Marvel temperaments: Difference between revisions

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[[toc]]
This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 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 5/4-9/7 versions of the augmented triad. 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.

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

[[POTE tuning|POTE temperament]]: ~15/14 = 125.608

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

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

[[POTE tuning|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 tuning|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, [[29edo|29]], [[48edo|48df]], [[77edo|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, [[85edo|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

=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 tuning|POTE temperament]]: 383.256

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

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

[[POTE tuning|POTE temperament]]: 383.232

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

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

[[POTE tuning|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 tuning|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 tuning|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, [[122edo|122g]], [[194edo|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: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|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, [[166edo|166g]], [[238edo|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 tuning|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 tuning|POTE temperament]]: 580.286

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

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

[[POTE tuning|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

=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 tuning|POTE temperament]]: 263.632

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

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

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

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

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

[[POTE tuning|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 tuning|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 tuning|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 tuning|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
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

Original HTML content:

<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:112:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 1em;"><a href="#Negri">Negri</a></div>
<!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Negri-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Negri-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 1em;"><a href="#Negril">Negril</a></div>
<!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Negril-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Negric">Negric</a></div>
<!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Negric-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Negroni">Negroni</a></div>
<!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Wizard">Wizard</a></div>
<!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Wizard-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Wizard-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 2em;"><a href="#Wizard-Lizard">Lizard</a></div>
<!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-17-limit">17-limit</a></div>
<!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-19-limit">19-limit</a></div>
<!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Wizard-Gizzard">Gizzard</a></div>
<!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-17-limit">17-limit</a></div>
<!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-19-limit">19-limit</a></div>
<!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Wizard-Mage">Mage</a></div>
<!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 1em;"><a href="#Triton">Triton</a></div>
<!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 2em;"><a href="#Triton-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 1em;"><a href="#Tritonic">Tritonic</a></div>
<!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 2em;"><a href="#Tritonic-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Tritonic-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 2em;"><a href="#Tritonic-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Tritonic-Tritoni">Tritoni</a></div>
<!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 1em;"><a href="#Merman">Merman</a></div>
<!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Merman-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Merman-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Merman-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 1em;"><a href="#Septimin">Septimin</a></div>
