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== Accidentals ==
; Wiki templates : {{Flat}} {{natural}} {{sharp}}
; Unicode characters : ♭ ♮ ♯
; Bravura font : <span class="bravura">&#xE260;</span> <span class="bravura">&#xE261;</span> <span class="bravura">&#xE262;</span>
; Heji font : <span class="heji">e</span> <span class="heji">n</span> <span class="heji">v</span>
== Template: Temperament data ==
{{User:FloraC/Temperament data
{{User:FloraC/Temperament data
| Subgroup = 2.3.5.7
| Subgroup = 2.3.5.7
Line 10: Line 17:
}}
}}


<span class="heji">n</span>
== Catalog of 5-limit rank-2 temperaments ==
Sintel's TE logflat badness.


<span class="bravura">&#xE264;</span>
Error > 25{{c}}, badness < 3
{| class="wikitable sortable center-2 center-3 center-4"
|-
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|  || 2.63 || 40.1 || .392 || {{mapping| 1 0 -1 | 0 1 2 }} || 10/9
|-
| Antitonic || 2.83 || 41.6 || .508 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|-
| University || 5.59 || 25.3 || 2.39 || {{mapping| 1 1 2 | 0 3 2 }} || 144/125
|}


== 5-limit rank-2 temperaments by TE simple badness ==
Complexity < 30, error < 25{{c}}, badness < 3
Breed's simple badness.


=== Junk temperaments ===
=== High-badness temperaments ===
{| class="wikitable sortable center-2 center-3 center-4"
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
| Father || 3.17 || 20.4 || .349 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
|-
|-
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
| Dicot || 3.73 || 11.0 || .306 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
|-
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| Bug || 4.30 || 17.9 || .769 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
|-
|-
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
| Meantone || 5.08 || 2.44 || .173 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
| Mavila || 5.68 || 9.36 || .928 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
| Augmented || 6.40 || 3.71 || .523 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
| Porcupine || 6.86 || 4.14 || .722 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
|-
|-
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 -5 -6 }} || 2048/1875
| Blackwood || 7.29 || 7.14 || 1.50 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 -4 1 }} || 3125/2916
| Diminished || 7.54 || 4.79 || 1.11 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
| Supersharp || 7.58 || 12.3 || 2.88 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
|-
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| Diaschismic || 8.76 || 1.29 || .467 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
| Magic || 9.98 || 1.71 || .919 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|}
 
=== Main sequence ===
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
| Hanson || 11.1 || .422 || .310 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
| Negri || 11.3 || 2.61 || 2.04 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
|-
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
| Tetracot || 11.5 || 1.39 || 1.14 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
| Helmholtz || 12.8 || .0881 || .0999 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
| Sensipent || 14.1 || .550 || .826 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
| Würschmidt || 16.3 || .404 || .952 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
| Amity || 16.4 || .217 || .515 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
|-
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
| Valentine || 16.7 || 1.14 || 2.88 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
| Compton || 17.4 || .778 || 2.22 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
| Orson || 17.5 || .332 || .957 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
| Misty || 21.3 || .476 || 2.50 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
| Gravity || 21.4 || .415 || 2.19 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
|-
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
| Parakleismic || 24.8 || .123 || 1.02 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
|-
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
| Quartonic || 24.9 || .331 || 2.75 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
|-
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
| Escapade || 25.8 || .213 || 1.97 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
| Vishnuzmic || 26.5 || .0727 || .731 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
|-
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
| Vulture || 27.3 || .0890 || .972 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
| Unidecmic || 29.3 || .143 || 1.93 || {{mapping| 2 5 8 | 0 6 11 }} || {{monzo| -7 22 -12 }}
|}
 
