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 [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full p-limit groups. =Terrain= Subgroup: 2.9/5.9/7 Commas: 250047/250000 Sval name: 6&21 Related temperament: [[xenharmonic/Minortonic family#Domain|domain]] [[Tp tuning|POT2 generator]]: ~10/9 = 182.461 [[Gencom]]: [63/50 10/9; 250047/250000] Gencom map: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|] 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 [[Tp tuning#T2%20tuning|RMS error]]: 0.00844 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. [[image:terrain_3558edo.png]] [[xenharmonic/terrain9|Nine note albitonic scale]] [[xenharmonic/terrain15|Fifteen note chromatic scale]] [[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/|5 5 1 mode of 33 equal (with video)]] [[http://micro.soonlabel.com/33edo/20130827_551of33.mp3|play]] by [[Chris Vaisvil]] =Petrtri= Subgroup: 2.11/5.13/5 Comma: 2200/2197 Svalname: 3&5 [[Tp tuning|POT2 generator]]: ~13/10 = 455.012 [[Gencom]]: [2 13/10; 2200/2197] Gencom map: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|] Map: [<1 0 1|, <0 3 1|] EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c [[Tp tuning#T2%20tuning|RMS error]]: 0.0749 cents [[image:petrtri_385edo.png]] [[xenharmonic/petrtri5|Five note haplotonic scale]] [[xenharmonic/petrtri8|Eight note albitonic scale]] [[xenharmonic/petrtri13|Thirteen note chromatic scale]] =Barton= Subgroup: 2.5.11.13 Commas: 2200/2197, 6656/6655 Svalname: 11&13 [[Tp tuning|POT2 generator]]: ~11/8 = 551.699 Gencom: [2 11/8; 2200/2197 6656/6655] Gencom map: [<1 0 6 0 3 6|, <0 0 -8 0 1 -5|] Map: [<1 6 3 6|, <0 -8 1 -5|] EDOs: 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd [[Tp tuning#T2%20tuning|RMS error]]: 0.0822 cents [[xenharmonic/barton5|Five note haplotonic scale]] [[xenharmonic/barton7|Seven note albitonic scale]] [[xenharmonic/barton9|Nine note mega albitonic scale]] [[xenharmonic/barton11|Eleven note chromatic scale]] [[xenharmonic/barton13|Thirteen note mega chromatic scale]] =Tridec= Subgroup: 2.7/5.11/5.13/5 Commas: 847/845, 1001/1000 Sval name: 5&8 [[Tp tuning|POT2 generator]]: ~13/10 = 454.556 [[Gencom]]: [2 13/10; 847/845 1001/1000] Gencom map: [<1 0 -3/4 5/4 -3/4 1/4|, <0 0 0 -4 3 1|] Map: [<1 2 0 1|, <0 -4 3 1|] EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc [[Tp tuning#T2%20tuning|RMS error]]: 0.1613 cents [[image:tridec_235edo.png]] [[xenharmonic/Tridec8|Eight note albitonic scale]] [[xenharmonic/Tridec13|Thirteen note chromatic scale]] =Nestoria= Subgroup: 2.3.5.19 Commas: 361/360, 513/512 Sval name: 12&29 Related temperament: [[xenharmonic/Schismatic family|schismatic]] [[Tp tuning|POT2 generator]]: ~3/2 = 701.746 [[Gencom]]: [2 3/2; 361/360 513/512] Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 0 -3|] Map: [<1 0 15 9|, <0 1 -8 -3|] EDOs: 7, 12, 17, 29, 41, 53, 118, 171, 460d, 631d [[Tp tuning#T2%20tuning|RMS error]]: 0.1763 cents [[image:nestoria_171edo.png]] [[xenharmonic/nestoria7|Seven note albitonic scale]] [[xenharmonic/nestoria12|Twelve note chromatic scale]] [[xenharmonic/nestoria17|Seventeen note mega chromatic scale]] =Orgone= Subgroup: 2.7.11 Commas: 65536/65219 Svals: 4&7 Related temperament: [[Gamelismic clan#superkleismic|superkleismic]] [[Tp tuning|POT2 generator]]: ~77/64 = 323.372 [[Gencom]]: [2 77/64; 65536/65219] Gencom map: [<1 0 0 2 4|, <0 0 0 3 -2|] Map: [<1 2 4|, <0 3 -2|] EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc [[Tp tuning#T2%20tuning|RMS error]]: 0.1888 cents [[image:orgone_308edo.jpg]] [[xenharmonic/orgone7|Seven note albitonic scale]] [[xenharmonic/orgone11|Eleven note chromatic scale]] [[xenharmonic/orgone15|Fifteen note mega chromatic scale]] =Marveltwintri= Subgroup: 2.5/3.13/9 Comma: 325/324 Svalname: 3&4 [[Tp tuning|POT2 generator]]: ~6/5 = 317.139 [[Gencom]]: [2 6/5; 325/324] Gencom map: [<1 -1/6 5/6 0 0 -1/3|, <0 -1/2 -3/2 0 0 1|] Map: [<1 0 2|, <0 1 -2|] EDOs: 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b [[Tp tuning#T2%20tuning|RMS error]]: 0.2444 cents [[image:marveltwintri_321edo.png]] [[xenharmonic/marveltwintri7|Seven note albitonic scale]] [[xenharmonic/marveltwintri11|Eleven note chromatic scale]] [[xenharmonic/marveltwintri15|Fifteen note mega chromatic scale]] =Cata= Subgroup: 2.3.5.13 Commas: 325/324, 625/624 Sval name: 15&19 Related temperament: [[xenharmonic/Kleismic family|catakleismic]] [[Tp tuning|POT2 generator]]: ~6/5 = 317.076 [[Gencom]]: [2 6/5; 325/324 625/624] Gencom map: [<1 0 1 0 0 0|, <0 6 5 0 0 14|] Map: [<1 0 1 0|, <0 6 5 14|] EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd [[Tp tuning#T2%20tuning|RMS error]]: 0.2450 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]] =Bridgetown= Subgroup: 2.3.11/5.13/5 Commas: 352/351, 676/675 Sval name: 5&24 Related temperaments: [[Chromatic pairs#Haumea|haumea]], [[xenharmonic/The Archipelago|barbados]] [[Tp tuning|POT2 generator]]: ~15/13 = 248.399 [[Gencom]]: [2 15/13; 352/351 676/675] Gencom map: [<1 2 -5/3 0 4/3 1/3|, <0 -2 4 0 -5 1|] Map: [<1 0 -6 -1|, <0 2 9 3|] EDOs: 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 [[Tp tuning#T2%20tuning|RMS error]]: 0.2513 cents [[image:bridgetown_29edo.png]] [[xenharmonic/bridgetown9|Nine note albitonic scale]] [[xenharmonic/bridgetown14|Fourteen note chromatic scale]] ==Music== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3|Paint in the Water 29]]</span></span> by [[xenharmonic/Igliashon Jones|Igliashon Jones]] <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3|Route 14 in Bridgetown]]</span></span> by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]] =Haumea= Subgroup: 2.3.7/5.11/5.13/5 Commas: 352/351, 676/675, 847/845 Related temperaments: [[Chromatic pairs#Bridgetown|bridgetown]], [[Hemifamity family#Namaka|namaka]], hemigari, barbados, parizekmic [[Tp tuning|POT2 generator]]: ~15/13 = 248.491 [[Gencom]]: [2 15/13; 352/351 676/675 847/845] Gencom map: [<1 2 -3/4 -11/4 9/4 5/4|, <0 -2 0 12 -9 -3|] Map: [<1 0 10 -6 -1|, <0 2 -12 9 3|] EDOs: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd [[Tp tuning#T2%20tuning|RMS error]]: 0.2668 cents [[xenharmonic/haumea5|Five note haplotonic scale]] [[xenharmonic/haumea9|Nine note albitonic scale]] [[xenharmonic/haumea14|Fourteen note chromatic scale]] [[xenharmonic/haumea19|Nineteen note mega chromatic scale]] =Neutraltet= Subgroup: 2.3.11 Commas: 243/242 Svalname: 7&17 [[Tp tuning|POT2 generator]]: ~11/9 = 350.525 [[Gencom]]: [2 11/9; 243/242] Gencom map: [<1 1 0 0 2|, <0 2 0 0 5|] Map: [<1 1 2|, <0 2 5|] EDOs: 7, 17, 24, 65, 89, 202, 291, 380 [[Tp tuning#T2%20tuning|RMS error]]: 0.3021 cents [[image:neutraltet_380edo.png]] [[xenharmonic/neutraltet7|Seven note albitonic scale]] [[xenharmonic/neutraltet10|Ten note chromatic scale]] [[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] ==Music== [[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in Neutraltet[7], 24et tuning =Slendric= Subgroup: 2.3.7 Comma: 1029/1024 Sval name: 5&21 [[Tp tuning|POT2 generator]]: ~8/7 = 233.688 [[Gencom]]: [2 8/7; 1029/1024] Gencom map: [<1 1 0 3|, <0 3 0 -1|] Map: [<1 1 3|, <0 3 -1|] EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190 [[Tp tuning#T2%20tuning|RMS error]]: 0.3202 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== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/tuning-survey/daily20111026-the-11th-slendric-fanfare.mp3|The 11th Slendric Fanfare]]</span></span> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3|16 Slendric Virgins]]</span></span> by [[xenharmonic/Chris Vaisvil|Chris Vaisvil]] =Huntington= Subgroup: 2.5.7.13 Commas: 640/637, 10985/10976 Sval name: 10&27 [[Tp tuning|POT2 generator]]: ~16/13 = 357.002 [[Gencom]]: [2 16/13; 640/637 10985/10976] Gencom map: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|] Map: [<1 5 4 4|, <0 -9 -4 -1|] EDOs: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd [[Tp tuning#T2%20tuning|RMS error]]: 0.3452 cents [[image:huntington_400edo.jpg]] [[xenharmonic/huntington7|Seven note haplotonic scale]] [[xenharmonic/huntington10|Ten note albitonic scale]] [[xenharmonic/huntington17|Seventeen note chromatic scale]] =Tobago= Subgroup: 2.3.11.13/5 Commas: 243/242, 676/675 Sval name: 10&14 Related temperaments: [[Chromatic pairs#Neutraltet|neutraltet]], [[xenharmonic/The Archipelago|barbados]] [[Tp tuning|POT2 generator]]: ~15/13 = 249.312 [[Gencom]]: [55/39 15/13; 243/242 676/675] Gencom map: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|] Map: [<2 0 -1 -2], <0 2 5 3]] EDOs: 10, 14, 24, 58, 82, 130 [[Tp tuning#T2%20tuning|RMS error]]: 0.3533 cents [[xenharmonic/tobago6|Six note haplotonic scale]] [[xenharmonic/tobago10|Ten note albitonic scale]] [[xenharmonic/tobago14|Fourteen note chromatic scale]] [[xenharmonic/tobago24|Twentyfour note quatertone 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. [[Tp tuning|POT2 generator]]: ~3/2 = 703.856 [[Gencom]]: [2 3/2; 352/351 364/363] Gencom map: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|] Map: [<1 0 7 12|, <0 1 -4 -7|] EDOs: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd [[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents [[image:pepperoni_271edo.png]] [[xenharmonic/pepperoni7|Seven note albitonic scale]] [[xenharmonic/pepperoni12|Twelve note chromatic scale]] =Wizz= Subgroup: 2.5.11 Commas: 15625/15488 Sval name: 6&16 Related temperaments: [[Marvel temperaments#Wizard-11-limit|wizard]] Generator: ~5/4 = 383.768 [[Gencom]]: [125/88 5/4; 15625/15488] Gencom map: [<2 0 4 0 5| <0 0 1 0 3|] Map: [<2 0 -7|, <0 1 3|] EDOs: 6, 16, 22, 28, 50, 122, 172, 222 [[Tp tuning#T2%20tuning|RMS error]]: 0.3997 [[xenharmonic/wizz6|Six note haplotonic scale]] [[xenharmonic/wizz10|Ten note albitonic scale]] [[xenharmonic/wizz16|Sixteen note chromatic scale]] =Bossier= Subgroup: 2.7.11.13 Commas: 1573/1568, 15488/15379 Sval name: 3&17 [[Tp tuning|POT2 generator]]: ~14/11 = 421.309 [[Gencom]]: [2 14/11; 1573/1568 15488/15379] Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|] Map: [<1 0 1 3|, <0 8 7 2|] EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd [[Tp tuning#T2%20tuning|RMS error]]: 0.4043 cents [[image:bossier_225edo.jpg]] [[xenharmonic/bossier8|Eight note albitonic scale]] [[xenharmonic/bossier11|Eleven note chromatic scale]] [[xenharmonic/bossier14|Fourteen note mega chromatic scale]] =Penta= Subgroup: 2.9.7.11 Commas: 896/891, 26411/26244 Svalname: 8&11 [[Tp tuning|POT2 generator]]: ~9/7 = 438.465 [[Gencom]]: [2 9/7; 896/891 26411/26244] Gencom map: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|] Map: [<1 0 -1 6|, <0 5 6 -4|] EDOs: 8, 11, 30, 41, 52 [[Tp tuning#T2%20tuning|RMS error]]: 0.4262 cents [[xenharmonic/penta5|Five note haplotonic scale]] [[xenharmonic/penta8|Eight note albitonic scale]] [[xenharmonic/penta11|Eleven note chromatic scale]] [[xenharmonic/penta19|Nineteen note mega chromatic scale]] =Marveltri= Subgroup: 2.5.9/7 Comma: 225/224 Sval name: 3&13 Related temperaments: marvel, 22&47, magic [[Tp tuning|POT2 generator]]: ~5/4 = 383.638 [[Gencom]]: [2 5/4; 225/224] Gencom map: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|] Map: [<1 0 5|, <0 1 -2|] EDOs: 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc [[Tp tuning#T2%20tuning|RMS error]]: 0.4801 cents [[xenharmonic/marveltri7|Seven note albitonic scale]] [[xenharmonic/marveltri10|Ten note chromatic scale]] [[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] =Edson= Subgroup: 2.3.7/5.11/5.13/5 Commas: 196/195, 352/351, 364/363 Related temperaments: [[Hemifamity family#Pele|pele]], cassandra [[Tp tuning|POT2 generator]]: ~3/2 = 703.414 [[Gencom]]: [2 3/2; 196/195, 352/351, 364/363] Gencom map: [<1 1 -5 -1 2 4|, <0 1 29/4 5/4 -11/4 -23/4|] Map: [<1 0 10 17 22|, <0 1 -6 -10 -13|] EDOs: 12, 17, 29, 621bcde [[Tp tuning#T2%20tuning|RMS error]]: 0.5102 cents [[xenharmonic/edson5|Five note haplotonic scale]] [[xenharmonic/edson7|Seven note albitonic scale]] [[xenharmonic/edson12|Twelve note chromatic scale]] [[xenharmonic/edson17|Seventeen note mega 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]] [[Tp tuning|POT2 generator]]: ~3/2 = 701.470 [[Gencom]]: [2 3/2; 171/170 256/255 324/323] Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|] Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|] EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d [[Tp tuning#T2%20tuning|RMS error]]: 0.5374 cents [[image:photia_65edo.png]] [[xenharmonic/photia7|Seven note albitonic scale]] [[xenharmonic/photia12|Twelve note chromatic scale]] =Shoe= Subgroup: 2.5.7.11.13 Commas: 176/175, 640/637, 847/845 Sval name: 16&21 [[Tp tuning|POT2 generator]]: ~8/7 = 227.108 [[Gencom]]: [2 8/7; 176/175 640/637 847/845] Gencom map: [<1 0 1 3 1 2|, <0 0 7 -1 13 9|] Map: [<1 1 3 1 2|, <0 7 -1 13 9|] EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce [[Tp tuning#T2%20tuning|RMS error]]: 0.5433 cents [[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/Würschmidt family|Hemiwürschmidt]] [[Tp tuning|POT2 generator]]: ~28/25 = 194.594 [[Gencom]]: [2 28/25; 176/175 1375/1372 640/637] Gencom map: [<1 0 2 2 2 5|, <0 0 2 5 9 -8|] Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|] EDOs: 6, 7, 13, 19, 25, 31, 37 [[Tp tuning#T2%20tuning|RMS error]]: 0.5567 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]] =Silver= Subgroup: 2.5.7.13.17 Commas: 170/169, 640/637, 5525/5488 Sval name: 10&27 [[Tp tuning|POT2 generator]]: ~13/8 = 842.711 [[Gencom]]: [2 13/8; 170/169 640/637 5525/5488] Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|] Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, 178e, 309cde, [[xenharmonic/487edo|487bcdee]] [[Tp tuning#T2%20tuning|RMS error]]: 0.5886 cents [[image:silver_487edo.jpg]] [[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]] =Baldy= Subgroup: 2.9.5.7.13 Commas: 225/224, 325/324, 640/637 Sval name: 6&35 Related temperament: [[xenharmonic/Schismatic family|Garibaldi]] [[Tp tuning|POT2 generator]]: ~9/8 = 204.090 [[Gencom]]: [2 9/8; 225/224 325/324 640/637] Gencom map: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|] 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]], 488cd, 635cd [[Tp tuning#T2%20tuning|RMS error]]: 0.5999 cents [[image:baldy_147edo.jpg]] [[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]] =Guanyintet= Subgroup: 2.5.7/3.11/3 Commas: 176/175, 540/539 Svalname: 4&9 Related temperaments: guanyin, orwell [[Tp tuning|POT2 generator]]: ~7/6 = 270.093 [[Gencom]]: [2 7/6; 176/175 540/539] Gencom map: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|] Map: [<1 0 2 -2|, <0 3 -1 5|] EDOs: 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd [[Tp tuning#T2%20tuning|RMS error]]: 0.6028 cents [[xenharmonic/guanyintet5|Five note haplotonic scale]] [[xenharmonic/guanyintet9|Nine note albitonic scale]] [[xenharmonic/guanyintet13|Thirteen note chromatic scale]] =Radon= Subgroup: 2.3.7.11 Commas: 896/891, 1029/1024 Sval name: 5&36 Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] [[Tp tuning|POT2 generator]]: ~8/7 = 234.381 [[Gencom]]: [2 8/7; 896/891 1029/1024] Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|] Map: [<1 1 3 6|, <0 3 -1 -13|] EDOs: 5, 36, 41, 87, 128 [[Tp tuning#T2%20tuning|RMS error]]: 0.6502 cents [[image:radon_128edo.jpg]] [[xenharmonic/radon5|Five note haplotonic scale]] [[xenharmonic/radon11|Eleven note albitonic scale]] [[xenharmonic/radon16|Sixteen note chromatic scale]] =Gariberttet= Subgroup: 2.5/3.7/3.13/11 Commas: 275/273, 847/845 Svalname: 4&29 [[Tp tuning|POT2 generator]]: ~13/11 = 293.679 [[Gencom]]: [2 13/11; 275/273 847/845] Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|] Map: [<1 0 0 0|, <0 3 5 1|] EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd [[Tp tuning#T2%20tuning|RMS error]]: 0.6914 cents [[xenharmonic/gariberttet5|Five note haplotonic scale]] [[xenharmonic/gariberttet9|Nine note albitonic scale]] [[xenharmonic/gariberttet13|Thirteen note chromatic scale]] =Namo= Subgroup: 2.3.11.13 Commas: 144/143, 243/242 Related temperament: [[Valinorismic temperaments#Mandos|mandos]], mohajira, hemif [[Tp tuning|POT2 generator]]: ~11/9 = 351.488 [[Gencom]]: [2 11/9; 144/143 243/242] Gencom map: [<1 1 0 0 2 4|, <0 2 0 0 5 -1|] Map: [<1 1 2 4|, <0 2 5 -1|] EDOs: 7, 10, 17, 41, 58, 99cd [[Tp tuning#T2%20tuning|RMS error]]: 0.7038 cents [[xenharmonic/namo7|Seven note haplotonic scale]] [[xenharmonic/namo10|Ten note albitonic scale]] [[xenharmonic/namo17|Seventeen note chromatic scale]] =Sentry= Group: 2.5/3.9/7 Commas: 245/243 Svalname: 3&5 Related temperaments: sensi [[Tp tuning|POT2 generator]]: ~9/7 = 440.902 [[Gencom]]: [2 9/7; 245/243] Gencom map: [<1 0 0 0|, <0 0 2 -1|] Map: [<1 0 0|, <0 2 1|] EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc [[Tp tuning#T2%20tuning|RMS error]]: 0.7105 cents [[xenharmonic/sentry5|Five note haplotonic scale]] [[xenharmonic/sentry8|Eight note albitonic scale]] [[xenharmonic/sentry11|Eleven note note chromatic scale]] =Hemif= Subgroup: 2.3.7.11.13 Commas: 144/143, 243/242, 364/363 Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo [[Tp tuning|POT2 generator]]: ~11/9 = 351.691 [[Gencom]]: [2 11/9; 144/143 243/242 364/363] Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] EDOs: 7, 10, 17, 24, 41, 58 [[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents [[image:hemif_58edo.jpg]] [[xenharmonic/hemif7|Seven note haplotonic scale]] [[xenharmonic/hemif10|Ten note albitonic scale]] [[xenharmonic/hemif17|Seventeen note chromatic scale]] =Garibaldi= Group: 2.3.5.7 Commas: 225/224, 3125/3087 Val name: 12&29 [[Tp tuning|POT2 generator]]: ~3/2 = 702.085 [[Gencom]]: [2 3/2; 225/224 3125/3087] Gencom map: [<1 1 7 11], <0 1 -8 -14|] Map: [<1 0 15 25|, <0 1 -8 -14|] EDOs: 7, 12, 17, 29, 41, 53, 94, 241c [[Tp tuning#T2%20tuning|RMS error]]: 0.7257 cents [[image:garibaldi_94edo.png]] [[xenharmonic/garibaldi12|Twelve note albitonic scale]] [[xenharmonic/garibaldi17|Seventeen note chromatic scale]] =Mabila= Subgroup: 2.5.7 Comma: 1071875/1048576 Sval name: 7&9 [[Tp tuning|POT2 generator]]: ~175/128 = 527.236 [[Gencom]]: [2 175/128; 1071875/1048576] Gencom map: [<1 0 1 5}, <0, 0, 3, -5|] Map: [<1 1 5|, <0 3 -5|] EDOs: 7, 9, 16, 25, 41, 66, 305bc [[Tp tuning#T2%20tuning|RMS error]]: 0.7729 cents [[image:mabila_66edo.jpg]] [[xenharmonic/mabila7|Seven note haplotonic scale]] [[xenharmonic/mabila9|Nine note albitonic scale]] [[xenharmonic/mabila16|Sixteen note chromatic scale]] =Indium= Subgroup: 2.5/3.7/3.11/3 Commas: 3025/3024, 3125/3087 Sval name: 8&33 [[Tp tuning|POT2 generator]]: ~12/11 = 147.010 [[Gencom]]: [2 12/11; 3025/3024 3125/3087] Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|] Map: [<1 0 0 2|, <0 6 10 -1|] EDOs: 33, 41, 49, 57, 106, 204, 253 [[Tp tuning#T2%20tuning|RMS error]]: 0.7788 cents [[image:indium_253edo.png]] [[xenharmonic/indium8|Eight note albitonic scale]] [[xenharmonic/indium17|Seventeen note chromatic scale]] ==Music== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3|The Cry of Indium]]</span></span> (in Indium 17) by [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=1532|details]] =Starlingtet= Group: 2.5/3.7/3 Comma: 126/125 Svalname: 4&15 Related temperaments: starling; becomes myna [[Tp tuning|POT2 generator]]: ~6/5 = 311.154 [[Gencom]]: [2 6/5; 126/125] Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|] Map: [<1 0 -1|, <0 1 3|] EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b [[Tp tuning#T2%20tuning|RMS error]]: 0.8398 cents [[xenharmonic/starlingtet4|Four note haplotonic scale]] [[xenharmonic/starlingtet7|Seven note albitonic scale]] [[xenharmonic/starlingtet11|Eleven note chromatic scale]] =Lovecraft= Group: 2.11.13 Commas: 1352/1331 [[Tp tuning|POT2 generator]]: ~13/11 = 279.318 [[Gencom]]: [2 13/11; 1352/1331] Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|] Map: [<1 1 0|, <0 2 3|] EDOS: 13, 30, 43, 73, 116b [[Tp tuning#T2%20tuning|RMS error]]: 0.8449 cents [[image:lovecraft_116edo.png]] [[xenharmonic/lovecraft5|Five note haplotonic scale]] [[xenharmonic/lovecraft9|Nine note albitonic scale]] [[xenharmonic/lovecraft13|Thirteen note chromatic scale]] =Laz= Subgroup: 2.5.7/3.11/3.13/3 Commas: 144/143, 176/175, 196/195 Related temperaments: [[Orwellismic family#Guanyin-Georgian|georgian]], winston [[Tp tuning|POT2 generator]]: ~7/6 = 269.300 [[Gencom]]: [2 7/6; 144/143 176/175 196/195] Gencom map: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|] Map: [<1 0 2 -2 6|, <0 3 -1 5 -5|] EDOs: 9, 31, 40, 49, 58, 156bde, 205bde [[Tp tuning#T2%20tuning|RMS error]]: 0.8790 cents [[xenharmonic/laz5|Five note haplotonic scale]] [[xenharmonic/laz9|Nine note albitonic scale]] [[xenharmonic/laz13|Thirteen note chromatic scale]] =Myna= Group: 2.3.5.7 Commas: 126/125, 1728/1715 Val name: 4&27 [[Tp tuning|POT2 generator]]: ~6/5 = 310.146 [[Gencom]]: [2 6/5; 126/125 1728/1715] Gencom map: [<1 -1 0 1|,<0 10 9 7|] Map: [<1 9 9 8|, <0 -10 -9 -7|] EDOs: 4, 27, 31, 58, 89, 236c, 325cd [[Tp tuning#T2%20tuning|RMS error]]: 0.9516 cents [[image:myna_89edo.jpg]] [[xenharmonic/myna7|Seven note haplotonic scale]] [[xenharmonic/myna11|Eleven note albitonic scale]] [[xenharmonic/myna15|Fifteen note chromatic scale]] =Greeley= Subgroup: 2.5/3.7/3.11/3 Commas: 121/120, 126/125 Related temperament: [[Porcupine family#Opossum|Opossum]], [[Starling temperaments#Nusecond%20temperament|Nusecond]] [[Tp tuning|POT2 generator]]: ~11/10 = 155.776 [[Gencom]]: [2 11/10; 121/120 126/125] Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|] Map: [<1 1 2 2|, <0 -2 -6 -1|] EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd [[Tp tuning#T2%20tuning|RMS error]]: 1.034 cents [[image:greeley_100edo.png]] [[xenharmonic/greeley8|Eight note albitonic scale]] [[xenharmonic/greeley15|Fifteen note chromatic scale]] ==Music== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3|A Greeley Steals Halloween]]</span></span> 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 [[Tp tuning|POT2 generator]]: ~13/10 = 453.242 [[Gencom]]: [2 13/10; 121/120 169/168 275/273] Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|] Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde, [[Tp tuning#T2%20tuning|RMS error]]: 1.052 cents [[image:semidim_770edo.png]] [[xenharmonic/semidim8|Eight note albitonic scale]] [[xenharmonic/semidim13|Thirteen note chromatic scale]] =Mothwelltri= Group: 2.7/3.11 Comma: 99/98 Svalname: 1&4 Related temperament: Orwell [[Tp tuning|POT2 generator]]: ~7/6 = 273.174 [[Gencom]]: [2 7/6; 99/98] Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|] Map: [<1 0 1|, <0 1 2|] EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc [[Tp tuning#T2%20tuning|RMS error]]: 1.064 cents [[xenharmonic/mothwelltri5|Five note haplotonic scale]] [[xenharmonic/mothwelltri9|Nine note albitonic scale]] [[xenharmonic/mothwelltri13|Thirteen note chromatic scale]] =Sulis= Subgroup: 2.5.9/7.11/9 Commas: 99/98, 176/175 Related temperament: [[Marvel family#Minerva|minerva]], würschmidt [[Tp tuning|POT2 generator]]: ~5/4 = 386.558 [[Gencom]]: [2 5/4; 99/98 176/175] Gencom map: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|] Map: [<1 0 5 -9|, <0 1 -2 4|] EDOs: 22, 25, 28, 31, 59, 90c, 149c [[Tp tuning#T2%20tuning|RMS error]]: 1.074 cents [[xenharmonic/sulis7|Seven note haplotonic scale]] [[xenharmonic/sulis10|Ten note albitonic scale]] [[xenharmonic/sulis13|Thirteen note chromatic scale]] =Skwares= Subgroup: 2.3.7.11 Commas: 99/98, 243/242 Related temperament: [[xenharmonic/Meantone family|squares]] [[Tp tuning|POT2 generator]]: ~9/7 = 425.244 [[Gencom]]: [2 9/7; 99/98 243/242] Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|] Map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd [[Tp tuning#T2%20tuning|RMS error]]: 1.099 cents [[image:skwares_206edo.png]] [[xenharmonic/skwares8|Eight note albitonic scale]] [[xenharmonic/skwares11|Eleven note mega albitonic scale]] [[xenharmonic/skwares14|Fourteen note chromatic scale]] =Orwell= Group: 2.3.5.7.11 Commas: 99/98, 121/120, 176/175 Val name: 9&22 [[Tp tuning|POT2 generator]]: ~7/6 = 271.426 [[Gencom]]: [2 7/6; 99/98 121/120 176/175] Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|] Map: [<1 0 3 1 3|, <0 7 -3 8 2|] EDOs: 9, 22, 31, 53, 84e [[Tp tuning#T2%20tuning|RMS error]]: 1.151 cents [[image:xenharmonic/orwell_84edo.png]] [[xenharmonic/orwell5|Five note haplotonic scale]] [[xenharmonic/orwell9|Nine note albitonic scale]] [[xenharmonic/orwell13|Thirteen note chromatic scale]] =Magicaltet= Group: 2.5/3.7.11 Commas: 100/99, 385/384 Related temperaments: 4&7&15, superkleismic, magic [[Tp tuning|POT2 generator]]: ~6/5 = 322.659 [[Gencom]]: [2 6/5; 100/99 385/384] Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|] Map: [<1 0 5 2|, <0 1 -3 2|] EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd [[Tp tuning#T2%20tuning|RMS error]]: 1.206 cents [[xenharmonic/magicaltet7|Seven note albitonic scale]] [[xenharmonic/magicaltet11|Eleven note chromatic scale]] [[xenharmonic/magicaltet15|Fifteen note mega scale]] =Magic= Group: 2.3.5.7.11 Commas: 100/99, 225/224, 245/243 Val name: 19&22 [[Tp tuning|POT2 generator]]: ~5/4 = 380.696 [[Gencom]]: [2 5/4; 100/99 225/224 245/243] Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|] Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] EDOs: 19, 22, 41, 104, 145 [[Tp tuning#T2%20tuning|RMS error]]: 1.226 cents [[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]] ==Music== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]</span> [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] =Kiribati= Subgroup: 2.9/5.7/3.11/9 Commas: 100/99, 245/242 Related temperament: [[Octagar family|nakika]], octacot [[Tp tuning|POT2 generator]]: ~21/20 = 87.892 [[Gencom]]: [2 21/20; 100/99 245/242] Gencom map: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|] Map: [<1 1 1 0|, <0 -2 3 4|] EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd [[Tp tuning#T2%20tuning|RMS error]]: 1.245 cents [[xenharmonic/kiribati13|Thirteen note chromatic scale]] [[xenharmonic/kiribati14|Fourteen note chromatic scale]] =Score= Subgroup: 2.7.11.13 Commas: 343/338, 847/832 [[Tp tuning|POT2 generator]]: ~11/8 = 540.099 [[Gencom]]: [2 11/8; 343/338 847/832] Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|] Map: [<1 1 3 1|, <0 4 1 6|] EDOs: 5, 7, 9, 11, 20 [[Tp tuning#T2%20tuning|RMS error]]: 1.282 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]] =Sensation= Group: 2.3.5.7.13 Commas: 91/90, 126/125, 169/168 Related temperaments: Sensi, Sensis, Sensus [[Tp tuning|POT2 generator]]: ~9/7 = 443.322 [[Gencom]]: [2 9/7; 91/90 126/125 169/168] Gencom map: [<1 -1 -1 -2 0 0|, <0 7 9 13 0 10|] Map: [<1 6 8 11 10|, <0 -7 -9 -13 -10|] EDOs: 19, 27, 46, 111de, 157de [[Tp tuning#T2%20tuning|RMS error]]: 1.321 cents [[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]] =Sensi= Group: 2.3.5.7 Commas: 126/125, 245/243 Val name: 19&27 [[Tp