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


Note:
{{Flat}}{{natural}}{{sharp}}
# Order: subgroup, [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], map to lattice, lattice basis, [[wedgie]], [[POTE generator]](s), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], vals, [[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 tuning are based on tonality diamond, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
# Replace "EDOs" with [[Template:Val list]].
# 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".


Get a family for:
♭♮♯
* <s>Ripple (3 different 7-limit extensions)</s> done
* <s>Smate (2 different 7-limit extensions)</s> done
* <s>Parakleismic (2 different 7-limit extensions)</s> canceled, not strong extensions
* <s>Superpyth (2 different 7-limit extensions)</s> canceled, not strong extensions


Who's next?
<span class="bravura">&#xE260;</span>
* <s>Meantone family</s>
<span class="bravura">&#xE261;</span>
* <s>Archytas clan</s>
<span class="bravura">&#xE262;</span>
* <s>Father family</s>
* <s>Trienstonic clan</s>
* <s>Septisemi temperaments</s>
* <s>Archytas family</s>
* <s>Slendro clan</s>
* <s>Semiphore family</s>
* <s>Marvel temperaments</s>
* <s>Marvel family</s>
* <s>Mint temperaments</s>
* <s>Mint family</s>
* <s>Gamelismic clan</s>
* <s>Gamelismic family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* <s>Didymus rank three family</s>
* <s>Kleismic family</s>
* <s>Kleismic rank three family</s>
* <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>
* <s>Starling temperaments</s>
* <s>Starling family</s>
* <s>Sensipent family</s>
* <s>Sensamagic clan</s>
* <s>Sensamagic family</s>
* <s>Magic family</s>
* <s>Unicorn family</s>
* <s>Trisedodge family</s>
* <s>Sycamore family</s>
* <s>Rastmic temperaments</s>
* <s>Semicomma family</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</s>
* <s>Hemimage temperaments</s>
* <s>Hemimage family</s>
* <s>Porwell temperaments</s>
* <s>Porwell family</s>
* <s>Hemifamity temperaments</s>
* <s>Hemifamity family</s>
* <s>Porcupine family</s>
* <s>Porcupine rank three family</s>
* <s>Tetracot family</s>
* <s>Misty family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic rank three family</s>
* <s>Amity family</s>
* <s>Lehmerismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Ragismic family</s>
* [[Ragismic microtemperaments]]
* <s>Landscape family</s>
* [[Landscape microtemperaments]]
* <s>Dimcomp family</s>
* <s>Mirkwai family</s>
* <s>Mirkwai clan</s>
* <s>Breed family</s>
* [[Breedsmic temperaments]]
* <s>Escapade family</s>
* <s>Gravity family</s>
* <s>Cataharry family</s>
* <s>Cataharry temperaments</s>
* <s>Varunismic temperaments</s>
* <s>Werckismic temperaments</s>
* <s>Valinorsmic temperaments</s>
* [[Wizmic microtemperaments]]
* [[Metric microtemperaments]]
* [[Vulture family]]
* [[Tricot family]]
 
== Regular temperament properties ==
{{Databox|Technical data|
; 3-limit
: Subgroup: 2.3
: Comma list: {{monzo| -49 31 }}
: Mapping: {{val| 31 49 }}
: TE octave stretch: +1.63¢
: TE absolute error (¢): 1.64
: TE relative error (%): 4.22


; 5-limit
<span class="heji">n</span>
: Subgroup: 2.3.5
: Comma list: 81/80, 393216/390625
: Mapping: [{{val| 31 49 72 }}]
: TE octave stretch: +0.98¢
: TE absolute error (¢): 1.63
: TE relative error (%): 4.20


; 7-limit
== Template: Temperament data ==
: Subgroup: 2.3.5.7
{{User:FloraC/Temperament data
: Comma list: 81/80, 126/125, 1029/1024
| Subgroup = 2.3.5.7
: Mapping: [{{val| 31 49 72 87 }}]
| Comma list = 81/80, 126/125
: TE octave stretch: +0.83¢
| Mapping = {{mapping| 1 0 -4 -13 | 0 1 4 10 }}
: TE absolute error (¢): 1.43
| Mapping generators = ~2, ~3
: TE relative error (%): 3.70
| CTE = ~3/2 = 696.9521
| Wedgie = 1 4 10 4 13 12
| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
| Badness = 0.0137
}}
}}


== Septimal meantone ==
== 5-limit rank-2 temperaments by TE simple badness ==
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>
Breed's simple badness.


{{main| Meantone }}
=== Junk temperaments ===
{{see also| Wikipedia: Septimal meantone temperament }}


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.


Subgroup: 2.3.5.7
=== High-badness temperaments ===
 
{| class="wikitable sortable center-2 center-3 center-4"
[[Comma list]]: 81/80, 126/125
|-
 
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]
|-
 
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
Mapping generators: ~2, ~3
|-
 
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
{{Multival|legend=1| 1 4 10 4 13 12 }}
|-
 
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
[[POTE generator]]: ~3/2 = 696.495
|-
 
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
[[Minimax tuning]]:
|-
* 7- and [[9-odd-limit]]
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
: [{{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
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
 
|-
[[Tuning ranges]]:
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
* 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 ||
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 -5 -6 }} || 2048/1875
|-
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 -4 1 }} || 3125/2916
|-
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
| || 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"
|-
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||  
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| || 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 Prime-Optimized Tunings
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
! Unskewed
! Skewed
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
! Equilateral
| CEOP: ~3/2 = 697.654¢<br>(1/5-comma)
| CEE: ~3/2 = 696.895¢<br>(4/17-comma)
| CSEE: ~3/2 = 696.453¢<br>(11/43-comma)
| CEC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
! Tenney
| CTOP: ~3/2 = 698.020¢
| CTE: ~3/2 = 697.214¢
| CWE: ~3/2 = 696.651¢
| CTC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 698.160¢<br>(3/17-comma)
| CBE: ~3/2 = 697.374¢<br>(36/169-comma)
| 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
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
! Unskewed
! Skewed
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
! Equilateral
| CEOP: ~3/2 = 697.344¢
| CEE: ~3/2 = 696.884¢
| CSEE: ~3/2 = 696.725¢
| CEC: ~3/2 = 696.883¢
|-
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
! Tenney
| CTOP: ~3/2 = 696.646¢
| CTE: ~3/2 = 696.952¢
| CWE: ~3/2 = 696.656¢
| CTC: ~3/2 = 696.883¢
|-
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 697.842¢
| CBE: ~3/2 = 697.015¢
| 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
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
| 2.3
| {{monzo| -49 31 }}
| {{mapping| 31 49 }}
| +1.63
| 1.64
| 4.22
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
| 2.3.5
| 81/80, 393216/390625
| {{mapping| 31 49 72 }}
| +0.98
| 1.63
| 4.20
|-
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
| 2.3.5.7
| 81/80, 126/125, 1029/1024
| {{mapping| 31 49 72 87 }}
| +0.83
| 1.43
| 3.70
|-
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
| 2.3.5.7.11
| 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]]
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