Marvel temperaments
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[[toc]] This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[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]], sharp [where?], [[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. 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= [[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 ==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 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 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 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
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<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:114:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Negri">Negri</a></div> <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Negri-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Negri-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 1em;"><a href="#Negril">Negril</a></div> <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 2em;"><a href="#Negril-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 1em;"><a href="#Negric">Negric</a></div> <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Negric-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Negroni">Negroni</a></div> <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Negroni-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Wizard">Wizard</a></div> <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Wizard-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 2em;"><a href="#Wizard-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Wizard-Lizard">Lizard</a></div> <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-17-limit">17-limit</a></div> <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 3em;"><a href="#Wizard-Lizard-19-limit">19-limit</a></div> <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 2em;"><a href="#Wizard-Gizzard">Gizzard</a></div> <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-17-limit">17-limit</a></div> <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 3em;"><a href="#Wizard-Gizzard-19-limit">19-limit</a></div> <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 2em;"><a href="#Wizard-Mage">Mage</a></div> <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 1em;"><a href="#Triton">Triton</a></div> <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Triton-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Tritonic">Tritonic</a></div> <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Tritonic-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Tritonic-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 2em;"><a href="#Tritonic-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Tritonic-Tritoni">Tritoni</a></div> <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 1em;"><a href="#Merman">Merman</a></div> <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 2em;"><a href="#Merman-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Merman-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 2em;"><a href="#Merman-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 1em;"><a href="#Septimin">Septimin</a></div> <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Septimin-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 2em;"><a href="#Septimin-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Septimin-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 1em;"><a href="#Slender">Slender</a></div> <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 2em;"><a href="#Slender-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Slender-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 1em;"><a href="#Marvo">Marvo</a></div> <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 2em;"><a href="#Marvo-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Marvo-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 1em;"><a href="#Marvolo">Marvolo</a></div> <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 2em;"><a href="#Marvolo-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Marvolo-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 1em;"><a href="#Amavil">Amavil</a></div> <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Amavil-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Amavil-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 1em;"><a href="#Enneaportent">Enneaportent</a></div> <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Enneaportent-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><div style="margin-left: 2em;"><a href="#Enneaportent-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --><div style="margin-left: 1em;"><a href="#Submajor">Submajor</a></div> <!