Marvel temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =[[225/224| 225/224]], the [[Marvel_family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone_family|meantone]], [[Miracle|miracle]], [[Magic_family|magic]], [[pajara|pajara]], [[Orwell|orwell]], [[Kleismic_family|catakleismic]], [[Garibaldi_temperament|garibaldi]], [[Augmented_family|august]], [[Pythagorean_family|compton]], [[Dicot_family|sharp]], [[Escapade_family|escapade]] and [[Pelogic_family|mavila]].
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-18 12:15:04 UTC</tt>.<br>
: The original revision id was <tt>602440728</tt>.<br>
: The revision comment was: <tt>removed tel links</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]
This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =[[225_224| 225/224]], the [[Marvel family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family|meantone]], [[Miracle|miracle]], [[Magic family|magic]], [[Pajara|pajara]], [[Orwell|orwell]], [[Kleismic family|catakleismic]], [[Garibaldi temperament|garibaldi]], [[Augmented family|august]], [[Pythagorean family|compton]], [[Dicot family|sharp]], [[Escapade family|escapade]] and [[Pelogic family|mavila]].


Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
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Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)


=Negri=  
=Negri=
[[Comma]]s: 49/48, 225/224
[[Comma|Comma]]s: 49/48, 225/224


[[POTE tuning|POTE temperament]]: ~15/14 = 125.608
[[POTE_tuning|POTE temperament]]: ~15/14 = 125.608
 
[[Map|Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
 
[[wedgie|Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||


[[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
[[Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||
EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]
EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]


==11-limit==  
==11-limit==
Commas: 45/44, 49/48, 56/55
Commas: 45/44, 49/48, 56/55


[[POTE tuning|POTE generator]]: ~15/14 = 126.474
[[POTE_tuning|POTE generator]]: ~15/14 = 126.474


Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
EDOs: 9, 10, 19
EDOs: 9, 10, 19
[[Badness]]: 0.0262


==13-limit==  
[[Badness|Badness]]: 0.0262
 
==13-limit==
Commas: 45/44, 49/48, 56/55, 78/77
Commas: 45/44, 49/48, 56/55, 78/77


[[POTE tuning|POTE generator]]: ~14/13 = 126.431
[[POTE_tuning|POTE generator]]: ~14/13 = 126.431


Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
EDOs: 9, 10, 19
EDOs: 9, 10, 19


=Negril=  
=Negril=
Commas: 49/48, 100/99, 225/224
Commas: 49/48, 100/99, 225/224


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Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]]
EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]]
Badness: 0.0387
Badness: 0.0387


==13-limit==  
==13-limit==
Commas: 49/48, 65/64, 91/90, 875/858
Commas: 49/48, 65/64, 91/90, 875/858


Line 56: Line 56:


Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]
Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]
EDOs: 9, 10, 19, 29, 48, 77
EDOs: 9, 10, 19, 29, 48, 77
Badness: 0.0244
Badness: 0.0244


=Negric=  
=Negric=
Commas: 33/32, 49/48, 77/75
Commas: 33/32, 49/48, 77/75


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Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]
Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]
EDOs: 9, 19, [[85edo|85]]
EDOs: 9, 19, [[85edo|85]]
Badness: 0.0306
Badness: 0.0306


==13-limit==  
==13-limit==
Commas: 33/32, 49/48, 65/64, 91/90
Commas: 33/32, 49/48, 65/64, 91/90


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Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
EDOs: 9, 19, 85
EDOs: 9, 19, 85
Badness: 0.0202
Badness: 0.0202


=Negroni=  
=Negroni=
Commas: 49/48, 55/54, 225/224
Commas: 49/48, 55/54, 225/224


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Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]
Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]
EDOs: 10, 19e, 29, 77cde
EDOs: 10, 19e, 29, 77cde
Badness: 0.0353
Badness: 0.0353


==13-limit==  
==13-limit==
Commas: 49/48, 55/54, 65/64, 91/90
Commas: 49/48, 55/54, 65/64, 91/90


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Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]
Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]
EDOs: 10, 19e, 29, 77cdef
EDOs: 10, 19e, 29, 77cdef
Badness: 0.0216
Badness: 0.0216


=Wizard=  
=Wizard=
Comma: 2197265625/2147483648
Comma: 2197265625/2147483648


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Map: [&lt;2 1 5|, &lt;0 6 -1|]
Map: [&lt;2 1 5|, &lt;0 6 -1|]
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc
Badness: 0.3864
Badness: 0.3864


==7-limit==  
==7-limit==
Commas: 225/224, 118098/117649
Commas: 225/224, 118098/117649


[[POTE tuning|POTE temperament]]: 383.256
[[POTE_tuning|POTE temperament]]: 383.256


Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]]
EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]]
Badness: 0.0408
Badness: 0.0408


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 4000/3993
Commas: 225/224, 385/384, 4000/3993


[[POTE tuning|POTE temperament]]: 383.232
[[POTE_tuning|POTE temperament]]: 383.232


Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]]
EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]]
Badness: 0.0185
Badness: 0.0185


==Lizard==  
==Lizard==
Commas: 225/224, 351/350, 364/363, 385/384
Commas: 225/224, 351/350, 364/363, 385/384


[[POTE tuning|POTE temperament]]: 383.389
[[POTE_tuning|POTE temperament]]: 383.389


Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]
Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]
EDOs: 22, 50, 72, 122, 194df
EDOs: 22, 50, 72, 122, 194df
Badness: 0.0218
Badness: 0.0218


===17-limit===  
===17-limit===
Commas: 221/220, 273/272, 289/288, 351/350, 375/374
Commas: 221/220, 273/272, 289/288, 351/350, 375/374


[[POTE tuning|POTE temperament]]: 383.381
[[POTE_tuning|POTE temperament]]: 383.381


Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]
Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]
EDOs: 22, 50, 72, 122g, 194dfg
EDOs: 22, 50, 72, 122g, 194dfg
Badness: 0.0145
Badness: 0.0145


===19-limit===  
===19-limit===
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


[[POTE tuning|POTE generator]]: ~5/4 = 383.477
[[POTE_tuning|POTE generator]]: ~5/4 = 383.477


Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]]
EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]]
Badness: 0.0157
Badness: 0.0157


==Gizzard==  
==Gizzard==
Commas: 225/224, 385/384, 325/324, 1573/1568
Commas: 225/224, 385/384, 325/324, 1573/1568