3 < badness < 6
 
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
| Avila || 7.79 || 16.7 || 4.27 || {{mapping| 1 0 -7 | 0 1 6 }} || 729/640
|-
|-
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
| Enipucrop || 8.16 || 11.5 || 3.38 || {{mapping| 1 2 2 | 0 3 -2 }} || 1125/1024
|-
|-
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
| Laconic || 8.87 || 10.1 || 3.80 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
|-
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
| Lafayette || 9.31 || 10.8 || 4.70 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
|-
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
| Symbolic || 9.38 || 9.40 || 4.19 || {{mapping| 1 3 2 | 0 4 -1 }} || 2048/1875
|-
|-
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
| Sixix || 9.81 || 7.06 || 3.59 || {{mapping| 1 3 4 | 0 5 6 }} || 3125/2916
|-
|-
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
| Whitewood || 10.1 || 6.49 || 3.63 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|-
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
| Ripple || 11.2 || 4.35 || 3.26 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
|-
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
| Progress || 11.9 || 6.38 || 5.77 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|-
|-
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
| Superpyth || 12.2 || 3.26 || 3.17 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
| Wesley || 13.6 || 4.25 || 5.81 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
|-
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
| Stump || 14.4 || 2.91 || 4.71 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
| Passion || 14.5 || 2.42 || 3.95 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
|-
|-
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
| Doublewide || 14.7 || 3.09 || 5.32 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
| Immunity || 17.2 || 1.59 || 4.33 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
| Shibboleth || 17.3 || 1.91 || 5.34 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
|-
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
| Unicorn || 18.0 || 1.12 || 3.53 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
|-
|-
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
| Mynic || 18.6 || 1.69 || 5.86 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
|-
|-
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
| Ampersand || 19.9 || .917 || 3.89 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
| Sycamore || 20.5 || 1.06 || 4.93 || {{mapping| 2 2 3 | 0 5 7 }} || 48828125/47775744
|-
|-
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
| Fifive || 20.8 || .992 || 4.83 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
| Rodan || 22.2 || .669 || 3.95 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
| Mabila || 23.8 || .753 || 5.45 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
| Ditonic || 26.3 || .399 || 3.92 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
|-
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
| Trisedodge || 27.7 || .518 || 5.92 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 -8 11 }} || {{monzo| -36 11 8 }}
| Demibuzzard || 28.6 || .243 || 3.06 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
|}
|}


== Tunings to be reviewed ==
30 < complexity < 60, badness < 3
{| class="wikitable mw-collapsible mw-collapsed"
 
