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Sintel's TE logflat badness.  
Sintel's TE logflat badness.  


Error > 25{{c}}, badness < 3
{| class="wikitable sortable center-2 center-3 center-4"
{| class="wikitable sortable center-2 center-3 center-4"
|-
|-
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
|  || 2.63 || 40.1 || .392 || {{mapping| 2 3 0 | 0 0 1 }} || 10/9
|  || 2.63 || 40.1 || .392 || {{mapping| 1 0 -1 | 0 1 2 }} || 10/9
|-
|-
| Antitonic || 2.83 || 41.6 || .508 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
| Antitonic || 2.83 || 41.6 || .508 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|-
| University || 5.59 || 25.3 || 2.39 || {{mapping| 1 1 2 | 0 3 2 }} || 144/125
|}
Complexity < 30, error < 25{{c}}, badness < 3
{| class="wikitable sortable center-2 center-3 center-4"
|-
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| Father || 3.17 || 20.4 || .349 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
| Father || 3.17 || 20.4 || .349 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
Line 49: Line 59:
|-
|-
| Diaschismic || 8.76 || 1.29 || .467 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
| Diaschismic || 8.76 || 1.29 || .467 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
| Magic || 9.98 || 1.71 || .919 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
| Hanson || 11.1 || .422 || .310 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
| Negri || 11.3 || 2.61 || 2.04 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
| Tetracot || 11.5 || 1.39 || 1.14 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
| Helmholtz || 12.8 || .0881 || .0999 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
| Sensipent || 14.1 || .550 || .826 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
| Würschmidt || 16.3 || .404 || .952 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
| Amity || 16.4 || .217 || .515 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
| Valentine || 16.7 || 1.14 || 2.88 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
| Compton || 17.4 || .778 || 2.22 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
| Orson || 17.5 || .332 || .957 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
| Misty || 21.3 || .476 || 2.50 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
| Gravity || 21.4 || .415 || 2.19 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
| Parakleismic || 24.8 || .123 || 1.02 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
| Quartonic || 24.9 || .331 || 2.75 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
| Escapade || 25.8 || .213 || 1.97 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
| Vishnuzmic || 26.5 || .0727 || .731 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
| Vulture || 27.3 || .0890 || .972 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
| 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"
|-
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
| Avila || 7.79 || 16.7 || 4.27 || {{mapping| 1 0 -7 | 0 1 6 }} || 729/640
|-
| Enipucrop || 8.16 || 11.5 || 3.38 || {{mapping| 1 2 2 | 0 3 -2 }} || 1125/1024
|-
|-
| Laconic || 8.87 || 10.1 || 3.80 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
| Laconic || 8.87 || 10.1 || 3.80 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
Line 57: Line 116:
|-
|-
| Sixix || 9.81 || 7.06 || 3.59 || {{mapping| 1 3 4 | 0 5 6 }} || 3125/2916
| Sixix || 9.81 || 7.06 || 3.59 || {{mapping| 1 3 4 | 0 5 6 }} || 3125/2916
|-
| Magic || 9.98 || 1.71 || .919 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
| Uncle || 10.0 || 11.6 || 6.33 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
|-
| Whitewood || 10.1 || 6.49 || 3.63 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| Whitewood || 10.1 || 6.49 || 3.63 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
| Hanson || 11.1 || .422 || .310 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| Ripple || 11.2 || 4.35 || 3.26 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
| Ripple || 11.2 || 4.35 || 3.26 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
|-
| Negri || 11.3 || 2.61 || 2.04 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
| Progress || 11.9 || 6.38 || 5.77 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|-
| Tetracot || 11.5 || 1.39 || 1.14 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|  || 11.9 || 6.38 || 5.77 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|-
|-
| Superpyth || 12.2 || 3.26 || 3.17 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
| Superpyth || 12.2 || 3.26 || 3.17 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
| Helmholtz || 12.8 || .0881 || .0999 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| Wesley || 13.6 || 4.25 || 5.81 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
| Wesley || 13.6 || 4.25 || 5.81 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
| Sensipent || 14.1 || .550 || .826 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| Stump || 14.4 || 2.91 || 4.71 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
