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== Notes for temperament pages ==
Comment: the example below looks great to me by the very formatting.


Note:
{{Flat}}{{natural}}{{sharp}}
# Order: subgroup, comma list, mapping, mapping generators (or simply "generators", this is the same thing), wedgie, minimax tuning, tuning ranges, algebraic generator, vals, badness, complexity spectrum.
# Comma list shows the simplest commas sufficient to define the temperament. This must be stated somewhere in this wiki.
# Mapping generators should show all the ratios as used in the mapping, including the period.
# Minimax tuning are based on tonality diamond, so it should explicitly state the ''odd'' limit, or a diamond function of ratios.
# Use <s>Template:Vals</s> > [[Template:Val list]].
 
Who's next?
* <s>Meantone family</s>
* [[Archytas clan]]
* [[Father family]]
* [[Trienstonic clan]]
* [[Septisemi temperaments]]
* [[Marvel temperaments]]
* [[Schismatic family]]
 
== Septimal meantone ==
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>


{{main| Meantone }}
&#x266D;&#x266E;&#x266F;
{{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 also tempers out the common 7-limit comma [[225/224]] and is in fact can be defined as the 7-limit temperament that tempers out 81/80 and 225/224.
<span class="bravura">&#xE260;</span>
<span class="bravura">&#xE261;</span>
<span class="bravura">&#xE262;</span>


Period: 1\1
<span class="heji">n</span>


Optimal ([[POTE]]) generator: ~3/2 = 696.495
== Template: Temperament data ==
{{User:FloraC/Temperament data
| Subgroup = 2.3.5.7
| Comma list = 81/80, 126/125
| Mapping = {{mapping| 1 0 -4 -13 | 0 1 4 10 }}
| Mapping generators = ~2, ~3
| CTE = ~3/2 = 696.9521
| Wedgie = 1 4 10 4 13 12
| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
| Badness = 0.0137
}}


EDO generators: [[12edo|7\12]], [[19edo|11\19]], [[31edo|18\31]], [[43edo|25\43]], [[50edo|29\50]]
== 5-limit rank-2 temperaments by TE simple badness ==
Breed's simple badness.


Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]
=== Junk temperaments ===


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
<div class="mw-collapsible-content">


{| class="wikitable right-1 right-2 sortable"
=== High-badness temperaments ===
|+
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
! #
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
! Cents<ref>octave-reduced</ref>
! class="unsortable"| Approximate ratios<ref>2.3.5.7, odd limit ≤ 27</ref>
|-
|-
| 0
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
| 0.0
| 1/1
|-
|-
| 1
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
| 696.5
| 3/2
|-
|-
| 2
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| 193.0
| 9/8, 10/9
|-
|-
| 3
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
| 889.5
| 5/3
|-
|-
| 4
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
| 386.0
| 5/4
|-
|-
| 5
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
| 1082.5
| 15/8, 28/15
|-
|-
| 6
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
| 579.0
| 7/5
|-
|-
| 7
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 -5 -6 }} || 2048/1875
| 75.5
| 21/20, 25/24, 28/27
|-
|-
| 8
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 -4 1 }} || 3125/2916
| 772.0
| 14/9, 25/16
|-
|-
| 9
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
| 268.5
| 7/6
|-
|-
| 10
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| 965.0
| 7/4
|-
|-
| 11
| || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
| 461.4
| 21/16
|}
|}
<references/></div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7
[[Comma]] list: 81/80, 126/125
[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]
Mapping generators: ~2, ~3
[[Wedgie]]: {{wedgie| 1 4 10 4 13 12 }}
[[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] (19 to 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, which comes to 503.4257 cents. The recurrence converges quickly.
{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
[[Badness]]: 0.0137
</div></div>
== Commas ==
41edo [[tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.


