Gamelismic clan
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[[toc]] The 2.3.7-[[Just intonation subgroups|subgroup]] comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, for the rank three [[Gamelismic family#Gamelan|gamelan temperament]] itself, and for the rank two 2.3.7 temperament [[slendric]], this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for gamelismic itself, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred. 7-limit minimax [|1 0 0 0>, |5/2 3/4 0 -3/4>, |5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>] Eigenmonzos: 2, 7/6, 6/5 9-limit minimax [|1 0 0 0>, |10/7 6/7 0 -3/7>, |10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>] Eigenmonzos: 2, 6/5, 9/7 Lattice basis: 8/7 0.5192 5/4 2.3219 Angle(8/7, 5/4) = 90 degrees Map to lattice: [<0 3 0 -1|, <0 0 1 0|] Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|] Generators: 2, 5, 7 No-fives [[POTE tuning|POTE generator]]: 233.688 EDOs: 5, 36, 77, 190 ==Full seven limit children== To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period. =Miracle= [[Comma|Commas]]: 1029/1024, 225/224 [[Minimax tuning]]: 7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>, |25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 6/5 9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>, |50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 [[POTE tuning|POTE generator]]: 116.675 Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15x^6-8x^4-12 Map: [<1 1 3 3|, <0 6 -7 -2|] Wedgie: <<6 -7 -2 -25 -20 15|| EDOs: 10, 21, 31, 41, 72, [[175edo|175]] Badness: 0.0167 ==11-limit== [[Comma|Commas]]: 1029/1024, 225/224, 243/242 [[Minimax tuning]]: [|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>, |50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>, |53/19 30/19 -15/19 0 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 10/9 [[POTE tuning|POTE generator]]: 116.633 Algebraic generator: Secor59 Map: [<1 1 3 3 2|, <0 6 -7 -2 15|] [[edo|EDOs]]: 10, 31, 41, [[72edo|72]], [[391edo|391bcde]] Badness: 0.0107 [[Chords of miracle]] ==Revelation== Commas: 99/98, 176/175, 1029/1024 POTE generator: ~15/14 = 116.277 Map: [<1 1 3 3 5|, <0 6 -7 -2 -16|] EDOs: 21, 31 Badness: 0.0329 ==Miraculous== Commas: 105/104, 144/143, 196/195, 275/273 POTE generator: ~15/14 = 116.747 Map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|] EDOs: 10, 31, 41, 72, 185 Badness: 0.0187 ==Benediction== Commas: 225/224, 243/242, 351/350, 441/440 POTE generator: ~15/14 = 116.574 Map: [<1 1 3 3 2 7|, <0 6 -7 2 15 -34|] EDOs: 10, 31, 72, 103, [[175edo|175f]] Badness: 0.0157 ==Manna== Commas: 225/224, 243/242, 325/324, 385/384 POTE generator: ~15/14 = 116.739 Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|] EDOs: 10, 31, 41, 72, 185, 257cf Badness: 0.0170 ==Music== By [[Gene Ward Smith]] [[http://www.archive.org/details/RachmaninoffPlaysBlackjack|Rachmaninoff Plays Blackjack]] [[http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3|play]] By [[Joseph Pehrson]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3|Black and Jill]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3|Blacklight]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3|Blackjack]] =Rodan= [[Comma|Commas]]: 1029/1024, 245/243 7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>, |25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 [[POTE tuning|POTE generator]]: 234.417 Algebraic generator: [[Algebraic number|larger root]] of 20x^2-36x+15, or (9+√6)/10. Map: [<1 1 -1 3|, <0 3 17 -1|] EDOs: 41, 87, 128 Badness: 0.0371 ==11-limit== [[Comma|Commas]]: 441/440, 245/243, 385/384 [[Minimax tuning]]: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>, |49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>, |62/19 -26/19 0 0 13/19>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/9 [[POTE tuning|POTE generator]]: 234.459 Algebraic generator: [[Algebraic number|positive root]] of x^2+16x-31, or √95-8. Map: [<1 1 -1 3 6|, <0 3 17 -1 -13|] EDOs: 41, 87, 389d Badness: 0.0231 [[Chords of rodan]] ==13-limit== Commas: 196/195, 245/243, 352/351, 364/363 13 and 15 limit minimax [|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>, |37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>, |45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>] Eigenmonzos: 2, 13/9 [[POTE tuning|POTE generator]]: 234.482 Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly. Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|] Generators: 2, 8/7 [[edo|Edos]]: 41, 46, [[87edo|87]] Badness: 0.0184 ===Music=== By [[Gene Ward Smith]] [[http://www.archive.org/details/Pianodactyl|Pianodactyl]] [[http://www.archive.org/download/Pianodactyl/pianodactyl.mp3|play]] ==Superduper== Commas: 91/90, 245/243, 385/384, 441/440 [[POTE tuning|POTE generator]]: 234.639 Map: [<1 1 -1 3 6 -1|, <0 3 17 -1 -13 24| EDOs: 46 Badness: 0.034 ==Varan== Commas: 100/99, 245/243, 2835/2816 POTE generator: ~8/7 = 234.145 Map: [<1 1 -1 3 -2|, <0 3 17 -1 28| EDOs: 41, 46e Badness: 0.0449 =Valentine= ==7-limit== [[Comma|Commas]]: 1029/1024, 126/125 [[Minimax tuning]]: 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>] Eigenmonzos: 2, 7/6 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>] Eigenmonzos: 2, 9/7 [[POTE tuning|POTE generator]]: 77.864 Algebraic generator: [[Algebraic number|smaller root]] of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents. Map: [<1 1 2 3|, <0 9 5 -3|] Wedgie: <<9 5 -3 -13 -30 -21|| EDOs: 15, 31, 46, 77, 185, 262cd Badness: 0.0311 ==11-limit== [[Comma|Commas]]: 121/120, 126/125, 176/175 [[Minimax tuning]]: [|1 0 0 0 0>, |1 0 0 -9/10 9/10>, |2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>] Eigenmonzos: 2, 11/7 [[POTE tuning|POTE generator]]: 77.881 Algebraic generator: [[Algebraic number|positive root]] of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5. Map: [<1 1 2 3 3|, <0 9 5 -3 7|] Generators: 2, 21/20 [[edo|Edos]]: 15, 31, 46, 77, 262cde, 339cde Badness: 0.0167 [[Chords of valentine]] =Unidec= ==7-limit== [[Comma|Commas]]: 1029/1024, 4375/4374 [[Minimax tuning]]: 7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>, |71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 [[POTE tuning|POTE generator]]: ~10/9 = 183.161 Map: [<2 5 8 5|, <0 -6 -11 2|] Wedgie: <<12 22 -4 7 -40 -71|| EDOs: 26, 46, 72, 118, 190 ==11-limit== [[Comma|Commas]]: 385/384, 441/440, 4375/4374 [[Minimax tuning]]: [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>, |20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 [[POTE tuning|POTE generator]]: 183.165 Map: [<2 5 8 5 6|, <0 -6 -11 2 3|] EDOs: 26, 46, 72, 118, 190 [[Chords of unidec]] ==Ekadash== Commas: 385/384, 441/440, 625/624, 729/728 [[POTE tuning|POTE generator]]: ~10/9 = 183.187 Map: [<2 5 8 5 6 19|, <0 -6 -11 2 3 -38|] EDOs: 20, 26, 46, 72, 118, 190, 262df, 452cdef Bad: 0.0204 ==Hendec== Commas: 169/168, 325/324, 364/363, 1716/1715 [[POTE tuning|POTE generator]]: ~10/9 = 183.187 Map: [<2 5 8 5 6 8|, <0 -6 -11 2 3 -2|] EDOs: 26, 46, 72 Bad: 0.0177 =Hemithirds= ==7-limit== [[Comma|Commas]]: 1029/1024, 3136/3125 [[Minimax tuning]]: 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/6 ==11-limit== [[Comma|Commas]]: 385/384, 441/440, 3136/3125 [[Minimax tuning]]: [|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>, |79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>] [[Eigenmonzo|Eigenmonzos]]: 2, 11/7 Map: [<1 4 2 2 7|, <0 -15 2 5 -22|] [[edo|Edos]]: [[118edo|118]], [[149edo|149]] [[Chords of hemithirds]] =Hemiseven= ==7-limit== Commas: 1029/1024, 19683/19600 POTE generator: ~320/243 = 483.267 Map: [<1 4 14 2|, <0 -6 -29 2|] Wedgie: <<6 29 -2 32 -20 -86|| EDOs: 72, 149, 221, 514bd, 735bcd Badness: 0.0566 ==11-limit== Commas: 385/384, 441/440, 19683/19600 POTE generator: ~320/243 = 483.276 Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|] EDOs: 67c, 72, 149, 221e, 293de Badness: 0.0285 =Tritikleismic= ==7-limit== [[Comma|Commas]]: 1029/1024, 15625/15552 [[Minimax tunings]]: 7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>, |8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 7/5 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>] [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 ==11-limit== [[Comma|Commas]]: 