Chromatic pairs
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[[toc|flat]] [[media type="custom" key="11052942"]] ---- =Definitions= By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with [[xenharmonic/Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give. =Terrain= Subgroup: 2.9/5.9/7 Commas: 250047/250000 Sval name: 6&21 Related temperament: [[xenharmonic/Minortonic family#Domain|domain]] [[xenharmonic/POTE generator|POTE generator]]: ~10/9 = 182.462 Map: [<3 0 -4|, <0 1 2|] EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 Error: 0.0443 cents Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic. [[xenharmonic/terrain9|Nine note albitonic scale]] [[xenharmonic/terrain15|Fifteen note chromatic scale]] =Orgone= Subgroup: 2.7.11 Commas: 65536/65219 Svals: 4&7 POTE generator: ~77/64 = 323.372 Map: [<1 2 4|, <0 3, -2|] EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308 Error: 0.7313 [[image:orgone_308edo.jpg]] [[xenharmonic/orgone7|Seven note albitonic scale]] [[xenharmonic/orgone11|Eleven note chromatic scale]] [[xenharmonic/orgone15|Fifteen note mega chromatic scale]] =Bridgetown= Subgroup: 2.3.11/5.13/5 Commas: 352/351, 676/675 Sval name: 5&24 Related temperament: [[xenharmonic/The Archipelago|barabados]] POTE generator: ~15/13 = 248.285 Map: [<1 0 -6 -1|, <0 2 9 3|] EDOs: 5, 9, 14, 19, 24, 29 Error: 0.8996 cents [[xenharmonic/bridgetown9|Nine note albitonic scale]] [[xenharmonic/bridgetown14|Fourteen note chromatic scale]] ==Music== [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]] by [[xenharmonic/Igliashon Jones|Igliashon Jones]] [[http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3|Route 14 in Bridgetown]] by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]] =Cata= Subgroup: 2.3.5.13 Commas: 325/324, 625/624 Sval name: 15&19 Related temperament: [[xenharmonic/Kleismic family|catakleismic]] POTE generator: ~6/5 = 317.076 Map: [<1 0 1 0|, <0 6 5 14|] EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 333 Error: 0.9355 cents [[image:xenharmonic/cata_246edo2.jpg]] [[xenharmonic/cata7|Seven note albitonic scale]] [[xenharmonic/cata11|Eleven note mega albitonic scale]] [[xenharmonic/cata15|Fifteen note chromatic scale]] [[xenharmonic/cata19|Nineteen note mega chromatic scale]] =Tridec= Subgroup: 2.7/5.11/5.13/5 Commas: 847/845, 1001/1000 Sval name: 5&8 POTE generator: ~13/10 = 454.461 Map: [<1 2 0 1|, <0 -4 3 1|] EDOs: 5, 8, 21, 29, 37, 66, 169, 235 Error: 1.057 [[xenharmonic/Tridec8|Eight note albitonic scale]] [[xenharmonic/Tridec13|Thirteen note chromatic scale]] =Pepperoni= Subgroup: 2.3.11/7.13/7 Commas: 352/351, 364/363 Sval name: 5&12 Related temperament: The [[xenharmonic/Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name. POTE generator: ~3/2 = 704.052 Map: [<1 0 7 12|, <0 1 -4 -7|] EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271 Error: 1.298 cents [[xenharmonic/pepperoni7|Seven note albitonic scale]] [[xenharmonic/pepperoni12|Twelve note chromatic scale]] =Slendric= Subgroup: 2.3.7 Comma: 1029/1024 Sval name: 5&21 POTE generator: ~8/7 = 233.688 Map: [<1 1 3|, <0 3 -1|] EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190 Error: 1.109 cents [[image:xenharmonic/slendric_190edo.jpg]] [[xenharmonic/slendric5|Five note haplotonic scale]] [[xenharmonic/slendric6|Six note haplotonic scale]] [[xenharmonic/slendric11|Eleven note albitonic scale]] [[xenharmonic/slendric16|Sixteen note chromatic scale]] ==Music== [[http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3|The 11th Slendric Fanfare]] [[http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3|16 Slendric Virgins]] by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]] =Nestoria= Subgroup: 2.3.5.19 Commas: 361/360, 513/512 Sval name: 12&29 Related temperament: [[xenharmonic/Schismatic family|schismatic]] POTE generator: ~3/2 = 701.746 Map: [<1 0 15 9|, <0 1 -8 -3|] EDOs: 7, 12, 17, 29, 41, 53, 118, 171 Error: 1.819 cents [[xenharmonic/nestoria7|Seven note albitonic scale]] [[xenharmonic/nestoria12|Twelve note chromatic scale]] =Photia= Subgroup: 2.3.5.17.19 Commas: 171/170, 256/255, 324/323 Sval name: 12&41 Related temperament: [[xenharmonic/Schismatic family|schismatic]] POTE generator: ~3/2 = 701.470 Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|] EDOs: 7, 12, 17, 29, 41, 53, 65 Error: 3.457 cents [[xenharmonic/photia7|Seven note albitonic scale]] [[xenharmonic/photia12|Twelve note chromatic scale]] =Huntington= Subgroup: 2.5.7.13 Commas: 640/637, 10985/10976 Sval name: 10&27 POTE generator: ~16/13 = 357.002 Map: [<1 5 4 4|, <0 -9 -4 -1|] EDOs: 7, 10, 17, 27, 37, 84, 121, 400 Error: 2.1001 cents [[image:huntington_400edo.jpg]] [[xenharmonic/huntington7|Seven note haplotonic scale]] [[xenharmonic/huntington10|Ten note albitonic scale]] [[xenharmonic/huntington17|Seventeen note chromatic scale]] =Shoe= Subgroup: 2.5.7.11.13 Commas: 176/175, 640/637, 847/845 Sval name: 16&21 POTE generator: ~8/7 = 227.108 Map: [<1 1 3 1 2|, <0 7 -1 13 9|] EDOs: 16, 21, 37 Error: 2.488 [[image:xenharmonic/shoe_37edo.jpg]] [[xenharmonic/shoe5|shoe5]] - five note mini [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/shoe6|shoe6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/shoe11|shoe11]] - eleven note note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/shoe16|shoe16]] - sixteen note [[xenharmonic/chromatic scale|chromatic scale]] =Roulette= Subgroup: 2.5.7.11.13 Commas: 176/175, 1375/1372, 640/637 Sval name: 6&25 Related temperament: [[xenharmonic/Wuerschmidt family|Hemiwuerschmidt]] POTE generator: ~28/25 = 194.594 Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|] EDOs: 6, 7, 13, 19, 25, 31, 37 Error: 2.555 cents [[image:xenharmonic/roulette_37edo.jpg]] [[xenharmonic/roulette6|roulette6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/roulette7|roulette7]] - seven note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/roulette13|roulette13]] - thirteen note [[xenharmonic/chromatic scale|chromatic scale]] [[xenharmonic/roulette19|roulette19]] - nineteen note [[xenharmonic/mega chromatic scale|mega chromatic scale]] =Garibaldi= Group: 2.3.5.7 Commas: 225/224, 3125/3087 Val name: 12&29 POTE generator: ~3/2 = 702.085 Map: [<1 0 15 25|, <0 1 -8 -14|] EDOs: 7, 12, 17, 29, 41, 53, 94 Error: 2.834 [[xenharmonic/garibaldi12|Twelve note albitonic scale]] [[xenharmonic/garibaldi17|Seventeen note chromatic scale]] =Baldy= Subgroup: 2.9.5.7.13 Commas: 225/224, 325/324, 640/637 Sval name: 6&35 Related temperament: [[xenharmonic/Schismatic family|Garibaldi]] POTE generator: ~9/8 = 204.090 Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|] EDOs: 6, 11, 17, 23, 29, 35, 41, [[xenharmonic/47edo|47]], 100, [[xenharmonic/147edo|147]] Error: 2.617 cents [[xenharmonic/baldy6|baldy6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/baldy11|baldy11]] - eleven note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/baldy17|baldy17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] =Bossier= Subgroup: 2.7.11.13 Commas: 1573/1569, 15488/15379 Sval name: 3&17 POTE generator: ~14/11 = 421.309 Map: [<1 0 1 3|, <0 8 7 2|] EDOs: 17, 20, 37, 57, 94, 225 Error: 2.665 cents [[xenharmonic/bossier8|Eight note albitonic scale]] [[xenharmonic/bossier11|Eleven note chromatic scale]] [[xenharmonic/bossier14|Fourteen note mega chromatic scale]] =Radon= Subgroup: 2.3.7.11 Commas: 896/891, 1029/1024 Sval name: 5&36 Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] POTE generator: ~8/7 = 234.381 Map: [<1 1 3 6|, <0 3 -1 -13|] EDOs: 5, 36, 41, 87, 128 Error: 2.925 cents [[xenharmonic/radon5|Five note haplotonic scale]] [[xenharmonic/radon11|Eleven note albitonic scale]] [[xenharmonic/radon16|Sixteen note chromatic scale]] =Myna= Group: 2.3.5.7 Commas: 126/125, 1728/1715 Val name: 4&27 POTE generator: ~6/5 = 310.146 Map: [<1 9 9 8|, <0 -10 -9 -7|] EDOs: 4, 27, 31, 58, 89 Error: 3.310 cents [[xenharmonic/myna7|Seven note haplotonic scale]] [[xenharmonic/myna11|Eleven note albitonic scale]] [[xenharmonic/myna15|Fifteen note chromatic scale]] =Silver= Subgroup: 2.5.7.13.17 Commas: 170/169, 640/637, 5525/5488 Sval name: 10&27 POTE generator: ~13/8 = 842.711 Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, [[xenharmonic/487edo|487]] Error: 3.437 [[xenharmonic/silver7|silver7]] -seven note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/silver10|silver10]] - ten note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/silver17|silver17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] =Mabila= Subgroup: 2.5.7 Comma: 1071875/1048576 Sval name: 7&9 POTE generator: ~175/128 = 527.236 Map: [<1 1 5|, <0 3 -5|] EDOs: 7, 9, 16, 25, 41, 66 Error: 3.560 [[xenharmonic/mabila7|Seven note haplotonic scale]] [[xenharmonic/mabila9|Nine note albitonic scale]] [[xenharmonic/mabila16|Sixteen note chromatic scale]] =Meantone= Group: 2.3.5.7 Commas: 81/80, 126/125 Val name: 12&19 POTE generator: 696.495 Map: [<1 0 -4 -13|, <0 1 4 10|] EDOs: 5, 7, 12, 19, 31, 81, 112, 143 Error: 3.585 [[xenharmonic/meantone5|Five note haplotonic scale]] [[xenharmonic/meantone7|Seven note albitonic scale]] [[xenharmonic/meantone12|Twelve note chromatic scale]] =Indium= Subgroup: 2.5/3.7/3.11/3 Commas: 3025/3024, 3125/3087 Sval name: 8&33 POTE generator: ~12/11 = 147.159 Map: [<1 0 0 2|, <0 6 10 -1|] EDOs: 33, 41, 49, 57, 106, 204, 253 Error: 3.968 cents [[xenharmonic/indium8|Eight note albitonic scale]] [[xenharmonic/indium17|Seventeen note chromatic scale]] Music [[http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3|The Cry of Indium]] (in Indium 17) by [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=1532|details]] =Magic= Group: 2.3.5.7.11 Commas: 100/99, 225/224, 245/243 Val name: 19&22 POTE generator: ~5/4 = 380.696 Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] EDOs: 19, 22, 41, 104, 145 Error: 4.489 [[image:xenharmonic/magic_145edo.jpg]] [[xenharmonic/magic7|Seven note haplotonic scale]] [[xenharmonic/magic10|Ten note albitonic scale]] [[xenharmonic/magic13|Thirteen note chromatic scale]] [[xenharmonic/magic16|Sixteen note mega chromatic scale]] =Hemif= Subgroup: 2.3.7.11.13 Commas: 144/143, 243/242, 364/363 Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]] POTE generator: ~11/9 = 351.691 Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] EDOs: 7, 10, 17, 24, 41, 58 Error: 4.867 cents [[xenharmonic/hemif7|Seven note haplotonic scale]] [[xenharmonic/hemif10|Ten note albitonic scale]] [[xenharmonic/hemif17|Seventeen note chromatic scale]] =Skwares= Subgroup: 2.3.7.11 Commas: 99/98, 243/242 Related temperament: [[xenharmonic/Meantone family|squares]] POTE generator: ~9/7 = 425.244 Map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 