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Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]]
EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]]
Badness: 0.0203
Badness: 0.0203


===17-limit===  
===17-limit===
Commas: 225/224, 289/288, 325/324, 375/374, 385/384
Commas: 225/224, 289/288, 325/324, 375/374, 385/384


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Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]]
EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]]
Badness: 0.0136
Badness: 0.0136


===19-limit===  
===19-limit===
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


Line 174: Line 201:


Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]
Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]
EDOs: 22f, 72, 94, 166g
EDOs: 22f, 72, 94, 166g
Badness: 0.0148
Badness: 0.0148


==Mage==  
==Mage==
Commas: 99/98, 176/175, 1331/1296
Commas: 99/98, 176/175, 1331/1296


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Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]
Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]
EDOs: 22, 72e, 94e
EDOs: 22, 72e, 94e
Badness: 0.0578
Badness: 0.0578


=Triton=  
=Triton=
Commas: 225/224, 1029/1000
Commas: 225/224, 1029/1000


[[POTE tuning|POTE temperament]]: ~7/5 = 568.865
[[POTE_tuning|POTE temperament]]: ~7/5 = 568.865


Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
EDOs: 17d, 19, 78bd, 97bd
EDOs: 17d, 19, 78bd, 97bd
Badness: 0.0592
Badness: 0.0592


==11-limit==  
==11-limit==
Commas: 45/44, 56/55, 1029/1000
Commas: 45/44, 56/55, 1029/1000


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Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
EDOs: 19, 59bde, 78bde, 97bde
EDOs: 19, 59bde, 78bde, 97bde
Badness: 0.0457
Badness: 0.0457


=Tritonic=  
=Tritonic=
Comnma: 553584375/536870912
Comnma: 553584375/536870912


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Map: [&lt;1 4 -3|, &lt;0 -5 11|]
Map: [&lt;1 4 -3|, &lt;0 -5 11|]
EDOs: 29, 31, 60, 91
EDOs: 29, 31, 60, 91
Badness: 0.3785
Badness: 0.3785


==7-limit==  
==7-limit==
Commas: 225/224, 50421/50000
Commas: 225/224, 50421/50000


[[POTE tuning|POTE temperament]]: 580.286
[[POTE_tuning|POTE temperament]]: 580.286


Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd
EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd


==11-limit==  
==11-limit==
Commas: 121/120, 225/224, 441/440
Commas: 121/120, 225/224, 441/440


[[POTE tuning|POTE generator]]: ~7/5 = 580.267
[[POTE_tuning|POTE generator]]: ~7/5 = 580.267


Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
EDOs: 29, 31, 60e
EDOs: 29, 31, 60e
Badness: 0.0237
Badness: 0.0237


==13-limit==  
==13-limit==
Commas: 105/104, 121/120, 196/195, 275/273
Commas: 105/104, 121/120, 196/195, 275/273


Line 238: Line 280:


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
EDOs: 29, 31, 60e, 151cde
EDOs: 29, 31, 60e, 151cde
Badness: 0.0230
Badness: 0.0230


==Tritoni==  
==Tritoni==
Commas: 225/224, 385/384, 27783/27500
Commas: 225/224, 385/384, 27783/27500


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Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
EDOs: 31, 91, 122
EDOs: 31, 91, 122
Badness: 0.0455
Badness: 0.0455


=Merman=  
=Merman=
Comma: 1121008359375/1099511627776
Comma: 1121008359375/1099511627776


Line 256: Line 302:


Map: [&lt;1 5 -5|, &lt;0 -7 15|]
Map: [&lt;1 5 -5|, &lt;0 -7 15|]
EDOs: 41, 84, 125, 209, 334c, 543bc
EDOs: 41, 84, 125, 209, 334c, 543bc
Badness: 0.4538
Badness: 0.4538


==7-limit==  
==7-limit==
Commas: 225/224, 2500000/2470629
Commas: 225/224, 2500000/2470629


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Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
EDOs: 41, 84, 125
EDOs: 41, 84, 125
Badness: 0.0551
Badness: 0.0551


==11-limit==  
==11-limit==
Commas: 225/224, 441/440, 1344/1331
Commas: 225/224, 441/440, 1344/1331


Line 275: Line 326:


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
EDOs: 41, 84, 125e
EDOs: 41, 84, 125e
Badness: 0.0364
Badness: 0.0364


==13-limit==  
==13-limit==
Commas: 144/143, 225/224, 364/363, 441/440
Commas: 144/143, 225/224, 364/363, 441/440


Line 284: Line 337:


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
EDOs: 41, 84, 125e, 209ef, 293ef
EDOs: 41, 84, 125e, 209ef, 293ef
Badness: 0.0275
Badness: 0.0275


=Septimin=  
=Septimin=
Comma: 35595703125/34359738368
Comma: 35595703125/34359738368


Line 293: Line 348:


Map: [&lt;1 4 1|, &lt;0 -11 6|]
Map: [&lt;1 4 1|, &lt;0 -11 6|]
EDOs: 9, 32, 41, 91, 132, 223c, 355bc
EDOs: 9, 32, 41, 91, 132, 223c, 355bc
Badness: 0.6709
Badness: 0.6709


==7-limit==  
==7-limit==
Commas: 225/224, 84035/82944
Commas: 225/224, 84035/82944


[[POTE tuning|POTE temperament]]: 263.632
[[POTE_tuning|POTE temperament]]: 263.632


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]]
EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]]


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 2401/2376
Commas: 225/224, 385/384, 2401/2376


[[POTE tuning|POTE temperament]]: 263.634
[[POTE_tuning|POTE temperament]]: 263.634


Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
EDOs: 9, 32, 41, 91, 223cdef
EDOs: 9, 32, 41, 91, 223cdef


==13-limit==  
==13-limit==
Commas: 105/104, 144/143, 196/195, 245/242
Commas: 105/104, 144/143, 196/195, 245/242


[[POTE tuning|POTE temperament]]: 263.700
[[POTE_tuning|POTE temperament]]: 263.700


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
EDOs: 9, 41, 91
EDOs: 9, 41, 91


=Slender=  
=Slender=
Commas: 225/224, 589824/588245
Commas: 225/224, 589824/588245


[[POTE tuning|POTE temperament]]: ~49/48 = 38.413
[[POTE_tuning|POTE temperament]]: ~49/48 = 38.413