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
{| class="wikitable sortable center-2 center-3 center-4"
|-
! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
|-
| Tenney || CTC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CTE<br>~3/2 = 697.2143¢ || CTOP<br>~3/2 = 698.0197¢
|-
| Tenney-Weil || CTWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CTWE<br>~3/2 = 696.6512¢ || CTWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
|-
| Equilateral || CEC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CEE<br>~3/2 = 696.8947¢<br>Eigenmonzo basis: 2.1875 (4/17-comma tuning) || CEOP<br>~3/2 = 697.6537¢<br>Eigenmonzo basis: 2.15 (1/5-comma tuning)
|-
|-
| Equilateral-Weil || CEWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CEWE<br>~3/2 = 696.4534¢<br>Eigenmonzo basis: 2.48828125/3 (11/43-comma tuning) || CEWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| Benedetti || CBC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CBE<br>~3/2 = 697.3738¢<br>Eigenmonzo basis: 2.{{monzo| 0 25 36 }} (36/169-comma tuning) || CBOP<br>~3/2 = 698.1598¢<br>Eigenmonzo basis: 2.30375 (3/17-comma tuning)
| Luna || 33.5 || .0239 || .483 || {{mapping| 1 4 2 | 0 15 -2 }} || {{monzo| 38 -2 -15 }}
|-
|-
| Benedetti-Weil || CBWC<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning) || CBWE<br>~3/2 = 696.7868¢<br>Eigenmonzo basis: 2.{{monzo| 0 5 31 }} (31/129-comma tuning) || CBWOP<br>~3/2 = 696.5784¢<br>Eigenmonzo basis: 2.5 (1/4-comma tuning)
| Enneadecal || 35.8 || .0454 || 1.12 || {{mapping| 19 0 14 | 0 1 1 }} || {{monzo| -14 -19 19 }}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
|-
|-
! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
| Gammic || 37.2 || .0740 || 2.06 || {{mapping| 1 1 2 | 0 20 11 }} || {{monzo| -29 -11 20 }}
|-
|-
| Tenney || CTC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CTE<br>~3/2 = 696.9521¢ || CTOP<br>~3/2 = 696.6458¢
| Ennealimmal || 38.7 || .0128 || .403 || {{mapping| 9 1 1 | 0 2 3 }} || {{monzo| 1 -27 18 }}
|-
|-
| Tenney-Weil || CTWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CTWE<br>~3/2 = 696.6562¢ || CTWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
| Alphatricot || 39.3 || .0330 || 1.08 || {{mapping| 1 0 -13 | 0 3 29 }} || {{monzo| 39 -29 3 }}
|-
|-
| Equilateral || CEC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CEE<br>~3/2 = 696.8843¢<br>Eigenmonzo basis: 2.{{monzo| 0 1 4 10 }} || CEOP<br>~3/2 = 697.3437¢<br>Eigenmonzo basis: 2.21
| Kwazy || 43.2 || .00762 || .331 || {{mapping| 2 1 6 | 0 8 -5 }} || {{monzo| -53 10 16 }}
|-
|-
| Equilateral-Weil || CEWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CEWE<br>~3/2 = 696.7248¢<br>Eigenmonzo basis: 2.4117715/9 || CEWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
| Minortone || 45.3 || .0139 || .698 || {{mapping| 1 16 32 | 0 17 35 }} || {{monzo| -16 35 -17 }}
|-
|-
| Benedetti || CBC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CBE<br>~3/2 = 697.0147¢<br>Eigenmonzo basis: 2.{{monzo| 0 1225 1764 2250 }} || CBOP<br>~3/2 = 697.8422¢<br>Eigenmonzo basis: 2.750141
| Monzismic || 51.7 || .00326 || .244 || {{mapping| 1 0 -27 | 0 2 37 }} || {{monzo| 54 -37 2 }}
|-
|-
| Benedetti-Weil || CBWC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CBWE<br>~3/2 = 696.6306¢<br>Eigenmonzo basis: 2.{{monzo| 0 -3290 3171 7215 }} || CBWOP<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7
| Vavoom || 54.2 || .0269 || 2.31 || {{mapping| 1 0 4 | 0 17 -18 }} || {{monzo| -68 18 17 }}
|}
|}


== Temperament pages ==
== 5-limit rank-2 temperaments by TE simple badness ==
Note:
Breed's TE simple badness.  
# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[optimal tuning]] ([[CTE]]), [[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", otherwise show "subgroup CTE" or "inharmonic CTE" instead.  


Get a family for:
=== Junk temperaments ===
* <s>Ripple (3 different 7-limit extensions)</s> done
=== High-badness temperaments ===
* <s>Smate (2 different 7-limit extensions)</s> done
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
* <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
|-
|-
! [[TE error|Absolute]] (¢)
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
| {{monzo| -49 31 }}
| {{mapping| 31 49 }}
| +1.63
| 1.64
| 4.22
|-
|-
| 2.3.5
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
| 81/80, 393216/390625
| {{mapping| 31 49 72 }}
| +0.98
| 1.63
| 4.20
|-
|-
| 2.3.5.7
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| 81/80, 126/125, 1029/1024
| {{mapping| 31 49 72 87 }}
| +0.83
| 1.43
| 3.70
|-
|-
| 2.3.5.7.11
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
| 81/80, 99/98, 121/120, 126/125
| {{mapping| 31 49 72 87 107 }}
| +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]]
 
(Bounded by branch depth = 7)
 