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --><div style="margin-left: 2em;"><a href="#Submajor-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><div style="margin-left: 2em;"><a href="#Submajor-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#Submajor-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 2em;"><a href="#Submajor-Interpental">Interpental</a></div> <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 3em;"><a href="#Submajor-Interpental-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --><div style="margin-left: 1em;"><a href="#Alphorn">Alphorn</a></div> <!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --><div style="margin-left: 2em;"><a href="#Alphorn-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --></div> <!-- ws:end:WikiTextTocRule:172 -->This page discusses some of the temperaments tempering out |-5 2 2 -1> =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/Marvel%20family">marvel</a> comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are <a class="wiki_link" href="/Meantone%20family">meantone</a>, <a class="wiki_link" href="/Miracle">miracle</a>, <a class="wiki_link" href="/Magic%20family">magic</a>, <a class="wiki_link" href="/Pajara">pajara</a>, <a class="wiki_link" href="/Orwell">orwell</a>, <a class="wiki_link" href="/Kleismic%20family">catakleismic</a>, <a class="wiki_link" href="/Garibaldi%20temperament">garibaldi</a>, <a class="wiki_link" href="/Augmented%20family">august</a>, <a class="wiki_link" href="/Pythagorean%20family">compton</a>, sharp [where?], <a class="wiki_link" href="/Escapade%20family">escapade</a> and <a class="wiki_link" href="/Pelogic%20family">mavila</a>.<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 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.<br /> <br /> 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.<br /> <br /> 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.)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><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>: [<1 2 2 3|, <0 -4 3 -2|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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:<h2> --><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: [<1 2 2 3 4|, <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:<h2> --><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: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]<br /> EDOs: 9, 10, 19<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><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: [<1 2 2 3 2|, <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:<h2> --><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: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]<br /> EDOs: 9, 10, 19, 29, 48, 77<br /> Badness: 0.0244<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><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: [<1 2 2 3 3|, <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:<h2> --><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: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]<br /> EDOs: 9, 19, 85<br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><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: [<1 2 2 3 5|, <0 -4 3 -2 -15|]<br /> EDOs: 10, 19e, 29, 77cde<br /> Badness: 0.0353<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Negroni-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h2> Commas: 49/48, 55/54, 65/64, 91/90<br /> <br /> POTE generator: ~15/14 = 124.545<br /> <br /> Map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]<br /> EDOs: 10, 19e, 29, 77cdef<br /> Badness: 0.0216<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:18 -->Wizard</h1> Comma: 2197265625/2147483648<br /> <br /> POTE generator: ~5/4 = 383.212<br /> <br /> Map: [<2 1 5|, <0 6 -1|]<br /> EDOs: 22, 50, 72, 166, 238c, 310c, 548bc<br /> Badness: 0.3864<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Wizard-7-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->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: [<2 1 5 2|, <0 6 -1 10|]<br /> Wedgie: <<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:22:<h2> --><h2 id="toc11"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->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: [<2 1 5 2 8|, <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:24:<h2> --><h2 