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
EDOs: 31, 94, 125
EDOs: 31, 94, 125
Badness: 0.0569
Badness: 0.0569


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 1331/1323
Commas: 225/224, 385/384, 1331/1323


[[POTE tuning|POTE temperament]]: ~49/48 = 38.387
[[POTE_tuning|POTE temperament]]: ~49/48 = 38.387


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
EDOs: 31, 63, 94, 125
EDOs: 31, 63, 94, 125
Badness: 25.342
Badness: 25.342


==13-limit==  
==13-limit==
Commas: 225/224, 275/273, 385/384, 1331/1323
Commas: 225/224, 275/273, 385/384, 1331/1323


Line 346: Line 412:


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
EDOs: 31, 63, 94
EDOs: 31, 63, 94
Badness: 25.913
Badness: 25.913


=Marvo=  
=Marvo=
Commas: 225/224, 78125000/78121827
Commas: 225/224, 78125000/78121827


[[POTE tuning|POTE temperament]]: ~27/20 = 516.694
[[POTE_tuning|POTE temperament]]: ~27/20 = 516.694


Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||
Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||
EDOs: 65, 72
EDOs: 65, 72


==11-limit==  
==11-limit==
Commas: 225/224, 243/242, 4000/3993
Commas: 225/224, 243/242, 4000/3993


[[POTE tuning|POTE temperament]]: ~27/20 = 516.699
[[POTE_tuning|POTE temperament]]: ~27/20 = 516.699


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
EDOs: 65, 72, 281, 497
EDOs: 65, 72, 281, 497


==13-limit==  
==13-limit==
Commas: 243/242, 225/224, 351/350, 1625/1617
Commas: 243/242, 225/224, 351/350, 1625/1617


Line 372: Line 443:


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
EDOs: 72, 137, 209, 281f, 490bcf
EDOs: 72, 137, 209, 281f, 490bcf
Badness: 0.0269
Badness: 0.0269


=Marvolo=  
=Marvolo=
Commas: 225/224, 156250000/155649627
Commas: 225/224, 156250000/155649627


Line 381: Line 454:


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
EDOs: 29, 43, 72, 619bcd, 691bcd
EDOs: 29, 43, 72, 619bcd, 691bcd
Badness: 0.0833
Badness: 0.0833


==11-limit==  
==11-limit==
Commas: 225/224, 441/440, 4000/3993
Commas: 225/224, 441/440, 4000/3993


Line 391: Line 467:


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
EDOs: 29, 43, 72
EDOs: 29, 43, 72
Badness: 0.0290
Badness: 0.0290


==13-limit==  
==13-limit==
Commas: 169/168, 225/224, 364/363, 441/440
Commas: 169/168, 225/224, 364/363, 441/440


Line 400: Line 478:


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
EDOs: 29, 43, 72, 115f
EDOs: 29, 43, 72, 115f
Badness: 0.0215
Badness: 0.0215


=Amavil=  
=Amavil=
Commas: 225/224, 17496/16807
Commas: 225/224, 17496/16807


Line 409: Line 489:


Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
EDOs: 9, 34d, 43, 77d
EDOs: 9, 34d, 43, 77d
Badness: 0.1096
Badness: 0.1096


==11-limit==  
==11-limit==
Commas: 99/98, 176/175, 864/847
Commas: 99/98, 176/175, 864/847


Line 419: Line 502:


Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]
Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]
EDOs: 9, 34d, 43, 77de
EDOs: 9, 34d, 43, 77de
Badness: 0.0426
Badness: 0.0426


==13-limit==  
==13-limit==
Commas: 78/77, 99/98, 144/143, 176/175
Commas: 78/77, 99/98, 144/143, 176/175


Line 428: Line 513:


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
EDOs: 9, 34d, 43, 77de
EDOs: 9, 34d, 43, 77de
Badness: 0.0258
Badness: 0.0258


=Enneaportent=  
=Enneaportent=
Commas: 225/224, 40353607/40310784
Commas: 225/224, 40353607/40310784


Line 437: Line 524:


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
EDOs: 9, 54, 63, 72, 495bcd
EDOs: 9, 54, 63, 72, 495bcd
Badness: 0.0937
Badness: 0.0937


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 12005/11979
Commas: 225/224, 385/384, 12005/11979


Line 447: Line 537:


Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
EDOs: 9, 54, 63, 72, 423cd, 495bcd
EDOs: 9, 54, 63, 72, 423cd, 495bcd
Badness: 0.0304
Badness: 0.0304


==13-limit==  
==13-limit==
Commas: 169/168, 225/224, 364/363, 1716/1715
Commas: 169/168, 225/224, 364/363, 1716/1715


Line 456: Line 548:


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
EDOs: 9, 54, 63, 72, 279cf
EDOs: 9, 54, 63, 72, 279cf
Badness: 0.0223
Badness: 0.0223


=Submajor=  
=Submajor=
Comma: 69198046875/68719476736
Comma: 69198046875/68719476736


Line 465: Line 559:


Map: [&lt;1 4 -1|, &lt;0 -8 11|]
Map: [&lt;1 4 -1|, &lt;0 -8 11|]
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc
Badness: 0.1302
Badness: 0.1302


==7-limit==  
==7-limit==
Commas: 225/224, 51200/50421
Commas: 225/224, 51200/50421


Line 474: Line 570:


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
EDOs: 10, 33, 43, 53
EDOs: 10, 33, 43, 53
Badness: 0.0605
Badness: 0.0605


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 6655/6561
Commas: 225/224, 385/384, 6655/6561


Line 484: Line 583:


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
EDOs: 10, 53, 116, 169de, 285cde
EDOs: 10, 53, 116, 169de, 285cde
Badness: 0.0506
Badness: 0.0506


==13-limit==  
==13-limit==
Commas: 169/168, 225/224, 275/273, 385/384
Commas: 169/168, 225/224, 275/273, 385/384


Line 493: Line 594:


Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
EDOs: 10, 53, 116, 169de, 285cdef
EDOs: 10, 53, 116, 169de, 285cdef
Badness: 0.0277
Badness: 0.0277


==Interpental==  
==Interpental==
Commas: 99/98, 176/175, 51200/50421
Commas: 99/98, 176/175, 51200/50421


Line 502: Line 605:


Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
EDOs: 43, 53, 96, 149d
EDOs: 43, 53, 96, 149d
Badness: 0.0518
Badness: 0.0518