{| class="wikitable center-all"
! colspan="7" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
|-
| 4\7 || || || || || || || 685.714 || 1 || 1 || 1.000 ||
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 5 6 }} || 2048/1875
|-
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 4 -1 }} || 3125/2916
|-
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
| Progress || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|}
 
=== Main sequence ===
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
|-
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| Diaschismic || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||  
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
|}
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 5-limit norm-based tunings
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
! Constrained
! Constrained & skewed
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
! Equilateral
| CEOP: ~3/2 = 697.654{{c}}<br>(1/5-comma)
| CEE: ~3/2 = 696.895{{c}}<br>(4/17-comma)
| CSEE: ~3/2 = 696.453{{c}}<br>(11/43-comma)
| CEC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
! Tenney
| CTOP: ~3/2 = 698.020{{c}}
| CTE: ~3/2 = 697.214{{c}}
| CWE: ~3/2 = 696.651{{c}}
| CTC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
! Benedetti, <br>Wilson
|-
| CBOP: ~3/2 = 698.160{{c}}<br>(3/17-comma)
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
| CBE: ~3/2 = 697.374{{c}}<br>(36/169-comma)
|-
| CSBE: ~3/2 = 696.787{{c}}<br>(31/129-comma)
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
| CBC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 7-limit norm-based tunings
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
! Constrained
! Constrained & skewed
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
! Equilateral
| CEOP: ~3/2 = 697.344{{c}}
| CEE: ~3/2 = 696.884{{c}}
| CSEE: ~3/2 = 696.725{{c}}
| CEC: ~3/2 = 696.883{{c}}
|-
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
! Tenney
| CTOP: ~3/2 = 696.646{{c}}
| CTE: ~3/2 = 696.952{{c}}
| CWE: ~3/2 = 696.656{{c}}
| CTC: ~3/2 = 696.883{{c}}
|-
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 697.842{{c}}
| CBE: ~3/2 = 697.015{{c}}
| CSBE: ~3/2 = 696.631{{c}}
| CBC: ~3/2 = 696.883{{c}}
|}
|}

Latest revision as of 12:07, 19 May 2026

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Template: Temperament data

Subgroup: 2.3.5.7

Comma list: 81/80, 126/125

Mapping: [⟨1 0 -4 -13], ⟨0 1 4 10]]

mapping generators: ~2, ~3

Wedgie: ⟨⟨ 1 4 10 4 13 12 ]]

Optimal tuning (CTE): ~3/2 = 696.9521

Optimal ET sequence: 12, 19, 31, 81, 112b, 143b

Badness: 0.0137

Catalog of 5-limit rank-2 temperaments

Sintel's TE logflat badness.

Error > 25 ¢, badness < 3

Temperament Complexity Error (¢) Badness Mapping Comma list
2.63 40.1 .392 [⟨1 0 -1], ⟨0 1 2]] 10/9
Antitonic 2.83 41.6 .508 [⟨2 3 0], ⟨0 0 1]] 9/8
University 5.59 25.3 2.39 [⟨1 1 2], ⟨0 3 2]] 144/125

