Xenharmonic Wiki

User:FloraC/Sandbox: Difference between revisions

← Older edit
VisualWikitext
Undo revision 176314 by FloraC (talk). Test complete
Tag: Undo
 
(76 intermediate revisions by 2 users not shown)
Line 1: Line 1:
== Primes in edo ==
 
{| class="wikitable center-all"
{{Flat}}{{natural}}{{sharp}}
|+Approximation of prime harmonics in 5edo
 
! colspan="2" | Prime
♭♮♯
! 2
 
! 3
<span class="bravura">&#xE260;</span>
! 5
<span class="bravura">&#xE261;</span>
! 7
<span class="bravura">&#xE262;</span>
! 11
 
! 13
<span class="heji">n</span>
! 17
 
! 19
== 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
}}
 
== 5-limit rank-2 temperaments by TE simple badness ==
Breed's simple badness.
 
=== 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 }}
|-
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
|-
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
|-
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
|-
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
|-
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|  || 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
|-
! 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)
|-
! 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)
|-
! 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
|-
! rowspan="2" |
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
! rowspan="2" | Error
! Unskewed
! absolute ([[¢]])
! Skewed
| +0
| +18
| +94
| -9
| -71
| +119
| -105
| -58
|-
|-
! [[Relative error|relative]] (%)
! Equilateral
| +0
| CEOP: ~3/2 = 697.344¢
| +8
| CEE: ~3/2 = 696.884¢
| +39
| CSEE: ~3/2 = 696.725¢
| -4
| CEC: ~3/2 = 696.883¢
| -30
| +50
| -44
| -24
|-
|-
! Mapping
! Tenney
! [[patent val]]<br>([[Octave reduction|reduced]])
| CTOP: ~3/2 = 696.646¢
| 5<br>(0)
| CTE: ~3/2 = 696.952¢
| 8<br>(3)
| CWE: ~3/2 = 696.656¢
| 12<br>(2)
| CTC: ~3/2 = 696.883¢
| 14<br>(4)
| 17<br>(2)
| 19<br>(4)
| 20<br>(0)
| 21<br>(1)
|-
|-
! colspan="2" | [[Fifthspan]]
! Benedetti, <br>Wilson
| 0
| CBOP: ~3/2 = 697.842¢
| +1
| CBE: ~3/2 = 697.015¢
| -1
| CSBE: ~3/2 = 696.631¢
| -2
| CBC: ~3/2 = 696.883¢
| -1
| -2
| 0
| +2
|}
|}


== Temperament pages ==
== Temperament pages ==
Databoxes has been canceled, but the cleanup will continue
Note:  
Note:  
# Order: subgroup, [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], map to lattice, lattice basis, [[wedgie]], [[POTE tuning]], [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], vals, [[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 tuning 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.
# 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 "CTE/CWE", otherwise show "subgroup/inharmonic CTE/CWE" instead.  
# 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:  
Get a family for:  
Line 70: 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>Undim</s> done
* <s>Superpyth (2 different 7-limit extensions)</s> canceled, not strong extensions
* <s>Quintaleap</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>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>
* [[Tricot family]]
* <s>Tricot family</s>
* [[Minortonic family]]
* <s>Minortonic family</s>
* <s>Gammic family</s>
* <s>Gammic family</s>
* [[Mirwomo temperaments]]
* <s>Vishnuzmic family</s>
* [[Augmented family]]
* <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>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 ==
== 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 172: 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 179: 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 186: 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 193: 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 200: Line 394:


== Scale tree ==
== Scale tree ==
(Bounded by branch depth = 7)
; 6-tone
: <s>1L 5s</s>, [[2L 4s]], <s>3L 3s</s>, [[4L 2s]], <s>5L 1s</s>


{| class="wikitable center-all"
; 7-tone
! colspan="7" | Generator
: <s>1L 6s</s>, <s>2L 5s</s>, <s>3L 4s</s>, <s>4L 3s</s>, <s>5L 2s</s>, <s>6L 1s</s>
! Cents
 
! L
; 8-tone
! s
: [[1L 7s]], <s>2L 6s</s>, [[3L 5s]], <s>4L 4s</s>, <s>5L 3s</s>, <s>6L 2s</s>, [[7L 1s]]
! L/s
 
! Comments
; 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]]
| 4\7 || || || || || || || 685.714 || 1 || 1 || 1.000 ||
 
|-
; 10-tone
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
: [[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]]
|-
 
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
; 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]]
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
 
|-
; 12-tone
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
: [[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]]
|-
| || || || || || || 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"