===13-limit===  
===13-limit===
Commas: 99/98, 169/168, 176/175, 640/637
Commas: 99/98, 169/168, 176/175, 640/637


Line 511: Line 616:


Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]
Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]
EDOs: 43, 53, 96, 149d
EDOs: 43, 53, 96, 149d
Badness: 0.0297
Badness: 0.0297


=Alphorn=  
=Alphorn=
Commas: 225/224, 5764801/5668704
Commas: 225/224, 5764801/5668704


Line 520: Line 627:


Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]
Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]
Wedgie: &lt;&lt;16 -5 22 -45 -10 65||
Wedgie: &lt;&lt;16 -5 22 -45 -10 65||
EDOs: 28d, 41, 151cd, 192cd, 233cd
EDOs: 28d, 41, 151cd, 192cd, 233cd
Badness: 0.1293
Badness: 0.1293


==11-limit==  
==11-limit==
Commas: 225/224, 385/384, 12250/11979
Commas: 225/224, 385/384, 12250/11979


Line 530: Line 640:


Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
EDOs: 41, 315cde
EDOs: 41, 315cde
Badness: 0.0735</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0735
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:114:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;/div&gt;
[[Category:marvel]]
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negri-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
[[Category:overview]]
&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negri-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Category:rank_2]]
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negril"&gt;Negril&lt;/a&gt;&lt;/div&gt;
[[Category:temperaments]]
&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negril-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negric-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negroni"&gt;Negroni&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negroni-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Lizard"&gt;Lizard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Lizard-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Lizard-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Gizzard"&gt;Gizzard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Gizzard-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Gizzard-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Mage"&gt;Mage&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triton"&gt;Triton&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triton-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Tritonic"&gt;Tritonic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-Tritoni"&gt;Tritoni&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Merman"&gt;Merman&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Septimin"&gt;Septimin&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;!-- ws:start:WikiTextTocRule:149: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Slender"&gt;Slender&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:149 --&gt;&lt;!-- ws:start:WikiTextTocRule:150: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slender-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:150 --&gt;&lt;!-- ws:start:WikiTextTocRule:151: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slender-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:151 --&gt;&lt;!-- ws:start:WikiTextTocRule:152: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvo"&gt;Marvo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvo-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvolo"&gt;Marvolo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvolo-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvolo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amavil"&gt;Amavil&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amavil-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amavil-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Enneaportent"&gt;Enneaportent&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Enneaportent-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Enneaportent-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Submajor"&gt;Submajor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-Interpental"&gt;Interpental&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Submajor-Interpental-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Alphorn"&gt;Alphorn&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alphorn-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:172 --&gt;This page discusses some of the temperaments tempering out |-5 2 2 -1&amp;gt; =&lt;a class="wiki_link" href="/225_224"&gt; 225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/Marvel%20family"&gt;marvel&lt;/a&gt; comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone&lt;/a&gt;, &lt;a class="wiki_link" href="/Miracle"&gt;miracle&lt;/a&gt;, &lt;a class="wiki_link" href="/Magic%20family"&gt;magic&lt;/a&gt;, &lt;a class="wiki_link" href="/Pajara"&gt;pajara&lt;/a&gt;, &lt;a class="wiki_link" href="/Orwell"&gt;orwell&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Garibaldi%20temperament"&gt;garibaldi&lt;/a&gt;, &lt;a class="wiki_link" href="/Augmented%20family"&gt;august&lt;/a&gt;, &lt;a class="wiki_link" href="/Pythagorean%20family"&gt;compton&lt;/a&gt;, &lt;a class="wiki_link" href="/Dicot%20family"&gt;sharp&lt;/a&gt;, &lt;a class="wiki_link" href="/Escapade%20family"&gt;escapade&lt;/a&gt; and &lt;a class="wiki_link" href="/Pelogic%20family"&gt;mavila&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.&lt;br /&gt;
&lt;br /&gt;
The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.&lt;br /&gt;
&lt;br /&gt;
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~15/14 = 125.608&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;4 -3 2 -14 -8 13||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Negri-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 49/48, 56/55&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/14 = 126.474&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0262&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Negri-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/13 = 126.431&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 4|, &amp;lt;0 -4 3 -2 -5 -3|]&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Negril"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negril&lt;/h1&gt;
Commas: 49/48, 100/99, 225/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.767&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 2|, &amp;lt;0 -4 3 -2 14|]&lt;br /&gt;
EDOs: 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48df&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77cdf&lt;/a&gt;&lt;br /&gt;
Badness: 0.0387&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Negril-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 65/64, 91/90, 875/858&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.716&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 2 4|, &amp;lt;0 -4 3 -2 14 -3|]&lt;br /&gt;
EDOs: 9, 10, 19, 29, 48, 77&lt;br /&gt;
Badness: 0.0244&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Negric&lt;/h1&gt;
Commas: 33/32, 49/48, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]&lt;br /&gt;
EDOs: 9, 19, &lt;a class="wiki_link" href="/85edo"&gt;85&lt;/a&gt;&lt;br /&gt;
Badness: 0.0306&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3 4|, &amp;lt;0 -4 3 -2 4 -3|]&lt;br /&gt;
EDOs: 9, 19, 85&lt;br /&gt;
Badness: 0.0202&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Negroni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Negroni&lt;/h1&gt;
Commas: 49/48, 55/54, 225/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 5|, &amp;lt;0 -4 3 -2 -15|]&lt;br /&gt;
EDOs: 10, 19e, 29, 77cde&lt;br /&gt;
Badness: 0.0353&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Negroni-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 55/54, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.545&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 5 4|, &amp;lt;0 -4 3 -2 -15 -3|]&lt;br /&gt;
EDOs: 10, 19e, 29, 77cdef&lt;br /&gt;
Badness: 0.0216&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Wizard&lt;/h1&gt;
Comma: 2197265625/2147483648&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.212&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5|, &amp;lt;0 6 -1|]&lt;br /&gt;
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc&lt;br /&gt;