Error: 4.942 cents [[xenharmonic/skwares8|Eight note albitonic scale]] [[xenharmonic/skwares11|Eleven note mega albitonic scale]] [[xenharmonic/skwares14|Fourteen note chromatic scale]] =Sensi= Group: 2.3.5.7 Commas: 126/126, 245/243 Val name: 19&27 POTE generator: ~9/7 = 443.383 Map: [<1 6 8 11|, <0 -7 -9 -13|] EDOs: 5, 8, 11, 19, 27, 46 Error: 5.019 [[image:xenharmonic/sensi_46edo.jpg]] [[xenharmonic/sensi5|Five note haplotonic scale]] [[xenharmonic/sensi8|Eight note albitonic scale]] [[xenharmonic/sensi11|Eleven note mega albitonic scale]] [[xenharmonic/sensi19|Nineteen note chromatic scale]] =Greeley= Subgroup: 2.5/3.7/3.11/3 Commas: 121/120, 126/125 POTE generator: ~11/10 = 156.055 Map: [<1 1 2 2|, <0 -2 -6 -1|] EDOs: 8, 15, 23, 77, 100 Error: 5.404 cents [[xenharmonic/greeley8|Eight note albitonic scale]] [[xenharmonic/greeley15|Fifteen note chromatic scale]] ==Music== [[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3|A Greeley Steals Halloween]] by [[@http://chrisvaisvil.com/?p=1485|Chris Vaisvil]] in Greeley 15 =Semidim= Subgroup: 2.5/3.7/3.11/3.13/3 Commas: 121/120, 169/168, 275/273 Sval name: 8&29 POTE generator: ~13/10 = 453.190 Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] EDOs: 5, 8, 13, 21, 29, 37, 45 Error: 5.433 cents [[xenharmonic/semidim8|Eight note albitonic scale]] [[xenharmonic/semidim13|Thirteen note chromatic scale]] =Orwell= Group: 2.3.5.7.11 Commas: 99/98, 121/120, 176/175 Val name: 9&22 POTE generator: ~7/6 = 271.426 Map: [<1 0 3 1 3|, <0 7 -3 8 2|] EDOs: 9, 22, 31, 53, 84 Error: 5.584 [[xenharmonic/orwell5|Five note haplotonic scale]] [[xenharmonic/orwell9|Nine note albitonic scale]] [[xenharmonic/orwell13|Thirteen note chromatic scale]] =Bleu= Group: 2.3.7.11.13 Commas: 78/77, 99/98, 144/143 Sval name: 9&17 POTE generator: ~13/12 = 139.990 Map: [<1 1 2 3 3|, <0 5 7 4 6|] EDOs: [[xenharmonic/9edo|9]], [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60]] Error: 6.361 [[xenharmonic/bleu8|bleu8]] - Eight note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/bleu9|bleu9]] - Nine note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/bleu17|bleu17]] - Seventeen note [[xenharmonic/chromatic scale|chromatic scale]] =Mohaha= Subgroup: 2.3.5.11 Commas: 81/80, 121/120 Related temperament: [[xenharmonic/Meantone family|mohajira]] POTE generator: ~11/9 = 348.094 Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 7, 10, 17, 24, 31, 131 Error: 6.733 cents [[xenharmonic/mohaha7|Seven note albitonic scale]] [[xenharmonic/mohaha10|Ten note chromatic scale]] ==Mohoho== Subgroup: 2.3.5.11.13 Commas: 66/65, 81/80, 121/120 POTE generator: ~11/9 = 348.916 Map: [<1 1 0 2 4|, <0 2 8 5 -1|] EDOs: 7, 10, 17, 24, 31, 55 Error: 9.556 cents =Tutone= Subgroup: 2.9.5.7.11 Commas: 81/80, 99/98, 126/125 Related temperament: [[xenharmonic/Meantone family|meantone]] POTE generator: ~9/8 = 193.937 Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] EDOs: 6, 7, 13, 19, 25, 31, 99 Error: 7.047 cents [[xenharmonic/tutone6|Six note haplotonic scale]] [[xenharmonic/tutone7|Seven note albitonic scale]] [[xenharmonic/tutone13|Thirteen note chromatic scale]] =Leantone= Subgroup: 2.9.5.7.11 Commas: 45/44, 56/55, 81/80 Related temperament: [[meanenneadecal]] POTE generator: ~9/8 = 192.500 Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] EDOs: 6, 7, 13, 19, 25, 31, 56, 81 Error: 20.338 cents [[xenharmonic/leantone6|Six note haplotonic scale]] [[xenharmonic/leantone7|Seven note albitonic scale]] [[xenharmonic/leantone13|Thirteen note chromatic scale]] =Score= Subgroup: 2.7.11.13 Commas: 343/338, 847/832 POTE generator: ~11/8 = 540.099 Map: [<1 1 3 1|, <0 4 1 6|] EDOs: 5, 7, 9, 11, 20 Error: 8.052 cents [[image:xenharmonic/score_20edo.jpg]] [[xenharmonic/score5|Five note haplotonic scale]] [[xenharmonic/score7|Seven note albitonic scale]] [[xenharmonic/score9|Nine note mega albitonic scale]] [[xenharmonic/score11|Eleven note chromatic scale]] =Supra= Subgroup: 2.3.7.11 Commas: 64/63, 99/98 Related temperament: [[xenharmonic/suprapyth|suprapyth]] POTE generator: ~3/2 = 707.192 Map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 7, 12, 17, 22, 39, 56 Error: 9.795 cents [[xenharmonic/supra7|Seven note albitonic scale]] [[xenharmonic/supra12|Twelve note chromatic scale]] ==Supraphon== Subgroup: 2.3.7.11.13 Commas: 64/63, 78/77, 99/98 POTE generator: ~3/2 = 706.137 Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] EDOs: 5, 7, 12, 17 Error: 10.534 cents ==Machine== Subgroup: 2.9.7.11 Commas: 64/63, 99/98 POTE generator: ~9/8 = 214.384 Map: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 Error: 10.100 cents [[xenharmonic/machine5|Five note haplotonic scale]] [[xenharmonic/machine6|Six note albitonic scale]] [[xenharmonic/machine11|Eleven note chromatic scale]] =Antikythera= Subgroup: 2.9.5.7 Commas: 50/49, 64/63 Related temperament: [[xenharmonic/pajara|pajara]] POTE generator: ~8/7 = 214.095 Map: [<2 0 11 12|, <0 1 -1 -1|] EDOS: 4, 6, 10, 16, 22, 28 Error: 11.508 cents [[xenharmonic/antikythera6|Six note haplotonic scale]] [[xenharmonic/antikythera10|Ten note albitonic scale]] [[xenharmonic/antikythera16|Sixteen note chromatic scale]] =Deutone= Subgroup: 2.9.5.7.13 Commas: 65/64, 81/80, 91/90 Related temperament: [[xenharmonic/Meantone family|meanpop]] POTE generator: ~9/8 = 191.059 Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] EDOs: 6, 7, 13, 19, 25, 44, 69 Error: 12.145 cents [[xenharmonic/deutone6|Six note haplotonic scale]] [[xenharmonic/deutone7|seven note albitonic scale]] [[xenharmonic/deutone13|Thirteen note chromatic scale]] =Semiphore= Subgroup: 2.3.7 Comma: 49/48 POTE generator: ~7/6 = 250.385 Map: [<1 0 2|, <0 2 1|] EDOs: 5, 9, 14, 19, 24 Error: 12.428 [[xenharmonic/semiphore5|Five note haplotonic scale]] [[xenharmonic/semiphore9|Nine note albitonic scale]] [[xenharmonic/semiphore14|Fourteen note chromatic scale]] =Augment= Subgroup: 2.5.7.11 Commas: 56/55, 128/125 Related temperament: [[xenharmonic/Augmented family|augmented]] POTE generator: ~8/7 = 228.275 Map: [<3 7 0 2|, <0 0 1 1|] EDOs: 3, 6, 9, 15, 21 Error: 12.830 cents [[xenharmonic/augment6|Six note haplotonic scale]] [[xenharmonic/augment9|Nine note albitonic scale]] [[xenharmonic/augment12|Twelve note chromatic scale]]
Original HTML content:
<html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:91:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Semiphore">Semiphore</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/11052942?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;11052942&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> </script><!-- ws:end:WikiTextMediaRule:0 --><br /> <hr /> <br /> <!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definitions</h1> By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups">subgroup temperament</a>) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:3:<h1> --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1> Subgroup: 2.9/5.9/7<br /> Commas: 250047/250000<br /> Sval name: 6&21<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortonic%20family#Domain">domain</a><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/POTE%20generator">POTE generator</a>: ~10/9 = 182.462<br /> <br /> Map: [<3 0 -4|, <0 1 2|]<br /> EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br /> Error: 0.0443 cents<br /> <br /> Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:5:<h1> --><h1 id="toc2"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:5 -->Orgone</h1> Subgroup: 2.7.11<br /> Commas: 65536/65219<br /> Svals: 4&7<br /> <br /> POTE generator: ~77/64 = 323.372<br /> <br /> Map: [<1 2 4|, <0 3, -2|]<br /> EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308<br /> Error: 0.7313<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:139:<img src="/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg" alt="" title="" /> --><img src="/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg" alt="orgone_308edo.jpg" title="orgone_308edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:139 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orgone15">Fifteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:7:<h1> --><h1 id="toc3"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:7 -->Bridgetown</h1> Subgroup: 2.3.11/5.13/5<br /> Commas: 352/351, 676/675<br /> Sval name: 5&24<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barabados</a><br /> <br /> POTE generator: ~15/13 = 248.285<br /> <br /> Map: [<1 0 -6 -1|, <0 2 9 3|]<br /> EDOs: 5, 9, 14, 19, 24, 29<br /> Error: 0.8996 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:9:<h2> --><h2 id="toc4"><a name="Bridgetown-Music"></a><!-- ws:end:WikiTextHeadingRule:9 -->Music</h2> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Igliashon%20Jones">Igliashon Jones</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3" rel="nofollow">Route 14 in Bridgetown</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:11:<h1> --><h1 id="toc5"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:11 -->Cata</h1> Subgroup: 2.3.5.13<br /> Commas: 325/324, 625/624<br /> Sval name: 15&19<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kleismic%20family">catakleismic</a><br /> <br /> POTE generator: ~6/5 = 317.076<br /> <br /> Map: [<1 0 1 0|, <0 6 5 14|]<br /> EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 333<br /> Error: 0.9355 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:140:<img src="http://xenharmonic.wikispaces.com/file/view/cata_246edo2.jpg/270809448/cata_246edo2.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/cata_246edo2.jpg/270809448/cata_246edo2.jpg" alt="cata_246edo2.jpg" title="cata_246edo2.jpg" /><!-- ws:end:WikiTextLocalImageRule:140 --><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata11">Eleven note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata15">Fifteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/cata19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:13:<h1> --><h1 id="toc6"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:13 -->Tridec</h1> Subgroup: 2.7/5.11/5.13/5<br /> Commas: 847/845, 1001/1000<br /> Sval name: 5&8<br /> <br /> POTE generator: ~13/10 = 454.461<br /> <br /> Map: [<1 2 0 1|, <0 -4 3 1|]<br /> EDOs: 5, 8, 21, 29, 37, 66, 169, 235<br /> Error: 1.057<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tridec8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tridec13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:15:<h1> --><h1 id="toc7"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:15 -->Pepperoni</h1> Subgroup: 2.3.11/7.13/7<br /> Commas: 352/351, 364/363<br /> Sval name: 5&12<br /> Related temperament: The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Peppermint-24">Pepper fifth</a>, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.