id="toc12"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:24 -->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: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]<br /> EDOs: 22, 50, 72, 122, 194df<br /> Badness: 0.0218<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h3> --><h3 id="toc13"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->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: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]<br /> EDOs: 22, 50, 72, 122g, 194dfg<br /> Badness: 0.0145<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h3> --><h3 id="toc14"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->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: [<2 1 5 2 8 11 6 2|, <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:30:<h2> --><h2 id="toc15"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:30 -->Gizzard</h2> Commas: 225/224, 385/384, 325/324, 1573/1568<br /> <br /> POTE generator: ~5/4 = 383.170<br /> <br /> Map: [<2 1 5 2 8 -2|, <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:32:<h3> --><h3 id="toc16"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->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: [<2 1 5 2 8 -2 6|, <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:34:<h3> --><h3 id="toc17"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]<br /> EDOs: 22f, 72, 94, 166g<br /> Badness: 0.0148<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Wizard-Mage"></a><!-- ws:end:WikiTextHeadingRule:36 -->Mage</h2> Commas: 99/98, 176/175, 1331/1296<br /> <br /> POTE generator: ~55/48 = 216.876<br /> <br /> Map: [<2 1 5 2 4|, <0 6 -1 10 8|]<br /> EDOs: 22, 72e, 94e<br /> Badness: 0.0578<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:38 -->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: [<1 0 6 7|, <0 3 -7 -8|]<br /> Wedgie: <<3 -7 -8 -18 -21 1||<br /> EDOs: 17d, 19, 78bd, 97bd<br /> Badness: 0.0592<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Triton-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> Commas: 45/44, 56/55, 1029/1000<br /> <br /> POTE generator: ~7/5 = 569.144<br /> <br /> Map: [<1 0 6 7 4|, <0 3 -7 -8 -1|]<br /> EDOs: 19, 59bde, 78bde, 97bde<br /> Badness: 0.0457<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:42 -->Tritonic</h1> Comnma: 553584375/536870912<br /> <br /> POTE generator: ~45/32 = 580.219<br /> <br /> Map: [<1 4 -3|, <0 -5 11|]<br /> EDOs: 29, 31, 60, 91<br /> Badness: 0.3785<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Tritonic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->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: [<1 4 -3 -3|, <0 -5 11 12|]<br /> Wedgie: <<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:46:<h2> --><h2 id="toc23"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->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: [<1 4 -3 -3 2|, <0 -5 11 12 3|]<br /> EDOs: 29, 31, 60e<br /> Badness: 0.0237<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><h2 id="toc24"><a name="Tritonic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->13-limit</h2> Commas: 105/104, 121/120, 196/195, 275/273<br /> <br /> POTE generator: ~7/5 = 580.108<br /> <br /> Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|]<br /> EDOs: 29, 31, 60e, 151cde<br /> Badness: 0.0230<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:50 -->Tritoni</h2> Commas: 225/224, 385/384, 27783/27500<br /> <br /> POTE generator: ~7/5 = 580.389<br /> <br /> Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]<br /> EDOs: 31, 91, 122<br /> Badness: 0.0455<br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h1> --><h1 id="toc26"><a name="Merman"></a><!-- ws:end:WikiTextHeadingRule:52 -->Merman</h1> Comma: 1121008359375/1099511627776<br /> <br /> POTE generator: ~45/32 = 585.634<br /> <br /> Map: [<1 5 -5|, <0 -7 15|]<br /> EDOs: 41, 84, 125, 209, 334c, 543bc<br /> Badness: 0.4538<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h2> --><h2 id="toc27"><a name="Merman-7-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->7-limit</h2> Commas: 225/224, 2500000/2470629<br /> <br /> POTE generator: ~7/5 = 585.585<br /> <br /> Map: [<1 5 -5 -5|, <0 -7 15 16|]<br /> Wedgie: <<7 -15 -16 -40 -45 5||<br /> EDOs: 41, 84, 125<br /> Badness: 0.0551<br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc28"><a name="Merman-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> Commas: 225/224, 441/440, 1344/1331<br /> <br /> POTE generator: ~7/5 = 585.606<br /> <br /> Map: [<1 5 -5 -5 2|, <0 -7 15 16 3]]<br /> EDOs: 41, 84, 125e<br /> Badness: 0.0364<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="Merman-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> Commas: 144/143, 225/224, 364/363, 441/440<br /> <br /> POTE generator: ~7/5 = 585.657<br /> <br /> Map: [<1 5 -5 -5 2 12|, <0 -7 15 16 3 -17|]<br /> EDOs: 41, 84, 125e, 209ef, 293ef<br /> Badness: 0.0275<br /> <br /> <!