
|7/6
|266.871
|
|
|
|
|
|
|
|
|
|
|-
|-
|Major 3rd
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 -5 -6 }} || 2048/1875
| +4
|81/64
|407.820
|5/4
|386.313
|9/7
|435.084
|80/63
|413.578
|
|
|64/49
|462.348
|
|
|
|
|-
|-
|Diminished 4th
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 -4 1 }} || 3125/2916
| -8
|
|
|
|
|
|
|56/45
|378.602
|32/25
|427.373
|
|
|
|
|
|
|-
|-
|Perfect 4th
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
| -1
|4/3
|498.045
|27/20
|519.551
|21/16
|470.781
|
|
|
|
|
|
|35/27
|449.275
|
|
|-
|-
|Augmented 4th
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| +6
|
|
|45/32
|590.224
|81/56
|638.994
|10/7
|617.488
|
|
|
|
|
|
|
|
|-
|-
|Diminshed 5th
| || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
| -6
|}
|
 
|
=== Main sequence ===
|64/45
{| class="wikitable sortable center-2 center-3 center-4"
|609.776
|112/81
|561.006
|7/5
|582.512
|
|
|
|
|
|
|
|
|-
|-
|Perfect 5th
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
| +1
|3/2
|701.955
|40/27
|680.449
|32/21
|729.219
|
|
|
|
|
|
|54/35
|750.725
|
|
|-
|-
|Augmented 5th
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
| +8
|
|
|
|
|
|
|45/28
|821.398
|25/16
|772.627
|
|
|
|
|
|
|-
|-
|Minor 6th
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
| -4
|128/81
|792.180
|8/5
|813.687
|14/9
|764.916
|63/40
|786.422
|
|
|49/32
|737.652
|
|
|
|
|-
|-
|Major 6th
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
| +3
|27/16
|905.865
|5/3
|884.339
|12/7
|933.129
|
|
|
|
|
|
|
|
|
|
|-
|-
|Diminished 7th
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
| -9
|
|
|
|
|
|
|
|
|128/75
|925.418
|
|
|
|
|
|
|-
|-
|Minor 7th
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
| -2
|16/9
|996.090
|9/5
|1017.596
|7/4
|968.826
|
|
|
|
|
|
|140/81
|947.320
|
|
|-
|-
|Major 7th
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
| +5
|
|
|15/8
|1088.269
|27/14
|1131.039
|40/21
|1115.533
|50/27
|1066.762
|96/49
|1164.303
|
|
|
|
|-
|-
|Diminished 8ve
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
| -7
|
|
|
|
|
|
|28/15
|1080.557
|48/25
|1129.328
|49/27
|1031.787
|
|
|
|
|-
|-
|Perfect 8ve
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|0
|2/1
|1200
|160/81
|1178.494
|63/32
|1172.736
|
|
|
|
|
|
|35/18
|1151.230
|
|
|-
|-
|Diminished 9th
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
| -12
|-
|
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|
|-
|
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
|
|-
|
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
|
|-
|
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|
|-
|
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|
|-
|
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|
|
|
|49/25
|1165.028
|}
 
== Intervals of 87edo ==
{| class="wikitable right-2 right-4"
!#
!Cents
!Approximated Ratios
!Ups and Downs Notation
!Solfege
|-
|-
|0
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
|0.000
|1/1
|D
|
|-
|-
|1
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|13.793
|126/125, 100/99, 91/90
|^D
|
|-
|-
|2
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|27.586
|81/80, 64/63, 49/48, 55/54, 65/64
|^^D
|
|-
|-
|3
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
|41.379
|50/49, 45/44
|^^^D/vvvEb
|
|-
|-
|4
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|55.172
|28/27, 36/35, 33/32
|vvEb
|
|-
|-
|5
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|68.966
|25/24, 27/26, 26/25
|vEb
|
|-
|-
|6
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
|82.759
|21/20, 22/21
|Eb
|
|-
|-
|7
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|96.552
|35/33
|^Eb
|
|-
|-
|8