<!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Septimin-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Septimin-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 2em;"><a href="#Septimin-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 1em;"><a href="#Slender">Slender</a></div>
<!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Slender-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Slender-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Marvo">Marvo</a></div>
<!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Marvo-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Marvo-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 1em;"><a href="#Marvolo">Marvolo</a></div>
<!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Marvolo-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Marvolo-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 1em;"><a href="#Amavil">Amavil</a></div>
<!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 2em;"><a href="#Amavil-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Amavil-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 1em;"><a href="#Enneaportent">Enneaportent</a></div>
<!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Enneaportent-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Enneaportent-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 1em;"><a href="#Submajor">Submajor</a></div>
<!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Submajor-7-limit">7-limit</a></div>
<!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Submajor-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 2em;"><a href="#Submajor-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Submajor-Interpental">Interpental</a></div>
<!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 3em;"><a href="#Submajor-Interpental-13-limit">13-limit</a></div>
<!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 1em;"><a href="#Alphorn">Alphorn</a></div>
<!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div>
<!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --></div>
<!-- ws:end:WikiTextTocRule:169 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/marvel%20comma">marvel comma</a> or <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>. 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.<br />
<br />
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. 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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 225/224<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~15/14 = 125.608<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;4 -3 2 -14 -8 13||<br />
EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/86edo">86</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2>
 Commas: 45/44, 49/48, 56/55<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~15/14 = 126.474<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />
EDOs: 9, 10, 19<br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0262<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2>
 Commas: 45/44, 49/48, 56/55, 78/77<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~14/13 = 126.431<br />
<br />
Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]<br />
EDOs: 9, 10, 19<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Negril"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negril</h1>
 Commas: 49/48, 100/99, 225/224<br />
<br />
POTE generator: ~15/14 = 124.767<br />
<br />
Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]<br />
EDOs: 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/48edo">48df</a>, <a class="wiki_link" href="/77edo">77cdf</a><br />
Badness: 0.0387<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negril-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2>
 Commas: 49/48, 65/64, 91/90, 875/858<br />
<br />
POTE generator: ~15/14 = 124.716<br />
<br />
Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]<br />
EDOs: 9, 10, 19, 29, 48, 77<br />
Badness: 0.0244<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:10 -->Negric</h1>
 Commas: 33/32, 49/48, 77/75<br />
<br />
POTE generator: ~15/14 = 127.039<br />
<br />
Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br />
EDOs: 9, 19, <a class="wiki_link" href="/85edo">85</a><br />
Badness: 0.0306<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2>
 Commas: 33/32, 49/48, 65/64, 91/90<br />
<br />
POTE generator: ~15/14 = 127.039<br />
<br />
Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]<br />
EDOs: 9, 19, 85<br />
Badness: 0.0202<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Negroni"></a><!-- ws:end:WikiTextHeadingRule:14 -->Negroni</h1>
 Commas: 49/48, 55/54, 225/224<br />
<br />
POTE generator: ~15/14 = 124.539<br />
<br />
Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]<br />
EDOs: 10, 19e, 29, 77cde<br />
Badness: 0.0353<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:16 -->Wizard</h1>
 Comma: 2197265625/2147483648<br />
<br />
POTE generator: ~5/4 = 383.212<br />
<br />
Map: [&lt;2 1 5|, &lt;0 6 -1|]<br />