-- ws:start:WikiTextHeadingRule:60:<h1> --><h1 id="toc30"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:60 -->Septimin</h1> Comma: 35595703125/34359738368<br /> <br /> POTE generator: ~75/64 = 263.658<br /> <br /> Map: [<1 4 1|, <0 -11 6|]<br /> EDOs: 9, 32, 41, 91, 132, 223c, 355bc<br /> Badness: 0.6709<br /> <br /> <!-- ws:start:WikiTextHeadingRule:62:<h2> --><h2 id="toc31"><a name="Septimin-7-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->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: [<1 4 1 5|, <0 -11 6 -10|]<br /> Wedgie: <<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:64:<h2> --><h2 id="toc32"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->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: [<1 4 1 5 5|, <0 -11 6 -10 -7|]<br /> EDOs: 9, 32, 41, 91, 223cdef<br /> <br /> <!-- ws:start:WikiTextHeadingRule:66:<h2> --><h2 id="toc33"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->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: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]<br /> EDOs: 9, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:68:<h1> --><h1 id="toc34"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:68 -->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: [<1 2 2 3|, <0 -13 10 -6|]<br /> Wedgie: <<13 -10 6 -46 -27 42||<br /> EDOs: 31, 94, 125<br /> Badness: 0.0569<br /> <br /> <!-- ws:start:WikiTextHeadingRule:70:<h2> --><h2 id="toc35"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->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: [<1 2 2 3 4|, <0 -13 10 -6 -17|]<br /> EDOs: 31, 63, 94, 125<br /> Badness: 25.342<br /> <br /> <!-- ws:start:WikiTextHeadingRule:72:<h2> --><h2 id="toc36"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->13-limit</h2> Commas: 225/224, 275/273, 385/384, 1331/1323<br /> <br /> POTE generator: ~49/48 = 38.314<br /> <br /> Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|]<br /> EDOs: 31, 63, 94<br /> Badness: 25.913<br /> <br /> <!-- ws:start:WikiTextHeadingRule:74:<h1> --><h1 id="toc37"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:74 -->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: [<1 5 12 29|, <0 -6 -17 -46|]<br /> Wedgie: <<6, 17, 46, 13, 56 59||<br /> EDOs: 65, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:76:<h2> --><h2 id="toc38"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:76 -->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: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]<br /> EDOs: 65, 72, 281, 497<br /> <br /> <!-- ws:start:WikiTextHeadingRule:78:<h2> --><h2 id="toc39"><a name="Marvo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->13-limit</h2> Commas: 243/242, 225/224, 351/350, 1625/1617<br /> <br /> POTE generator: ~27/20 = 516.730<br /> <br /> Map: [<1 5 12 29 12 39|, <0 -6 -17 -46 -15 -62|]<br /> EDOs: 72, 137, 209, 281f, 490bcf<br /> Badness: 0.0269<br /> <br /> <!-- ws:start:WikiTextHeadingRule:80:<h1> --><h1 id="toc40"><a name="Marvolo"></a><!-- ws:end:WikiTextHeadingRule:80 -->Marvolo</h1> Commas: 225/224, 156250000/155649627<br /> <br /> POTE generator: ~21/20 = 83.348<br /> <br /> Map: [<1 2 1 1|, <0 -6 19 26|]<br /> Wedgie: <<6 -19 -26 -44 -58 -7||<br /> EDOs: 29, 43, 72, 619bcd, 691bcd<br /> Badness: 0.0833<br /> <br /> <!-- ws:start:WikiTextHeadingRule:82:<h2> --><h2 id="toc41"><a name="Marvolo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:82 -->11-limit</h2> Commas: 225/224, 441/440, 4000/3993<br /> <br /> POTE generator: ~21/20 = 83.340<br /> <br /> Map: [<1 2 1 1 2|, <0 -6 19 26 21|]<br /> EDOs: 29, 43, 72<br /> Badness: 0.0290<br /> <br /> <!-- ws:start:WikiTextHeadingRule:84:<h2> --><h2 id="toc42"><a name="Marvolo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->13-limit</h2> Commas: 169/168, 225/224, 364/363, 441/440<br /> <br /> POTE generator: ~21/20 = 83.330<br /> <br /> Map: [<1 2 1 1 2 3|, <0 -6 19 26 21 10|]<br /> EDOs: 29, 43, 72<br /> Badness: 0.0215<br /> <br /> <!-- ws:start:WikiTextHeadingRule:86:<h1> --><h1 id="toc43"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:86 -->Amavil</h1> Commas: 225/224, 17496/16807<br /> <br /> POTE generator: ~48/35 = 529.979<br /> <br /> Map: [<1 6 1 9|, <0 -10 3 -14|]<br /> Wedgie: <<10 -3 14 -28 -6 41||<br /> EDOs: 9, 34d, 43, 77d<br /> Badness: 0.1096<br /> <br /> <!