Complexity < 30, error < 25 ¢, badness < 3

Temperament Complexity Error (¢) Badness Mapping Comma list
Father 3.17 20.4 .349 [⟨1 0 4], ⟨0 1 -1]] 16/15
Dicot 3.73 11.0 .306 [⟨1 1 2], ⟨0 2 1]] 25/24
Bug 4.30 17.9 .769 [⟨1 0 0], ⟨0 2 3]] 27/25
Meantone 5.08 2.44 .173 [⟨1 0 -4], ⟨0 1 4]] 81/80
Mavila 5.68 9.36 .928 [⟨1 0 7], ⟨0 1 -3]] 135/128
Augmented 6.40 3.71 .523 [⟨3 0 7], ⟨0 1 0]] 128/125
Porcupine 6.86 4.14 .722 [⟨1 2 3], ⟨0 3 5]] 250/243
Blackwood 7.29 7.14 1.50 [⟨5 8 0], ⟨0 0 1]] 256/243
Diminished 7.54 4.79 1.11 [⟨4 0 3], ⟨0 1 1]] 648/625
Supersharp 7.58 12.3 2.88 [⟨2 0 -5], ⟨0 1 3]] 800/729
Diaschismic 8.76 1.29 .467 [⟨2 0 11], ⟨0 1 -2]] 2048/2025
Magic 9.98 1.71 .919 [⟨1 0 2], ⟨0 5 1]] 3125/3072
Hanson 11.1 .422 .310 [⟨1 0 1], ⟨0 6 5]] 15625/15552
Negri 11.3 2.61 2.04 [⟨1 2 2], ⟨0 4 -3]] 16875/16384
Tetracot 11.5 1.39 1.14 [⟨1 1 1], ⟨0 4 9]] 20000/19683
Helmholtz 12.8 .0881 .0999 [⟨1 0 15], ⟨0 1 -8]] 32805/32768
Sensipent 14.1 .550 .826 [⟨1 6 8], ⟨0 7 9]] 78732/78125
Würschmidt 16.3 .404 .952 [⟨1 7 3], ⟨0 8 1]] 393216/390625
Amity 16.4 .217 .515 [⟨1 3 6], ⟨0 5 13]] 1600000/1594323
Valentine 16.7 1.14 2.88 [⟨1 1 2], ⟨0 9 5]] 1990656/1953125
Compton 17.4 .778 2.22 [⟨12 19 0], ⟨0 0 1]] 531441/524288
Orson 17.5 .332 .957 [⟨1 0 3], ⟨0 7 -3]] 2109375/2097152
Misty 21.3 .476 2.50 [⟨3 0 26], ⟨0 1 -4]] 67108864/66430125
Gravity 21.4 .415 2.19 [⟨1 5 12], ⟨0 6 17]] 129140163/128000000
Parakleismic 24.8 .123 1.02 [⟨1 5 6], ⟨0 13 14]] [8 14 -13⟩
Quartonic 24.9 .331 2.75 [⟨1 2 3], ⟨0 11 18]] [3 -18 11⟩
Escapade 25.8 .213 1.97 [⟨1 2 2], ⟨0 9 -7]] [32 -7 -9⟩
Vishnuzmic 26.5 .0727 .731 [⟨2 4 5], ⟨0 7 3]] [23 6 -14⟩
Vulture 27.3 .0890 .972 [⟨1 0 -6], ⟨0 4 21]] [24 -21 4⟩
Unidecmic 29.3 .143 1.93 [⟨2 5 8], ⟨0 6 11]] [-7 22 -12⟩