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc<br />
Badness: 0.3864<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Wizard-7-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->7-limit</h2>
 Commas: 225/224, 118098/117649<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br />
<br />
Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br />
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br />
EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a>, <a class="wiki_link" href="/382edo">382c</a><br />
Badness: 0.0408<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2>
 Commas: 225/224, 385/384, 4000/3993<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br />
<br />
Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br />
EDOs: 22, 50, 72, 94, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238c</a>, <a class="wiki_link" href="/310edo">310c</a><br />
Badness: 0.0185<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:22 -->Lizard</h2>
 Commas: 225/224, 351/350, 364/363, 385/384<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br />
<br />
Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]<br />
EDOs: 22, 50, 72, 122, 194df<br />
Badness: 0.0218<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->17-limit</h3>
 Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br />
<br />
Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]<br />
EDOs: 22, 50, 72, 122g, 194dfg<br />
Badness: 0.0145<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->19-limit</h3>
 Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~5/4 = 383.477<br />
<br />
Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]<br />
EDOs: 22h, 50, 72, <a class="wiki_link" href="/122edo">122g</a>, <a class="wiki_link" href="/194edo">194dfg</a><br />
Badness: 0.0157<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:28 -->Gizzard</h2>
 Commas: 225/224, 385/384, 325/324, 1573/1568<br />
<br />
POTE generator: ~5/4 = 383.170<br />
<br />
Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]<br />
EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/26edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/238edo">238cf</a><br />
Badness: 0.0203<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->17-limit</h3>
 Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br />
<br />
POTE generator: ~5/4 = 383.175<br />
<br />
Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]<br />
EDOs: 22f, 72, 94, <a class="wiki_link" href="/166edo">166g</a>, <a class="wiki_link" href="/238edo">238cfg</a><br />
Badness: 0.0136<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->19-limit</h3>
 Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399<br />
<br />
POTE generator: ~5/4 = 383.138<br />
<br />
Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]<br />
EDOs: 22f, 72, 94, 166g<br />
Badness: 0.0148<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Wizard-Mage"></a><!-- ws:end:WikiTextHeadingRule:34 -->Mage</h2>
 Commas: 99/98, 176/175, 1331/1296<br />
<br />
POTE generator: ~55/48 = 216.876<br />
<br />
Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]<br />
EDOs: 22, 72e, 94e<br />
Badness: 0.0578<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:36 -->Triton</h1>
 Commas: 225/224, 1029/1000<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~7/5 = 568.865<br />
<br />
Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]<br />
Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||<br />
EDOs: 17d, 19, 78bd, 97bd<br />
Badness: 0.0592<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Triton-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2>
 Commas: 45/44, 56/55, 1029/1000<br />
<br />
POTE generator: ~7/5 = 569.144<br />
<br />
Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]<br />
EDOs: 19, 59bde, 78bde, 97bde<br />
Badness: 0.0457<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:40 -->Tritonic</h1>
 Comnma: 553584375/536870912<br />
<br />
POTE generator: ~45/32 = 580.219<br />
<br />
Map: [&lt;1 4 -3|, &lt;0 -5 11|]<br />
EDOs: 29, 31, 60, 91<br />
Badness: 0.3785<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Tritonic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->7-limit</h2>
 Commas: 225/224, 50421/50000<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br />
<br />
Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br />
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br />
EDOs: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, 213bcd<br />
<br />
<!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2>
 Commas: 121/120, 225/224, 441/440<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/5 = 580.267<br />
<br />
Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]<br />
EDOs: 29, 31, 60e<br />
Badness: 0.0237<br />
<br />
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Tritonic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2>
 Commas: 105/104, 121/120, 196/195, 275/273<br />
<br />
POTE generator: ~7/5 = 580.108<br />
<br />
Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]<br />
EDOs: 29, 31, 60e, 151cde<br />
Badness: 0.0230<br />
<br />
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:48 -->Tritoni</h2>
 Commas: 225/224, 385/384, 27783/27500<br />
<br />
POTE generator: ~7/5 = 580.389<br />
<br />
Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br />
EDOs: 31, 91, 122<br />
Badness: 0.0455<br />
<br />
<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Merman"></a><!-- ws:end:WikiTextHeadingRule:50 -->Merman</h1>
 Comma: 1121008359375/1099511627776<br />
<br />
POTE generator: ~45/32 = 585.634<br />
<br />
Map: [&lt;1 5 -5|, &lt;0 -7 15|]<br />
EDOs: 41, 84, 125, 209, 334c, 543bc<br />
Badness: 0.4538<br />
<br />
<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Merman-7-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->7-limit</h2>
 Commas: 225/224, 2500000/2470629<br />
<br />
POTE generator: ~7/5 = 585.585<br />
<br />
Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]<br />
Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||<br />
EDOs: 41, 84, 125<br />
Badness: 0.0551<br />
<br />
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Merman-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2>
 Commas: 225/224, 441/440, 1344/1331<br />
<br />
POTE generator: ~7/5 = 585.606<br />
<br />
Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]<br />
EDOs: 41, 84, 125e<br />
Badness: 0.0364<br />
<br />
<!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Merman-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2>
 Commas: 144/143, 225/224, 364/363, 441/440<br />
<br />
POTE generator: ~7/5 = 585.657<br />
<br />
Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]<br />
EDOs: 41, 84, 125e, 209ef, 293ef<br />
<br />
<!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:58 -->Septimin</h1>
 Comma: 35595703125/34359738368<br />
<br />
POTE generator: ~75/64 = 263.658<br />
<br />
Map: [&lt;1 4 1|, &lt;0 -11 6|]<br />
EDOs: 9, 32, 41, 91, 132, 223c, 355bc<br />
Badness: 0.6709<br />
<br />
<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Septimin-7-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->7-limit</h2>
 Commas: 225/224, 84035/82944<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br />
<br />
Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br />
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br />
EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2>
 Commas: 225/224, 385/384, 2401/2376<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br />
<br />
Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]<br />
EDOs: 9, 32, 41, 91, 223cdef<br />
<br />
<!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2>
 Commas: 105/104, 144/143, 196/195, 245/242<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br />
<br />
Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]<br />
EDOs: 9, 41, 91<br />
<br />
<!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:66 -->Slender</h1>
 Commas: 225/225, 589824/588245<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.413<br />
<br />
Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]<br />
Wedgie: &lt;&lt;13 -10 6 -46 -27 42||<br />
EDOs: 31, 94, 125<br />
Badness: 0.0569<br />
<br />
<!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->11-limit</h2>
 Commas: 225/224, 385/384, 1331/1323<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.387<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]<br />
EDOs: 31, 63, 94, 125<br />
Badness: 25.342<br />
<br />
<!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->13-limit</h2>
 Commas: 225/224, 275/273, 385/384, 1331/1323<br />
<br />
POTE generator: ~49/48 = 38.314<br />
<br />
Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]<br />
EDOs: 31, 63, 94<br />
Badness: 25.913<br />
<br />
<!-- ws:start:WikiTextHeadingRule:72:&lt;h1&gt; --><h1 id="toc36"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:72 -->Marvo</h1>
 Commas: 225/224, 78125000/78121827<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.694<br />
<br />
Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]<br />
Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||<br />
EDOs: 65, 72<br />
<br />
<!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->11-limit</h2>
 Commas: 225/224, 243/242, 4000/3993<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~27/20 = 516.699<br />
<br />
Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]<br />
EDOs: 65, 72, 281, 497<br />
<br />
<!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Marvo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->13-limit</h2>
 Commas: 243/242, 225/224, 351/350, 1625/1617<br />
<br />
POTE generator: ~27/20 = 516.730<br />
<br />
Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]<br />
EDOs: 72, 137, 209, 281f, 490bcf<br />
Badness: 0.0269<br />
<br />
<!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="Marvolo"></a><!-- ws:end:WikiTextHeadingRule:78 -->Marvolo</h1>
 Commas: 225/224, 156250000/155649627<br />
<br />
POTE generator: ~21/20 = 83.348<br />