385/384, 441/440, 4000/3993 [[Minimax tuning]]: [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>, |20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>] [[Eigenmonzo|Eigenmonzos]]: 2, 9/7 Map: [<3 0 3 10 8|, <0 6 5 -2 3|] [[edo|EDOs]]: [[72edo|72]], [[159edo|159]], [[231edo|231]] ==13-limit== Commas: 325/324, 364/363, 441/440, 625/624 Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] EDOs: 15, 72, 87, 159 =Superkleismic= Commas: 1029/1024, 875/864 POTE generator: ~6/5 = 321.930 Map: [<1 4 5 2|, <0 -9 -10 3|] EDOs: 11, 15, 26, 41 Badness: 0.0479 ==11-limit== Commas: 100/99, 245/242, 385/384 POTE generator: ~6/5 = 321.847 Map: [<1 4 5 2 4|, <0 -9 -10 3 -2|] EDOs: 15, 26, 41, 261 Badness: 0.0257 ==13-limit== Commas: 100/99, 105/104, 245/243, 1188/1183 POTE generator: ~6/5 = 321.994 Map: [<1 4 5 2 4 8|, <0 -9 -10 3 -2 -16|] EDOs: 11, 15, 26, 41 Badness: 0.0215 =Gorgo= Commas: 36/35, 1029/1024 [[POTE tuning|POTE generator]]: 228.337 Map: [<1 1 1 3|, <0 3 7 -1|] Wedgie: <<3 7 -1 4 -10 -22|| EDOs: 5, 16, 21, 226, 247 ==11-limit== Commas: 36/35, 45/44, 1029/1024 POTE generator: ~8/7 = 227.373 Map: [<1 1 1 3 1|, <0 3 7 -1 13|> EDOs: 16, 21, 37b Badness: 0.0495 ==13-limit== Commas: 27/26, 36/35, 45/55, 507/500 POTE generator: ~8/7 = 227.230 Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|> EDOs 16, 21, 37b Badness: 0.0327 ==Music== [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3|Gorgo Example]] by [[Herman Miller]] =Lemba= Commas: 50/49, 525/512 [[POTE tuning|POTE generator]]: 232.089 Map: [<2 2 5 6|, <3 -1 -1|] Wedgie: <<6 -2 -2 -17 -20 1|| EDOs: 10, 16, 26 ==Music== By [[Herman Miller]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3|Lemba Galatsia]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3|GPO Lemba]] =Gidorah= Commas: 21/20, 144/125 POTE generator: ~8/7 = 230.762 Map: [<1 1 2 3|, <0 3 2 -1|] EDOs: 5, 11, 21, 26 Badness: 0.0623 =Clyndro= Commas: 1029/1024, 135/128 POTE generator: ~8/7 = 226.469 Map: [<1 1 4 3|, <0 3 -9 -1|] EDOs: 16
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<html><head><title>Gamelismic clan</title></head><body><!-- ws:start:WikiTextTocRule:86:<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:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#x-Full seven limit children">Full seven limit children</a></div> <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Miracle">Miracle</a></div> <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Miracle-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Miracle-Revelation">Revelation</a></div> <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Miracle-Miraculous">Miraculous</a></div> <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 2em;"><a href="#Miracle-Benediction">Benediction</a></div> <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Miracle-Manna">Manna</a></div> <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Miracle-Music">Music</a></div> <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 1em;"><a href="#Rodan">Rodan</a></div> <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Rodan-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Rodan-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 3em;"><a href="#Rodan-13-limit-Music">Music</a></div> <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Rodan-Superduper">Superduper</a></div> <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 2em;"><a href="#Rodan-Varan">Varan</a></div> <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 1em;"><a href="#Valentine">Valentine</a></div> <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Valentine-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Valentine-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Unidec">Unidec</a></div> <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Unidec-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Unidec-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 2em;"><a href="#Unidec-Ekadash">Ekadash</a></div> <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Unidec-Hendec">Hendec</a></div> <!