<br /> <br /> POTE generator: ~3/2 = 704.052<br /> <br /> Map: [<1 0 7 12|, <0 1 -4 -7|]<br /> EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br /> Error: 1.298 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pepperoni7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pepperoni12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:17:<h1> --><h1 id="toc8"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:17 -->Slendric</h1> Subgroup: 2.3.7<br /> Comma: 1029/1024<br /> Sval name: 5&21<br /> <br /> POTE generator: ~8/7 = 233.688<br /> <br /> Map: [<1 1 3|, <0 3 -1|]<br /> EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190<br /> Error: 1.109 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:141:<img src="http://xenharmonic.wikispaces.com/file/view/slendric_190edo.jpg/270813524/slendric_190edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/slendric_190edo.jpg/270813524/slendric_190edo.jpg" alt="slendric_190edo.jpg" title="slendric_190edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:141 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/slendric16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:19:<h2> --><h2 id="toc9"><a name="Slendric-Music"></a><!-- ws:end:WikiTextHeadingRule:19 -->Music</h2> <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3" rel="nofollow">The 11th Slendric Fanfare</a><br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3" rel="nofollow">16 Slendric Virgins</a><br /> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:21:<h1> --><h1 id="toc10"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:21 -->Nestoria</h1> Subgroup: 2.3.5.19<br /> Commas: 361/360, 513/512<br /> Sval name: 12&29<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> <br /> POTE generator: ~3/2 = 701.746<br /> <br /> Map: [<1 0 15 9|, <0 1 -8 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br /> Error: 1.819 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:23:<h1> --><h1 id="toc11"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:23 -->Photia</h1> Subgroup: 2.3.5.17.19<br /> Commas: 171/170, 256/255, 324/323<br /> Sval name: 12&41<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> <br /> POTE generator: ~3/2 = 701.470<br /> <br /> Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 65<br /> Error: 3.457 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:25:<h1> --><h1 id="toc12"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:25 -->Huntington</h1> Subgroup: 2.5.7.13<br /> Commas: 640/637, 10985/10976<br /> Sval name: 10&27<br /> <br /> POTE generator: ~16/13 = 357.002<br /> <br /> Map: [<1 5 4 4|, <0 -9 -4 -1|]<br /> EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br /> Error: 2.1001 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:142:<img src="/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg" alt="" title="" /> --><img src="/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg" alt="huntington_400edo.jpg" title="huntington_400edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:142 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:27:<h1> --><h1 id="toc13"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:27 -->Shoe</h1> Subgroup: 2.5.7.11.13<br /> Commas: 176/175, 640/637, 847/845<br /> Sval name: 16&21<br /> <br /> POTE generator: ~8/7 = 227.108<br /> <br /> Map: [<1 1 3 1 2|, <0 7 -1 13 9|]<br /> EDOs: 16, 21, 37<br /> Error: 2.488<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:143:<img src="http://xenharmonic.wikispaces.com/file/view/shoe_37edo.jpg/270828948/shoe_37edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/shoe_37edo.jpg/270828948/shoe_37edo.jpg" alt="shoe_37edo.jpg" title="shoe_37edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:143 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe5">shoe5</a> - five note mini <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe6">shoe6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe11">shoe11</a> - eleven note note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/shoe16">shoe16</a> - sixteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:29:<h1> --><h1 id="toc14"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:29 -->Roulette</h1> Subgroup: 2.5.7.11.13<br /> Commas: 176/175, 1375/1372, 640/637<br /> Sval name: 6&25<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Wuerschmidt%20family">Hemiwuerschmidt</a><br /> <br /> POTE generator: ~28/25 = 194.594<br /> <br /> Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 37<br /> Error: 2.555 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:144:<img src="http://xenharmonic.wikispaces.com/file/view/roulette_37edo.jpg/270817184/roulette_37edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/roulette_37edo.jpg/270817184/roulette_37edo.jpg" alt="roulette_37edo.jpg" title="roulette_37edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:144 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette6">roulette6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette7">roulette7</a> - seven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette13">roulette13</a> - thirteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/roulette19">roulette19</a> - nineteen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mega%20chromatic%20scale">mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:31:<h1> --><h1 