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|110.345
|16/15
|^^Eb
|
|-
|-
|9
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
|124.138
|15/14, 14/13
|^^^Eb
|
|-
|-
|10
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|137.931
|13/12
|^^^^Eb
|
|-
|-
|11
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|151.724
|12/11
|vvvvE
|
|-
|-
|12
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
|165.517
|11/10
|vvvE
|
|-
|-
|13
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
|179.310
|10/9
|vvE
|
|-
|-
|14
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|193.103
|28/25
|vE
|
|-
|-
|15
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|206.897
|9/8
|E
|
|-
|-
|16
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|220.690
|25/22
|^E
|
|-
|-
|17
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
|234.483
|8/7
|^^E
|
|-
|-
|18
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|248.276
|15/13
|^^^E/vvvF
|
|-
|-
|19
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|262.089
|7/6
|vvF
|
|-
|-
|20
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
|275.862
|75/64
|vF
|
|-
|-
|21
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
|289.655
|33/28, 13/11
|F
|
|-
|-
|22
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
|303.448
|25/21, 105/88
|^F
|
|-
|-
|23
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
|317.241
|6/5
|^^F
|
|-
|-
|24
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
|331.034
|63/52
|^^^F
|
|-
|-
|25
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
|344.828
|11/9, 39/32
|^^^^F
|
|-
|-
|26
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|358.621
|27/22, 16/13
|vvvvF#
|
|-
|-
|27
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|372.414
|26/21
|vvvF#
|
|-
|-
|28
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 -8 11 }} || {{monzo| -36 11 8 }}
|386.207
|}
|5/4
 
|vvF#
== Tunings ==
|
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
|-
|-
|29
! rowspan="2" |  
|400.000
! rowspan="2" | Manhattan
|63/50, 44/35
! colspan="2" | Euclidean
|vF#
! rowspan="2" | Chebyshevian
|
|-
|-
|30
! Unskewed
|413.793
! Skewed
|14/11, 33/26
|F#
|
|-
|-
|31
! Equilateral
|427.586
| CEOP: ~3/2 = 697.654¢<br>(1/5-comma)
|32/25
| CEE: ~3/2 = 696.895¢<br>(4/17-comma)
|^F#
| CSEE: ~3/2 = 696.453¢<br>(11/43-comma)
|
| CEC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
|32
! Tenney
|441.379
| CTOP: ~3/2 = 698.020¢
|9/7
| CTE: ~3/2 = 697.214¢
|^^F#
| CWE: ~3/2 = 696.651¢
|
| CTC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
|33
! Benedetti, <br>Wilson
|455.172
| CBOP: ~3/2 = 698.160¢<br>(3/17-comma)
|13/10
| CBE: ~3/2 = 697.374¢<br>(36/169-comma)
|^^^F#/vvvG
| CSBE: ~3/2 = 696.787¢<br>(31/129-comma)
|
| CBC: ~3/2 = 696.578¢<br>(1/4-comma)
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
|-
|-
|34
! rowspan="2" |  
|468.966
! rowspan="2" | Manhattan
|21/16
! colspan="2" | Euclidean
|vvG
! rowspan="2" | Chebyshevian
|
|-
|-
|35
! Unskewed
|482.759
! Skewed
|33/25
|vG
|
|-
|-
|36
! Equilateral
|496.552
| CEOP: ~3/2 = 697.344¢
|4/3
| CEE: ~3/2 = 696.884¢
|G
| CSEE: ~3/2 = 696.725¢
|
| CEC: ~3/2 = 696.883¢
|-
|-
|37
! Tenney
|510.345
| CTOP: ~3/2 = 696.646¢
|75/56
| CTE: ~3/2 = 696.952¢
|^G
| CWE: ~3/2 = 696.656¢
|
| CTC: ~3/2 = 696.883¢
|-
|-
|38
! Benedetti, <br>Wilson
|524.138
| CBOP: ~3/2 = 697.842¢
|27/20
| CBE: ~3/2 = 697.015¢
|^^G
| CSBE: ~3/2 = 696.631¢
|
| CBC: ~3/2 = 696.883¢
|}
 
== Temperament pages ==
Note:
# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[optimal tuning]]s ([[CTE]], [[CWE]]/[[POTE]]), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], [[optimal ET sequence]], [[badness]], [[complexity spectrum]], and others.