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Hemithirds">Hemithirds</a></div> <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Hemithirds-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Hemithirds-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 1em;"><a href="#Hemiseven">Hemiseven</a></div> <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 2em;"><a href="#Hemiseven-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 2em;"><a href="#Hemiseven-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 1em;"><a href="#Tritikleismic">Tritikleismic</a></div> <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 2em;"><a href="#Tritikleismic-7-limit">7-limit</a></div> <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Tritikleismic-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 2em;"><a href="#Tritikleismic-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 1em;"><a href="#Superkleismic">Superkleismic</a></div> <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Superkleismic-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 2em;"><a href="#Superkleismic-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 1em;"><a href="#Gorgo">Gorgo</a></div> <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Gorgo-11-limit">11-limit</a></div> <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 2em;"><a href="#Gorgo-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Gorgo-Music">Music</a></div> <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 1em;"><a href="#Lemba">Lemba</a></div> <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Lemba-Music">Music</a></div> <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 1em;"><a href="#Gidorah">Gidorah</a></div> <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 1em;"><a href="#Clyndro">Clyndro</a></div> <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --></div> <!-- ws:end:WikiTextTocRule:130 --><br /> The 2.3.7-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3>. For any member of the clan, for the rank three <a class="wiki_link" href="/Gamelismic%20family#Gamelan">gamelan temperament</a> itself, and for the rank two 2.3.7 temperament <a class="wiki_link" href="/slendric">slendric</a>, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. <a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred.<br /> <br /> 7-limit minimax<br /> [|1 0 0 0>, |5/2 3/4 0 -3/4>,<br /> |5/2 -1/4 1 -3/4>, |5/2 -1/4 0 1/4>]<br /> Eigenmonzos: 2, 7/6, 6/5<br /> <br /> 9-limit minimax<br /> [|1 0 0 0>, |10/7 6/7 0 -3/7>,<br /> |10/7 -1/7 1 -3/7>, |20/7 -2/7 0 1/7>]<br /> Eigenmonzos: 2, 6/5, 9/7<br /> <br /> Lattice basis: 8/7 0.5192 5/4 2.3219<br /> Angle(8/7, 5/4) = 90 degrees<br /> Map to lattice: [<0 3 0 -1|, <0 0 1 0|]<br /> <br /> Map: [<1 1 0 3|, <0 3 0 -1|, < 0 0 1 0|]<br /> Generators: 2, 5, 7<br /> <br /> No-fives <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 233.688<br /> EDOs: 5, 36, 77, 190<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Full seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Full seven limit children</h2> To the gamelisma itself we need to add the comma which appears next on the modified <a class="wiki_link" href="/Normal%20lists">normal comma list</a>, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Miracle"></a><!-- ws:end:WikiTextHeadingRule:2 -->Miracle</h1> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 225/224<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> 7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>,<br /> |25/13 -7/13 7/13 0>, |35/13 -2/13 2/13 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 6/5<br /> <br /> 9-limit: [|1 0 0 0>, |25/19 12/19 -6/19 0>,<br /> |50/19 -14/19 7/19 0>, |55/19 -4/19 2/19 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 116.675<br /> Algebraic generator: Secor59, <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 15x^6-8x^4-12<br /> <br /> Map: [<1 1 3 3|, <0 6 -7 -2|]<br /> Wedgie: <<6 -7 -2 -25 -20 15||<br /> EDOs: 10, 21, 31, 41, 72, <a class="wiki_link" href="/175edo">175</a><br /> Badness: 0.0167<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Miracle-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 