<br />
Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]<br />
Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||<br />
EDOs: 29, 43, 72, 619bcd, 691bcd<br />
Badness: 0.0833<br />
<br />
<!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Marvolo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->11-limit</h2>
 Commas: 225/224, 441/440, 4000/3993<br />
<br />
POTE generator: ~21/20 = 83.340<br />
<br />
Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]<br />
EDOs: 29, 43, 72<br />
Badness: 0.0290<br />
<br />
<!-- ws:start:WikiTextHeadingRule:82:&lt;h2&gt; --><h2 id="toc41"><a name="Marvolo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->13-limit</h2>
 Commas: 169/168, 225/224, 364/363, 441/440<br />
<br />
POTE generator: ~21/20 = 83.330<br />
<br />
Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]<br />
EDOs: 29, 43, 72<br />
Badness: 0.0215<br />
<br />
<!-- ws:start:WikiTextHeadingRule:84:&lt;h1&gt; --><h1 id="toc42"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:84 -->Amavil</h1>
 Commas: 225/224, 17496/16807<br />
<br />
POTE generator: ~48/35 = 529.979<br />
<br />
Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]<br />
Wedgie: &lt;&lt;10 -3 14 -28 -6 41||<br />
EDOs: 9, 34d, 43, 77d<br />
Badness: 0.1096<br />
<br />
<!-- ws:start:WikiTextHeadingRule:86:&lt;h2&gt; --><h2 id="toc43"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:86 -->11-limit</h2>
 Commas: 99/98, 176/175, 864/847<br />
<br />
POTE generator: ~15/11 = 529.974<br />
<br />
Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]<br />
EDOs: 9, 34d, 43, 77de<br />
Badness: 0.0426<br />
<br />
<!-- ws:start:WikiTextHeadingRule:88:&lt;h2&gt; --><h2 id="toc44"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->13-limit</h2>
 Commas: 78/77, 99/98, 144/143, 176/175<br />
<br />
POTE generator: ~15/11 = 529.951<br />
<br />
Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]<br />
EDOs: 9, 34d, 43, 77de<br />
Badness: 0.0258<br />
<br />
<!-- ws:start:WikiTextHeadingRule:90:&lt;h1&gt; --><h1 id="toc45"><a name="Enneaportent"></a><!-- ws:end:WikiTextHeadingRule:90 -->Enneaportent</h1>
 Commas: 225/224, 40353607/40310784<br />
<br />
POTE generator: ~5/4 = 383.165<br />
<br />
Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]<br />
Wedgie: &lt;&lt;18 -9 18 -56 -22 67||<br />
EDOs: 9, 54, 63, 72, 495bcd<br />
Badness: 0.0937<br />
<br />
<!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Enneaportent-11-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->11-limit</h2>
 Commas: 225/224, 385/384, 12005/11979<br />
<br />
POTE generator: ~5/4 = 383.146<br />
<br />
Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]<br />
EDOs: 9, 54, 63, 72, 423cd, 495bcd<br />
Badness: 0.0304<br />
<br />
<!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Enneaportent-13-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->13-limit</h2>
 Commas: 169/168 225/224 364/363 1716/1715<br />
<br />
POTE generator: ~5/4 = 383.047<br />
<br />
Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]<br />
EDOs: 9, 54, 63, 72, 279cf<br />
Badness: 0.0223<br />
<br />
<!-- ws:start:WikiTextHeadingRule:96:&lt;h1&gt; --><h1 id="toc48"><a name="Submajor"></a><!-- ws:end:WikiTextHeadingRule:96 -->Submajor</h1>
 Comma: 69198046875/68719476736<br />
<br />
POTE generator: ~10125/8192 = 362.321<br />
<br />
Map: [&lt;1 4 -1|, &lt;0 -8 11|]<br />
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc<br />
Badness: 0.1302<br />
<br />
<!-- ws:start:WikiTextHeadingRule:98:&lt;h2&gt; --><h2 id="toc49"><a name="Submajor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->7-limit</h2>
 Commas: 225/224, 51200/50421<br />
<br />
POTE generator: ~49/40 = 362.255<br />
<br />
Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]<br />
Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||<br />
EDOs: 10, 33, 43, 53<br />
Badness: 0.0605<br />
<br />
<!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Submajor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->11-limit</h2>
 Commas: 225/224, 385/384, 6655/6561<br />
<br />
POTE generator: ~27/22 = 362.101<br />
<br />
Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]<br />
EDOs: 10, 53, 116, 169de, 285cde<br />
Badness: 0.0506<br />
<br />
<!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Submajor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->13-limit</h2>
 Commas: 169/168, 225/224, 275/273, 385/384<br />
<br />
POTE generator: ~16/13 = 362.105<br />
<br />
Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]<br />
EDOs: 10, 53, 116, 169de, 285cdef<br />
Badness: 0.0277<br />
<br />
<!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Submajor-Interpental"></a><!-- ws:end:WikiTextHeadingRule:104 -->Interpental</h2>
 Commas: 99/98, 176/175, 51200/50421<br />
<br />
POTE generator: ~49/40 = 362.418<br />
<br />
Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]<br />
EDOs: 43, 53, 96, 149d<br />
Badness: 0.0518<br />
<br />