3 < badness < 6

Temperament Complexity Error (¢) Badness Mapping Comma list
Avila 7.79 16.7 4.27 [⟨1 0 -7], ⟨0 1 6]] 729/640
Enipucrop 8.16 11.5 3.38 [⟨1 2 2], ⟨0 3 -2]] 1125/1024
Laconic 8.87 10.1 3.80 [⟨1 1 1], ⟨0 3 7]] 2187/2000
Lafayette 9.31 10.8 4.70 [⟨1 1 2], ⟨0 5 3]] 3456/3125
Symbolic 9.38 9.40 4.19 [⟨1 3 2], ⟨0 4 -1]] 2048/1875
Sixix 9.81 7.06 3.59 [⟨1 3 4], ⟨0 5 6]] 3125/2916
Whitewood 10.1 6.49 3.63 [⟨7 11 0], ⟨0 0 1]] 2187/2048
Ripple 11.2 4.35 3.26 [⟨1 2 3], ⟨0 5 8]] 6561/6250
Progress 11.9 6.38 5.77 [⟨1 0 5], ⟨0 3 -5]] 32768/30375
Superpyth 12.2 3.26 3.17 [⟨1 0 -12], ⟨0 1 9]] 20480/19683
Wesley 13.6 4.25 5.81 [⟨1 4 3], ⟨0 7 2]] 78125/73728
Stump 14.4 2.91 4.71 [⟨1 0 6], ⟨0 3 -7]] 273375/262144
Passion 14.5 2.42 3.95 [⟨1 2 2], ⟨0 5 -4]] 262144/253125
Doublewide 14.7 3.09 5.32 [⟨2 1 3], ⟨0 4 3]] 390625/373248
Immunity 17.2 1.59 4.33 [⟨1 0 -8], ⟨0 2 13]] 1638400/1594323
Shibboleth 17.3 1.91 5.34 [⟨1 4 5], ⟨0 9 10]] 1953125/1889568
Unicorn 18.0 1.12 3.53 [⟨1 2 3], ⟨0 8 13]] 1594323/1562500
Mynic 18.6 1.69 5.86 [⟨1 9 9], ⟨0 10 9]] 10077696/9765625
Ampersand 19.9 .917 3.89 [⟨1 1 3], ⟨0 6 -7]] 34171875/33554432
Sycamore 20.5 1.06 4.93 [⟨2 2 3], ⟨0 5 7]] 48828125/47775744
Fifive 20.8 .992 4.83 [⟨2 2 3], ⟨0 5 7]] 9765625/9565938
Rodan 22.2 .669 3.95 [⟨1 1 -1], ⟨0 3 17]] [20 -17 3⟩
Mabila 23.8 .753 5.45 [⟨1 6 1], ⟨0 10 -3]] [28 -3 -10⟩
Ditonic 26.3 .399 3.92 [⟨1 6 3], ⟨0 13 2]] [-27 -2 13⟩
Trisedodge 27.7 .518 5.92 [⟨5 1 7], ⟨0 3 2]] [19 10 -15⟩
Demibuzzard 28.6 .243 3.06 [⟨1 4 -1], ⟨0 8 -11]] [-36 11 8⟩

30 < complexity < 60, badness < 3

Temperament Complexity Error (¢) Badness Mapping Comma list
Luna 33.5 .0239 .483 [⟨1 4 2], ⟨0 15 -2]] [38 -2 -15⟩
Enneadecal 35.8 .0454 1.12 [⟨19 0 14], ⟨0 1 1]] [-14 -19 19⟩
Gammic 37.2 .0740 2.06 [⟨1 1 2], ⟨0 20 11]] [-29 -11 20⟩
Ennealimmal 38.7 .0128 .403 [⟨9 1 1], ⟨0 2 3]] [1 -27 18⟩
Alphatricot 39.3 .0330 1.08 [⟨1 0 -13], ⟨0 3 29]] [39 -29 3⟩
Kwazy 43.2 .00762 .331 [⟨2 1 6], ⟨0 8 -5]] [-53 10 16⟩
Minortone 45.3 .0139 .698 [⟨1 16 32], ⟨0 17 35]] [-16 35 -17⟩
Monzismic 51.7 .00326 .244 [⟨1 0 -27], ⟨0 2 37]] [54 -37 2⟩
Vavoom 54.2 .0269 2.31 [⟨1 0 4], ⟨0 17 -18]] [-68 18 17⟩

5-limit rank-2 temperaments by TE simple badness

Breed's TE simple badness.

