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== Temperament pages ==
== Accidentals ==
Databoxes has been canceled, but the cleanup will continue
; 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>


Note:  
== Template: Temperament data ==
# Order: subgroup, [[comma list]], [[mapping]], mapping generators, gencom mapping, [[gencom]], map to lattice, lattice basis, [[wedgie]], [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], vals, [[badness]], [[complexity spectrum]].  
{{User:FloraC/Temperament data
# Comma list shows the simplest commas sufficient to define the temperament, stated in [[Normal lists #Normal interval list]].
| Subgroup = 2.3.5.7
# Mapping generators should show all the ratios as used in the mapping, including the period.
| Comma list = 81/80, 126/125
# Minimax tuning are based on tonality diamond, so it should explicitly state the ''odd'' limit, or a diamond function of ratios.
| Mapping = {{mapping| 1 0 -4 -13 | 0 1 4 10 }}
# Use [[Template:Val list]].
| Mapping generators = ~2, ~3
# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "POTE", otherwise show "POL2" or "POT2" instead of "POTE".  
| CTE = ~3/2 = 696.9521
| Wedgie = 1 4 10 4 13 12
| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
| Badness = 0.0137
}}


Get a family for:
== Catalog of 5-limit rank-2 temperaments ==
* <s>Ripple (3 different 7-limit extensions)</s>
Sintel's TE logflat badness.
* <s>Smate (2 different 7-limit extensions)</s>
* Maybe [[parakleismic]] (2 different 7-limit extensions)
* Maybe [[superpyth]] (2 different 7-limit extensions)


Who's next?
Error > 25{{c}}, badness < 3
* <s>Meantone family</s>
{| class="wikitable sortable center-2 center-3 center-4"
* <s>Archytas clan</s>
|-
* <s>Father family</s>
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
* <s>Trienstonic clan</s>
|-
* <s>Septisemi temperaments</s>
|  || 2.63 || 40.1 || .392 || {{mapping| 1 0 -1 | 0 1 2 }} || 10/9
* <s>Archytas family</s>
|-
* <s>Slendro clan</s>
| Antitonic || 2.83 || 41.6 || .508 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
* <s>Semiphore family</s>
|-
* <s>Marvel temperaments</s>
| University || 5.59 || 25.3 || 2.39 || {{mapping| 1 1 2 | 0 3 2 }} || 144/125
* <s>Marvel family</s>
|}
* <s>Mint temperaments</s>
* <s>Mint family</s>
* [[Gamelismic clan]]
* <s>Gamelismic family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* <s>Didymus rank three family</s>
* <s>Kleismic family</s>
* [[Kleismic rank three family]]
* <s>Shibboleth family</s>
* <s>Keemic temperaments</s>
* <s>Keemic family</s>
* <s>Schismatic family</s>
* <s>Hemimean clan</s>
* <s>Hemimean family</s>
* <s>Luna family</s>
* <s>Canousmic temperaments</s>
* <s>Canou family</s>
* [[Starling temperaments]]
* [[Starling family]]
* <s>Sensipent family</s>
* [[Sensamagic clan]]
* [[Sensamagic family]]
* [[Magic family]]
* [[Unicorn family]]
* [[Trisedodge family]]


== Septimal meantone ==
Complexity < 30, error < 25{{c}}, badness < 3
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>


{{main| Meantone }}
{| class="wikitable sortable center-2 center-3 center-4"
{{see also| Wikipedia: Septimal meantone temperament }}
|-
 
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the tritone, and [[21/16]], C-E#, the augmented third. Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.
|-
 
| Father || 3.17 || 20.4 || .349 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
Subgroup: 2.3.5.7
|-
 
| Dicot || 3.73 || 11.0 || .306 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
[[Comma list]]: 81/80, 126/125
 
[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]
 
Mapping generators: ~2, ~3
 
{{Multival|legend=1| 1 4 10 4 13 12 }}
 
[[POTE generator]]: ~3/2 = 696.495
 
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]
: [[Eigenmonzo]]s: 2, 5
 
[[Tuning ranges]]:
* valid range: [694.737, 700.000] (11\19 to 7\12)
* nice range: [694.786, 701.955]
* strict range: [694.786, 700.000]
 
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.
 