tuning|POT2 generator]]: ~9/7 = 443.383 [[Gencom]]: [2 9/7; 126/125 245/243] Gencom map: [<1 -1 -1 -2|, <0 7 9 13|] Map: [<1 6 8 11|, <0 -7 -9 -13|] EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd [[Tp tuning#T2%20tuning|RMS error]]: 1.323 cents [[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]] =Meantone= Group: 2.3.5.7 Commas: 81/80, 126/125 Val name: 12&19 [[Tp tuning|POT2 generator]]: ~3/2 = 696.495 [[Gencom]]: [2 3/2; 81/80 126/125] Gencom map: [<1 1 0 -3|, <0 1 4 10|] Map: [<1 0 -4 -13|, <0 1 4 10|] EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b [[Tp tuning#T2%20tuning|RMS error]]: 1.382 cents [[image:meantone_31edo.jpg]] [[xenharmonic/meantone5|Five note haplotonic scale]] [[xenharmonic/meantone7|Seven note albitonic scale]] [[xenharmonic/meantone12|Twelve note chromatic scale]] =Mohaha= Subgroup: 2.3.5.11 Commas: 81/80, 121/120 Related temperament: [[xenharmonic/Meantone family|mohajira]] [[Tp tuning|POT2 generator]]: ~11/9 = 348.094 [[Gencom]]: [2 11/9; 81/80 121/120] Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|] Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 24, 31, 55, 69d, 100d, 131bd [[Tp tuning#T2%20tuning|RMS error]]: 1.392 cents [[image:mohaha_131edo.png]] [[xenharmonic/mohaha7|Seven note albitonic scale]] [[xenharmonic/mohaha10|Ten note chromatic scale]] ==Music== [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]] =Tutone= Subgroup: 2.9.5.7.11 Commas: 81/80, 99/98, 126/125 Related temperaments: [[xenharmonic/Meantone family|meantone]], [[Hemimean family#Belobog|belobog]], hemithirds, hemiwürschmidt [[Tp tuning|POT2 generator]]: ~9/8 = 193.937 [[Gencom]]: [2 9/8; 81/80 99/98 126/125] Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|] Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] EDOs: 25, 31, 68b, 99b [[Tp tuning#T2%20tuning|RMS error]]: 1.439 cents [[xenharmonic/tutone6|Six note haplotonic scale]] [[xenharmonic/tutone7|Seven note albitonic scale]] [[xenharmonic/tutone13|Thirteen note chromatic scale]] [[image:tutone_99edo.png]] =Stacks= Subgroup: 2.9.15.7.11.13 Commas: 100/99, 105/104, 144/143, 196/195 Related temperament: [[Magic family#Magic-13-limit|magic]] Svalname: 11&30 [[Tp tuning|POT2 generator]]: ~9/7 = 439.146 [[Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195] Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef [[Tp tuning#T2%20tuning|RMS error]]: 1.540 cents [[xenharmonic/stacks5|Five note haplotonic scale]] [[xenharmonic/stacks8|Eight note albitonic scale]] [[xenharmonic/stacks11|Eleven note note chromatic scale]] [[xenharmonic/stacks19|Nineteen note note mega chromatic scale]] =Bleu= Group: 2.3.7.11.13 Commas: 78/77, 99/98, 144/143 Sval name: 9&17 [[Tp tuning|POL2 generator]]: ~13/12 = 139.990 [[Gencom]]: [2 13/12; 78/77 99/98 144/143] Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] Map: [<1 1 2 3 3|, <0 5 7 4 6|] EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] [[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents [[image:blue_60edo.png]] [[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]] [[http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3|On a Well Worn Riff (Bleu 17)]] by [[http://chrisvaisvil.com/on-a-well-worn-riff-bleu-17/|Chris Vaisvil]] =Sephiroth= Subgroup: 2.5.11.13.17 Commas: 65/64, 170/169, 221/220 Related temperament: muggles [[Tp tuning|POT2 generator]]: ~5/4 = 372.236 [[Gencom]]: [2 5/4; 65/64 170/169 221/220] Gencom map: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|] Map: [<1 0 15 6 11|, <0 1 -5 -1 -3|] EDOs: 10, 13, 16, 29c [[Tp tuning#T2%20tuning|RMS error]]: 1.774 cents [[xenharmonic/sephiroth7|Seven note haplotonic scale]] [[xenharmonic/sephiroth10|Ten note albitonic scale]] [[xenharmonic/sephiroth13|Thirteen note chromatic scale]] [[xenharmonic/sephiroth16|Sixteen note mega chromatic scale]] =Archy= Subgroup: 2.3.7 Comma: 64/63 [[Tp tuning|POT2 generator]]: ~3/2 = 709.321 Gencom: [2 3/2; 64/63] Gencom mapping: [<1 1 0 4|, <0 1 0 -2|] Map: [<1 2 2|, <0 -1 2|] EDOs: 5, 12, 17, 22, 27, 137bc [[Tp tuning#T2%20tuning|RMS error]]: 1.856 cents [[xenharmonic/archy5|Five note haplotonic scale]] [[xenharmonic/archy7|Seven note albitonic scale]] [[xenharmonic/archy12|Twelve note chromatic scale]] =Suhajira= Subgroup: 2.3.7.11 Commas: 64/63, 243/242 [[Tp tuning|POL2 generator]]: ~11/9 = 353.958 [[Gencom]]: [2 11/9; 64/63 243/242] Gencom map: [<1 1 0 4 2|, <0 2 0 -4 5|] Map: [<1 1 4 2|, <0 2 -4 5|] EDOs: 7, 10, 17, 61de [[Tp tuning#T2%20tuning|RMS error]]: 1.968 cents [[suhajira7]] - Seven note [[xenharmonic/haplotonic scale|haplotonic scale]] [[suhajira10]] - Ten note [[xenharmonic/albitonic scale|albitonic scale]] [[suhajira17]] - note [[xenharmonic/chromatic scale|chromatic scale]] =Mohoho= Subgroup: 2.3.5.11.13 Commas: 66/65, 81/80, 121/120 [[Tp tuning|POT2 generator]]: ~11/9 = 348.916 [[Gencom]]: [2 11/9; 66/65 81/80 121/120] Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|] Map: [<1 1 0 2 4|, <0 2 8 5 -1|] EDOs: 17c, 24, 31, 55, 86de, 141cde [[Tp tuning#T2%20tuning|RMS error]]: 1.971 cents =Supra= Subgroup: 2.3.7.11 Commas: 64/63, 99/98 Related temperament: [[xenharmonic/suprapyth|suprapyth]] [[Tp tuning|POT2 generator]]: ~3/2 = 707.192 [[Gencom]]: [2 3/2; 64/63 99/98] Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|] Map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c [[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents [[image:supra_56edo.png]] [[xenharmonic/supra7|Seven note albitonic scale]] [[xenharmonic/supra12|Twelve note chromatic scale]] =Machine= Subgroup: 2.9.7.11 Commas: 64/63, 99/98 [[Tp tuning|POT2 generator]]: ~9/8 = 214.384 [[Gencom]]: [2 9/8; 64/63 99/98] Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] Map: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 [[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents [[image:machine_28edo.png]] [[xenharmonic/machine5|Five note haplotonic scale]] [[xenharmonic/machine6|Six note albitonic scale]] [[xenharmonic/machine11|Eleven note chromatic scale]] =Deutone= Subgroup: 2.9.5.7.13 Commas: 65/64, 81/80, 91/90 Related temperament: [[xenharmonic/Meantone family|meanpop]] [[Tp tuning|POT2 generator]]: ~9/8 = 191.059 [[Gencom]]: [2 9/8; 65/64 81/80 91/90] Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|] Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] EDOs: 6, 7, 13, 19, 25e, 44de [[Tp tuning#T2%20tuning|RMS error]]: 2.003 cents [[image:deutone_44edo.png]] [[xenharmonic/deutone6|Six note haplotonic scale]] [[xenharmonic/deutone7|seven note albitonic scale]] [[xenharmonic/deutone13|Thirteen note chromatic scale]] =Supraphon= Subgroup: 2.3.7.11.13 Commas: 64/63, 78/77, 99/98 [[Tp tuning|POT2 generator]]: ~3/2 = 706.137 [[Gencom]]: [2 3/2; 64/63 78/77 99/98] Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|] Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] EDOs: 5, 7, 12, 17 [[Tp tuning#T2%20tuning|RMS error]]: 2.095 cents =Negra= Subgroup: 2.3.5.7.13 Commas: 49/48, 65/64, 91/90 Related temperament: [[Marvel temperaments#Negri-13-limit|negri]] [[Tp tuning|POT2 generator]]: ~14/13~13/12 = 125.567 cents [[Gencom]]: [2 14/13; Gencom map: [<1 2 2 3 0 4|, <0 -4 3 -2 0 -3|] Map: [<1 2 2 3 4|, <0 -4 3 -2 -3|] EDOs: 9, 10, 19, 29, 67cd*f, 86cd*f [[Tp tuning#T2%20tuning|RMS error]]: 2.147 cents =Joan= Subgroup: 2.9.5.7.11 Commas: 81/80, 99/98, 9317/9216 Related temperaments: casablanca, euterpe [[Tp tuning|POT2 generator]]: ~11/8 = 541.703 cents Gencom: [2 11/8; 81/80 99/98 9317/9216] Gencom map: [<1 0 -4 1 3|, <0 7/2 14 4 1|] Map: [<1 0 -4 1 3|, <0 7 14 4 1|] EDOs: 11, 20, 31, 113be, 144be [[Tp tuning#T2%20tuning|RMS error]]: 2.176 cents [[xenharmonic/joan5|Five note haplotonic scale]] [[xenharmonic/joan7|Seven note albitonic scale]] [[xenharmonic/joan9|Nine note mega albitonic scale]] [[xenharmonic/joan11|Eleven note chromatic scale]] =Porkypine= Subgroup: 2.3.5.11 Commas: 55/54, 100/99 [[Tp tuning|POT2 generator]]: ~10/9 = 164.078 [[Gencom]]: [2 10/9; 55/54 100/99] Gencom map: [<1 2 3 0 4|], <0 -3 -5 0 -4|] Map: [<1 2 3 4|, <0 3 5 4|] EDOs: 7, 15, 22, 73cd, 95cd, 117bcd, 256bcdd [[Tp tuning#T2%20tuning|RMS error]]: 2.287 cents [[xenharmonic/porkypine7|Seven note haplotonic scale]] [[xenharmonic/porkypine8|Eight note albitonic scale]] [[xenharmonic/porkypine15|Fifteen note chromatic scale]] =Skateboard= Subgroup: 2.5/3.7/3.11.13/9 Commas: 56/55, 91/90, 100/99 Related temperament: [[Starling family#Thrasher-13-limit|thrasher]] [[Tp tuning|POT2 generator]]: ~6/5 = 313.842 [[Gencom]]: [2 6/5; 56/55 91/90 100/99] Gencom map: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|] Map: [<1 0 -1 2 2|, <0 1 3 2 -2|] EDOs: 11, 15, 19, 23, 42d, 65d [[Tp tuning#T2%20tuning|RMS error]]: 2.396 cents [[xenharmonic/skateboard7|Seven note haplotonic scale]] [[xenharmonic/skateboard11|Eleven note albitonic scale]] [[xenharmonic/skateboard15|Fifteen note chromatic scale]] =Augment= Subgroup: 2.5.7.11 Commas: 56/55, 128/125 Related temperament: [[xenharmonic/Augmented family|augmented]] [[Tp tuning|POT2 generator]]: ~8/7 = 228.275 [[Gencom]]: [5/4 8/7; 56/55 128/125] Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|] Map: [<3 7 0 2|, <0 0 1 1|] EDOs: 3, 6, 9, 15, 21 [[Tp tuning#T2%20tuning|RMS error]]: 2.422 cents [[image:augment_21edo.png]] [[xenharmonic/augment6|Six note haplotonic scale]] [[xenharmonic/augment9|Nine note albitonic scale]] [[xenharmonic/augment12|Twelve note chromatic scale]] =Semaphore= Subgroup: 2.3.7 Comma: 49/48 [[Tp tuning|POT2 generator]]: ~7/6 = 250.385 [[Gencom]]: [2 7/6; 49/48] Gencom map: [<1 2 0 3}, <0 -2 0 -1|] Map: [<1 0 2|, <0 2 1|] EDOs: 5, 9, 14, 19, 24, 67c, 91c [[Tp tuning#T2%20tuning|RMS error]]: 2.523 cents [[image:semaphore_24edo.png]] [[xenharmonic/semiphore5|Five note haplotonic scale]] [[xenharmonic/semiphore9|Nine note albitonic scale]] [[xenharmonic/semiphore14|Fourteen note chromatic scale]] =Kryptonite= Subgroup: 2.5.7/3.11/3.13/3 Commas: 56/55, 78/77, 91/90 Related temperaments: [[Sengic family|krypton]] [[Tp tuning|POT2 generator]]: ~13/12 = 132.428 [[Gencom]]: [2 13/12; 56/55 78/77 91/90] Gencom map: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|] Map: [<1 2 1 2 2|, <0 -3 -2 1 -1|] EDOs: 9, 63, 82bd, 91bde [[Tp tuning#T2%20tuning|RMS error]]: 2.545 cents [[kryptonite9|Nine note albitonic scale]] [[kryptonite10|Ten note albitonic scale]] [[kryptonite19|Nineteen note mega chromatic scale]] =Oregon= Subgroup: 2.9.15.7.11 Commas: 55/54, 64/63, 100/99 [[Tp tuning|POT2 generator]]: ~6/5 = 325.495 [[Gencom]]: [2 6/5; 55/54 64/63 100/99] Gencom map: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|] Map: [<1 1 1 5 2|, <0 3 4 -3 2|] EDOs: 7, 11, 37b, 48b, 59b [[Tp tuning#T2%20tuning|RMS error]]: 2.550 cents [[xenharmonic/oregon7|Seven note haplotonic scale]] [[xenharmonic/oregon11|Eleven note albitonic scale]] [[xenharmonic/oregon15|Fifteen note chromatic scale]] =Antikythera= Subgroup: 2.9.5.7 Commas: 50/49, 64/63 Related temperament: [[xenharmonic/pajara|pajara]] [[Tp tuning|POT2 generator]]: ~8/7 = 214.095 [[Gencom]]: [7/5 8/7; 50/49 64/63] Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|] Map: [<2 0 11 12|, <0 1 -1 -1|] EDOS: 4, 6, 10, 16, 22, 28 [[Tp tuning#T2%20tuning|RMS error]]: 2.572 cents [[image:antikythera_28edo.png]] [[xenharmonic/antikythera6|Six note haplotonic scale]] [[xenharmonic/antikythera10|Ten note albitonic scale]] [[xenharmonic/antikythera16|Sixteen note chromatic scale]] =Glacial= Subgroup: 2.9.5.11.13 Commas: 45/44, 65/64, 81/80 [[Tp tuning|POT2 generator]]: ~9/8 = 186.151 [[Gencom]]: [2 9/8; 45/44 65/64 81/80] Gencom map: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|] Map: [<1 0 -4 -6 10|, <0 1 2 3 -2|] EDOs: 6, 13, 45be, 58bce, 71bce, 84bce [[Tp tuning#T2%20tuning|RMS error]]: 2.887 cents [[glacial6|Six note haplotonic scale]] [[glacial7|Seven note albitonic scale]] [[glacial13|Thirteen note chromatic scale]] =Leantone= Subgroup: 2.9.5.7.11 Commas: 45/44, 56/55, 81/80 Related temperament: [[meanenneadecal]] [[Tp tuning|POT2 generator]]: ~9/8 = 192.500 [[Gencom]]: [2 9/8; 45/44 56/55 81/80] Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|] Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] EDOs: 6, 7, 13, 19, 25, 31, 56, 81 [[Tp tuning#T2%20tuning|RMS error]]: 3.882 cents [[image:leantone_81edo.png]] [[xenharmonic/leantone6|Six note haplotonic scale]] [[xenharmonic/leantone7|Seven note albitonic scale]] [[xenharmonic/leantone13|Thirteen note chromatic scale]]