| Stump || 14.4 || 2.91 || 4.71 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
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|-
|-
| Doublewide || 14.7 || 3.09 || 5.32 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
| Doublewide || 14.7 || 3.09 || 5.32 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
| Würschmidt || 16.3 || .404 || .952 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
| Amity || 16.4 || .217 || .515 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
| Valentine || 16.7 || 1.14 || 2.88 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| Immunity || 17.2 || 1.59 || 4.33 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
| Immunity || 17.2 || 1.59 || 4.33 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| Shibboleth || 17.3 || 1.91 || 5.34 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
| Shibboleth || 17.3 || 1.91 || 5.34 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
| Compton || 17.4 || .778 || 2.22 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
| Orson || 17.5 || .332 || .957 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| Unicorn || 18.0 || 1.12 || 3.53 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
| Unicorn || 18.0 || 1.12 || 3.53 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
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|-
|-
| Ampersand || 19.9 || .917 || 3.89 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
| Ampersand || 19.9 || .917 || 3.89 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
| Sycamore || 20.5 || 1.06 || 4.93 || {{mapping| 2 2 3 | 0 5 7 }} || 48828125/47775744
|-
|-
| Fifive || 20.8 || .992 || 4.83 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
| Fifive || 20.8 || .992 || 4.83 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| Misty || 21.3 || .476 || 2.50 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
| Rodan || 22.2 || .669 || 3.95 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
| Mabila || 23.8 || .753 || 5.45 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
| Ditonic || 26.3 || .399 || 3.92 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
|-
| Gravity || 21.4 || .415 || 2.19 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
| Trisedodge || 27.7 || .518 || 5.92 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| Rodan || 22.2 || .669 || 3.95 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
| 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"
|-
|-
| Python || 22.2 || 1.17 || 6.92 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
|-
| Mabila || 23.8 || .753 || 5.45 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
| Luna || 33.5 || .0239 || .483 || {{mapping| 1 4 2 | 0 15 -2 }} || {{monzo| 38 -2 -15 }}
|-
|-
| Parakleismic || 24.8 || .123 || 1.02 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
| Enneadecal || 35.8 || .0454 || 1.12 || {{mapping| 19 0 14 | 0 1 1 }} || {{monzo| -14 -19 19 }}
|-
|-
| Quartonic || 24.9 || .331 || 2.75 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
| Gammic || 37.2 || .0740 || 2.06 || {{mapping| 1 1 2 | 0 20 11 }} || {{monzo| -29 -11 20 }}
|-
|-
| Escapade || 25.8 || .213 || 1.97 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
| Ennealimmal || 38.7 || .0128 || .403 || {{mapping| 9 1 1 | 0 2 3 }} || {{monzo| 1 -27 18 }}
|-
|-
| Ditonic || 26.3 || .399 || 3.92 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
| Alphatricot || 39.3 || .0330 || 1.08 || {{mapping| 1 0 -13 | 0 3 29 }} || {{monzo| 39 -29 3 }}
|-
|-
| Vishnuzmic || 26.5 || .0727 || .731 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
| Kwazy || 43.2 || .00762 || .331 || {{mapping| 2 1 6 | 0 8 -5 }} || {{monzo| -53 10 16 }}
|-
|-
| Vulture || 27.3 || .0890 || .972 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
| Minortone || 45.3 || .0139 || .698 || {{mapping| 1 16 32 | 0 17 35 }} || {{monzo| -16 35 -17 }}
|-
|-
| Trisedodge || 27.7 || .518 || 5.92 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
| Monzismic || 51.7 || .00326 || .244 || {{mapping| 1 0 -27 | 0 2 37 }} || {{monzo| 54 -37 2 }}
|-
|-
| || 28.6 || .243 || 3.06 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
| Vavoom || 54.2 || .0269 || 2.31 || {{mapping| 1 0 4 | 0 17 -18 }} || {{monzo| -68 18 17 }}
|}
|}


Line 168: Line 214:
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
| 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
| Progress || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|}
|}


Line 325: Line 371:
| CBC: ~3/2 = 696.883{{c}}
| CBC: ~3/2 = 696.883{{c}}
|}
|}
== Temperament pages ==
Note:
# Order: [[subgroup]], [[comma list]], [[mapping]], mapping generators, (subgroup-val mapping, gencom mapping), lattice basis, [[optimal tuning]]s ([[WE]] and [[CWE]]), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]] (?), [[optimal ET sequence]], [[badness]], [[complexity spectrum]], and others.
# Comma list should be the Tenney-minimal commas sufficient to define the temperament, stated in [[Normal forms #Normal forms for commas]].