Badness: 0.3864&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Wizard-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.256&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2|, &amp;lt;0 6 -1 10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;12 -2 20 -31 -2 52||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238c&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310c&lt;/a&gt;, &lt;a class="wiki_link" href="/382edo"&gt;382c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0408&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.232&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8|, &amp;lt;0 6 -1 10 -3|]&lt;br /&gt;
EDOs: 22, 50, 72, 94, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238c&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0185&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Wizard-Lizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Lizard&lt;/h2&gt;
Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.389&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11|, &amp;lt;0 6 -1 10 -3 -10|]&lt;br /&gt;
EDOs: 22, 50, 72, 122, 194df&lt;br /&gt;
Badness: 0.0218&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Wizard-Lizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;17-limit&lt;/h3&gt;
Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.381&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11 6|, &amp;lt;0 6 -1 10 -3 -10 6|]&lt;br /&gt;
EDOs: 22, 50, 72, 122g, 194dfg&lt;br /&gt;
Badness: 0.0145&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Wizard-Lizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;19-limit&lt;/h3&gt;
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 383.477&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11 6 2|, &amp;lt;0 6 -1 10 -3 -10 6 18|]&lt;br /&gt;
EDOs: 22h, 50, 72, &lt;a class="wiki_link" href="/122edo"&gt;122g&lt;/a&gt;, &lt;a class="wiki_link" href="/194edo"&gt;194dfg&lt;/a&gt;&lt;br /&gt;
Badness: 0.0157&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Wizard-Gizzard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Gizzard&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 1573/1568&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.170&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2|, &amp;lt;0 6 -1 10 -3 26|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238cf&lt;/a&gt;&lt;br /&gt;
Badness: 0.0203&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Wizard-Gizzard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;17-limit&lt;/h3&gt;
Commas: 225/224, 289/288, 325/324, 375/374, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.175&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2 6|, &amp;lt;0 6 -1 10 -3 26 6|]&lt;br /&gt;
EDOs: 22f, 72, 94, &lt;a class="wiki_link" href="/166edo"&gt;166g&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238cfg&lt;/a&gt;&lt;br /&gt;
Badness: 0.0136&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="Wizard-Gizzard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;19-limit&lt;/h3&gt;
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.138&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2 6 15|, &amp;lt;0 6 -1 10 -3 26 6 -18|]&lt;br /&gt;
EDOs: 22f, 72, 94, 166g&lt;br /&gt;
Badness: 0.0148&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Wizard-Mage"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Mage&lt;/h2&gt;
Commas: 99/98, 176/175, 1331/1296&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~55/48 = 216.876&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 4|, &amp;lt;0 6 -1 10 8|]&lt;br /&gt;
EDOs: 22, 72e, 94e&lt;br /&gt;
Badness: 0.0578&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Triton&lt;/h1&gt;
Commas: 225/224, 1029/1000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~7/5 = 568.865&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 6 7|, &amp;lt;0 3 -7 -8|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 -7 -8 -18 -21 1||&lt;br /&gt;
EDOs: 17d, 19, 78bd, 97bd&lt;br /&gt;
Badness: 0.0592&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Triton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 569.144&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 6 7 4|, &amp;lt;0 3 -7 -8 -1|]&lt;br /&gt;
EDOs: 19, 59bde, 78bde, 97bde&lt;br /&gt;
Badness: 0.0457&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Tritonic&lt;/h1&gt;
Comnma: 553584375/536870912&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~45/32 = 580.219&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3|, &amp;lt;0 -5 11|]&lt;br /&gt;
EDOs: 29, 31, 60, 91&lt;br /&gt;
Badness: 0.3785&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Tritonic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.286&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3|, &amp;lt;0 -5 11 12|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 -11 -12 -29 -33 3||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;, &lt;a class="wiki_link" href="/91edo"&gt;91&lt;/a&gt;, &lt;a class="wiki_link" href="/122edo"&gt;122&lt;/a&gt;, 213bcd&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
Commas: 121/120, 225/224, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/5 = 580.267&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 2|, &amp;lt;0 -5 11 12 3|]&lt;br /&gt;
EDOs: 29, 31, 60e&lt;br /&gt;
Badness: 0.0237&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Tritonic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 121/120, 196/195, 275/273&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 580.108&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 2 -5|, &amp;lt;0 -5 11 12 3 18|]&lt;br /&gt;
EDOs: 29, 31, 60e, 151cde&lt;br /&gt;
Badness: 0.0230&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Tritonic-Tritoni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Tritoni&lt;/h2&gt;
Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 580.389&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 17|, &amp;lt;0 -5 11 12 -28|]&lt;br /&gt;
EDOs: 31, 91, 122&lt;br /&gt;
Badness: 0.0455&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Merman"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Merman&lt;/h1&gt;
Comma: 1121008359375/1099511627776&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~45/32 = 585.634&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5|, &amp;lt;0 -7 15|]&lt;br /&gt;
EDOs: 41, 84, 125, 209, 334c, 543bc&lt;br /&gt;
Badness: 0.4538&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Merman-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 2500000/2470629&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.585&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5|, &amp;lt;0 -7 15 16|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;7 -15 -16 -40 -45 5||&lt;br /&gt;
EDOs: 41, 84, 125&lt;br /&gt;
Badness: 0.0551&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Merman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.606&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5 2|, &amp;lt;0 -7 15 16 3]]&lt;br /&gt;
EDOs: 41, 84, 125e&lt;br /&gt;
Badness: 0.0364&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Merman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 225/224, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.657&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5 2 12|, &amp;lt;0 -7 15 16 3 -17|]&lt;br /&gt;
EDOs: 41, 84, 125e, 209ef, 293ef&lt;br /&gt;
Badness: 0.0275&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Septimin&lt;/h1&gt;
Comma: 35595703125/34359738368&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~75/64 = 263.658&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1|, &amp;lt;0 -11 6|]&lt;br /&gt;
EDOs: 9, 32, 41, 91, 132, 223c, 355bc&lt;br /&gt;
Badness: 0.6709&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Septimin-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.632&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5|, &amp;lt;0 -11 6 -10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;11 -6 10 -35 -15 40||&lt;br /&gt;
EDOs: 9, &lt;a class="wiki_link" href="/32edo"&gt;32&lt;/a&gt;, 41, 91, &lt;a class="wiki_link" href="/132edo"&gt;132&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.634&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5 5|, &amp;lt;0 -11 6 -10 -7|]&lt;br /&gt;