-- ws:start:WikiTextHeadingRule:88:<h2> --><h2 id="toc44"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:88 -->11-limit</h2> Commas: 99/98, 176/175, 864/847<br /> <br /> POTE generator: ~15/11 = 529.974<br /> <br /> Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0426<br /> <br /> <!-- ws:start:WikiTextHeadingRule:90:<h2> --><h2 id="toc45"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->13-limit</h2> Commas: 78/77, 99/98, 144/143, 176/175<br /> <br /> POTE generator: ~15/11 = 529.951<br /> <br /> Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0258<br /> <br /> <!-- ws:start:WikiTextHeadingRule:92:<h1> --><h1 id="toc46"><a name="Enneaportent"></a><!-- ws:end:WikiTextHeadingRule:92 -->Enneaportent</h1> Commas: 225/224, 40353607/40310784<br /> <br /> POTE generator: ~5/4 = 383.165<br /> <br /> Map: [<9 0 28 11|, <0 2 -1 2|]<br /> Wedgie: <<18 -9 18 -56 -22 67||<br /> EDOs: 9, 54, 63, 72, 495bcd<br /> Badness: 0.0937<br /> <br /> <!-- ws:start:WikiTextHeadingRule:94:<h2> --><h2 id="toc47"><a name="Enneaportent-11-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->11-limit</h2> Commas: 225/224, 385/384, 12005/11979<br /> <br /> POTE generator: ~5/4 = 383.146<br /> <br /> Map: [<9 0 28 11 24|, <0 2 -1 2 1|]<br /> EDOs: 9, 54, 63, 72, 423cd, 495bcd<br /> Badness: 0.0304<br /> <br /> <!-- ws:start:WikiTextHeadingRule:96:<h2> --><h2 id="toc48"><a name="Enneaportent-13-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->13-limit</h2> Commas: 169/168 225/224 364/363 1716/1715<br /> <br /> POTE generator: ~5/4 = 383.047<br /> <br /> Map: [<9 0 28 11 24 19|, <0 2 -1 2 1 2|]<br /> EDOs: 9, 54, 63, 72, 279cf<br /> Badness: 0.0223<br /> <br /> <!-- ws:start:WikiTextHeadingRule:98:<h1> --><h1 id="toc49"><a name="Submajor"></a><!-- ws:end:WikiTextHeadingRule:98 -->Submajor</h1> Comma: 69198046875/68719476736<br /> <br /> POTE generator: ~10125/8192 = 362.321<br /> <br /> Map: [<1 4 -1|, <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:100:<h2> --><h2 id="toc50"><a name="Submajor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->7-limit</h2> Commas: 225/224, 51200/50421<br /> <br /> POTE generator: ~49/40 = 362.255<br /> <br /> Map: [<1 4 -1 1|, <0 -8 11 6|]<br /> Wedgie: <<8 -11 -6 -36 -32 17||<br /> EDOs: 10, 33, 43, 53<br /> Badness: 0.0605<br /> <br /> <!-- ws:start:WikiTextHeadingRule:102:<h2> --><h2 id="toc51"><a name="Submajor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->11-limit</h2> Commas: 225/224, 385/384, 6655/6561<br /> <br /> POTE generator: ~27/22 = 362.101<br /> <br /> Map: [<1 4 -1 1 11|, <0 -8 11 6 -25|]<br /> EDOs: 10, 53, 116, 169de, 285cde<br /> Badness: 0.0506<br /> <br /> <!-- ws:start:WikiTextHeadingRule:104:<h2> --><h2 id="toc52"><a name="Submajor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:104 -->13-limit</h2> Commas: 169/168, 225/224, 275/273, 385/384<br /> <br /> POTE generator: ~16/13 = 362.105<br /> <br /> Map: [<1 4 -1 1 11 4|, <0 -8 11 6 -25 -1|]<br /> EDOs: 10, 53, 116, 169de, 285cdef<br /> Badness: 0.0277<br /> <br /> <!-- ws:start:WikiTextHeadingRule:106:<h2> --><h2 id="toc53"><a name="Submajor-Interpental"></a><!-- ws:end:WikiTextHeadingRule:106 -->Interpental</h2> Commas: 99/98, 176/175, 51200/50421<br /> <br /> POTE generator: ~49/40 = 362.418<br /> <br /> Map: [<1 4 -1 1 -5|, <0 -8 11 6 28|]<br /> EDOs: 43, 53, 96, 149d<br /> Badness: 0.0518<br /> <br /> <!-- ws:start:WikiTextHeadingRule:108:<h3> --><h3 id="toc54"><a name="Submajor-Interpental-13-limit"></a><!-- ws:end:WikiTextHeadingRule:108 -->13-limit</h3> Commas: 99/98, 169/168, 176/175, 640/637<br /> <br /> POTE generator: ~16/13 = 362.402<br /> <br /> Map: [<1 4 -1 1 -5 4|, <0 -8 11 6 28 -1|]<br /> EDOs: 43, 53, 96, 149d<br /> Badness: 0.0297<br /> <br /> <!-- ws:start:WikiTextHeadingRule:110:<h1> --><h1 id="toc55"><a name="Alphorn"></a><!-- ws:end:WikiTextHeadingRule:110 -->Alphorn</h1> Commas: 225/224, 5764801/5668704<br /> <br /> POTE generator: ~48/35 = 556.221<br /> <br /> Map: [<1 9 0 13|, <0 -16 5 -22|]<br /> Wedgie: <<16 -5 22 -45 -10 65||<br /> EDOs: 28d, 41, 151cd, 192cd, 233cd<br /> Badness: 0.1293<br /> <br /> <!-- ws:start:WikiTextHeadingRule:112:<h2> --><h2 id="toc56"><a name="Alphorn-11-limit"></a><!-- ws:end:WikiTextHeadingRule:112 -->11-limit</h2> Commas: 225/224, 385/384, 12250/11979<br /> <br /> POTE generator: ~11/8 = 556.144<br /> <br /> Map: [<1 9 0 13 3|, <0 -16 5 -22 1|]<br /> EDOs: 41, 315cde<br /> Badness: 0.0735</body></html>