# Mapping generators should show all the ratios as used in the mapping, including the period.
# For subgroup temperaments, "mapping" becomes "subgroup-val mapping" and "gencom mapping"".
* If the subgroup is trivial, simply show "WE"/"CWE", otherwise show "subgroup/inharmonic WE/CWE" instead.
# Cent symbol in tunings.
# Since minimax tunings are based on tonality diamonds, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
# Algebraic generators are to be discussed later.
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-3 family (perhaps)
Progress:
* <s>Meantone family</s>
* <s>Didymus rank-3 family</s>
* <s>Archytas clan</s>
* <s>Archytas family</s>
* <s>Father family</s>
* <s>Trienstonic clan</s>
* <s>Septisemi temperaments</s>
* <s>Semaphoresmic clan</s>
* <s>Semaphoresmic family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* [[Mint temperaments]]
* [[Mint family]]
* <s>Augmented family</s>
* <s>Diminished family</s>
* <s>Passion family</s>
* <s>Ripple family</s>
* <s>Dicot family</s>
* <s>Bug family</s>
* <s>Mavila family</s>
* [[Smate family]]
* <s>Gamelismic clan</s>
* <s>Gamelismic family</s>
* [[Marvel temperaments]]
* [[Marvel family]]
* [[Starling temperaments]]
* [[Starling family]]
* <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>
* [[Schismatic family]]
* [[Kleismic family]]
* [[Kleismic rank-3 family]]
* [[Würschmidt family]]
* [[Unicorn family]]
* [[Immunity family]]
* [[Fifive family]]
* [[Trisedodge family]]
* [[Quintosec family]]
* [[Quintile family]]
* [[Sycamore family]]
* [[Semicomma family]]
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</s>
* [[Hemimean clan]]
* [[Hemimean family]]
* <s>Hemifamity temperaments</s>
* <s>Hemifamity family</s>
* [[Porwell temperaments]]
* [[Porwell family]]
* [[Hemimage temperaments]]
* [[Hemimage family]]
* <s>Porcupine family</s>
* <s>Porcupine rank-3 family</s>
* [[Tetracot family]]
* <s>Diaschismic family</s>
* <s>Diaschismic rank-3 family</s>
* <s>Compton family</s>
* [[Amity family]]
* [[Misty family]]
* [[Undim family]]
* [[Lehmerismic temperaments]]
* [[Kalismic temperaments]]
* [[Ragismic microtemperaments]]
* [[Ragismic family]]
* [[Landscape microtemperaments]]
* [[Landscape family]]
* [[Dimcomp family]]
* [[Mirkwai clan]]
* [[Mirkwai family]]
* [[Quince clan]]
* [[Breedsmic temperaments]]
* [[Breed family]]
* [[Escapade family]]
* <s>Gravity family</s>
* <s>Buzzardsmic clan</s>
* [[Cataharry temperaments]]
* [[Cataharry family]]
* [[Varunismic temperaments]]
* <s>Rastmic rank-3 clan</s>
* [[Biyatismic clan]]
* [[Ptolemismic clan]]
* [[Valinorsmic clan]]
* [[Pentacircle clan]]
* [[Keenanismic temperaments]]
* [[Werckismic temperaments]]
* [[Swetismic temperaments]]
* [[Wizmic microtemperaments]]
* [[Metric microtemperaments]]
* [[Horwell temperaments]]
* [[Horwell family]]
* [[Luna family]]
* <s>Vulture family</s>
* <s>Alphatricot family</s>
* [[Minortonic family]]
* [[Gammic family]]
* [[Vishnuzmic family]]
* [[Garischismic clan]]
* [[Canousmic temperaments]]
* [[Canou family]]
* [[Semicanousmic clan]]
* [[Semiporwellismic clan]]
* [[Olympic clan]]
* [[Alphaxenic rank-3 clan]]
* [[Mirwomo temperaments]]
* <s>Gariboh clan</s>
* <s>Gariboh family</s>
* [[Octagar temperaments]]
* [[Octagar family]]
* <s>Whitewood family</s>
* [[Wesley family]]
* [[Mabila family]]
* [[Maquila family]]
* [[Maja family]]
* [[Ditonmic family]]
* [[Greenwoodmic temperaments]]
* <s>Avicennmic temperaments</s>
* <s>Very low accuracy temperaments</s>
* [[Very high accuracy temperaments]]
* [[Equivalence continuum|Equivalence continua]]
* [[Fractional-octave temperaments]]
* [[Subgroup temperaments]]
== 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]]
Retrieved from "https://en.xen.wiki/w/User:FloraC/Sandbox"