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{{Flat}}{{natural}}{{sharp}}
♭♮♯
<span class="bravura">&#xE260;</span>
<span class="bravura">&#xE261;</span>
<span class="bravura">&#xE262;</span>
<span class="heji">n</span>
== Template: Temperament data ==
{{User:FloraC/Temperament data
{{User:FloraC/Temperament data
| Subgroup = 2.3.5.7
| Subgroup = 2.3.5.7
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}}
}}


== Tunings to be reviewed ==
== 5-limit rank-2 temperaments by TE simple badness ==
{| class="wikitable mw-collapsible mw-collapsed"
Breed's simple badness.
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
 
=== Junk temperaments ===
 
 
=== High-badness temperaments ===
{| class="wikitable sortable center-2 center-3 center-4"
|-
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
| 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
|-
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
|-
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
|-
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 -5 -6 }} || 2048/1875
|-
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 -4 1 }} || 3125/2916
|-
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|  || 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"
|-
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
|-
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
|-
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
|-
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
|-
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
|-
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
|-
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
|-
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
|-
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
|-
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
|-
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|  || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|-
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
|-
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
|-
|-
! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
|-
|-
| 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¢
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| 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)
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
|-
|-
| 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)
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
|-
|-
| 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)
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| 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)
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -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)
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 -8 11 }} || {{monzo| -36 11 8 }}
|}
|}


== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
|+style=white-space:nowrap | 5-limit Prime-Optimized Tunings
|-
! rowspan="2" |
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
! Unskewed
! Skewed
|-
! 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)
|-
|-
! Weight-skew\Order !! Chebyshevian !! Euclidean !! Manhattan
! 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)
|-
|-
| Tenney || CTC<br>~3/2 = 696.8826¢<br>Eigenmonzo basis: 2.7 || CTE<br>~3/2 = 696.9521¢ || CTOP<br>~3/2 = 696.6458¢
! 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
|-
|-
| 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
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| 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
! Unskewed
! Skewed
|-
|-
| 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
! Equilateral
| CEOP: ~3/2 = 697.344¢
| CEE: ~3/2 = 696.884¢
| CSEE: ~3/2 = 696.725¢
| CEC: ~3/2 = 696.883¢
|-
|-
| 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
! Tenney
| CTOP: ~3/2 = 696.646¢
| CTE: ~3/2 = 696.952¢
| CWE: ~3/2 = 696.656¢
| CTC: ~3/2 = 696.883¢
|-
|-
| 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
! 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 ==
== Temperament pages ==
Note:  
Note:  
# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[POTE generator]], [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], [[Optimal ET sequence]], [[badness]], [[complexity spectrum]], and others.  
# 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]].  
# 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.  
# 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.
# 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 "POTE", otherwise show "POL2" or "POT2" instead of "POTE".  
# 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:  
Get a family for:  
Line 59: Line 225:
* <s>Smate (2 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>Passion (4 different 7-limit extensions, 3 strong and 1 weak)</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
* <s>Undim</s> done
* <s>Undim</s> done
* <s>Quintaleap</s> done
* <s>Quintaleap</s> done
* <s>Quindromeda</s> done
* <s>Quindromeda</s> done
* Parakleismic (many reasonable but unnamed 7-limit extensions)
* Schismatic rank three family (perhaps)