<!-- ws:start:WikiTextHeadingRule:106:&lt;h3&gt; --><h3 id="toc53"><a name="Submajor-Interpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:106 -->13-limit</h3>
 Commas: 99/98, 169/168, 176/175, 640/637<br />
<br />
POTE generator: ~16/13 = 362.402<br />
<br />
Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]<br />
EDOs: 43, 53, 96, 149d<br />
Badness: 0.0297<br />
<br />
<!-- ws:start:WikiTextHeadingRule:108:&lt;h1&gt; --><h1 id="toc54"><a name="Alphorn"></a><!-- ws:end:WikiTextHeadingRule:108 -->Alphorn</h1>
 Commas: 225/224, 5764801/5668704<br />
<br />
POTE generator: ~48/35 = 556.221<br />
<br />
Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]<br />
Wedgie: &lt;&lt;16 -5 22 -45 -10 65||<br />
EDOs: 28d, 41, 151cd, 192cd, 233cd<br />
Badness: 0.1293<br />
<br />
<!-- ws:start:WikiTextHeadingRule:110:&lt;h2&gt; --><h2 id="toc55"><a name="Alphorn-11-limit"></a><!-- ws:end:WikiTextHeadingRule:110 -->11-limit</h2>
 Commas: 225/224, 385/384, 12250/11979<br />
<br />
POTE generator: ~11/8 = 556.144<br />
<br />
Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]<br />
EDOs: 41, 315cde<br />
Badness: 0.0735</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-20 19:21:43 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-17 21:38:37 UTC</tt>.<br>
-: The original revision id was <tt>337659208</tt>.<br>
+: The original revision id was <tt>353613468</tt>.<br>
 : The revision comment was: <tt></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 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.
@@ Line 15: / Line 14: @@
 [[Comma]]s: 49/48, 225/224
-[[POTE tuning|POTE temperament]]: 125.608
+[[POTE tuning|POTE temperament]]: ~15/14 = 125.608
 [[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
@@ Line 24: / Line 23: @@
 Commas: 45/44, 49/48, 56/55
-[[POTE tuning|POTE generator]]: 126.474
+[[POTE tuning|POTE generator]]: ~15/14 = 126.474
 Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
@@ Line 33: / Line 32: @@
 Commas: 45/44, 49/48, 56/55, 78/77
-[[POTE tuning|POTE generator]]: 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|]
@@ Line 74: / Line 73: @@
 Badness: 0.0202
 =Negroni=
 Commas: 49/48, 55/54, 225/224
@@ Line 92: / Line 91: @@
 Badness: 0.3864
 ==7-limit==
 Commas: 225/224, 118098/117649
@@ Line 184: / Line 183: @@
 Badness: 0.0592
 ==11-limit==
 Commas: 45/44, 56/55, 1029/1000
@@ Line 202: / Line 201: @@
 Badness: 0.3785
 ==7-limit==
 Commas: 225/224, 50421/50000
@@ Line 247: / Line 246: @@
 Badness: 0.4538
 ==7-limit==
 Commas: 225/224, 2500000/2470629
@@ Line 257: / Line 256: @@
 Badness: 0.0551
 ==11-limit==
 Commas: 225/224, 441/440, 1344/1331
@@ Line 266: / Line 265: @@
 Badness: 0.0364
 ==13-limit==
 Commas: 144/143, 225/224, 364/363, 441/440
@@ Line 283: / Line 282: @@
 Badness: 0.6709
 ==7-limit==
 Commas: 225/224, 84035/82944
@@ Line 437: / Line 436: @@
 Badness: 0.0304
 ==13-limit==
 Commas: 169/168 225/224 364/363 1716/1715
@@ Line 446: / Line 445: @@
 Badness: 0.0223
 =Submajor=
 Comma: 69198046875/68719476736
@@ Line 455: / Line 454: @@
 Badness: 0.1302
 ==7-limit==
-Commas:  225/224, 51200/50421
+Commas: 225/224, 51200/50421
 POTE generator: ~49/40 = 362.255
@@ Line 465: / Line 464: @@
 Badness: 0.0605
 ==11-limit==
 Commas: 225/224, 385/384, 6655/6561
@@ Line 474: / Line 473: @@
 Badness: 0.0506
 ==13-limit==
 Commas: 169/168, 225/224, 275/273, 385/384
@@ Line 483: / Line 482: @@
 Badness: 0.0277
 ==Interpental==
 Commas: 99/98, 176/175, 51200/50421
@@ Line 492: / Line 491: @@
 Badness: 0.0518
 ===13-limit===
 Commas: 99/98, 169/168, 176/175, 640/637
@@ Line 501: / Line 500: @@
 Badness: 0.0297
 =Alphorn=
 Commas: 225/224, 5764801/5668704
@@ Line 511: / Line 510: @@
 Badness: 0.1293
 ==11-limit==
 Commas: 225/224, 385/384, 12250/11979
@@ Line 518: / Line 517: @@
 Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
 EDOs: 41, 315cde
-Badness: 0.0735
+Badness: 0.0735</pre></div>
-</pre></div>
 <h4>Original HTML 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;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:112:&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:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;/div&gt;
@@ Line 578: / Line 576: @@
 &lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&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:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;/div&gt;
-&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:169 --&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%20comma"&gt;marvel comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;. 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.&lt;br /&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%20comma"&gt;marvel comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;. 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.&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 5/4-9/7 versions of the augmented triad. 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;
@@ Line 586: / Line 583: @@
   &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;: 125.608&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;