225/224, 243/242<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> [|1 0 0 0 0>, |25/19 12/19 -6/19 0 0>,<br /> |50/19 -14/19 7/19 0 0>, |55/19 -4/19 2/19 0 0>,<br /> |53/19 30/19 -15/19 0 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 10/9<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 116.633<br /> Algebraic generator: Secor59<br /> <br /> Map: [<1 1 3 3 2|, <0 6 -7 -2 15|]<br /> <a class="wiki_link" href="/edo">EDOs</a>: 10, 31, 41, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/391edo">391bcde</a><br /> Badness: 0.0107<br /> <br /> <a class="wiki_link" href="/Chords%20of%20miracle">Chords of miracle</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Miracle-Revelation"></a><!-- ws:end:WikiTextHeadingRule:6 -->Revelation</h2> Commas: 99/98, 176/175, 1029/1024<br /> <br /> POTE generator: ~15/14 = 116.277<br /> <br /> Map: [<1 1 3 3 5|, <0 6 -7 -2 -16|]<br /> EDOs: 21, 31<br /> Badness: 0.0329<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Miracle-Miraculous"></a><!-- ws:end:WikiTextHeadingRule:8 -->Miraculous</h2> Commas: 105/104, 144/143, 196/195, 275/273<br /> <br /> POTE generator: ~15/14 = 116.747<br /> <br /> Map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|]<br /> EDOs: 10, 31, 41, 72, 185<br /> Badness: 0.0187<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Miracle-Benediction"></a><!-- ws:end:WikiTextHeadingRule:10 -->Benediction</h2> Commas: 225/224, 243/242, 351/350, 441/440<br /> <br /> POTE generator: ~15/14 = 116.574<br /> <br /> Map: [<1 1 3 3 2 7|, <0 6 -7 2 15 -34|]<br /> EDOs: 10, 31, 72, 103, <a class="wiki_link" href="/175edo">175f</a><br /> Badness: 0.0157<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Miracle-Manna"></a><!-- ws:end:WikiTextHeadingRule:12 -->Manna</h2> Commas: 225/224, 243/242, 325/324, 385/384<br /> <br /> POTE generator: ~15/14 = 116.739<br /> <br /> Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|]<br /> EDOs: 10, 31, 41, 72, 185, 257cf<br /> Badness: 0.0170<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Miracle-Music"></a><!-- ws:end:WikiTextHeadingRule:14 -->Music</h2> <br /> By <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> <a class="wiki_link_ext" href="http://www.archive.org/details/RachmaninoffPlaysBlackjack" rel="nofollow">Rachmaninoff Plays Blackjack</a> <a class="wiki_link_ext" href="http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3" rel="nofollow">play</a><br /> By <a class="wiki_link" href="/Joseph%20Pehrson">Joseph Pehrson</a><br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/blackandjill.mp3" rel="nofollow">Black and Jill</a><br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blacklight.mp3" rel="nofollow">Blacklight</a><br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Pehrson/josephpehrson+blackjack.mp3" rel="nofollow">Blackjack</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Rodan"></a><!-- ws:end:WikiTextHeadingRule:16 -->Rodan</h1> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 245/243<br /> <br /> 7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>,<br /> |25/9 0 17/18 -17/18>, |25/9 0 -1/18 1/18>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.417<br /> Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">larger root</a> of 20x^2-36x+15, or (9+√6)/10.<br /> <br /> Map: [<1 1 -1 3|, <0 3 17 -1|]<br /> EDOs: 41, 87, 128<br /> Badness: 0.0371<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Rodan-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 441/440, 245/243, 385/384<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>: [|1 0 0 0 0>, |31/19 6/19 0 0 -3/19>,<br /> |49/19 34/19 0 0 -17/19>, |53/19 -2/19 0 0 1/19>,<br /> |62/19 -26/19 0 0 13/19>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/9<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.459<br /> Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of x^2+16x-31, or √95-8.