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<html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:165:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --> | <a href="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --> | <a href="#Barton">Barton</a><!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --> | <a href="#Haumea">Haumea</a><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --> | <a href="#Neutraltet">Neutraltet</a><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --> | <a href="#Tobago">Tobago</a><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --> | <a href="#Wizz">Wizz</a><!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --> | <a href="#Penta">Penta</a><!-- ws:end:WikiTextTocRule:187 --><!-- ws:start:WikiTextTocRule:188: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:188 --><!-- ws:start:WikiTextTocRule:189: --> | <a href="#Edson">Edson</a><!-- ws:end:WikiTextTocRule:189 --><!-- ws:start:WikiTextTocRule:190: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:190 --><!-- ws:start:WikiTextTocRule:191: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:191 --><!-- ws:start:WikiTextTocRule:192: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:192 --><!-- ws:start:WikiTextTocRule:193: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:193 --><!-- ws:start:WikiTextTocRule:194: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:194 --><!-- ws:start:WikiTextTocRule:195: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:195 --><!-- ws:start:WikiTextTocRule:196: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:196 --><!-- ws:start:WikiTextTocRule:197: --> | <a href="#Gariberttet">Gariberttet</a><!-- ws:end:WikiTextTocRule:197 --><!-- ws:start:WikiTextTocRule:198: --> | <a href="#Namo">Namo</a><!-- ws:end:WikiTextTocRule:198 --><!-- ws:start:WikiTextTocRule:199: --> | <a href="#Sentry">Sentry</a><!-- ws:end:WikiTextTocRule:199 --><!-- ws:start:WikiTextTocRule:200: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:200 --><!-- ws:start:WikiTextTocRule:201: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:201 --><!-- ws:start:WikiTextTocRule:202: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:202 --><!-- ws:start:WikiTextTocRule:203: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:203 --><!-- ws:start:WikiTextTocRule:204: --><!-- ws:end:WikiTextTocRule:204 --><!-- ws:start:WikiTextTocRule:205: --> | <a href="#Starlingtet">Starlingtet</a><!-- ws:end:WikiTextTocRule:205 --><!-- ws:start:WikiTextTocRule:206: --> | <a href="#Lovecraft">Lovecraft</a><!-- ws:end:WikiTextTocRule:206 --><!-- ws:start:WikiTextTocRule:207: --> | <a href="#Laz">Laz</a><!-- ws:end:WikiTextTocRule:207 --><!-- ws:start:WikiTextTocRule:208: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:208 --><!-- ws:start:WikiTextTocRule:209: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:209 --><!-- ws:start:WikiTextTocRule:210: --><!-- ws:end:WikiTextTocRule:210 --><!-- ws:start:WikiTextTocRule:211: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:211 --><!-- ws:start:WikiTextTocRule:212: --> | <a href="#Mothwelltri">Mothwelltri</a><!-- ws:end:WikiTextTocRule:212 --><!-- ws:start:WikiTextTocRule:213: --> | <a href="#Sulis">Sulis</a><!-- ws:end:WikiTextTocRule:213 --><!-- ws:start:WikiTextTocRule:214: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:214 --><!-- ws:start:WikiTextTocRule:215: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:215 --><!-- ws:start:WikiTextTocRule:216: --> | <a href="#Magicaltet">Magicaltet</a><!-- ws:end:WikiTextTocRule:216 --><!-- ws:start:WikiTextTocRule:217: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:217 --><!-- ws:start:WikiTextTocRule:218: --><!-- ws:end:WikiTextTocRule:218 --><!-- ws:start:WikiTextTocRule:219: --> | <a href="#Kiribati">Kiribati</a><!-- ws:end:WikiTextTocRule:219 --><!-- ws:start:WikiTextTocRule:220: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:220 --><!-- ws:start:WikiTextTocRule:221: --> | <a href="#Sensation">Sensation</a><!-- ws:end:WikiTextTocRule:221 --><!-- ws:start:WikiTextTocRule:222: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:222 --><!-- ws:start:WikiTextTocRule:223: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:223 --><!-- ws:start:WikiTextTocRule:224: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:224 --><!-- ws:start:WikiTextTocRule:225: --><!-- ws:end:WikiTextTocRule:225 --><!-- ws:start:WikiTextTocRule:226: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:226 --><!-- ws:start:WikiTextTocRule:227: --> | <a href="#Stacks">Stacks</a><!-- ws:end:WikiTextTocRule:227 --><!-- ws:start:WikiTextTocRule:228: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:228 --><!-- ws:start:WikiTextTocRule:229: --> | <a href="#Sephiroth">Sephiroth</a><!-- ws:end:WikiTextTocRule:229 --><!-- ws:start:WikiTextTocRule:230: --> | <a href="#Archy">Archy</a><!-- ws:end:WikiTextTocRule:230 --><!-- ws:start:WikiTextTocRule:231: --> | <a href="#Suhajira">Suhajira</a><!-- ws:end:WikiTextTocRule:231 --><!-- ws:start:WikiTextTocRule:232: --> | <a href="#Mohoho">Mohoho</a><!-- ws:end:WikiTextTocRule:232 --><!-- ws:start:WikiTextTocRule:233: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:233 --><!-- ws:start:WikiTextTocRule:234: --> | <a href="#Machine">Machine</a><!-- ws:end:WikiTextTocRule:234 --><!-- ws:start:WikiTextTocRule:235: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:235 --><!-- ws:start:WikiTextTocRule:236: --> | <a href="#Supraphon">Supraphon</a><!-- ws:end:WikiTextTocRule:236 --><!-- ws:start:WikiTextTocRule:237: --> | <a href="#Negra">Negra</a><!-- ws:end:WikiTextTocRule:237 --><!-- ws:start:WikiTextTocRule:238: --> | <a href="#Joan">Joan</a><!-- ws:end:WikiTextTocRule:238 --><!-- ws:start:WikiTextTocRule:239: --> | <a href="#Porkypine">Porkypine</a><!-- ws:end:WikiTextTocRule:239 --><!-- ws:start:WikiTextTocRule:240: --> | <a href="#Skateboard">Skateboard</a><!-- ws:end:WikiTextTocRule:240 --><!-- ws:start:WikiTextTocRule:241: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:241 --><!-- ws:start:WikiTextTocRule:242: --> | <a href="#Semaphore">Semaphore</a><!-- ws:end:WikiTextTocRule:242 --><!-- ws:start:WikiTextTocRule:243: --> | <a href="#Kryptonite">Kryptonite</a><!-- ws:end:WikiTextTocRule:243 --><!-- ws:start:WikiTextTocRule:244: --> | <a href="#Oregon">Oregon</a><!-- ws:end:WikiTextTocRule:244 --><!-- ws:start:WikiTextTocRule:245: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:245 --><!-- ws:start:WikiTextTocRule:246: --> | <a href="#Glacial">Glacial</a><!-- ws:end:WikiTextTocRule:246 --><!-- ws:start:WikiTextTocRule:247: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:247 --><!-- ws:start:WikiTextTocRule:248: --> <!-- ws:end:WikiTextTocRule:248 --><!-- 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 <a class="wiki_link" href="/Tp%20tuning#T2 tuning">RMS error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<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="/Tp%20tuning">POT2 generator</a>: ~10/9 = 182.461<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [63/50 10/9; 250047/250000]<br /> Gencom map: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|]<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 /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.00844 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 /> <!-- ws:start:WikiTextLocalImageRule:250:<img src="/file/view/terrain_3558edo.png/284858244/terrain_3558edo.png" alt="" title="" /> --><img src="/file/view/terrain_3558edo.png/284858244/terrain_3558edo.png" alt="terrain_3558edo.png" title="terrain_3558edo.png" /><!-- ws:end:WikiTextLocalImageRule:250 --><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 /> <a class="wiki_link_ext" href="http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/" rel="nofollow">5 5 1 mode of 33 equal (with video)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/33edo/20130827_551of33.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:5:<h1> --><h1 id="toc2"><a name="Petrtri"></a><!-- ws:end:WikiTextHeadingRule:5 -->Petrtri</h1> Subgroup: 2.11/5.13/5<br /> Comma: 2200/2197<br /> Svalname: 3&5<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/10 = 455.012<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/10; 2200/2197]<br /> Gencom map: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|]<br /> <br /> Map: [<1 0 1|, <0 3 1|]<br /> EDOs: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0749 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:251:<img src="/file/view/petrtri_385edo.png/284586314/petrtri_385edo.png" alt="" title="" /> --><img src="/file/view/petrtri_385edo.png/284586314/petrtri_385edo.png" alt="petrtri_385edo.png" title="petrtri_385edo.png" /><!-- ws:end:WikiTextLocalImageRule:251 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:7:<h1> --><h1 id="toc3"><a name="Barton"></a><!-- ws:end:WikiTextHeadingRule:7 -->Barton</h1> Subgroup: 2.5.11.13<br /> Commas: 2200/2197, 6656/6655<br /> Svalname: 11&13<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/8 = 551.699<br /> <br /> Gencom: [2 11/8; 2200/2197 6656/6655]<br /> Gencom map: [<1 0 6 0 3 6|, <0 0 -8 0 1 -5|]<br /> <br /> Map: [<1 6 3 6|, <0 -8 1 -5|]<br /> EDOs: 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0822 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/barton5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/barton7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/barton9">Nine note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/barton11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/barton13">Thirteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:9:<h1> --><h1 id="toc4"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:9 -->Tridec</h1> Subgroup: 2.7/5.11/5.13/5<br /> Commas: 847/845, 1001/1000<br /> Sval name: 5&8<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/10 = 454.556<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/10; 847/845 1001/1000]<br /> Gencom map: [<1 0 -3/4 5/4 -3/4 1/4|, <0 0 0 -4 3 1|]<br /> <br /> Map: [<1 2 0 1|, <0 -4 3 1|]<br /> EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.1613 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:252:<img src="/file/view/tridec_235edo.png/284860428/tridec_235edo.png" alt="" title="" /> --><img src="/file/view/tridec_235edo.png/284860428/tridec_235edo.png" alt="tridec_235edo.png" title="tridec_235edo.png" /><!-- ws:end:WikiTextLocalImageRule:252 --><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:11:<h1> --><h1 id="toc5"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:11 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 701.746<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 361/360 513/512]<br /> Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 0 -3|]<br /> <br /> Map: [<1 0 15 9|, <0 1 -8 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 118, 171, 460d, 631d<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.1763 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:253:<img src="/file/view/nestoria_171edo.png/284862598/nestoria_171edo.png" alt="" title="" /> --><img src="/file/view/nestoria_171edo.png/284862598/nestoria_171edo.png" alt="nestoria_171edo.png" title="nestoria_171edo.png" /><!-- ws:end:WikiTextLocalImageRule:253 --><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 /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria17">Seventeen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:13:<h1> --><h1 id="toc6"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:13 -->Orgone</h1> Subgroup: 2.7.11<br /> Commas: 65536/65219<br /> Svals: 4&7<br /> Related temperament: <a class="wiki_link" href="/Gamelismic%20clan#superkleismic">superkleismic</a><br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~77/64 = 323.372<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 77/64; 65536/65219]<br /> Gencom map: [<1 0 0 2 4|, <0 0 0 3 -2|]<br /> <br /> Map: [<1 2 4|, <0 3 -2|]<br /> EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.1888 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:254:<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:254 --><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:15:<h1> --><h1 id="toc7"><a name="Marveltwintri"></a><!-- ws:end:WikiTextHeadingRule:15 -->Marveltwintri</h1> Subgroup: 2.5/3.13/9<br /> Comma: 325/324<br /> Svalname: 3&4<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 317.139<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 325/324]<br /> Gencom map: [<1 -1/6 5/6 0 0 -1/3|, <0 -1/2 -3/2 0 0 1|]<br /> <br /> Map: [<1 0 2|, <0 1 -2|]<br /> EDOs: 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2444 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:255:<img src="/file/view/marveltwintri_321edo.png/284588650/marveltwintri_321edo.png" alt="" title="" /> --><img src="/file/view/marveltwintri_321edo.png/284588650/marveltwintri_321edo.png" alt="marveltwintri_321edo.png" title="marveltwintri_321edo.png" /><!-- ws:end:WikiTextLocalImageRule:255 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltwintri7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltwintri11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltwintri15">Fifteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:17:<h1> --><h1 id="toc8"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:17 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 317.076<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 325/324 625/624]<br /> Gencom map: [<1 0 1 0 0 0|, <0 6 5 0 0 14|]<br /> <br /> Map: [<1 0 1 0|, <0 6 5 14|]<br /> EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2450 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:256:<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:256 --><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:19:<h1> --><h1 id="toc9"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:19 -->Bridgetown</h1> Subgroup: 2.3.11/5.13/5<br /> Commas: 352/351, 676/675<br /> Sval name: 5&24<br /> Related temperaments: <a class="wiki_link" href="/Chromatic%20pairs#Haumea">haumea</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barbados</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~15/13 = 248.399<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 15/13; 352/351 676/675]<br /> Gencom map: [<1 2 -5/3 0 4/3 1/3|, <0 -2 4 0 -5 1|]<br /> <br /> Map: [<1 0 -6 -1|, <0 2 9 3|]<br /> EDOs: 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2513 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:257:<img src="/file/view/bridgetown_29edo.png/284859430/bridgetown_29edo.png" alt="" title="" /> --><img src="/file/view/bridgetown_29edo.png/284859430/bridgetown_29edo.png" alt="bridgetown_29edo.png" title="bridgetown_29edo.png" /><!