Junk temperaments

High-badness temperaments

Temperament Complexity Error (¢) Badness (moct) Mapping Comma list
Yo .367 26.0 7.95 [⟨1 0 -1], ⟨0 1 -2]] 10/9
Antitonic .395 27.0 8.89 [⟨2 3 0], ⟨0 0 1]] 9/8
Father .443 13.2 4.87 [⟨1 0 4], ⟨0 1 -1]] 16/15
Bug .602 11.6 5.81 [⟨1 0 0], ⟨0 2 3]] 27/25
Supersharp 1.06 7.94 7.01 [⟨2 0 -5], ⟨0 1 3]] 800/729
Laconic 1.24 6.52 6.74 [⟨1 1 1], ⟨0 3 7]] 2187/2000
Lafayette 1.30 7.00 7.60 [⟨1 1 2], ⟨0 5 3]] 3456/3125
Symbolic 1.31 6.09 6.66 [⟨1 3 4], ⟨0 5 6]] 2048/1875
Sixix 1.37 4.57 5.22 [⟨1 3 2], ⟨0 4 -1]] 3125/2916
Uncle 1.40 7.53 8.80 [⟨1 0 12], ⟨0 1 -6]] 4096/3645
Whitewood 1.42 4.20 4.95 [⟨7 11 0], ⟨0 0 1]] 2187/2048
Progress 1.66 4.13 5.72 [⟨1 0 5], ⟨0 3 -5]] 32768/30375

Main sequence

Temperament Complexity Error (¢) Badness (moct) Mapping Comma list
Dicot .521 7.09 3.08 [⟨1 1 2], ⟨0 2 1]] 25/24
Meantone .711 1.58 .937 [⟨1 0 -4], ⟨0 1 4]] 81/80
Mavila .795 6.06 4.02 [⟨1 0 7], ⟨0 1 -3]] 135/128
Augmented .894 2.40 1.79 [⟨3 0 7], ⟨0 1 0]] 128/125
Porcupine .960 2.68 2.14 [⟨1 2 3], ⟨0 3 5]] 250/243
Blackwood 1.02 4.63 3.93 [⟨5 8 0], ⟨0 0 1]] 256/243
Diminished 1.05 3.10 2.73 [⟨4 0 3], ⟨0 1 1]] 648/625
Diaschismic 1.22 .835 .852 [⟨2 0 11], ⟨0 1 -2]] 2048/2025
Magic 1.40 1.11 1.29 [⟨1 0 2], ⟨0 5 1]] 3125/3072
Hanson 1.55 .274 .353 [⟨1 0 1], ⟨0 6 5]] 15625/15552
Ripple 1.56 2.82 3.66 [⟨1 2 3], ⟨0 5 8]] 6561/6250
Negri 1.58 1.69 2.23 [⟨1 2 2], ⟨0 4 -3]] 16875/16384
Tetracot 1.61 .900 1.21 [⟨1 1 1], ⟨0 4 9]] 20000/19683
Superpyth 1.70 2.11 2.99 [⟨1 0 -12], ⟨0 1 9]] 20480/19683
Helmholtz 1.79 .0570 .0851 [⟨1 0 15], ⟨0 1 -8]] 32805/32768
Wesley 1.91 2.75 4.37 [⟨1 4 3], ⟨0 7 2]] 78125/73728
Sensipent 1.97 .356 .584 [⟨1 6 8], ⟨0 7 9]] 78732/78125
Stump 2.02 1.88 3.16 [⟨1 0 6], ⟨0 3 -7]] 273375/262144
Passion 2.02 1.57 2.64 [⟨1 2 2], ⟨0 5 -4]] 262144/253125
Doublewide 2.06 2.00 3.43 [⟨2 1 3], ⟨0 4 3]] 390625/373248
Würschmidt 2.29 .262 .499 [⟨1 7 3], ⟨0 8 1]] 393216/390625
Amity 2.29 .140 .268 [⟨1 3 6], ⟨0 5 13]] 1600000/1594323
Valentine 2.34 .736 1.44 [⟨1 1 2], ⟨0 9 5]] 1990656/1953125
Immunity 2.40 1.03 2.06 [⟨1 0 -8], ⟨0 2 13]] 1638400/1594323
Shibboleth 2.42 1.24 2.50 [⟨1 4 5], ⟨0 9 10]] 1953125/1889568
Compton 2.44 .504 1.02 [⟨12 19 0], ⟨0 0 1]] 531441/524288
Orson 2.44 .215 .438 [⟨1 0 3], ⟨0 7 -3]] 2109375/2097152
Unicorn 2.52 .725 1.52 [⟨1 2 3], ⟨0 8 13]] 1594323/1562500
Mynic 2.60 1.10 2.37 [⟨1 9 9], ⟨0 10 9]] 10077696/9765625
Ampersand 2.78 .594 1.38 [⟨1 1 3], ⟨0 6 -7]] 34171875/33554432
Fifive 2.91 .643 1.56 [⟨2 2 3], ⟨0 5 7]] 9765625/9565938
Misty 2.99 .308 .767 [⟨3 0 26], ⟨0 1 -4]] 67108864/66430125
Gravity 2.99 .269 .669 [⟨1 5 12], ⟨0 6 17]] 129140163/128000000
Rodan 3.10 .433 1.12 [⟨1 1 -1], ⟨0 3 17]] [20 -17 3⟩
3.11 .757 1.96 [⟨1 0 -23], ⟨0 1 16]] [-23 16 -1⟩
Mabila 3.32 .488 1.35 [⟨1 6 1], ⟨0 10 -3]] [28 -3 -10⟩
Parakleismic 3.47 .0798 .231 [⟨1 5 6], ⟨0 13 14]] [8 14 -13⟩
Quartonic 3.48 .214 .621 [⟨1 2 3], ⟨0 11 18]] [3 -18 11⟩
Escapade 3.60 .138 .414 [⟨1 2 2], ⟨0 9 -7]] [32 -7 -9⟩
Ditonic 3.68 .258 .792 [⟨1 6 3], ⟨0 13 2]] [-27 -2 13⟩
Vishnuzmic 3.71 .0471 .145 [⟨2 4 5], ⟨0 7 3]] [23 6 -14⟩
Vulture 3.81 .0576 .183 [⟨1 0 -6], ⟨0 4 21]] [24 -21 4⟩
Trisedodge 3.87 .336 1.08 [⟨5 1 7], ⟨0 3 2]] [19 10 -15⟩
4.00 .157 .524 [⟨1 4 -1], ⟨0 8 -11]] [-36 11 8⟩