id="toc15"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:31 -->Garibaldi</h1> Group: 2.3.5.7<br /> Commas: 225/224, 3125/3087<br /> Val name: 12&29<br /> <br /> POTE generator: ~3/2 = 702.085<br /> <br /> Map: [<1 0 15 25|, <0 1 -8 -14|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 94<br /> Error: 2.834<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi12">Twelve note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:33:<h1> --><h1 id="toc16"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:33 -->Baldy</h1> Subgroup: 2.9.5.7.13<br /> Commas: 225/224, 325/324, 640/637<br /> Sval name: 6&35<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br /> <br /> POTE generator: ~9/8 = 204.090<br /> <br /> Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]<br /> EDOs: 6, 11, 17, 23, 29, 35, 41, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 100, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/147edo">147</a><br /> Error: 2.617 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy6">baldy6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy11">baldy11</a> - eleven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/baldy17">baldy17</a> - seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:35:<h1> --><h1 id="toc17"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:35 -->Bossier</h1> Subgroup: 2.7.11.13<br /> Commas: 1573/1569, 15488/15379<br /> Sval name: 3&17<br /> <br /> POTE generator: ~14/11 = 421.309<br /> <br /> Map: [<1 0 1 3|, <0 8 7 2|]<br /> EDOs: 17, 20, 37, 57, 94, 225<br /> Error: 2.665 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier14">Fourteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:37:<h1> --><h1 id="toc18"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:37 -->Radon</h1> Subgroup: 2.3.7.11<br /> Commas: 896/891, 1029/1024<br /> Sval name: 5&36<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gamelismic%20clan">Rodan</a><br /> <br /> POTE generator: ~8/7 = 234.381<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> Error: 2.925 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/radon16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:39:<h1> --><h1 id="toc19"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:39 -->Myna</h1> Group: 2.3.5.7<br /> Commas: 126/125, 1728/1715<br /> Val name: 4&27<br /> <br /> POTE generator: ~6/5 = 310.146<br /> <br /> Map: [<1 9 9 8|, <0 -10 -9 -7|]<br /> EDOs: 4, 27, 31, 58, 89<br /> Error: 3.310 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:41:<h1> --><h1 id="toc20"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:41 -->Silver</h1> Subgroup: 2.5.7.13.17<br /> Commas: 170/169, 640/637, 5525/5488<br /> Sval name: 10&27<br /> <br /> POTE generator: ~13/8 = 842.711<br /> <br /> Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]<br /> EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487</a><br /> Error: 3.437<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver7">silver7</a> -seven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver10">silver10</a> - ten note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/silver17">silver17</a> - seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:43:<h1> --><h1 id="toc21"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:43 -->Mabila</h1> Subgroup: 2.5.7<br /> Comma: 1071875/1048576<br /> Sval name: 7&9<br /> <br /> POTE generator: ~175/128 = 527.236<br /> <br /> Map: [<1 1 5|, <0 3 -5|]<br /> EDOs: 7, 9, 16, 25, 41, 66<br /> Error: 3.560<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:45:<h1> --><h1 id="toc22"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:45 -->Meantone</h1> Group: 2.3.5.7<br /> Commas: 81/80, 126/125<br /> Val name: 12&19<br /> <br /> POTE generator: 696.495<br /> <br /> Map: [<1 0 -4 -13|, <0 1 4 10|]<br /> EDOs: 5, 7, 12, 19, 31, 81, 112, 143<br /> Error: 3.585<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:47:<h1> --><h1 id="toc23"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:47 -->Indium</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 3025/3024, 3125/3087<br /> Sval name: 8&33<br /> <br /> POTE generator: ~12/11 = 147.159<br /> <br /> Map: [<1 0 0 2|, <0 6 10 -1|]<br /> EDOs: 33, 41, 49, 57, 106, 204, 253<br /> Error: 3.968 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/indium8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/indium17">Seventeen note chromatic scale</a><br /> <br /> Music<br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3" rel="nofollow">The Cry of Indium</a> (in Indium 17) by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a> => <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1532" rel="nofollow" target="_blank">details</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:49:<h1> --><h1 id="toc24"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:49 -->Magic</h1> Group: 2.3.5.7.11<br /> Commas: 100/99, 225/224, 245/243<br /> Val name: 19&22<br /> <br /> POTE generator: ~5/4 = 380.696<br /> <br /> Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> EDOs: 19, 22, 41, 104, 145<br /> Error: 4.489<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:145:<img