<br /> <br /> Map: [<1 1 -1 3 6|, <0 3 17 -1 -13|]<br /> EDOs: 41, 87, 389d<br /> Badness: 0.0231<br /> <br /> <a class="wiki_link" href="/Chords%20of%20rodan">Chords of rodan</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Rodan-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> Commas: 196/195, 245/243, 352/351, 364/363<br /> <br /> 13 and 15 limit minimax<br /> [|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>,<br /> |37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>,<br /> |45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>]<br /> Eigenmonzos: 2, 13/9<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.482<br /> Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.<br /> <br /> Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|]<br /> Generators: 2, 8/7<br /> <a class="wiki_link" href="/edo">Edos</a>: 41, 46, <a class="wiki_link" href="/87edo">87</a><br /> Badness: 0.0184<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="Rodan-13-limit-Music"></a><!-- ws:end:WikiTextHeadingRule:22 -->Music</h3> By <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> <a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow">Pianodactyl</a> <a class="wiki_link_ext" href="http://www.archive.org/download/Pianodactyl/pianodactyl.mp3" rel="nofollow">play</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Rodan-Superduper"></a><!-- ws:end:WikiTextHeadingRule:24 -->Superduper</h2> Commas: 91/90, 245/243, 385/384, 441/440<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 234.639<br /> <br /> Map: [<1 1 -1 3 6 -1|, <0 3 17 -1 -13 24|<br /> EDOs: 46<br /> Badness: 0.034<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Rodan-Varan"></a><!-- ws:end:WikiTextHeadingRule:26 -->Varan</h2> Commas: 100/99, 245/243, 2835/2816<br /> <br /> POTE generator: ~8/7 = 234.145<br /> <br /> Map: [<1 1 -1 3 -2|, <0 3 17 -1 28|<br /> EDOs: 41, 46e<br /> Badness: 0.0449<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="Valentine"></a><!-- ws:end:WikiTextHeadingRule:28 -->Valentine</h1> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="Valentine-7-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->7-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 126/125<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>,<br /> |17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>]<br /> Eigenmonzos: 2, 7/6<br /> <br /> 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,<br /> |47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]<br /> Eigenmonzos: 2, 9/7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.864<br /> Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">smaller root</a> of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.<br /> <br /> Map: [<1 1 2 3|, <0 9 5 -3|]<br /> Wedgie: <<9 5 -3 -13 -30 -21||<br /> EDOs: 15, 31, 46, 77, 185, 262cd<br /> Badness: 0.0311<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Valentine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 121/120, 126/125, 176/175<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> [|1 0 0 0 0>, |1 0 0 -9/10 9/10>,<br /> |2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]<br /> Eigenmonzos: 2, 11/7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 77.881<br /> Algebraic generator: <a class="wiki_link" href="/Algebraic%20number">positive root</a> of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.<br /> <br /> Map: [<1 1 2 3 3|, <0 9 5 -3 7|]<br /> Generators: 2, 21/20<br /> <a class="wiki_link" href="/edo">Edos</a>: 15, 31, 46, 77, 262cde, 339cde<br /> Badness: 0.0167<br /> <br /> <a class="wiki_link" href="/Chords%20of%20valentine">Chords of valentine</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="Unidec"></a><!