-- ws:end:WikiTextLocalImageRule:257 --><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:21:<h2> --><h2 id="toc10"><a name="Bridgetown-Music"></a><!-- ws:end:WikiTextHeadingRule:21 -->Music</h2> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Igliashon%20Jones">Igliashon Jones</a><br /> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3" rel="nofollow">Route 14 in Bridgetown</a></span></span> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:23:<h1> --><h1 id="toc11"><a name="Haumea"></a><!-- ws:end:WikiTextHeadingRule:23 -->Haumea</h1> Subgroup: 2.3.7/5.11/5.13/5<br /> Commas: 352/351, 676/675, 847/845<br /> Related temperaments: <a class="wiki_link" href="/Chromatic%20pairs#Bridgetown">bridgetown</a>, <a class="wiki_link" href="/Hemifamity%20family#Namaka">namaka</a>, hemigari, barbados, parizekmic<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~15/13 = 248.491<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 15/13; 352/351 676/675 847/845]<br /> Gencom map: [<1 2 -3/4 -11/4 9/4 5/4|, <0 -2 0 12 -9 -3|]<br /> <br /> Map: [<1 0 10 -6 -1|, <0 2 -12 9 3|]<br /> EDOs: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2668 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea14">Fourteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:25:<h1> --><h1 id="toc12"><a name="Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:25 -->Neutraltet</h1> Subgroup: 2.3.11<br /> Commas: 243/242<br /> Svalname: 7&17<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 350.525<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 243/242]<br /> Gencom map: [<1 1 0 0 2|, <0 2 0 0 5|]<br /> <br /> Map: [<1 1 2|, <0 2 5|]<br /> EDOs: 7, 17, 24, 65, 89, 202, 291, 380<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3021 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:258:<img src="/file/view/neutraltet_380edo.png/284587504/neutraltet_380edo.png" alt="" title="" /> --><img src="/file/view/neutraltet_380edo.png/284587504/neutraltet_380edo.png" alt="neutraltet_380edo.png" title="neutraltet_380edo.png" /><!-- ws:end:WikiTextLocalImageRule:258 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10">Ten note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:27:<h2> --><h2 id="toc13"><a name="Neutraltet-Music"></a><!-- ws:end:WikiTextHeadingRule:27 -->Music</h2> <a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow">Mo - Happy - Happy</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow">play</a> by Jake Freivald in Neutraltet[7], 24et tuning<br /> <br /> <!-- ws:start:WikiTextHeadingRule:29:<h1> --><h1 id="toc14"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:29 -->Slendric</h1> Subgroup: 2.3.7<br /> Comma: 1029/1024<br /> Sval name: 5&21<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~8/7 = 233.688<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 1029/1024]<br /> Gencom map: [<1 1 0 3|, <0 3 0 -1|]<br /> <br /> Map: [<1 1 3|, <0 3 -1|]<br /> EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3202 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:259:<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:259 --><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:31:<h2> --><h2 id="toc15"><a name="Slendric-Music"></a><!-- ws:end:WikiTextHeadingRule:31 -->Music</h2> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span><br /> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/tuning-survey/daily20111026-16-slendric-virgins.mp3" rel="nofollow">16 Slendric Virgins</a></span></span><br /> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Chris%20Vaisvil">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:33:<h1> --><h1 id="toc16"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:33 -->Huntington</h1> Subgroup: 2.5.7.13<br /> Commas: 640/637, 10985/10976<br /> Sval name: 10&27<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~16/13 = 357.002<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 16/13; 640/637 10985/10976]<br /> Gencom map: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|]<br /> <br /> Map: [<1 5 4 4|, <0 -9 -4 -1|]<br /> EDOs: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3452 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:260:<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:260 --><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:35:<h1> --><h1 id="toc17"><a name="Tobago"></a><!-- ws:end:WikiTextHeadingRule:35 -->Tobago</h1> Subgroup: 2.3.11.13/5<br /> Commas: 243/242, 676/675<br /> Sval name: 10&14<br /> Related temperaments: <a class="wiki_link" href="/Chromatic%20pairs#Neutraltet">neutraltet</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barbados</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~15/13 = 249.312<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [55/39 15/13; 243/242 676/675]<br /> Gencom map: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|]<br /> <br /> Map: [<2 0 -1 -2], <0 2 5 3]]<br /> EDOs: 10, 14, 24, 58, 82, 130<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3533 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tobago6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tobago10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tobago14">Fourteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tobago24">Twentyfour note quatertone scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:37:<h1> --><h1 id="toc18"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:37 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 703.856<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 352/351 364/363]<br /> Gencom map: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|]<br /> <br /> Map: [<1 0 7 12|, <0 1 -4 -7|]<br /> EDOs: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3789 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:261:<img src="/file/view/pepperoni_271edo.png/284861296/pepperoni_271edo.png" alt="" title="" /> --><img src="/file/view/pepperoni_271edo.png/284861296/pepperoni_271edo.png" alt="pepperoni_271edo.png" title="pepperoni_271edo.png" /><!-- ws:end:WikiTextLocalImageRule:261 --><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:39:<h1> --><h1 id="toc19"><a name="Wizz"></a><!-- ws:end:WikiTextHeadingRule:39 -->Wizz</h1> Subgroup: 2.5.11<br /> Commas: 15625/15488<br /> Sval name: 6&16<br /> Related temperaments: <a class="wiki_link" href="/Marvel%20temperaments#Wizard-11-limit">wizard</a><br /> <br /> Generator: ~5/4 = 383.768<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [125/88 5/4; 15625/15488]<br /> Gencom map: [<2 0 4 0 5| <0 0 1 0 3|]<br /> <br /> Map: [<2 0 -7|, <0 1 3|]<br /> EDOs: 6, 16, 22, 28, 50, 122, 172, 222<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3997<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/wizz6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/wizz10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/wizz16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:41:<h1> --><h1 id="toc20"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:41 -->Bossier</h1> Subgroup: 2.7.11.13<br /> Commas: 1573/1568, 15488/15379<br /> Sval name: 3&17<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~14/11 = 421.309<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 14/11; 1573/1568 15488/15379]<br /> Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]<br /> <br /> Map: [<1 0 1 3|, <0 8 7 2|]<br /> EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4043 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:262:<img src="/file/view/bossier_225edo.jpg/271202010/bossier_225edo.jpg" alt="" title="" /> --><img src="/file/view/bossier_225edo.jpg/271202010/bossier_225edo.jpg" alt="bossier_225edo.jpg" title="bossier_225edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:262 --><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:43:<h1> --><h1 id="toc21"><a name="Penta"></a><!-- ws:end:WikiTextHeadingRule:43 -->Penta</h1> Subgroup: 2.9.7.11<br /> Commas: 896/891, 26411/26244<br /> Svalname: 8&11<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 438.465<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 896/891 26411/26244]<br /> Gencom map: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]<br /> <br /> Map: [<1 0 -1 6|, <0 5 6 -4|]<br /> EDOs: 8, 11, 30, 41, 52<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4262 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:45:<h1> --><h1 id="toc22"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:45 -->Marveltri</h1> Subgroup: 2.5.9/7<br /> Comma: 225/224<br /> Sval name: 3&13<br /> Related temperaments: marvel, 22&47, magic<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~5/4 = 383.638<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 225/224]<br /> Gencom map: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]<br /> <br /> Map: [<1 0 5|, <0 1 -2|]<br /> EDOs: 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4801 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri10">Ten note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri13">Thirteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:47:<h1> --><h1 id="toc23"><a name="Edson"></a><!-- ws:end:WikiTextHeadingRule:47 -->Edson</h1> Subgroup: 2.3.7/5.11/5.13/5<br /> Commas: 196/195, 352/351, 364/363<br /> Related temperaments: <a class="wiki_link" href="/Hemifamity%20family#Pele">pele</a>, cassandra<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 703.414<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 196/195, 352/351, 364/363]<br /> Gencom map: [<1 1 -5 -1 2 4|, <0 1 29/4 5/4 -11/4 -23/4|]<br /> <br /> Map: [<1 0 10 17 22|, <0 1 -6 -10 -13|]<br /> EDOs: 12, 17, 29, 621bcde<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5102 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/edson5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/edson7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/edson12">Twelve note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/edson17">Seventeen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:49:<h1> --><h1 id="toc24"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:49 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 701.470<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 171/170 256/255 324/323]<br /> Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|]<br /> <br /> Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5374 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:263:<img src="/file/view/photia_65edo.png/284863542/photia_65edo.png" alt="" title="" /> --><img src="/file/view/photia_65edo.png/284863542/photia_65edo.png" alt="photia_65edo.png" title="photia_65edo.png" /><!-- ws:end:WikiTextLocalImageRule:263 --><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:51:<h1> --><h1 id="toc25"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:51 -->Shoe</h1> Subgroup: 2.5.7.11.13<br /> Commas: 176/175, 640/637, 847/845<br /> Sval name: 16&21<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~8/7 = 227.108<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 176/175 640/637 847/845]<br /> Gencom map: [<1 0 1 3 1 2|, <0 0 7 -1 13 9|]<br /> <br /> Map: [<1 1 3 1 2|, <0 7 -1 13 9|]<br /> EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5433 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:264:<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:264 --><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:53:<h1> --><h1 id="toc26"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:53 -->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/W%C3%BCrschmidt%20family">Hemiwürschmidt</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~28/25 = 194.594<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 28/25; 176/175 1375/1372 640/637]<br /> Gencom map: [<1 0 2 2 2 5|, <0 0 2 5 9 -8|]<br /> <br /> Map: [<1 0 -3 -7 13|, <0 2 5 9 -8|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 37<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5567 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:265:<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:265 --><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:55:<h1> --><h1 id="toc27"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:55 -->Silver</h1> Subgroup: 2.5.7.13.17<br /> Commas: 170/169, 640/637, 5525/5488<br /> Sval name: 10&27<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/8 = 842.711<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/8; 170/169 640/637 5525/5488]<br /> Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]<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, 178e, 309cde, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487bcdee</a><br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5886 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:266:<img src="/file/view/silver_487edo.jpg/271264440/silver_487edo.jpg" alt="" title="" /> --><img src="/file/view/silver_487edo.jpg/271264440/silver_487edo.jpg" alt="silver_487edo.jpg" title="silver_487edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:266 --><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:57:<h1> --><h1 id="toc28"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:57 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 204.090<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 225/224 325/324 640/637]<br /> Gencom map: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]<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>, 488cd, 635cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5999 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:267:<img src="/file/view/baldy_147edo.jpg/271199372/baldy_147edo.jpg" alt="" title="" /> --><img src="/file/view/baldy_147edo.jpg/271199372/baldy_147edo.jpg" alt="baldy_147edo.jpg" title="baldy_147edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:267 --><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:59:<h1> --><h1 id="toc29"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:59 -->Guanyintet</h1> Subgroup: 2.5.7/3.11/3<br /> Commas: 176/175, 540/539<br /> Svalname: 4&9<br /> Related temperaments: guanyin, orwell<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~7/6 = 270.093<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 176/175 540/539]<br /> Gencom map: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|]<br /> <br /> Map: [<1 0 2 -2|, <0 3 -1 5|]<br /> EDOs: 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6028 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:61:<h1> --><h1 id="toc30"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:61 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~8/7 = 234.381<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 896/891 1029/1024]<br /> Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|]<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6502 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:268:<img src="/file/view/radon_128edo.jpg/271207646/radon_128edo.jpg" alt="" title="" /> --><img src="/file/view/radon_128edo.jpg/271207646/radon_128edo.jpg" alt="radon_128edo.jpg" title="radon_128edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:268 --><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:63:<h1> --><h1 id="toc31"><a name="Gariberttet"></a><!-- ws:end:WikiTextHeadingRule:63 -->Gariberttet</h1> Subgroup: 2.5/3.7/3.13/11<br /> Commas: 275/273, 847/845<br /> Svalname: 4&29<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/11 = 293.679<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/11; 275/273 847/845]<br /> Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|]<br /> <br /> Map: [<1 0 0 0|, <0 3 5 1|]<br /> EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6914 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:65:<h1> --><h1 id="toc32"><a name="Namo"></a><!-- ws:end:WikiTextHeadingRule:65 -->Namo</h1> Subgroup: 2.3.11.13<br /> Commas: 144/143, 243/242<br /> Related temperament: <a class="wiki_link" href="/Valinorismic%20temperaments#Mandos">mandos</a>, mohajira, hemif<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 351.488<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242]<br /> Gencom map: [<1 1 0 0 2 4|, <0 2 0 0 5 -1|]<br /> <br /> Map: [<1 1 2 4|, <0 2 5 -1|]<br /> EDOs: 7, 10, 17, 41, 58, 99cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7038 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/namo7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/namo10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/namo17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:67:<h1> --><h1 id="toc33"><a name="Sentry"></a><!-- ws:end:WikiTextHeadingRule:67 -->Sentry</h1> Group: 2.5/3.9/7<br /> Commas: 245/243<br /> Svalname: 3&5<br /> Related temperaments: sensi<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 440.902<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 245/243]<br /> Gencom map: [<1 0 0 0|, <0 0 2 -1|]<br /> <br /> Map: [<1 0 0|, <0 2 1|]<br /> EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7105 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sentry5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sentry8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sentry11">Eleven note note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:69:<h1> --><h1 id="toc34"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:69 -->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>, namo<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 351.691<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br /> Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7167 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:269:<img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="" title="" /> --><img src="/file/view/hemif_58edo.jpg/272176886/hemif_58edo.jpg" alt="hemif_58edo.jpg" title="hemif_58edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:269 --><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:71:<h1> --><h1 id="toc35"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:71 -->Garibaldi</h1> Group: 2.3.5.7<br /> Commas: 225/224, 3125/3087<br /> Val name: 12&29<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 702.085<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 225/224 3125/3087]<br /> Gencom map: [<1 1 7 11], <0 1 -8 -14|]<br /> <br /> Map: [<1 0 15 25|, <0 1 -8 -14|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 94, 241c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7257 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:270:<img src="/file/view/garibaldi_94edo.png/284865722/garibaldi_94edo.png" alt="" title="" /> --><img src="/file/view/garibaldi_94edo.png/284865722/garibaldi_94edo.png" alt="garibaldi_94edo.png" title="garibaldi_94edo.png" /><!-- ws:end:WikiTextLocalImageRule:270 --><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:73:<h1> --><h1 id="toc36"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:73 -->Mabila</h1> Subgroup: 2.5.7<br /> Comma: 1071875/1048576<br /> Sval name: 7&9<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~175/128 = 527.236<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 175/128; 1071875/1048576]<br /> Gencom map: [<1 0 1 5}, <0, 0, 3, -5|]<br /> <br /> Map: [<1 1 5|, <0 3 -5|]<br /> EDOs: 7, 9, 16, 25, 41, 66, 305bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7729 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:271:<img src="/file/view/mabila_66edo.jpg/271267504/mabila_66edo.jpg" alt="" title="" /> --><img src="/file/view/mabila_66edo.jpg/271267504/mabila_66edo.jpg" alt="mabila_66edo.jpg" title="mabila_66edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:271 --><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:75:<h1> --><h1 id="toc37"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:75 -->Indium</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 3025/3024, 3125/3087<br /> Sval name: 8&33<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~12/11 = 147.010<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 12/11; 3025/3024 3125/3087]<br /> Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|]<br /> <br /> Map: [<1 0 0 2|, <0 6 10 -1|]<br /> EDOs: 33, 41, 49, 57, 106, 204, 253<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7788 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:272:<img src="/file/view/indium_253edo.png/284867050/indium_253edo.png" alt="" title="" /> --><img src="/file/view/indium_253edo.png/284867050/indium_253edo.png" alt="indium_253edo.png" title="indium_253edo.png" /><!-- ws:end:WikiTextLocalImageRule:272 --><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 /> <!-- ws:start:WikiTextHeadingRule:77:<h2> --><h2 id="toc38"><a name="Indium-Music"></a><!-- ws:end:WikiTextHeadingRule:77 -->Music</h2> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3" rel="nofollow">The Cry of Indium</a></span></span> (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:79:<h1> --><h1 id="toc39"><a name="Starlingtet"></a><!-- ws:end:WikiTextHeadingRule:79 -->Starlingtet</h1> Group: 2.5/3.7/3<br /> Comma: 126/125<br /> Svalname: 4&15<br /> Related temperaments: starling; becomes myna<br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 311.154<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125]<br /> Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]<br /> <br /> Map: [<1 0 -1|, <0 1 3|]<br /> EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.8398 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4">Four note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:81:<h1> --><h1 id="toc40"><a name="Lovecraft"></a><!-- ws:end:WikiTextHeadingRule:81 -->Lovecraft</h1> Group: 2.11.13<br /> Commas: 1352/1331<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/11 = 279.318<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/11; 1352/1331]<br /> Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]<br /> <br /> Map: [<1 1 0|, <0 2 3|]<br /> EDOS: 13, 30, 43, 73, 116b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.8449 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:273:<img src="/file/view/lovecraft_116edo.png/284590430/lovecraft_116edo.png" alt="" title="" /> --><img src="/file/view/lovecraft_116edo.png/284590430/lovecraft_116edo.png" alt="lovecraft_116edo.png" title="lovecraft_116edo.png" /><!-- ws:end:WikiTextLocalImageRule:273 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/lovecraft13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:83:<h1> --><h1 id="toc41"><a name="Laz"></a><!-- ws:end:WikiTextHeadingRule:83 -->Laz</h1> Subgroup: 2.5.7/3.11/3.13/3<br /> Commas: 144/143, 176/175, 196/195<br /> Related temperaments: <a class="wiki_link" href="/Orwellismic%20family#Guanyin-Georgian">georgian</a>, winston<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~7/6 = 269.300<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 144/143 176/175 196/195]<br /> Gencom map: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|]<br /> <br /> Map: [<1 0 2 -2 6|, <0 3 -1 5 -5|]<br /> EDOs: 9, 31, 40, 49, 58, 156bde, 205bde<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.8790 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/laz5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/laz9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/laz13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:85:<h1> --><h1 id="toc42"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:85 -->Myna</h1> Group: 2.3.5.7<br /> Commas: 126/125, 1728/1715<br /> Val name: 4&27<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 310.146<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125 1728/1715]<br /> Gencom map: [<1 -1 0 1|,<0 10 9 7|]<br /> <br /> Map: [<1 9 9 8|, <0 -10 -9 -7|]<br /> EDOs: 4, 27, 31, 58, 89, 236c, 325cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.9516 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:274:<img src="/file/view/myna_89edo.jpg/271260474/myna_89edo.jpg" alt="" title="" /> --><img src="/file/view/myna_89edo.jpg/271260474/myna_89edo.jpg" alt="myna_89edo.jpg" title="myna_89edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:274 --><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:87:<h1> --><h1 id="toc43"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:87 -->Greeley</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 121/120, 126/125<br /> Related temperament: <a class="wiki_link" href="/Porcupine%20family#Opossum">Opossum</a>, <a class="wiki_link" href="/Starling%20temperaments#Nusecond%20temperament">Nusecond</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/10 = 155.776<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/10; 121/120 126/125]<br /> Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.034 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:275:<img src="/file/view/greeley_100edo.png/284867960/greeley_100edo.png" alt="" title="" /> --><img src="/file/view/greeley_100edo.png/284867960/greeley_100edo.png" alt="greeley_100edo.png" title="greeley_100edo.png" /><!-- ws:end:WikiTextLocalImageRule:275 --><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:89:<h2> --><h2 id="toc44"><a name="Greeley-Music"></a><!-- ws:end:WikiTextHeadingRule:89 -->Music</h2> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><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></span></span> 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:91:<h1> --><h1 id="toc45"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:91 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/10 = 453.242<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/10; 121/120 169/168 275/273]<br /> Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]<br /> <br /> Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]<br /> EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde,<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.052 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:276:<img src="/file/view/semidim_770edo.png/284868918/semidim_770edo.png" alt="" title="" /> --><img src="/file/view/semidim_770edo.png/284868918/semidim_770edo.png" alt="semidim_770edo.png" title="semidim_770edo.png" /><!-- ws:end:WikiTextLocalImageRule:276 --><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:93:<h1> --><h1 id="toc46"><a name="Mothwelltri"></a><!