src="http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/magic_145edo.jpg/270820174/magic_145edo.jpg" alt="magic_145edo.jpg" title="magic_145edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:145 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic13">Thirteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magic16">Sixteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:51:<h1> --><h1 id="toc25"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:51 -->Hemif</h1> Subgroup: 2.3.7.11.13<br /> Commas: 144/143, 243/242, 364/363<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a><br /> <br /> POTE generator: ~11/9 = 351.691<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> Error: 4.867 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/hemif17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:53:<h1> --><h1 id="toc26"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:53 -->Skwares</h1> Subgroup: 2.3.7.11<br /> Commas: 99/98, 243/242<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">squares</a><br /> <br /> POTE generator: ~9/7 = 425.244<br /> <br /> Map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br /> Error: 4.942 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skwares8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skwares11">Eleven note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skwares14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:55:<h1> --><h1 id="toc27"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:55 -->Sensi</h1> Group: 2.3.5.7<br /> Commas: 126/126, 245/243<br /> Val name: 19&27<br /> <br /> POTE generator: ~9/7 = 443.383<br /> <br /> Map: [<1 6 8 11|, <0 -7 -9 -13|]<br /> EDOs: 5, 8, 11, 19, 27, 46<br /> Error: 5.019<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:146:<img src="http://xenharmonic.wikispaces.com/file/view/sensi_46edo.jpg/270823804/sensi_46edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/sensi_46edo.jpg/270823804/sensi_46edo.jpg" alt="sensi_46edo.jpg" title="sensi_46edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:146 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi11">Eleven note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sensi19">Nineteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:57:<h1> --><h1 id="toc28"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:57 -->Greeley</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 121/120, 126/125<br /> <br /> POTE generator: ~11/10 = 156.055<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 77, 100<br /> Error: 5.404 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greeley8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/greeley15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:59:<h2> --><h2 id="toc29"><a name="Greeley-Music"></a><!-- ws:end:WikiTextHeadingRule:59 -->Music</h2> <a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3" rel="nofollow">A Greeley Steals Halloween</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1485" rel="nofollow" target="_blank">Chris Vaisvil</a> in Greeley 15<br /> <br /> <!-- ws:start:WikiTextHeadingRule:61:<h1> --><h1 id="toc30"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:61 -->Semidim</h1> Subgroup: 2.5/3.7/3.11/3.13/3<br /> Commas: 121/120, 169/168, 275/273<br /> Sval name: 8&29<br /> <br /> POTE generator: ~13/10 = 453.190<br /> <br /> Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]<br /> EDOs: 5, 8, 13, 21, 29, 37, 45<br /> Error: 5.433 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semidim8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semidim13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:63:<h1> --><h1 id="toc31"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:63 -->Orwell</h1> Group: 2.3.5.7.11<br /> Commas: 99/98, 121/120, 176/175<br /> Val name: 9&22<br /> <br /> POTE generator: ~7/6 = 271.426<br /> <br /> Map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> EDOs: 9, 22, 31, 53, 84<br /> Error: 5.584<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/orwell13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:65:<h1> --><h1 id="toc32"><a name="Bleu"></a><!-- ws:end:WikiTextHeadingRule:65 -->Bleu</h1> Group: 2.3.7.11.13<br /> Commas: 78/77, 99/98, 144/143<br /> Sval name: 9&17<br /> <br /> POTE generator: ~13/12 = 139.990<br /> <br /> Map: [<1 1 2 3 3|, <0 5 7 4 6|]<br /> EDOs: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/9edo">9</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo">43</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo">60</a><br /> Error: 6.361<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu8">bleu8</a> - Eight note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu9">bleu9</a> - Nine note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu17">bleu17</a> - Seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:67:<h1> --><h1 id="toc33"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:67 -->Mohaha</h1> Subgroup: 2.3.5.11<br /> Commas: 81/80, 121/120<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">mohajira</a><br /> <br /> POTE generator: ~11/9 = 348.094<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 7, 10, 17, 24, 31, 131<br /> Error: 6.733 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohaha7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mohaha10">Ten