{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
 
[[Badness]]: 0.0137
 
Scales: [[meantone5]], [[meantone7]], [[meantone12]]
 
== Archytas ==
{{main| Archytas }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 64/63
 
[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
 
Mapping generators: ~2, ~3, ~5
 
Map to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
 
Lattice basis:
: 3/2 length = 1.0508, 5/4 length = 2.3219
: Angle (3/2, 5/4) = 90 degrees
 
[[POTE generator]]s: ~3/2 = 709.3213, ~5/4 = 393.3747
 
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
: [[Eigenmonzo]]s: 2, 6/5, 7/5
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 }}, {{monzo| 3/2 -1/2 1 -1/4 }}, {{monzo| 3 -1 0 1/2 }}]
: [[Eigenmonzo]]s: 2, 6/5, 9/7
 
{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 49 }}
 
Scales: [[archytas12]], [[archytas12synch]]
 
== Scale tree ==
(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 ||
| Bug || 4.30 || 17.9 || .769 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
|-
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
| Meantone || 5.08 || 2.44 || .173 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
| Mavila || 5.68 || 9.36 || .928 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
| Augmented || 6.40 || 3.71 || .523 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
| Porcupine || 6.86 || 4.14 || .722 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
|-
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
| Blackwood || 7.29 || 7.14 || 1.50 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
| Diminished || 7.54 || 4.79 || 1.11 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
| Supersharp || 7.58 || 12.3 || 2.88 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
| Diaschismic || 8.76 || 1.29 || .467 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
| Magic || 9.98 || 1.71 || .919 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
| Hanson || 11.1 || .422 || .310 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| Negri || 11.3 || 2.61 || 2.04 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| Tetracot || 11.5 || 1.39 || 1.14 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
| Helmholtz || 12.8 || .0881 || .0999 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| Sensipent || 14.1 || .550 || .826 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| Würschmidt || 16.3 || .404 || .952 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| Amity || 16.4 || .217 || .515 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| Valentine || 16.7 || 1.14 || 2.88 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| Compton || 17.4 || .778 || 2.22 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| Orson || 17.5 || .332 || .957 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| Misty || 21.3 || .476 || 2.50 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
| Gravity || 21.4 || .415 || 2.19 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| Parakleismic || 24.8 || .123 || 1.02 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||
| Quartonic || 24.9 || .331 || 2.75 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
| Escapade || 25.8 || .213 || 1.97 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| Vishnuzmic || 26.5 || .0727 || .731 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| Vulture || 27.3 || .0890 || .972 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| 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"
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| Avila || 7.79 || 16.7 || 4.27 || {{mapping| 1 0 -7 | 0 1 6 }} || 729/640
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| Enipucrop || 8.16 || 11.5 || 3.38 || {{mapping| 1 2 2 | 0 3 -2 }} || 1125/1024
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| Laconic || 8.87 || 10.1 || 3.80 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
| Lafayette || 9.31 || 10.8 || 4.70 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| Symbolic || 9.38 || 9.40 || 4.19 || {{mapping| 1 3 2 | 0 4 -1 }} || 2048/1875
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
| Sixix || 9.81 || 7.06 || 3.59 || {{mapping| 1 3 4 | 0 5 6 }} || 3125/2916
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| Whitewood || 10.1 || 6.49 || 3.63 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| Ripple || 11.2 || 4.35 || 3.26 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| Progress || 11.9 || 6.38 || 5.77 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| Superpyth || 12.2 || 3.26 || 3.17 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| Wesley || 13.6 || 4.25 || 5.81 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| Stump || 14.4 || 2.91 || 4.71 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| Passion || 14.5 || 2.42 || 3.95 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| Doublewide || 14.7 || 3.09 || 5.32 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
| Immunity || 17.2 || 1.59 || 4.33 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
| Shibboleth || 17.3 || 1.91 || 5.34 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| Unicorn || 18.0 || 1.12 || 3.53 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| Mynic || 18.6 || 1.69 || 5.86 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| Ampersand || 19.9 || .917 || 3.89 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| Sycamore || 20.5 || 1.06 || 4.93 || {{mapping| 2 2 3 | 0 5 7 }} || 48828125/47775744
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| Fifive || 20.8 || .992 || 4.83 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
| Rodan || 22.2 || .669 || 3.95 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
| Mabila || 23.8 || .753 || 5.45 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
| Ditonic || 26.3 || .399 || 3.92 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
| Trisedodge || 27.7 || .518 || 5.92 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
| Demibuzzard || 28.6 || .243 || 3.06 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
|}
 