-- ws:end:WikiTextHeadingRule:34 -->Unidec</h1> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Unidec-7-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->7-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 4375/4374<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> 7-limit: [|1 0 0 0>, |47/26 0 6/13 -6/13>,<br /> |71/26 0 11/13 -11/13>, |71/26 0 -2/13 2/13>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br /> <br /> 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,<br /> |57/28 11/7 0 -11/14>, |20/7 -2/7 0 1/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.161<br /> <br /> Map: [<2 5 8 5|, <0 -6 -11 2|]<br /> Wedgie: <<12 22 -4 7 -40 -71||<br /> EDOs: 26, 46, 72, 118, 190<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Unidec-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4375/4374<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |57/28 11/7 0 -11/14 0>,<br /> |20/7 -2/7 0 1/7 0>, |99/28 -3/7 0 3/14 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 183.165<br /> <br /> Map: [<2 5 8 5 6|, <0 -6 -11 2 3|]<br /> EDOs: 26, 46, 72, 118, 190<br /> <br /> <br /> <a class="wiki_link" href="/Chords%20of%20unidec">Chords of unidec</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Unidec-Ekadash"></a><!-- ws:end:WikiTextHeadingRule:40 -->Ekadash</h2> Commas: 385/384, 441/440, 625/624, 729/728<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.187<br /> <br /> Map: [<2 5 8 5 6 19|, <0 -6 -11 2 3 -38|]<br /> EDOs: 20, 26, 46, 72, 118, 190, 262df, 452cdef<br /> Bad: 0.0204<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h2> --><h2 id="toc21"><a name="Unidec-Hendec"></a><!-- ws:end:WikiTextHeadingRule:42 -->Hendec</h2> Commas: 169/168, 325/324, 364/363, 1716/1715<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 183.187<br /> <br /> Map: [<2 5 8 5 6 8|, <0 -6 -11 2 3 -2|]<br /> EDOs: 26, 46, 72<br /> Bad: 0.0177<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h1> --><h1 id="toc22"><a name="Hemithirds"></a><!-- ws:end:WikiTextHeadingRule:44 -->Hemithirds</h1> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="Hemithirds-7-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->7-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 3136/3125<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> 7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>,<br /> |11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br /> <br /> 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,<br /> |82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/6<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h2> --><h2 id="toc24"><a name="Hemithirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 3136/3125<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> [|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>,<br /> |79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 11/7<br /> <br /> Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]<br /> <br /> <a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/149edo">149</a><br /> <br /> <a class="wiki_link" href="/Chords%20of%20hemithirds">Chords of hemithirds</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h1> --><h1 id="toc25"><a name="Hemiseven"></a><!-- ws:end:WikiTextHeadingRule:50 -->Hemiseven</h1> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="Hemiseven-7-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->7-limit</h2> Commas: 1029/1024, 19683/19600<br /> <br /> POTE generator: ~320/243 = 483.267<br /> <br /> Map: [<1 4 14 2|, <0 -6 -29 2|]<br /> Wedgie: <<6 29 -2 32 -20 -86||<br /> EDOs: 72, 149, 221, 514bd, 735bcd<br /> Badness: 0.0566<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h2> --><h2 id="toc27"><a name="Hemiseven-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> Commas: 385/384, 441/440, 19683/19600<br /> <br /> POTE generator: ~320/243 = 483.276<br /> <br /> Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|]<br /> EDOs: 67c, 72, 149, 221e, 293de<br /> Badness: 0.0285<br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h1> --><h1 id="toc28"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:56 -->Tritikleismic</h1> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="Tritikleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->7-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 15625/15552<br /> <br /> <a class="wiki_link" href="/Minimax%20tunings">Minimax tunings</a>:<br /> 7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>,<br /> |8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7/5<br /> <br /> 9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>,<br /> |46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:60:<h2> --><h2 id="toc30"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4000/3993<br /> <br /> <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> [|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>,<br /> |20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> <br /> Map: [<3 0 3 10 8|, <0 6 5 -2 3|]<br /> <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:62:<h2> --><h2 id="toc31"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2> Commas: 325/324, 364/363, 441/440, 625/624<br /> <br /> Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|]<br /> EDOs: 15, 72, 87, 159<br /> <br /> <!-- ws:start:WikiTextHeadingRule:64:<h1> --><h1 id="toc32"><a name="Superkleismic"></a><!-- ws:end:WikiTextHeadingRule:64 -->Superkleismic</h1> Commas: 1029/1024, 875/864<br /> <br /> POTE generator: ~6/5 = 321.930<br /> <br /> Map: [<1 4 5 2|, <0 -9 -10 3|]<br /> EDOs: 11, 15, 26, 41<br /> Badness: 0.0479<br /> <br /> <!-- ws:start:WikiTextHeadingRule:66:<h2> --><h2 id="toc33"><a name="Superkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2> Commas: 100/99, 245/242, 385/384<br /> <br /> POTE generator: ~6/5 = 321.847<br /> <br /> Map: [<1 4 5 2 4|, <0 -9 -10 3 -2|]<br /> EDOs: 15, 26, 41, 261<br /> Badness: 0.0257<br /> <br /> <!-- ws:start:WikiTextHeadingRule:68:<h2> --><h2 id="toc34"><a name="Superkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2> Commas: 100/99, 105/104, 245/243, 1188/1183<br /> <br /> POTE generator: ~6/5 = 321.994<br /> <br /> Map: [<1 4 5 2 4 8|, <0 -9 -10 3 -2 -16|]<br /> EDOs: 11, 15, 26, 41<br /> Badness: 0.0215<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:70:<h1> --><h1 id="toc35"><a name="Gorgo"></a><!-- ws:end:WikiTextHeadingRule:70 -->Gorgo</h1> Commas: 36/35, 1029/1024<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 228.337<br /> <br /> Map: [<1 1 1 3|, <0 3 7 -1|]<br /> Wedgie: <<3 7 -1 4 -10 -22||<br /> EDOs: 5, 16, 21, 226, 247<br /> <br /> <!-- ws:start:WikiTextHeadingRule:72:<h2> --><h2 id="toc36"><a name="Gorgo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2> Commas: 36/35, 45/44, 1029/1024<br /> <br /> POTE generator: ~8/7 = 227.373<br /> <br /> Map: [<1 1 1 3 1|, <0 3 7 -1 13|><br /> EDOs: 16, 21, 37b<br /> Badness: 0.0495<br /> <br /> <!-- ws:start:WikiTextHeadingRule:74:<h2> --><h2 id="toc37"><a name="Gorgo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2> Commas: 27/26, 36/35, 45/55, 507/500<br /> <br /> POTE generator: ~8/7 = 227.230<br /> <br /> Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|><br /> EDOs 16, 21, 37b<br /> Badness: 0.0327<br /> <br /> <!-- ws:start:WikiTextHeadingRule:76:<h2> --><h2 id="toc38"><a name="Gorgo-Music"></a><!-- ws:end:WikiTextHeadingRule:76 -->Music</h2> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3" rel="nofollow">Gorgo Example</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:78:<h1> --><h1 id="toc39"><a name="Lemba"></a><!-- ws:end:WikiTextHeadingRule:78 -->Lemba</h1> Commas: 50/49, 525/512<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 232.089<br /> <br /> Map: [<2 2 5 6|, <3 -1 -1|]<br /> Wedgie: <<6 -2 -2 -17 -20 1||<br /> EDOs: 10, 16, 26<br /> <br /> <!-- ws:start:WikiTextHeadingRule:80:<h2> --><h2 id="toc40"><a name="Lemba-Music"></a><!-- ws:end:WikiTextHeadingRule:80 -->Music</h2> By <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3" rel="nofollow">Lemba Galatsia</a><br /> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3" rel="nofollow">GPO Lemba</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:82:<h1> --><h1 id="toc41"><a name="Gidorah"></a><!-- ws:end:WikiTextHeadingRule:82 -->Gidorah</h1> Commas: 21/20, 144/125<br /> <br /> POTE generator: ~8/7 = 230.762<br /> <br /> Map: [<1 1 2 3|, <0 3 2 -1|]<br /> EDOs: 5, 11, 21, 26<br /> Badness: 0.0623<br /> <br /> <!-- ws:start:WikiTextHeadingRule:84:<h1> --><h1 id="toc42"><a name="Clyndro"></a><!-- ws:end:WikiTextHeadingRule:84 -->Clyndro</h1> Commas: 1029/1024, 135/128<br /> <br /> POTE generator: ~8/7 = 226.469<br /> <br /> Map: [<1 1 4 3|, <0 3 -9 -1|]<br /> EDOs: 16</body></html>