@@ Line 595: / Line 592: @@
   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;: 126.474&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;
@@ Line 604: / Line 601: @@
   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;: 126.431&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;
@@ Line 646: / Line 643: @@
 &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;
+ Commas: 49/48, 55/54, 225/224&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~15/14 = 124.539&lt;br /&gt;
@@ Line 664: / Line 661: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Wizard-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
-Commas: 225/224, 118098/117649&lt;br /&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;
@@ Line 756: / Line 753: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Triton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
-Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
+ Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 569.144&lt;br /&gt;
@@ Line 774: / Line 771: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Tritonic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;7-limit&lt;/h2&gt;
-Commas: 225/224, 50421/50000&lt;br /&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;
@@ Line 819: / Line 816: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Merman-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;7-limit&lt;/h2&gt;
-Commas: 225/224, 2500000/2470629&lt;br /&gt;
+ Commas: 225/224, 2500000/2470629&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 585.585&lt;br /&gt;
@@ Line 829: / Line 826: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Merman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
+ Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~7/5 = 585.606&lt;br /&gt;
@@ Line 838: / Line 835: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Merman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
-Commas: 144/143, 225/224, 364/363, 441/440&lt;br /&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;
@@ Line 855: / Line 852: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Septimin-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
-Commas: 225/224, 84035/82944&lt;br /&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;
@@ Line 1,009: / Line 1,006: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Enneaportent-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;13-limit&lt;/h2&gt;
-Commas: 169/168 225/224 364/363 1716/1715&lt;br /&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;
@@ Line 1,018: / Line 1,015: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Submajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Submajor&lt;/h1&gt;
-Comma: 69198046875/68719476736&lt;br /&gt;
+ Comma: 69198046875/68719476736&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~10125/8192 = 362.321&lt;br /&gt;
@@ Line 1,027: / Line 1,024: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Submajor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;7-limit&lt;/h2&gt;
-Commas:  225/224, 51200/50421 &lt;br /&gt;
+ Commas: 225/224, 51200/50421&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~49/40 = 362.255&lt;br /&gt;
@@ Line 1,037: / Line 1,034: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Submajor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
+ Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~27/22 = 362.101&lt;br /&gt;
@@ Line 1,046: / Line 1,043: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Submajor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;13-limit&lt;/h2&gt;
-Commas: 169/168, 225/224, 275/273, 385/384&lt;br /&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;
@@ Line 1,055: / Line 1,052: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Submajor-Interpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;Interpental&lt;/h2&gt;
-Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
+ Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~49/40 = 362.418&lt;br /&gt;
@@ Line 1,064: / Line 1,061: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc53"&gt;&lt;a name="Submajor-Interpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;13-limit&lt;/h3&gt;
-Commas: 99/98, 169/168, 176/175, 640/637&lt;br /&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;
@@ Line 1,073: / Line 1,070: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc54"&gt;&lt;a name="Alphorn"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;Alphorn&lt;/h1&gt;
-Commas: 225/224, 5764801/5668704&lt;br /&gt;
+ Commas: 225/224, 5764801/5668704&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~48/35 = 556.221&lt;br /&gt;
@@ Line 1,083: / Line 1,080: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Alphorn-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;11-limit&lt;/h2&gt;
-Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
+ Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~11/8 = 556.144&lt;br /&gt;

Marvel temperaments: Difference between revisions

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