EDOs: 9, 32, 41, 91, 223cdef&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.700&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5 5 7|, &amp;lt;0 -11 6 -10 -7 -15|]&lt;br /&gt;
EDOs: 9, 41, 91&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Slender&lt;/h1&gt;
Commas: 225/224, 589824/588245&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.413&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -13 10 -6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;13 -10 6 -46 -27 42||&lt;br /&gt;
EDOs: 31, 94, 125&lt;br /&gt;
Badness: 0.0569&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.387&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -13 10 -6 -17|]&lt;br /&gt;
EDOs: 31, 63, 94, 125&lt;br /&gt;
Badness: 25.342&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Slender-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 275/273, 385/384, 1331/1323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/48 = 38.314&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 3|, &amp;lt;0 -13 10 -6 -17 22|]&lt;br /&gt;
EDOs: 31, 63, 94&lt;br /&gt;
Badness: 25.913&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Marvo&lt;/h1&gt;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~27/20 = 516.694&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29|, &amp;lt;0 -6 -17 -46|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6, 17, 46, 13, 56 59||&lt;br /&gt;
EDOs: 65, 72&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~27/20 = 516.699&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29 12|, &amp;lt;0 -6 -17 -46 -15|]&lt;br /&gt;
EDOs: 65, 72, 281, 497&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Marvo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h2&gt;
Commas: 243/242, 225/224, 351/350, 1625/1617&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 516.730&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29 12 39|, &amp;lt;0 -6 -17 -46 -15 -62|]&lt;br /&gt;
EDOs: 72, 137, 209, 281f, 490bcf&lt;br /&gt;
Badness: 0.0269&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc40"&gt;&lt;a name="Marvolo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Marvolo&lt;/h1&gt;
Commas: 225/224, 156250000/155649627&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.348&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1|, &amp;lt;0 -6 19 26|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 -19 -26 -44 -58 -7||&lt;br /&gt;
EDOs: 29, 43, 72, 619bcd, 691bcd&lt;br /&gt;
Badness: 0.0833&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Marvolo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 441/440, 4000/3993&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.340&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1 2|, &amp;lt;0 -6 19 26 21|]&lt;br /&gt;
EDOs: 29, 43, 72&lt;br /&gt;
Badness: 0.0290&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Marvolo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.330&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1 2 3|, &amp;lt;0 -6 19 26 21 10|]&lt;br /&gt;
EDOs: 29, 43, 72, 115f&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Amavil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Amavil&lt;/h1&gt;
Commas: 225/224, 17496/16807&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 529.979&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9|, &amp;lt;0 -10 3 -14|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 -3 14 -28 -6 41||&lt;br /&gt;
EDOs: 9, 34d, 43, 77d&lt;br /&gt;
Badness: 0.1096&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Amavil-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
Commas: 99/98, 176/175, 864/847&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 529.974&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9 7|, &amp;lt;0 -10 3 -14 -8|]&lt;br /&gt;
EDOs: 9, 34d, 43, 77de&lt;br /&gt;
Badness: 0.0426&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Amavil-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
Commas: 78/77, 99/98, 144/143, 176/175&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 529.951&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9 7 9|, &amp;lt;0 -10 3 -14 -8 -12|]&lt;br /&gt;
EDOs: 9, 34d, 43, 77de&lt;br /&gt;
Badness: 0.0258&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc46"&gt;&lt;a name="Enneaportent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;Enneaportent&lt;/h1&gt;
Commas: 225/224, 40353607/40310784&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.165&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11|, &amp;lt;0 2 -1 2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;18 -9 18 -56 -22 67||&lt;br /&gt;
EDOs: 9, 54, 63, 72, 495bcd&lt;br /&gt;
Badness: 0.0937&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Enneaportent-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 12005/11979&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.146&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11 24|, &amp;lt;0 2 -1 2 1|]&lt;br /&gt;
EDOs: 9, 54, 63, 72, 423cd, 495bcd&lt;br /&gt;
Badness: 0.0304&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Enneaportent-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 364/363, 1716/1715&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.047&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11 24 19|, &amp;lt;0 2 -1 2 1 2|]&lt;br /&gt;
EDOs: 9, 54, 63, 72, 279cf&lt;br /&gt;
Badness: 0.0223&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc49"&gt;&lt;a name="Submajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;Submajor&lt;/h1&gt;
Comma: 69198046875/68719476736&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10125/8192 = 362.321&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1|, &amp;lt;0 -8 11|]&lt;br /&gt;
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc&lt;br /&gt;
Badness: 0.1302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Submajor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 51200/50421&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.255&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1|, &amp;lt;0 -8 11 6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;8 -11 -6 -36 -32 17||&lt;br /&gt;
EDOs: 10, 33, 43, 53&lt;br /&gt;
Badness: 0.0605&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Submajor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/22 = 362.101&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 11|, &amp;lt;0 -8 11 6 -25|]&lt;br /&gt;
EDOs: 10, 53, 116, 169de, 285cde&lt;br /&gt;
Badness: 0.0506&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Submajor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 275/273, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.105&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 11 4|, &amp;lt;0 -8 11 6 -25 -1|]&lt;br /&gt;
EDOs: 10, 53, 116, 169de, 285cdef&lt;br /&gt;
Badness: 0.0277&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Submajor-Interpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Interpental&lt;/h2&gt;
Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.418&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 -5|, &amp;lt;0 -8 11 6 28|]&lt;br /&gt;
EDOs: 43, 53, 96, 149d&lt;br /&gt;
Badness: 0.0518&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc54"&gt;&lt;a name="Submajor-Interpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;13-limit&lt;/h3&gt;
Commas: 99/98, 169/168, 176/175, 640/637&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.402&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 -5 4|, &amp;lt;0 -8 11 6 28 -1|]&lt;br /&gt;
EDOs: 43, 53, 96, 149d&lt;br /&gt;
Badness: 0.0297&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc55"&gt;&lt;a name="Alphorn"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;Alphorn&lt;/h1&gt;
Commas: 225/224, 5764801/5668704&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 556.221&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 9 0 13|, &amp;lt;0 -16 5 -22|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;16 -5 22 -45 -10 65||&lt;br /&gt;
EDOs: 28d, 41, 151cd, 192cd, 233cd&lt;br /&gt;
Badness: 0.1293&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc56"&gt;&lt;a name="Alphorn-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 556.144&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 9 0 13 3|, &amp;lt;0 -16 5 -22 1|]&lt;br /&gt;
EDOs: 41, 315cde&lt;br /&gt;
Badness: 0.0735&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