-- ws:end:WikiTextHeadingRule:93 -->Mothwelltri</h1> Group: 2.7/3.11<br /> Comma: 99/98<br /> Svalname: 1&4<br /> Related temperament: Orwell<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~7/6 = 273.174<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 99/98]<br /> Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]<br /> <br /> Map: [<1 0 1|, <0 1 2|]<br /> EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.064 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mothwelltri13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:95:<h1> --><h1 id="toc47"><a name="Sulis"></a><!-- ws:end:WikiTextHeadingRule:95 -->Sulis</h1> Subgroup: 2.5.9/7.11/9<br /> Commas: 99/98, 176/175<br /> Related temperament: <a class="wiki_link" href="/Marvel%20family#Minerva">minerva</a>, würschmidt<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~5/4 = 386.558<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 99/98 176/175]<br /> Gencom map: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|]<br /> <br /> Map: [<1 0 5 -9|, <0 1 -2 4|]<br /> EDOs: 22, 25, 28, 31, 59, 90c, 149c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.074 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sulis7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sulis10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sulis13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:97:<h1> --><h1 id="toc48"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:97 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 425.244<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 99/98 243/242]<br /> Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|]<br /> <br /> Map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.099 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:277:<img src="/file/view/skwares_206edo.png/284589566/skwares_206edo.png" alt="" title="" /> --><img src="/file/view/skwares_206edo.png/284589566/skwares_206edo.png" alt="skwares_206edo.png" title="skwares_206edo.png" /><!-- ws:end:WikiTextLocalImageRule:277 --><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:99:<h1> --><h1 id="toc49"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:99 -->Orwell</h1> Group: 2.3.5.7.11<br /> Commas: 99/98, 121/120, 176/175<br /> Val name: 9&22<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~7/6 = 271.426<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 99/98 121/120 176/175]<br /> Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> <br /> Map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> EDOs: 9, 22, 31, 53, 84e<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.151 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:278:<img src="http://xenharmonic.wikispaces.com/file/view/orwell_84edo.png/279497768/orwell_84edo.png" alt="" title="" /> --><img src="http://xenharmonic.wikispaces.com/file/view/orwell_84edo.png/279497768/orwell_84edo.png" alt="orwell_84edo.png" title="orwell_84edo.png" /><!-- ws:end:WikiTextLocalImageRule:278 --><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:101:<h1> --><h1 id="toc50"><a name="Magicaltet"></a><!-- ws:end:WikiTextHeadingRule:101 -->Magicaltet</h1> Group: 2.5/3.7.11<br /> Commas: 100/99, 385/384<br /> Related temperaments: 4&7&15, superkleismic, magic<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 322.659<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 100/99 385/384]<br /> Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|]<br /> <br /> Map: [<1 0 5 2|, <0 1 -3 2|]<br /> EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.206 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/magicaltet15">Fifteen note mega scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:103:<h1> --><h1 id="toc51"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:103 -->Magic</h1> Group: 2.3.5.7.11<br /> Commas: 100/99, 225/224, 245/243<br /> Val name: 19&22<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~5/4 = 380.696<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 100/99 225/224 245/243]<br /> Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> <br /> Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> EDOs: 19, 22, 41, 104, 145<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.226 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:279:<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:279 --><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:105:<h2> --><h2 id="toc52"><a name="Magic-Music"></a><!-- ws:end:WikiTextHeadingRule:105 -->Music</h2> <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3" rel="nofollow">Chromatic piece in magic 16</a></span> <a class="wiki_link_ext" href="http://www.chrisvaisvil.com/" rel="nofollow" target="_blank">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:107:<h1> --><h1 id="toc53"><a name="Kiribati"></a><!-- ws:end:WikiTextHeadingRule:107 -->Kiribati</h1> Subgroup: 2.9/5.7/3.11/9<br /> Commas: 100/99, 245/242<br /> Related temperament: <a class="wiki_link" href="/Octagar%20family">nakika</a>, octacot<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~21/20 = 87.892<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 21/20; 100/99 245/242]<br /> Gencom map: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|]<br /> <br /> Map: [<1 1 1 0|, <0 -2 3 4|]<br /> EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.245 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/kiribati13">Thirteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/kiribati14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:109:<h1> --><h1 id="toc54"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:109 -->Score</h1> Subgroup: 2.7.11.13<br /> Commas: 343/338, 847/832<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/8 = 540.099<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/8; 343/338 847/832]<br /> Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]<br /> <br /> Map: [<1 1 3 1|, <0 4 1 6|]<br /> EDOs: 5, 7, 9, 11, 20<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.282 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:280:<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:280 --><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:111:<h1> --><h1 id="toc55"><a name="Sensation"></a><!-- ws:end:WikiTextHeadingRule:111 -->Sensation</h1> Group: 2.3.5.7.13<br /> Commas: 91/90, 126/125, 169/168<br /> Related temperaments: Sensi, Sensis, Sensus<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 443.322<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 91/90 126/125 169/168]<br /> Gencom map: [<1 -1 -1 -2 0 0|, <0 7 9 13 0 10|]<br /> <br /> Map: [<1 6 8 11 10|, <0 -7 -9 -13 -10|]<br /> EDOs: 19, 27, 46, 111de, 157de<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.321 cents<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:113:<h1> --><h1 id="toc56"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:113 -->Sensi</h1> Group: 2.3.5.7<br /> Commas: 126/125, 245/243<br /> Val name: 19&27<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 443.383<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 126/125 245/243]<br /> Gencom map: [<1 -1 -1 -2|, <0 7 9 13|]<br /> <br /> Map: [<1 6 8 11|, <0 -7 -9 -13|]<br /> EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.323 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:281:<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:281 --><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:115:<h1> --><h1 id="toc57"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:115 -->Meantone</h1> Group: 2.3.5.7<br /> Commas: 81/80, 126/125<br /> Val name: 12&19<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 696.495<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 81/80 126/125]<br /> Gencom map: [<1 1 0 -3|, <0 1 4 10|]<br /> <br /> Map: [<1 0 -4 -13|, <0 1 4 10|]<br /> EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.382 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:282:<img src="/file/view/meantone_31edo.jpg/272175716/meantone_31edo.jpg" alt="" title="" /> --><img src="/file/view/meantone_31edo.jpg/272175716/meantone_31edo.jpg" alt="meantone_31edo.jpg" title="meantone_31edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:282 --><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:117:<h1> --><h1 id="toc58"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:117 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 348.094<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 81/80 121/120]<br /> Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|]<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 24, 31, 55, 69d, 100d, 131bd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.392 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:283:<img src="/file/view/mohaha_131edo.png/284869856/mohaha_131edo.png" alt="" title="" /> --><img src="/file/view/mohaha_131edo.png/284869856/mohaha_131edo.png" alt="mohaha_131edo.png" title="mohaha_131edo.png" /><!-- ws:end:WikiTextLocalImageRule:283 --><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:119:<h2> --><h2 id="toc59"><a name="Mohaha-Music"></a><!-- ws:end:WikiTextHeadingRule:119 -->Music</h2> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3" rel="nofollow">Mohaha10ping2</a> by <a class="wiki_link" href="/Billy%20Stiltner">Billy Stiltner</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:121:<h1> --><h1 id="toc60"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:121 -->Tutone</h1> Subgroup: 2.9.5.7.11<br /> Commas: 81/80, 99/98, 126/125<br /> Related temperaments: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meantone</a>, <a class="wiki_link" href="/Hemimean%20family#Belobog">belobog</a>, hemithirds, hemiwürschmidt<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 193.937<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 81/80 99/98 126/125]<br /> Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|]<br /> <br /> Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]<br /> EDOs: 25, 31, 68b, 99b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.439 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:WikiTextLocalImageRule:284:<img src="/file/view/tutone_99edo.png/284592004/tutone_99edo.png" alt="" title="" /> --><img src="/file/view/tutone_99edo.png/284592004/tutone_99edo.png" alt="tutone_99edo.png" title="tutone_99edo.png" /><!-- ws:end:WikiTextLocalImageRule:284 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:123:<h1> --><h1 id="toc61"><a name="Stacks"></a><!-- ws:end:WikiTextHeadingRule:123 -->Stacks</h1> Subgroup: 2.9.15.7.11.13<br /> Commas: 100/99, 105/104, 144/143, 196/195<br /> Related temperament: <a class="wiki_link" href="/Magic%20family#Magic-13-limit">magic</a><br /> Svalname: 11&30<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 439.146<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 100/99 105/104 144/143 196/195]<br /> Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]<br /> <br /> Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]<br /> EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.540 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/stacks5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/stacks8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/stacks11">Eleven note note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/stacks19">Nineteen note note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:125:<h1> --><h1 id="toc62"><a name="Bleu"></a><!-- ws:end:WikiTextHeadingRule:125 -->Bleu</h1> Group: 2.3.7.11.13<br /> Commas: 78/77, 99/98, 144/143<br /> Sval name: 9&17<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POL2 generator</a>: ~13/12 = 139.990<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/12; 78/77 99/98 144/143]<br /> Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]<br /> <br /> Map: [<1 1 2 3 3|, <0 5 7 4 6|]<br /> EDOs: <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">60c</a><br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.752 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:285:<img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="" title="" /> --><img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="blue_60edo.png" title="blue_60edo.png" /><!-- ws:end:WikiTextLocalImageRule:285 --><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 /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3" rel="nofollow">On a Well Worn Riff (Bleu 17)</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/on-a-well-worn-riff-bleu-17/" rel="nofollow">Chris Vaisvil</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:127:<h1> --><h1 id="toc63"><a name="Sephiroth"></a><!-- ws:end:WikiTextHeadingRule:127 -->Sephiroth</h1> Subgroup: 2.5.11.13.17<br /> Commas: 65/64, 170/169, 221/220<br /> Related temperament: muggles<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~5/4 = 372.236<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 65/64 170/169 221/220]<br /> Gencom map: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|]<br /> <br /> Map: [<1 0 15 6 11|, <0 1 -5 -1 -3|]<br /> EDOs: 10, 13, 16, 29c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.774 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sephiroth7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sephiroth10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sephiroth13">Thirteen note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/sephiroth16">Sixteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:129:<h1> --><h1 id="toc64"><a name="Archy"></a><!