# Comma list should show the simplest commas sufficient to define the temperament, stated in [[Normal lists #Normal interval list]].
# Mapping generators should show all the ratios as used in the mapping, including the period.
# Since minimax tunings are based on tonality diamond, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "CTE/CWE", otherwise show "subgroup/inharmonic CTE/CWE" instead.
 
Get a family for:
* <s>Ripple (3 different 7-limit extensions)</s> done
* <s>Smate (2 different 7-limit extensions)</s> done
* <s>Passion (4 different 7-limit extensions, 3 strong and 1 weak)</s> done
* <s>Undim</s> done
* <s>Quintaleap</s> done
* <s>Quindromeda</s> done
* Parakleismic (many reasonable but unnamed 7-limit extensions)
* Schismatic rank three family (perhaps)
 
Who's next?
* <s>Meantone family</s>
* <s>Didymus rank three family</s>
* <s>Archytas clan</s>
* <s>Archytas family</s>
* <s>Father family</s>
* <s>Trienstonic clan</s>
* <s>Septisemi temperaments</s>
* <s>Slendro clan</s>
* <s>Semiphore family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* <s>Mint temperaments</s>
* <s>Mint family</s>
* <s>Ripple family</s>
* <s>Smate family</s>
* <s>Augmented family</s>
* <s>Dimipent family</s>
* <s>Dicot family</s>
* <s>Bug family</s>
* <s>Pelogic family</s>
* <s>Marvel temperaments</s>
* <s>Marvel family</s>
* <s>Gamelismic clan</s>
* <s>Gamelismic family</s>
* <s>Starling temperaments</s>
* <s>Starling family</s>
* <s>Sensamagic clan</s>
* <s>Sensamagic family</s>
* <s>Magic family</s>
* <s>Sensipent family</s>
* <s>Keemic temperaments</s>
* <s>Keemic family</s>
* <s>Sengic family</s>
* <s>Schismatic family</s>
* <s>Kleismic family</s>
* <s>Kleismic rank three family</s>
* <s>Würschmidt family</s>
* <s>Unicorn family</s>
* <s>Shibboleth family</s>
* <s>Immunity family</s>
* <s>Fifive family</s>
* <s>Trisedodge family</s>
* <s>Quintosec family</s>
* <s>Pental family</s>
* <s>Sycamore family</s>
* <s>Semicomma family</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</s>
* <s>Hemimean clan</s>
* <s>Hemimean family</s>
* <s>Hemifamity temperaments</s>
* <s>Hemifamity family</s>
* <s>Porwell temperaments</s>
* <s>Porwell family</s>
* <s>Hemimage temperaments</s>
* <s>Hemimage family</s>
* <s>Porcupine family</s>
* <s>Porcupine rank three family</s>
* <s>Tetracot family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic rank three family</s>
* <s>Compton family</s>
* <s>Amity family</s>
* <s>Misty family</s>
* <s>Undim family</s>
* <s>Lehmerismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Ragismic microtemperaments</s>
* <s>Ragismic family</s>
* <s>Landscape microtemperaments</s>
* <s>Landscape family</s>
* <s>Dimcomp family</s>
* <s>Mirkwai clan</s>
* <s>Mirkwai family</s>