{| class="commatable wikitable center-1"
=== Main sequence ===
! [[Prime limit|Prime <br> limit]]
{| class="wikitable sortable center-2 center-3 center-4"
! [[Ratio]]<ref>Ratios with more than 9 digits are presented in monzos</ref>
! Name(s)
|-
|-
| 3
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
| <abbr title="36893488147419103232/36472996377170786403">{{monzo| 65 -41 }}</abbr>
| [[41-comma]]
|-
|-
| 5
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
| <abbr title="1953125/1889568">{{Monzo| -5 -10 9 }}</abbr>
| [[Shibboleth]]
|-
|-
| 5
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
| <abbr title="34171875/33554432">{{Monzo| -25 7 6 }}</abbr>
| [[Ampersand]]
|-
|-
| 5
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
| [[3125/3072]]
| Magic comma
|-
|-
| 5
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
| <abbr title="20000/19683">{{Monzo| 5 -9 4 }}</abbr>
| [[Tetracot comma]]
|-
|-
| 5
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
| <abbr title="131072000/129140163">{{Monzo| 20 -17 3 }}</abbr>
| [[Roda]]
|-
|-
| 5
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
| <abbr title="32805/32768">{{Monzo| -15 8 1 }}</abbr>
| [[Schisma]]
|-
|-
| 7
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
| <abbr title="15625/15309">{{Monzo| 0 -7 6 -1 }}</abbr>
| [[Great BP diesis]]
|-
|-
| 7
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
| <abbr title="854296875/843308032">{{Monzo| -10 7 8 -7 }}</abbr>
| [[Blackjackisma]]
|-
|-
| 7
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
| [[875/864]]
| Keema
|-
|-
| 7
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
| [[3125/3087]]
| Gariboh
|-
|-
| 7
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
| <abbr title="179200/177147">{{Monzo| 10 -11 2 1 }}</abbr>
| [[Tolerma]]
|-
|-
| 7
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
| <abbr title="33075/32768">{{Monzo| -15 3 2 2 }}</abbr>
| [[Mirwomo comma]]
|-
|-
| 7
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
| [[245/243]]
| Sensamagic
|-
|-
| 7
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
| [[4000/3969]]
| Octagar
|-
|-
| 7
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
| <abbr title="823543/819200">{{Monzo| -15 0 -2 7 }}</abbr>
| [[Quince]]
|-
|-
| 7
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
| [[1029/1024]]
| Gamelisma
|-
|-
| 7
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
| [[225/224]]
| Marvel comma
|-
|-
| 7
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
| <abbr title="16875/16807">{{Monzo| 0 3 4 -5 }}</abbr>
| [[Mirkwai]]
|-
|-
| 7
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
| <abbr title="10976/10935">{{Monzo| 5 -7 -1 3 }}</abbr>
| [[Hemimage]]
|-
|-
| 7
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
| [[5120/5103]]
| Hemifamity
|-
|-
| 7
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
| <abbr title="33554432/33480783">{{Monzo| 25 -14 0 -1 }}</abbr>
| [[Garischisma]]
|-
|-
| 7
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
| [[2401/2400]]
| Breedsma
|-
|-
| 11
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
| <abbr title="163840/161051">{{Monzo| 15 0 1 0 -5 }}</abbr>
| [[Thuja comma]]
|-
|-
| 11
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
| [[245/242]]
| Cassacot
|-
|-
| 11
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
| [[100/99]]
| Ptolemisma
|-
|-
| 11
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
| [[1344/1331]]
| Hemimin
|-
|-
| 11
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
| [[896/891]]
| Pentacircle
|-
|-
| 11
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
| <abbr title="65536/65219">{{Monzo| 16 0 0 -2 -3 }}</abbr>
| [[Orgonisma]]
|-
|-
| 11
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