This page discusses some of the temperaments tempering out |-5 2 2 -1> = 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.

Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)

Negri

Commas: 49/48, 225/224

POTE temperament: ~15/14 = 125.608

Map: [<1 2 2 3|, <0 -4 3 -2|]

Wedgie: <<4 -3 2 -14 -8 13||

EDOs: 9, 10, 19, 86

11-limit

Commas: 45/44, 49/48, 56/55

POTE generator: ~15/14 = 126.474

Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]

EDOs: 9, 10, 19

Badness: 0.0262

13-limit

Commas: 45/44, 49/48, 56/55, 78/77

POTE generator: ~14/13 = 126.431

Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]

EDOs: 9, 10, 19

Negril

Commas: 49/48, 100/99, 225/224

POTE generator: ~15/14 = 124.767

Map: [<1 2 2 3 2|, <0 -4 3 -2 14|]

EDOs: 19, 29, 48df, 77cdf

Badness: 0.0387

13-limit

Commas: 49/48, 65/64, 91/90, 875/858

POTE generator: ~15/14 = 124.716

Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]

EDOs: 9, 10, 19, 29, 48, 77

Badness: 0.0244

Negric

Commas: 33/32, 49/48, 77/75

POTE generator: ~15/14 = 127.039

Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]

EDOs: 9, 19, 85

Badness: 0.0306

13-limit

Commas: 33/32, 49/48, 65/64, 91/90

POTE generator: ~15/14 = 127.039

Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]

EDOs: 9, 19, 85

Badness: 0.0202

Negroni

Commas: 49/48, 55/54, 225/224

POTE generator: ~15/14 = 124.539

Map: [<1 2 2 3 5|, <0 -4 3 -2 -15|]

EDOs: 10, 19e, 29, 77cde

Badness: 0.0353

13-limit

Commas: 49/48, 55/54, 65/64, 91/90

POTE generator: ~15/14 = 124.545

Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]

EDOs: 10, 19e, 29, 77cdef

Badness: 0.0216

Wizard

Comma: 2197265625/2147483648

POTE generator: ~5/4 = 383.212

Map: [<2 1 5|, <0 6 -1|]

EDOs: 22, 50, 72, 166, 238c, 310c, 548bc

Badness: 0.3864

7-limit

Commas: 225/224, 118098/117649

POTE temperament: 383.256

Map: [<2 1 5 2|, <0 6 -1 10|]

Wedgie: <<12 -2 20 -31 -2 52||

EDOs: 22, 50, 72, 94, 166, 238c, 310c, 382c

Badness: 0.0408

11-limit

Commas: 225/224, 385/384, 4000/3993

POTE temperament: 383.232

Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]

EDOs: 22, 50, 72, 94, 166, 238c, 310c

Badness: 0.0185

Lizard

Commas: 225/224, 351/350, 364/363, 385/384

POTE temperament: 383.389

Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]

EDOs: 22, 50, 72, 122, 194df

Badness: 0.0218

17-limit

Commas: 221/220, 273/272, 289/288, 351/350, 375/374

POTE temperament: 383.381

Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]

EDOs: 22, 50, 72, 122g, 194dfg

Badness: 0.0145

19-limit

Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

POTE generator: ~5/4 = 383.477

Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]

EDOs: 22h, 50, 72, 122g, 194dfg

Badness: 0.0157

Gizzard

Commas: 225/224, 385/384, 325/324, 1573/1568

POTE generator: ~5/4 = 383.170

Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|]

EDOs: 22, 72, 94, 166, 238cf

Badness: 0.0203

17-limit

Commas: 225/224, 289/288, 325/324, 375/374, 385/384

POTE generator: ~5/4 = 383.175

Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|]

EDOs: 22f, 72, 94, 166g, 238cfg

Badness: 0.0136

19-limit

Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399

POTE generator: ~5/4 = 383.138

Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]

EDOs: 22f, 72, 94, 166g

Badness: 0.0148

Mage

Commas: 99/98, 176/175, 1331/1296

POTE generator: ~55/48 = 216.876

Map: [<2 1 5 2 4|, <0 6 -1 10 8|]

EDOs: 22, 72e, 94e

Badness: 0.0578

Triton

Commas: 225/224, 1029/1000

POTE temperament: ~7/5 = 568.865

Map: [<1 0 6 7|, <0 3 -7 -8|]

Wedgie: <<3 -7 -8 -18 -21 1||

EDOs: 17d, 19, 78bd, 97bd

Badness: 0.0592

11-limit

Commas: 45/44, 56/55, 1029/1000

POTE generator: ~7/5 = 569.144

Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|]

EDOs: 19, 59bde, 78bde, 97bde

Badness: 0.0457

Tritonic

Comnma: 553584375/536870912

POTE generator: ~45/32 = 580.219

Map: [<1 4 -3|, <0 -5 11|]

EDOs: 29, 31, 60, 91

Badness: 0.3785

7-limit

Commas: 225/224, 50421/50000

POTE temperament: 580.286

Map: [<1 4 -3 -3|, <0 -5 11 12|]

Wedgie: <<5 -11 -12 -29 -33 3||

EDOs: 29, 31, 60, 91, 122, 213bcd

11-limit

Commas: 121/120, 225/224, 441/440

POTE generator: ~7/5 = 580.267

Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|]

EDOs: 29, 31, 60e

Badness: 0.0237

13-limit

Commas: 105/104, 121/120, 196/195, 275/273

POTE generator: ~7/5 = 580.108

Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|]

EDOs: 29, 31, 60e, 151cde

Badness: 0.0230

Tritoni

Commas: 225/224, 385/384, 27783/27500

POTE generator: ~7/5 = 580.389

Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]

EDOs: 31, 91, 122

Badness: 0.0455

Merman

Comma: 1121008359375/1099511627776

POTE generator: ~45/32 = 585.634

Map: [<1 5 -5|, <0 -7 15|]

EDOs: 41, 84, 125, 209, 334c, 543bc

Badness: 0.4538

7-limit

Commas: 225/224, 2500000/2470629

POTE generator: ~7/5 = 585.585

Map: [<1 5 -5 -5|, <0 -7 15 16|]

Wedgie: <<7 -15 -16 -40 -45 5||

EDOs: 41, 84, 125

Badness: 0.0551

11-limit

Commas: 225/224, 441/440, 1344/1331

POTE generator: ~7/5 = 585.606

Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]]

EDOs: 41, 84, 125e

Badness: 0.0364

13-limit

Commas: 144/143, 225/224, 364/363, 441/440

POTE generator: ~7/5 = 585.657

Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|]