note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:69:<h2> --><h2 id="toc34"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:69 -->Mohoho</h2> Subgroup: 2.3.5.11.13<br /> Commas: 66/65, 81/80, 121/120<br /> <br /> POTE generator: ~11/9 = 348.916<br /> <br /> Map: [<1 1 0 2 4|, <0 2 8 5 -1|]<br /> EDOs: 7, 10, 17, 24, 31, 55<br /> Error: 9.556 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:71:<h1> --><h1 id="toc35"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:71 -->Tutone</h1> Subgroup: 2.9.5.7.11<br /> Commas: 81/80, 99/98, 126/125<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meantone</a><br /> <br /> POTE generator: ~9/8 = 193.937<br /> <br /> Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 99<br /> Error: 7.047 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:73:<h1> --><h1 id="toc36"><a name="Leantone"></a><!-- ws:end:WikiTextHeadingRule:73 -->Leantone</h1> Subgroup: 2.9.5.7.11<br /> Commas: 45/44, 56/55, 81/80<br /> Related temperament: <a class="wiki_link" href="/meanenneadecal">meanenneadecal</a><br /> <br /> POTE generator: ~9/8 = 192.500<br /> <br /> Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> Error: 20.338 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:75:<h1> --><h1 id="toc37"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:75 -->Score</h1> Subgroup: 2.7.11.13<br /> Commas: 343/338, 847/832<br /> <br /> POTE generator: ~11/8 = 540.099<br /> <br /> Map: [<1 1 3 1|, <0 4 1 6|]<br /> EDOs: 5, 7, 9, 11, 20<br /> Error: 8.052 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:147:<img src="http://xenharmonic.wikispaces.com/file/view/score_20edo.jpg/270826026/score_20edo.jpg" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/score_20edo.jpg/270826026/score_20edo.jpg" alt="score_20edo.jpg" title="score_20edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:147 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score9">Nine note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/score11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:77:<h1> --><h1 id="toc38"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:77 -->Supra</h1> Subgroup: 2.3.7.11<br /> Commas: 64/63, 99/98<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/suprapyth">suprapyth</a><br /> <br /> POTE generator: ~3/2 = 707.192<br /> <br /> Map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 7, 12, 17, 22, 39, 56<br /> Error: 9.795 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/supra7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/supra12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:79:<h2> --><h2 id="toc39"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:79 -->Supraphon</h2> Subgroup: 2.3.7.11.13<br /> Commas: 64/63, 78/77, 99/98<br /> <br /> POTE generator: ~3/2 = 706.137<br /> <br /> Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]<br /> EDOs: 5, 7, 12, 17<br /> Error: 10.534 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:81:<h2> --><h2 id="toc40"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:81 -->Machine</h2> Subgroup: 2.9.7.11<br /> Commas: 64/63, 99/98<br /> <br /> POTE generator: ~9/8 = 214.384<br /> <br /> Map: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> Error: 10.100 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine6">Six note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/machine11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:83:<h1> --><h1 id="toc41"><a name="Antikythera"></a><!-- ws:end:WikiTextHeadingRule:83 -->Antikythera</h1> Subgroup: 2.9.5.7<br /> Commas: 50/49, 64/63<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pajara">pajara</a><br /> <br /> POTE generator: ~8/7 = 214.095<br /> <br /> Map: [<2 0 11 12|, <0 1 -1 -1|]<br /> EDOS: 4, 6, 10, 16, 22, 28<br /> Error: 11.508 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/antikythera16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:85:<h1> --><h1 id="toc42"><a name="Deutone"></a><!-- ws:end:WikiTextHeadingRule:85 -->Deutone</h1> Subgroup: 2.9.5.7.13<br /> Commas: 65/64, 81/80, 91/90<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meanpop</a><br /> <br /> POTE generator: ~9/8 = 191.059<br /> <br /> Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]<br /> EDOs: 6, 7, 13, 19, 25, 44, 69<br /> Error: 12.145 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone7">seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/deutone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:87:<h1> --><h1 id="toc43"><a name="Semiphore"></a><!-- ws:end:WikiTextHeadingRule:87 -->Semiphore</h1> Subgroup: 2.3.7<br /> Comma: 49/48<br /> <br /> POTE generator: ~7/6 = 250.385<br /> <br /> Map: [<1 0 2|, <0 2 1|]<br /> EDOs: 5, 9, 14, 19, 24<br /> Error: 12.428<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/semiphore14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:89:<h1> --><h1 id="toc44"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:89 -->Augment</h1> Subgroup: 2.5.7.11<br /> Commas: 56/55, 128/125<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Augmented%20family">augmented</a><br /> <br /> POTE generator: ~8/7 = 228.275<br /> <br /> Map: [<3 7 0 2|, <0 0 1 1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> Error: 12.830 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment12">Twelve note chromatic scale</a></body></html>