-- ws:end:WikiTextHeadingRule:129 -->Archy</h1> Subgroup: 2.3.7<br /> Comma: 64/63<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 709.321<br /> <br /> Gencom: [2 3/2; 64/63]<br /> Gencom mapping: [<1 1 0 4|, <0 1 0 -2|]<br /> <br /> Map: [<1 2 2|, <0 -1 2|]<br /> EDOs: 5, 12, 17, 22, 27, 137bc<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.856 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/archy5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/archy7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/archy12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:131:<h1> --><h1 id="toc65"><a name="Suhajira"></a><!-- ws:end:WikiTextHeadingRule:131 -->Suhajira</h1> Subgroup: 2.3.7.11<br /> Commas: 64/63, 243/242<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POL2 generator</a>: ~11/9 = 353.958<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 64/63 243/242]<br /> Gencom map: [<1 1 0 4 2|, <0 2 0 -4 5|]<br /> <br /> Map: [<1 1 4 2|, <0 2 -4 5|]<br /> EDOs: 7, 10, 17, 61de<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.968 cents<br /> <br /> <a class="wiki_link" href="/suhajira7">suhajira7</a> - Seven note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="/suhajira10">suhajira10</a> - Ten note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="/suhajira17">suhajira17</a> - note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:133:<h1> --><h1 id="toc66"><a name="Mohoho"></a><!-- ws:end:WikiTextHeadingRule:133 -->Mohoho</h1> Subgroup: 2.3.5.11.13<br /> Commas: 66/65, 81/80, 121/120<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 348.916<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 66/65 81/80 121/120]<br /> Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|]<br /> <br /> Map: [<1 1 0 2 4|, <0 2 8 5 -1|]<br /> EDOs: 17c, 24, 31, 55, 86de, 141cde<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.971 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:135:<h1> --><h1 id="toc67"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:135 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 707.192<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 64/63 99/98]<br /> Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|]<br /> <br /> Map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:286:<img src="/file/view/supra_56edo.png/284870878/supra_56edo.png" alt="" title="" /> --><img src="/file/view/supra_56edo.png/284870878/supra_56edo.png" alt="supra_56edo.png" title="supra_56edo.png" /><!-- ws:end:WikiTextLocalImageRule:286 --><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:137:<h1> --><h1 id="toc68"><a name="Machine"></a><!-- ws:end:WikiTextHeadingRule:137 -->Machine</h1> Subgroup: 2.9.7.11<br /> Commas: 64/63, 99/98<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 214.384<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 64/63 99/98]<br /> Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]<br /> <br /> Map: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:287:<img src="/file/view/machine_28edo.png/284594814/machine_28edo.png" alt="" title="" /> --><img src="/file/view/machine_28edo.png/284594814/machine_28edo.png" alt="machine_28edo.png" title="machine_28edo.png" /><!-- ws:end:WikiTextLocalImageRule:287 --><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:139:<h1> --><h1 id="toc69"><a name="Deutone"></a><!-- ws:end:WikiTextHeadingRule:139 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 191.059<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 65/64 81/80 91/90]<br /> Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]<br /> <br /> Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]<br /> EDOs: 6, 7, 13, 19, 25e, 44de<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.003 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:288:<img src="/file/view/deutone_44edo.png/284596634/deutone_44edo.png" alt="" title="" /> --><img src="/file/view/deutone_44edo.png/284596634/deutone_44edo.png" alt="deutone_44edo.png" title="deutone_44edo.png" /><!-- ws:end:WikiTextLocalImageRule:288 --><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:141:<h1> --><h1 id="toc70"><a name="Supraphon"></a><!-- ws:end:WikiTextHeadingRule:141 -->Supraphon</h1> Subgroup: 2.3.7.11.13<br /> Commas: 64/63, 78/77, 99/98<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~3/2 = 706.137<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 64/63 78/77 99/98]<br /> Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|]<br /> <br /> Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]<br /> EDOs: 5, 7, 12, 17<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.095 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:143:<h1> --><h1 id="toc71"><a name="Negra"></a><!-- ws:end:WikiTextHeadingRule:143 -->Negra</h1> Subgroup: 2.3.5.7.13<br /> Commas: 49/48, 65/64, 91/90<br /> Related temperament: <a class="wiki_link" href="/Marvel%20temperaments#Negri-13-limit">negri</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~14/13~13/12 = 125.567 cents<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 14/13;<br /> Gencom map: [<1 2 2 3 0 4|, <0 -4 3 -2 0 -3|]<br /> <br /> Map: [<1 2 2 3 4|, <0 -4 3 -2 -3|]<br /> EDOs: 9, 10, 19, 29, 67cd*f, 86cd*f<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.147 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:145:<h1> --><h1 id="toc72"><a name="Joan"></a><!-- ws:end:WikiTextHeadingRule:145 -->Joan</h1> Subgroup: 2.9.5.7.11<br /> Commas: 81/80, 99/98, 9317/9216<br /> Related temperaments: casablanca, euterpe<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/8 = 541.703 cents<br /> <br /> Gencom: [2 11/8; 81/80 99/98 9317/9216]<br /> Gencom map: [<1 0 -4 1 3|, <0 7/2 14 4 1|]<br /> <br /> Map: [<1 0 -4 1 3|, <0 7 14 4 1|]<br /> EDOs: 11, 20, 31, 113be, 144be<br /> <br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.176 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/joan5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/joan7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/joan9">Nine note mega albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/joan11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:147:<h1> --><h1 id="toc73"><a name="Porkypine"></a><!-- ws:end:WikiTextHeadingRule:147 -->Porkypine</h1> Subgroup: 2.3.5.11<br /> Commas: 55/54, 100/99<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~10/9 = 164.078<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 10/9; 55/54 100/99]<br /> Gencom map: [<1 2 3 0 4|], <0 -3 -5 0 -4|]<br /> <br /> Map: [<1 2 3 4|, <0 3 5 4|]<br /> EDOs: 7, 15, 22, 73cd, 95cd, 117bcd, 256bcdd<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.287 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porkypine7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porkypine8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/porkypine15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:149:<h1> --><h1 id="toc74"><a name="Skateboard"></a><!-- ws:end:WikiTextHeadingRule:149 -->Skateboard</h1> Subgroup: 2.5/3.7/3.11.13/9<br /> Commas: 56/55, 91/90, 100/99<br /> Related temperament: <a class="wiki_link" href="/Starling%20family#Thrasher-13-limit">thrasher</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 313.842<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 56/55 91/90 100/99]<br /> Gencom map: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|]<br /> <br /> Map: [<1 0 -1 2 2|, <0 1 3 2 -2|]<br /> EDOs: 11, 15, 19, 23, 42d, 65d<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.396 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skateboard7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skateboard11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/skateboard15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:151:<h1> --><h1 id="toc75"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:151 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~8/7 = 228.275<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [5/4 8/7; 56/55 128/125]<br /> Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|]<br /> <br /> Map: [<3 7 0 2|, <0 0 1 1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.422 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:289:<img src="/file/view/augment_21edo.png/284598188/augment_21edo.png" alt="" title="" /> --><img src="/file/view/augment_21edo.png/284598188/augment_21edo.png" alt="augment_21edo.png" title="augment_21edo.png" /><!-- ws:end:WikiTextLocalImageRule:289 --><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><br /> <br /> <!-- ws:start:WikiTextHeadingRule:153:<h1> --><h1 id="toc76"><a name="Semaphore"></a><!-- ws:end:WikiTextHeadingRule:153 -->Semaphore</h1> Subgroup: 2.3.7<br /> Comma: 49/48<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~7/6 = 250.385<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 49/48]<br /> Gencom map: [<1 2 0 3}, <0 -2 0 -1|]<br /> <br /> Map: [<1 0 2|, <0 2 1|]<br /> EDOs: 5, 9, 14, 19, 24, 67c, 91c<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.523 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:290:<img src="/file/view/semaphore_24edo.png/337342626/semaphore_24edo.png" alt="" title="" /> --><img src="/file/view/semaphore_24edo.png/337342626/semaphore_24edo.png" alt="semaphore_24edo.png" title="semaphore_24edo.png" /><!-- ws:end:WikiTextLocalImageRule:290 --><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:155:<h1> --><h1 id="toc77"><a name="Kryptonite"></a><!-- ws:end:WikiTextHeadingRule:155 -->Kryptonite</h1> Subgroup: 2.5.7/3.11/3.13/3<br /> Commas: 56/55, 78/77, 91/90<br /> Related temperaments: <a class="wiki_link" href="/Sengic%20family">krypton</a><br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~13/12 = 132.428<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/12; 56/55 78/77 91/90]<br /> Gencom map: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|]<br /> <br /> Map: [<1 2 1 2 2|, <0 -3 -2 1 -1|]<br /> EDOs: 9, 63, 82bd, 91bde<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.545 cents<br /> <br /> <a class="wiki_link" href="/kryptonite9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="/kryptonite10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="/kryptonite19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:157:<h1> --><h1 id="toc78"><a name="Oregon"></a><!-- ws:end:WikiTextHeadingRule:157 -->Oregon</h1> Subgroup: 2.9.15.7.11<br /> Commas: 55/54, 64/63, 100/99<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~6/5 = 325.495<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 55/54 64/63 100/99]<br /> Gencom map: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|]<br /> <br /> Map: [<1 1 1 5 2|, <0 3 4 -3 2|]<br /> EDOs: 7, 11, 37b, 48b, 59b<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.550 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/oregon7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/oregon11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/oregon15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:159:<h1> --><h1 id="toc79"><a name="Antikythera"></a><!-- ws:end:WikiTextHeadingRule:159 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~8/7 = 214.095<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [7/5 8/7; 50/49 64/63]<br /> Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|]<br /> <br /> Map: [<2 0 11 12|, <0 1 -1 -1|]<br /> EDOS: 4, 6, 10, 16, 22, 28<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.572 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:291:<img src="/file/view/antikythera_28edo.png/284595816/antikythera_28edo.png" alt="" title="" /> --><img src="/file/view/antikythera_28edo.png/284595816/antikythera_28edo.png" alt="antikythera_28edo.png" title="antikythera_28edo.png" /><!-- ws:end:WikiTextLocalImageRule:291 --><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:161:<h1> --><h1 id="toc80"><a name="Glacial"></a><!-- ws:end:WikiTextHeadingRule:161 -->Glacial</h1> Subgroup: 2.9.5.11.13<br /> Commas: 45/44, 65/64, 81/80<br /> <br /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 186.151<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 45/44 65/64 81/80]<br /> Gencom map: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|]<br /> <br /> Map: [<1 0 -4 -6 10|, <0 1 2 3 -2|]<br /> EDOs: 6, 13, 45be, 58bce, 71bce, 84bce<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.887 cents<br /> <br /> <a class="wiki_link" href="/glacial6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/glacial7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/glacial13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:163:<h1> --><h1 id="toc81"><a name="Leantone"></a><!-- ws:end:WikiTextHeadingRule:163 -->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 /> <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/8 = 192.500<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 45/44 56/55 81/80]<br /> Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]<br /> <br /> Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 3.882 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:292:<img src="/file/view/leantone_81edo.png/284593104/leantone_81edo.png" alt="" title="" /> --><img src="/file/view/leantone_81edo.png/284593104/leantone_81edo.png" alt="leantone_81edo.png" title="leantone_81edo.png" /><!-- ws:end:WikiTextLocalImageRule:292 --><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></body></html>