EDOs: 41, 84, 125e, 209ef, 293ef

Badness: 0.0275

Septimin

Comma: 35595703125/34359738368

POTE generator: ~75/64 = 263.658

Map: [<1 4 1|, <0 -11 6|]

EDOs: 9, 32, 41, 91, 132, 223c, 355bc

Badness: 0.6709

7-limit

Commas: 225/224, 84035/82944

POTE temperament: 263.632

Map: [<1 4 1 5|, <0 -11 6 -10|]

Wedgie: <<11 -6 10 -35 -15 40||

EDOs: 9, 32, 41, 91, 132

11-limit

Commas: 225/224, 385/384, 2401/2376

POTE temperament: 263.634

Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|]

EDOs: 9, 32, 41, 91, 223cdef

13-limit

Commas: 105/104, 144/143, 196/195, 245/242

POTE temperament: 263.700

Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]

EDOs: 9, 41, 91

Slender

Commas: 225/224, 589824/588245

POTE temperament: ~49/48 = 38.413

Map: [<1 2 2 3|, <0 -13 10 -6|]

Wedgie: <<13 -10 6 -46 -27 42||

EDOs: 31, 94, 125

Badness: 0.0569

11-limit

Commas: 225/224, 385/384, 1331/1323

POTE temperament: ~49/48 = 38.387

Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|]

EDOs: 31, 63, 94, 125

Badness: 25.342

13-limit

Commas: 225/224, 275/273, 385/384, 1331/1323

POTE generator: ~49/48 = 38.314

Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|]

EDOs: 31, 63, 94

Badness: 25.913

Marvo

Commas: 225/224, 78125000/78121827

POTE temperament: ~27/20 = 516.694

Map: [<1 5 12 29|, <0 -6 -17 -46|]

Wedgie: <<6, 17, 46, 13, 56 59||

EDOs: 65, 72

11-limit

Commas: 225/224, 243/242, 4000/3993

POTE temperament: ~27/20 = 516.699

Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]

EDOs: 65, 72, 281, 497

13-limit

Commas: 243/242, 225/224, 351/350, 1625/1617

POTE generator: ~27/20 = 516.730

Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|]

EDOs: 72, 137, 209, 281f, 490bcf

Badness: 0.0269

Marvolo

Commas: 225/224, 156250000/155649627

POTE generator: ~21/20 = 83.348

Map: [<1 2 1 1|, <0 -6 19 26|]

Wedgie: <<6 -19 -26 -44 -58 -7||

EDOs: 29, 43, 72, 619bcd, 691bcd

Badness: 0.0833

11-limit

Commas: 225/224, 441/440, 4000/3993

POTE generator: ~21/20 = 83.340

Map: [<1 2 1 1 2|, <0 -6 19 26 21|]

EDOs: 29, 43, 72

Badness: 0.0290

13-limit

Commas: 169/168, 225/224, 364/363, 441/440

POTE generator: ~21/20 = 83.330

Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|]

EDOs: 29, 43, 72, 115f

Badness: 0.0215

Amavil

Commas: 225/224, 17496/16807

POTE generator: ~48/35 = 529.979

Map: [<1 6 1 9|, <0 -10 3 -14|]

Wedgie: <<10 -3 14 -28 -6 41||

EDOs: 9, 34d, 43, 77d

Badness: 0.1096

11-limit

Commas: 99/98, 176/175, 864/847

POTE generator: ~15/11 = 529.974

Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|]

EDOs: 9, 34d, 43, 77de

Badness: 0.0426

13-limit

Commas: 78/77, 99/98, 144/143, 176/175

POTE generator: ~15/11 = 529.951

Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|]

EDOs: 9, 34d, 43, 77de

Badness: 0.0258

Enneaportent

Commas: 225/224, 40353607/40310784

POTE generator: ~5/4 = 383.165

Map: [<9 0 28 11|, <0 2 -1 2|]

Wedgie: <<18 -9 18 -56 -22 67||

EDOs: 9, 54, 63, 72, 495bcd

Badness: 0.0937

11-limit

Commas: 225/224, 385/384, 12005/11979

POTE generator: ~5/4 = 383.146

Map: [<9 0 28 11 24|, <0 2 -1 2 1|]

EDOs: 9, 54, 63, 72, 423cd, 495bcd

Badness: 0.0304

13-limit

Commas: 169/168, 225/224, 364/363, 1716/1715

POTE generator: ~5/4 = 383.047

Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|]

EDOs: 9, 54, 63, 72, 279cf

Badness: 0.0223

Submajor

Comma: 69198046875/68719476736

POTE generator: ~10125/8192 = 362.321

Map: [<1 4 -1|, <0 -8 11|]

EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc

Badness: 0.1302

7-limit

Commas: 225/224, 51200/50421

POTE generator: ~49/40 = 362.255

Map: [<1 4 -1 1|, <0 -8 11 6|]

Wedgie: <<8 -11 -6 -36 -32 17||

EDOs: 10, 33, 43, 53

Badness: 0.0605

11-limit

Commas: 225/224, 385/384, 6655/6561

POTE generator: ~27/22 = 362.101

Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|]

EDOs: 10, 53, 116, 169de, 285cde

Badness: 0.0506

13-limit

Commas: 169/168, 225/224, 275/273, 385/384

POTE generator: ~16/13 = 362.105

Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|]

EDOs: 10, 53, 116, 169de, 285cdef

Badness: 0.0277

Interpental

Commas: 99/98, 176/175, 51200/50421

POTE generator: ~49/40 = 362.418

Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|]

EDOs: 43, 53, 96, 149d

Badness: 0.0518

13-limit

Commas: 99/98, 169/168, 176/175, 640/637

POTE generator: ~16/13 = 362.402

Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|]

EDOs: 43, 53, 96, 149d

Badness: 0.0297

Alphorn

Commas: 225/224, 5764801/5668704

POTE generator: ~48/35 = 556.221

Map: [<1 9 0 13|, <0 -16 5 -22|]

Wedgie: <<16 -5 22 -45 -10 65||

EDOs: 28d, 41, 151cd, 192cd, 233cd

Badness: 0.1293

11-limit

Commas: 225/224, 385/384, 12250/11979

POTE generator: ~11/8 = 556.144

Map: [<1 9 0 13 3|, <0 -16 5 -22 1|]

EDOs: 41, 315cde

Badness: 0.0735

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