* <s>Quince clan</s>
* <s>Breedsmic temperaments</s>
* <s>Breed family</s>
* <s>Escapade family</s>
* <s>Gravity family</s>
* <s>Cataharry temperaments</s>
* <s>Cataharry family</s>
* <s>Varunismic temperaments</s>
* <s>Rastmic rank three clan</s>
* <s>Biyatismic clan</s>
* <s>Ptolemismic clan</s>
* <s>Valinorsmic clan</s>
* <s>Pentacircle clan</s>
* <s>Keenanismic temperaments</s>
* <s>Werckismic temperaments</s>
* <s>Swetismic temperaments</s>
* <s>Wizmic microtemperaments</s>
* <s>Metric microtemperaments</s>
* <s>Horwell temperaments</s>
* <s>Horwell family</s>
* <s>Luna family</s>
* <s>Vulture family</s>
* <s>Tricot family</s>
* <s>Minortonic family</s>
* <s>Gammic family</s>
* <s>Vishnuzmic family</s>
* <s>Garischismic clan</s>
* <s>Canousmic temperaments</s>
* <s>Canou family</s>
* <s>Semicanousmic clan</s>
* <s>Semiporwellismic clan</s>
* <s>Olympic clan</s>
* <s>Alphaxenic rank three clan</s>
* <s>Mirwomo temperaments</s>
* <s>Gariboh clan</s>
* <s>Gariboh family</s>
* <s>Octagar temperaments</s>
* <s>Octagar family</s>
* <s>Wesley family</s>
* <s>Apotome family</s>
* [[Mabila family]]
* [[Maquila family]]
* [[Maja family]]
* [[Ditonmic family]]
* <s>Greenwoodmic temperaments</s>
* <s>Avicennmic temperaments</s>
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
|-
|39
! [[TE error|Absolute]] (¢)
|537.931
! [[TE simple badness|Relative]] (%)
|15/11
|^^^G
|
|-
|-
|40
| 2.3
|551.724
| {{monzo| -49 31 }}
|11/8
| {{mapping| 31 49 }}
|^^^^G
| +1.63
|
| 1.64
| 4.22
|-
|-
|41
| 2.3.5
|565.517
| 81/80, 393216/390625
|18/13
| {{mapping| 31 49 72 }}
|vvvvG#, vAb
| +0.98
|
| 1.63
| 4.20
|-
|-
|42
| 2.3.5.7
|579.310
| 81/80, 126/125, 1029/1024
|7/5, 39/28
| {{mapping| 31 49 72 87 }}
|vvvG#, Ab
| +0.83
|
| 1.43
| 3.70
|-
|-
|43
| 2.3.5.7.11
|593.103
| 81/80, 99/98, 121/120, 126/125
|45/32
| {{mapping| 31 49 72 87 107 }}
|vvG#, ^Ab
| +1.21
|
| 1.49
| 3.84
|}
|}
== Scale tree ==
; 6-tone
: <s>1L 5s</s>, [[2L 4s]], <s>3L 3s</s>, [[4L 2s]], <s>5L 1s</s>
; 7-tone
: <s>1L 6s</s>, <s>2L 5s</s>, <s>3L 4s</s>, <s>4L 3s</s>, <s>5L 2s</s>, <s>6L 1s</s>
; 8-tone
: [[1L 7s]], <s>2L 6s</s>, [[3L 5s]], <s>4L 4s</s>, <s>5L 3s</s>, <s>6L 2s</s>, [[7L 1s]]
; 9-tone
: [[1L 8s]], [[2L 7s]], <s>3L 6s</s>, <s>4L 5s</s>, <s>5L 4s</s>, <s>6L 3s</s>, [[7L 2s]], [[8L 1s]]
; 10-tone
: [[1L 9s]], <s>2L 8s</s>, <s>3L 7s</s>, <s>4L 6s</s>, <s>5L 5s</s>, <s>6L 4s</s>, <s>7L 3s</s>, [[8L 2s]], [[9L 1s]]
; 11-tone
: [[1L 10s]], [[2L 9s]], [[3L 8s]], <s>4L 7s</s>, <s>5L 6s</s>, <s>6L 5s</s>, <s>7L 4s</s>, [[8L 3s]], [[9L 2s]], [[10L 1s]]
; 12-tone
: [[1L 11s]], [[2L 10s]], [[3L 9s]], [[4L 8s]], <s>5L 7s</s>, <s>6L 6s</s>, <s>7L 5s</s>, [[8L 4s]], [[9L 3s]], [[10L 2s]], [[11L 1s]]
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