Who's next?  
Who's next?  
* <s>Meantone family</s>
* <s>Meantone family</s>
* <s>Didymus rank three family</s>
* <s>Archytas clan</s>
* <s>Archytas clan</s>
* <s>Archytas family</s>
* <s>Father family</s>
* <s>Father family</s>
* <s>Trienstonic clan</s>
* <s>Trienstonic clan</s>
* <s>Septisemi temperaments</s>
* <s>Septisemi temperaments</s>
* <s>Archytas family</s>
* <s>Slendro clan</s>
* <s>Slendro clan</s>
* <s>Semiphore family</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 temperaments</s>
* <s>Marvel family</s>
* <s>Marvel family</s>
* <s>Mint temperaments</s>
* <s>Mint family</s>
* <s>Gamelismic clan</s>
* <s>Gamelismic clan</s>
* <s>Gamelismic family</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 temperaments</s>
* <s>Starling family</s>
* <s>Starling family</s>
* <s>Sensipent family</s>
* <s>Sensamagic clan</s>
* <s>Sensamagic clan</s>
* <s>Sensamagic family</s>
* <s>Sensamagic family</s>
* <s>Magic 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>Unicorn family</s>
* <s>Shibboleth family</s>
* <s>Immunity family</s>
* <s>Fifive family</s>
* <s>Trisedodge family</s>
* <s>Trisedodge family</s>
* <s>Quintosec family</s>
* <s>Pental family</s>
* <s>Sycamore family</s>
* <s>Sycamore family</s>
* <s>Rastmic temperaments</s>
* <s>Semicomma family</s>
* <s>Semicomma family</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</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 temperaments</s>
* <s>Hemimage family</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 family</s>
* <s>Porcupine rank three family</s>
* <s>Porcupine rank three family</s>
* <s>Tetracot family</s>
* <s>Tetracot family</s>
* <s>Misty family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic rank three family</s>
* <s>Diaschismic rank three family</s>
* <s>Compton family</s>
* <s>Amity family</s>
* <s>Amity family</s>
* <s>Misty family</s>
* <s>Undim family</s>
* <s>Lehmerismic temperaments</s>
* <s>Lehmerismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Ragismic microtemperaments</s>
* <s>Ragismic family</s>
* <s>Ragismic family</s>
* [[Ragismic microtemperaments]]
* <s>Landscape microtemperaments</s>
* <s>Landscape family</s>
* <s>Landscape family</s>
* <s>Landscape microtemperaments</s>
* <s>Dimcomp family</s>
* <s>Dimcomp family</s>
* <s>Mirkwai clan</s>
* <s>Mirkwai family</s>
* <s>Mirkwai family</s>
* <s>Mirkwai clan</s>
* <s>Quince clan</s>
* <s>Breedsmic temperaments</s>
* <s>Breed family</s>
* <s>Breed family</s>
* <s>Breedsmic temperaments</s>
* <s>Escapade family</s>
* <s>Escapade family</s>
* <s>Gravity family</s>
* <s>Gravity family</s>
* <s>Cataharry temperaments</s>
* <s>Cataharry family</s>
* <s>Cataharry family</s>
* <s>Cataharry temperaments</s>
* <s>Varunismic temperaments</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>Werckismic temperaments</s>
* <s>Valinorsmic temperaments</s>
* <s>Swetismic temperaments</s>
* <s>Swetismic temperaments</s>
* <s>Wizmic microtemperaments</s>
* <s>Wizmic microtemperaments</s>
* <s>Metric microtemperaments</s>
* <s>Metric microtemperaments</s>
* <s>Horwell temperaments</s>
* <s>Horwell family</s>
* <s>Luna family</s>
* <s>Vulture family</s>
* <s>Vulture family</s>
* <s>Tricot family</s>
* <s>Tricot family</s>
* <s>Minortonic family</s>
* <s>Minortonic family</s>
* <s>Gammic family</s>
* <s>Gammic family</s>
* [[Mirwomo temperaments]]
* <s>Vishnuzmic family</s>
* <s>Augmented family</s>
* <s>Garischismic clan</s>
* [[Dimipent family]]
* <s>Canousmic temperaments</s>
* [[Dicot family]]
* <s>Canou family</s>
* <s>Bug family</s>
* <s>Semicanousmic clan</s>
* [[Pelogic family]]
* <s>Semiporwellismic clan</s>
* <s>Horwell family</s>
* <s>Olympic clan</s>
* [[Horwell temperaments]]
* <s>Alphaxenic rank three clan</s>
* [[Gariboh clan]]
* <s>Mirwomo temperaments</s>
* <s>Gariboh clan</s>
* <s>Gariboh family</s>
* <s>Gariboh family</s>
* [[Octagar temperaments]]
* <s>Octagar temperaments</s>
* <s>Octagar family</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 ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning Error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
Line 171: Line 366:
| 2.3
| 2.3
| {{monzo| -49 31 }}
| {{monzo| -49 31 }}
| [{{val| 31 49 }}]
| {{mapping| 31 49 }}
| +1.63
| +1.63
| 1.64
| 1.64
Line 178: Line 373:
| 2.3.5
| 2.3.5
| 81/80, 393216/390625
| 81/80, 393216/390625
| [{{val| 31 49 72 }}]
| {{mapping| 31 49 72 }}
| +0.98
| +0.98
| 1.63
| 1.63
Line 185: Line 380:
| 2.3.5.7
| 2.3.5.7
| 81/80, 126/125, 1029/1024
| 81/80, 126/125, 1029/1024
| [{{val| 31 49 72 87 }}]
| {{mapping| 31 49 72 87 }}
| +0.83
| +0.83
| 1.43
| 1.43
Line 192: Line 387:
| 2.3.5.7.11
| 2.3.5.7.11
| 81/80, 99/98, 121/120, 126/125
| 81/80, 99/98, 121/120, 126/125
| [{{val| 31 49 72 87 107 }}]
| {{mapping| 31 49 72 87 107 }}
| +1.21
| +1.21
| 1.49
| 1.49
Line 219: Line 414:
; 12-tone
; 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]]
: [[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 ||
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
|}
Retrieved from "https://en.xen.wiki/w/User:FloraC/Sandbox"