30 < complexity < 60, badness < 3
 
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
| Luna || 33.5 || .0239 || .483 || {{mapping| 1 4 2 | 0 15 -2 }} || {{monzo| 38 -2 -15 }}
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
| Enneadecal || 35.8 || .0454 || 1.12 || {{mapping| 19 0 14 | 0 1 1 }} || {{monzo| -14 -19 19 }}
|-
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
| Gammic || 37.2 || .0740 || 2.06 || {{mapping| 1 1 2 | 0 20 11 }} || {{monzo| -29 -11 20 }}
|-
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
| Ennealimmal || 38.7 || .0128 || .403 || {{mapping| 9 1 1 | 0 2 3 }} || {{monzo| 1 -27 18 }}
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
| Alphatricot || 39.3 || .0330 || 1.08 || {{mapping| 1 0 -13 | 0 3 29 }} || {{monzo| 39 -29 3 }}
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
| Kwazy || 43.2 || .00762 || .331 || {{mapping| 2 1 6 | 0 8 -5 }} || {{monzo| -53 10 16 }}
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
| Minortone || 45.3 || .0139 || .698 || {{mapping| 1 16 32 | 0 17 35 }} || {{monzo| -16 35 -17 }}
|-
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
| Monzismic || 51.7 || .00326 || .244 || {{mapping| 1 0 -27 | 0 2 37 }} || {{monzo| 54 -37 2 }}
|-
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
| Vavoom || 54.2 || .0269 || 2.31 || {{mapping| 1 0 4 | 0 17 -18 }} || {{monzo| -68 18 17 }}
|}
|}


== Commas ==
== 5-limit rank-2 temperaments by TE simple badness ==
Breed's TE simple badness.


41edo [[tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.
=== Junk temperaments ===
 
=== High-badness temperaments ===
{| class="commatable wikitable center-1"
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
! [[Prime limit|Prime <br> limit]]
|-
! [[Ratio]]<ref>Ratios with more than 9 digits are presented in monzos</ref>
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
! Name(s)
|-
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
|-
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|-
|-
| 3
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| <abbr title="36893488147419103232/36472996377170786403">{{monzo| 65 -41 }}</abbr>
| [[41-comma]]
|-
|-
| 5
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
| <abbr title="1953125/1889568">{{Monzo| -5 -10 9 }}</abbr>
| [[Shibboleth]]
|-
|-
| 5
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
| <abbr title="34171875/33554432">{{Monzo| -25 7 6 }}</abbr>
| [[Ampersand]]
|-
|-
| 5
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
| [[3125/3072]]
| Magic comma
|-
|-
| 5
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
| <abbr title="20000/19683">{{Monzo| 5 -9 4 }}</abbr>
| [[Tetracot comma]]
|-
|-
| 5
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 5 6 }} || 2048/1875
| <abbr title="131072000/129140163">{{Monzo| 20 -17 3 }}</abbr>
| [[Roda]]
|-
|-
| 5
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 4 -1 }} || 3125/2916
| <abbr title="32805/32768">{{Monzo| -15 8 1 }}</abbr>
| [[Schisma]]
|-
|-
| 7
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
| <abbr title="15625/15309">{{Monzo| 0 -7 6 -1 }}</abbr>
| [[Great BP diesis]]
|-
|-
| 7
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| <abbr title="854296875/843308032">{{Monzo| -10 7 8 -7 }}</abbr>
| [[Blackjackisma]]
|-
|-
| 7
| Progress || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
| [[875/864]]
|}
| Keema
 