| [[243/242]]
| Rastma
|-
|-
| 11
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
| [[385/384]]
| Keenanisma
|-
|-
| 11
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
| [[441/440]]
| Werckisma
|-
|-
| 11
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
| [[1375/1372]]
| Moctdel
|-
|-
| 11
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
| [[540/539]]
| Swetisma
|-
|-
| 11
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
| [[3025/3024]]
| Lehmerisma
|-
|-
| 11
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
| <abbr title="151263/151250">{{Monzo| -1 2 -4 5 -2 }}</abbr>
| [[Odiheim]]
|-
|-
| 13
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
| [[343/338]]
|  
|-
|-
| 13
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
| [[105/104]]
| Animist comma
|-
|-
| 13
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
| <abbr title="28672/28431">{{Monzo| 12 -7 0 1 0 -1 }}</abbr>
| [[Secorian]]
|-
|-
| 13
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
| [[275/273]]
| Gassorma
|-
|-
| 13
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
| [[144/143]]
| Grossma
|-
|-
| 13
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
| [[196/195]]
| Mynucuma
|-
|-
| 13
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
| [[640/637]]
| Huntma
|-
|-
| 13
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
| [[1188/1183]]
| Kestrel comma
|-
|-
| 13
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 -8 11 }} || {{monzo| -36 11 8 }}
| [[325/324]]
|}
| Marveltwin
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
|-
|-
| 13
! rowspan="2" |  
| [[352/351]]
! rowspan="2" | Manhattan
| Minthma
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| 13
! Unskewed
| [[364/363]]
! Skewed
| Gentle comma
|-
|-
| 13
! Equilateral
| [[847/845]]
| CEOP: ~3/2 = 697.654¢<br>(1/5-comma)
| Cuthbert
| 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)
|-
|-
| 13
! Tenney
| [[729/728]]
| CTOP: ~3/2 = 698.020¢
| Squbema
| CTE: ~3/2 = 697.214¢
| CWE: ~3/2 = 696.651¢
| CTC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
| 13
! Benedetti, <br>Wilson
| [[4096/4095]]
| CBOP: ~3/2 = 698.160¢<br>(3/17-comma)
| Schismina
| 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
|-
|-
| 13
! rowspan="2" |  
| <abbr title="10648/10647">{{Monzo| 3 -2 0 -1 3 -2 }}</abbr>
! rowspan="2" | Manhattan
| [[Harmonisma]]
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| 17
! Unskewed
| [[2187/2176]]
! Skewed
| Septendecimal schisma
|-
|-
| 17
! Equilateral
| [[256/255]]
| CEOP: ~3/2 = 697.344¢
| Septendecimal kleisma
| CEE: ~3/2 = 696.884¢
| CSEE: ~3/2 = 696.725¢
| CEC: ~3/2 = 696.883¢
|-
|-
| 17
! Tenney
| [[715/714]]
| CTOP: ~3/2 = 696.646¢
| Septendecimal bridge comma
| CTE: ~3/2 = 696.952¢
| CWE: ~3/2 = 696.656¢
| CTC: ~3/2 = 696.883¢
|-
|-
| 19
! Benedetti, <br>Wilson
| [[210/209]]
| CBOP: ~3/2 = 697.842¢
| Spleen comma
| 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
|-
|-
| 19
! [[TE error|Absolute]] (¢)
| [[361/360]]
! [[TE simple badness|Relative]] (%)
| Go comma
|-
|-
| 19
| 2.3
| [[513/512]]
| {{monzo| -49 31 }}
| Undevicesimal comma
| {{mapping| 31 49 }}
| +1.63
| 1.64
| 4.22
|-
|-
| 19
| 2.3.5
| [[1216/1215]]
| 81/80, 393216/390625
| Eratosthenes' comma
| {{mapping| 31 49 72 }}
| +0.98
| 1.63
| 4.20
|-
|-
| 23
| 2.3.5.7
| [[736/729]]
| 81/80, 126/125, 1029/1024
| Vicesimotertial comma
| {{mapping| 31 49 72 87 }}
| +0.83
| 1.43
| 3.70
|-
|-
| 29
| 2.3.5.7.11
| [[145/144]]
| 81/80, 99/98, 121/120, 126/125
| 29th-partial chroma
| {{mapping| 31 49 72 87 107 }}
| +1.21
| 1.49
| 3.84
|}
|}
<references/>
 
== 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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