Tunings

5-limit norm-based tunings
Manhattan Euclidean Chebyshevian
Constrained Constrained & skewed
Equilateral CEOP: ~3/2 = 697.654 ¢
(1/5-comma) 		CEE: ~3/2 = 696.895 ¢
(4/17-comma) 		CSEE: ~3/2 = 696.453 ¢
(11/43-comma) 		CEC: ~3/2 = 696.578 ¢
(1/4-comma)
Tenney CTOP: ~3/2 = 698.020 ¢ CTE: ~3/2 = 697.214 ¢ CWE: ~3/2 = 696.651 ¢ CTC: ~3/2 = 696.578 ¢
(1/4-comma)
Benedetti,
Wilson 		CBOP: ~3/2 = 698.160 ¢
(3/17-comma) 		CBE: ~3/2 = 697.374 ¢
(36/169-comma) 		CSBE: ~3/2 = 696.787 ¢
(31/129-comma) 		CBC: ~3/2 = 696.578 ¢
(1/4-comma)
7-limit norm-based tunings
Manhattan Euclidean Chebyshevian
Constrained Constrained & skewed
Equilateral CEOP: ~3/2 = 697.344 ¢ CEE: ~3/2 = 696.884 ¢ CSEE: ~3/2 = 696.725 ¢ CEC: ~3/2 = 696.883 ¢
Tenney CTOP: ~3/2 = 696.646 ¢ CTE: ~3/2 = 696.952 ¢ CWE: ~3/2 = 696.656 ¢ CTC: ~3/2 = 696.883 ¢
Benedetti,
Wilson 		CBOP: ~3/2 = 697.842 ¢ CBE: ~3/2 = 697.015 ¢ CSBE: ~3/2 = 696.631 ¢ CBC: ~3/2 = 696.883 ¢
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