Chromatic pairs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 350962506 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 350979052 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-06 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-06 19:54:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>350979052</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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[[xenharmonic/petrtri8|Eight note albitonic scale]] | [[xenharmonic/petrtri8|Eight note albitonic scale]] | ||
[[xenharmonic/petrtri13|Thirteen note chromatic scale]] | [[xenharmonic/petrtri13|Thirteen note chromatic scale]] | ||
=Garibaldi= | |||
Group: 2.3.5.7 | |||
Commas: 225/224, 3125/3087 | |||
Val name: 12&29 | |||
[[Lp tuning|POL2 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 | |||
[[Lp tuning#L2 tuning|L2 error]]: 0.2419 | |||
[[image:garibaldi_94edo.png]] | |||
[[xenharmonic/garibaldi12|Twelve note albitonic scale]] | |||
[[xenharmonic/garibaldi17|Seventeen note chromatic scale]] | |||
=Nestoria= | =Nestoria= | ||
| Line 266: | Line 285: | ||
[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] | [[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] | ||
= | =Roulette= | ||
Subgroup: 2.5. | Subgroup: 2.5.7.11.13 | ||
Commas: 176/175, 1375/1372, 640/637 | |||
Sval name: | Sval name: 6&25 | ||
Related | Related temperament: [[xenharmonic/Würschmidt family|Hemiwürschmidt]] | ||
[[Lp tuning|POL2 generator]]: ~5/4 = 383.638 | [[Lp tuning|POL2 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 | |||
[[Lp tuning#L2 tuning|L2 error]]: 0.6943 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]] | |||
=Marveltri= | |||
Subgroup: 2.5.9/7 | |||
Comma: 225/224 | |||
Sval name: 3&13 | |||
Related temperaments: marvel, 22&47, magic | |||
[[Lp tuning|POL2 generator]]: ~5/4 = 383.638 | |||
[[Gencom]]: [2 5/4; 225/224] | [[Gencom]]: [2 5/4; 225/224] | ||
| Line 324: | Line 365: | ||
[[xenharmonic/penta17|Seventeen note mega chromatic scale]] | [[xenharmonic/penta17|Seventeen note mega chromatic scale]] | ||
=Guanyintet= | =Shoe= | ||
Subgroup: 2.5.7/3.11/3 | Subgroup: 2.5.7.11.13 | ||
Commas: 176/175, 540/539 | Commas: 176/175, 640/637, 847/845 | ||
Sval name: 16&21 | |||
[[Lp tuning|POL2 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 | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.035 | |||
[[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]] | |||
=Guanyintet= | |||
Subgroup: 2.5.7/3.11/3 | |||
Commas: 176/175, 540/539 | |||
Svalname: 4&9 | Svalname: 4&9 | ||
Related temperaments: guanyin, orwell | Related temperaments: guanyin, orwell | ||
| Line 343: | Line 405: | ||
[[xenharmonic/guanyintet13|Thirteen note chromatic scale]] | [[xenharmonic/guanyintet13|Thirteen note chromatic scale]] | ||
= | =Baldy= | ||
Subgroup: 2.5.7 | Subgroup: 2.9.5.7.13 | ||
Commas: | Commas: 225/224, 325/324, 640/637 | ||
Sval name: | Sval name: 6&35 | ||
Related temperament: [[xenharmonic/Schismatic family|Garibaldi]] | |||
POTE generator: ~8 | POTE generator: ~9/8 = 204.090 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|] | ||
EDOs: | EDOs: 6, 11, 17, 23, 29, 35, 41, [[xenharmonic/47edo|47]], 100, [[xenharmonic/147edo|147]] | ||
Error: 2. | Error: 2.617 cents | ||
[[image: | [[image:baldy_147edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/baldy6|baldy6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] | ||
[[xenharmonic/baldy11|baldy11]] - eleven note [[xenharmonic/albitonic scale|albitonic scale]] | |||
[[xenharmonic/ | [[xenharmonic/baldy17|baldy17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | ||
[[xenharmonic/ | |||
= | =Bossier= | ||
Subgroup: 2 | Subgroup: 2.7.11.13 | ||
Commas: | Commas: 1573/1568, 15488/15379 | ||
Sval name: | Sval name: 3&17 | ||
POTE generator: ~ | POTE generator: ~14/11 = 421.309 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 1 3|, <0 8 7 2|] | ||
EDOs: | EDOs: 17, 20, 37, 57, 94, 225 | ||
Error: 2. | Error: 2.665 cents | ||
[[image: | [[image:bossier_225edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/bossier8|Eight note albitonic scale]] | ||
[[xenharmonic/bossier11|Eleven note chromatic scale]] | |||
[[xenharmonic/ | [[xenharmonic/bossier14|Fourteen note mega chromatic scale]] | ||
[[xenharmonic/ | |||
= | =Radon= | ||
Subgroup: 2.3.7.11 | |||
Commas: | Commas: 896/891, 1029/1024 | ||
Sval name: 5&36 | |||
Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] | |||
POTE generator: ~ | POTE generator: ~8/7 = 234.381 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 1 3 6|, <0 3 -1 -13|] | ||
EDOs: | EDOs: 5, 36, 41, 87, 128 | ||
Error: 2. | Error: 2.925 cents | ||
[[image: | [[image:radon_128edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/radon5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/radon11|Eleven note albitonic scale]] | ||
[[xenharmonic/radon16|Sixteen note chromatic scale]] | |||
= | =Myna= | ||