=== Main sequence ===
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
|-
|-
| 7
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
| [[3125/3087]]
| Gariboh
|-
|-
| 7
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
| <abbr title="179200/177147">{{Monzo| 10 -11 2 1 }}</abbr>
| [[Tolerma]]
|-
|-
| 7
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
| <abbr title="33075/32768">{{Monzo| -15 3 2 2 }}</abbr>
| [[Mirwomo comma]]
|-
|-
| 7
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
| [[245/243]]
| Sensamagic
|-
|-
| 7
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
| [[4000/3969]]
| Octagar
|-
|-
| 7
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
| <abbr title="823543/819200">{{Monzo| -15 0 -2 7 }}</abbr>
| [[Quince]]
|-
|-
| 7
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
| [[1029/1024]]
| Gamelisma
|-
|-
| 7
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
| [[225/224]]
| Marvel comma
|-
|-
| 7
| Diaschismic || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
| <abbr title="16875/16807">{{Monzo| 0 3 4 -5 }}</abbr>
| [[Mirkwai]]
|-
|-
| 7
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
| <abbr title="10976/10935">{{Monzo| 5 -7 -1 3 }}</abbr>
| [[Hemimage]]
|-
|-
| 7
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
| [[5120/5103]]
| Hemifamity
|-
|-
| 7
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
| <abbr title="33554432/33480783">{{Monzo| 25 -14 0 -1 }}</abbr>
| [[Garischisma]]
|-
|-
| 7
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
| [[2401/2400]]
| Breedsma
|-
|-
| 11
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
| <abbr title="163840/161051">{{Monzo| 15 0 1 0 -5 }}</abbr>
| [[Thuja comma]]
|-
|-
| 11
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
| [[245/242]]
| Cassacot
|-
|-
| 11
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
| [[100/99]]
| Ptolemisma
|-
|-
| 11
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
| [[1344/1331]]
| Hemimin
|-
|-
| 11
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
| [[896/891]]
| Pentacircle
|-
|-
| 11
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
| <abbr title="65536/65219">{{Monzo| 16 0 0 -2 -3 }}</abbr>
| [[Orgonisma]]
|-
|-
| 11
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
| [[243/242]]
| Rastma
|-
|-
| 11
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
| [[385/384]]
| Keenanisma
|-
|-
| 11
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
| [[441/440]]
| Werckisma
|-
|-
| 11
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
| [[1375/1372]]
| Moctdel
|-
|-
| 11
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
| [[540/539]]
| Swetisma
|-
|-
| 11
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
| [[3025/3024]]
| Lehmerisma
|-
|-
| 11
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
| <abbr title="151263/151250">{{Monzo| -1 2 -4 5 -2 }}</abbr>
| [[Odiheim]]
|-
|-
| 13
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
| [[343/338]]
|
|-
|-
| 13
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
| [[105/104]]
| Animist comma
|-
|-
| 13
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
| <abbr title="28672/28431">{{Monzo| 12 -7 0 1 0 -1 }}</abbr>
| [[Secorian]]
|-
|-
| 13
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
| [[275/273]]
| Gassorma
|-
|-
| 13
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
| [[144/143]]
| Grossma
|-
|-
| 13
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
| [[196/195]]
| Mynucuma
|-
|-
| 13
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
| [[640/637]]
| Huntma
|-
|-
| 13
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
| [[1188/1183]]
| Kestrel comma
|-
|-
| 13
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
| [[325/324]]
| Marveltwin
|-
|-
| 13
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
| [[352/351]]
| Minthma
|-
|-
| 13
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
| [[364/363]]
| Gentle comma
|-
|-
| 13
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
| [[847/845]]
| Cuthbert
|-
|-
| 13
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
| [[729/728]]
| Squbema
|-
|-
| 13
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
| [[4096/4095]]
| Schismina
|-
|-
| 13
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
| <abbr title="10648/10647">{{Monzo| 3 -2 0 -1 3 -2 }}</abbr>
| [[Harmonisma]]
|-
|-
| 17
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
| [[2187/2176]]
| Septendecimal schisma
|-
|-
| 17
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
| [[256/255]]
| Septendecimal kleisma
|-
|-
| 17
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
| [[715/714]]
| Septendecimal bridge comma
|-
|-
| 19
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
| [[210/209]]
|}
| Spleen comma
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 5-limit norm-based tunings
|-
! rowspan="2" |
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
! Constrained
! Constrained & skewed
|-
! 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)
|-
! 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)
|-
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 698.160{{c}}<br>(3/17-comma)
| CBE: ~3/2 = 697.374{{c}}<br>(36/169-comma)
| CSBE: ~3/2 = 696.787{{c}}<br>(31/129-comma)
| 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
|-
|-
| 19
! rowspan="2" |  
| [[361/360]]
! rowspan="2" | Manhattan
| Go comma
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| 19
! Constrained
| [[513/512]]
! Constrained & skewed
| Undevicesimal comma
|-
|-
| 19
! Equilateral
| [[1216/1215]]
| CEOP: ~3/2 = 697.344{{c}}
| Eratosthenes' comma
| CEE: ~3/2 = 696.884{{c}}
| CSEE: ~3/2 = 696.725{{c}}
| CEC: ~3/2 = 696.883{{c}}
|-
|-
| 23
! Tenney
| [[736/729]]
| CTOP: ~3/2 = 696.646{{c}}
| Vicesimotertial comma
| CTE: ~3/2 = 696.952{{c}}
| CWE: ~3/2 = 696.656{{c}}
| CTC: ~3/2 = 696.883{{c}}
|-
|-
| 29
! Benedetti, <br>Wilson
| [[145/144]]
| CBOP: ~3/2 = 697.842{{c}}
| 29th-partial chroma
| CBE: ~3/2 = 697.015{{c}}
| CSBE: ~3/2 = 696.631{{c}}
| CBC: ~3/2 = 696.883{{c}}
|}
|}
<references/>

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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