Group: 2.3.5.7 | |||
Commas: | Commas: 126/125, 1728/1715 | ||
Val name: 4&27 | |||
POTE generator: ~ | POTE generator: ~6/5 = 310.146 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 9 9 8|, <0 -10 -9 -7|] | ||
EDOs: | EDOs: 4, 27, 31, 58, 89 | ||
Error: | Error: 3.310 cents | ||
[[image: | [[image:myna_89edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/myna7|Seven note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/myna11|Eleven note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/myna15|Fifteen note chromatic scale]] | ||
= | =Silver= | ||
Subgroup: 2.7. | Subgroup: 2.5.7.13.17 | ||
Commas: | Commas: 170/169, 640/637, 5525/5488 | ||
Sval name: | Sval name: 10&27 | ||
POTE generator: ~ | POTE generator: ~13/8 = 842.711 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] | ||
EDOs: 17, | EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, [[xenharmonic/487edo|487]] | ||
Error: | Error: 3.437 | ||
[[image: | [[image:silver_487edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/silver7|silver7]] -seven note [[xenharmonic/haplotonic scale|haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/silver10|silver10]] - ten note [[xenharmonic/albitonic scale|albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/silver17|silver17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | ||
= | =Mabila= | ||
Subgroup: 2. | Subgroup: 2.5.7 | ||
Comma: 1071875/1048576 | |||
Sval name: | Sval name: 7&9 | ||
POTE generator: ~ | POTE generator: ~175/128 = 527.236 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 1 | Map: [<1 1 5|, <0 3 -5|] | ||
EDOs: | EDOs: 7, 9, 16, 25, 41, 66 | ||
Error: | Error: 3.560 | ||
[[image: | [[image:mabila_66edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/mabila7|Seven note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/mabila9|Nine note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/mabila16|Sixteen note chromatic scale]] | ||
= | =Meantone= | ||
Group: 2.3.5.7 | Group: 2.3.5.7 | ||
Commas: 126/125 | Commas: 81/80, 126/125 | ||
Val name: | Val name: 12&19 | ||
POTE generator: | POTE generator: 696.495 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 -4 -13|, <0 1 4 10|] | ||
EDOs: | EDOs: 5, 7, 12, 19, 31, 81, 112, 143 | ||
Error: 3. | Error: 3.585 | ||
[[image: | [[image:meantone_31edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/meantone5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/meantone7|Seven note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/meantone12|Twelve note chromatic scale]] | ||
= | =Starlingtet= | ||
Group: 2.5/3.7/3 | |||
Comma: 126/125 | |||
Svalname: 4&15 | |||
Related temperaments: starling; becomes myna | |||
POTE generator: ~ | POTE generator: ~6/5 = 311.213 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 -1|, <0 1 3|] | ||
EDOs: | EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b | ||
Error: | Error: 311.213 | ||
[[ | [[xenharmonic/starlingtet4|Four note haplotonic scale]] | ||
[[xenharmonic/starlingtet7|Seven note albitonic scale]] | |||
[[xenharmonic/starlingtet11|Eleven note chromatic scale]] | |||
=Indium= | |||
Subgroup: 2.5/3.7/3.11/3 | |||
Commas: 3025/3024, 3125/3087 | |||
Sval name: 8&33 | |||
POTE generator: ~12/11 = 147.159 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 0 2|, <0 6 10 -1|] | ||
EDOs: | EDOs: 33, 41, 49, 57, 106, 204, 253 | ||
Error: 3. | Error: 3.968 cents | ||
[[image: | [[image:indium_253edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/indium8|Eight note albitonic scale]] | ||
[[xenharmonic/indium17|Seventeen note chromatic scale]] | |||
[[xenharmonic/ | |||
= | ==Music== | ||
Group: 2.3.5.7 | <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]] | ||
Commas: | |||
Val name: | =Magic= | ||
Group: 2.3.5.7.11 | |||
Commas: 100/99, 225/224, 245/243 | |||
Val name: 19&22 | |||
POTE generator: 696 | POTE generator: ~5/4 = 380.696 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 - | Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | ||
EDOs: | EDOs: 19, 22, 41, 104, 145 | ||
Error: | Error: 4.489 | ||
[[image: | [[image:xenharmonic/magic_145edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/magic7|Seven note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/magic10|Ten note albitonic scale]] | ||
[[xenharmonic/ | [[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]] | |||
Svalname: 4& | =Gariberttet= | ||
Subgroup: 2.5/3.7/3.13/11 | |||
POTE generator: ~ | Commas: 275/273, 847/845 | ||
Svalname: 4&29 | |||
POTE generator: ~13/11 = 292.418 | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 0 0|, <0 3 5 1|] | ||
EDOs: | EDOs: 29, 33, 37, 41, 78 | ||
Error: | Error: 4.473 | ||
[[xenharmonic/ | [[xenharmonic/gariberttet5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/gariberttet9|Nine note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/gariberttet13|Thirteen note chromatic scale]] | ||
= | =Hemif= | ||
Subgroup: 2. | Subgroup: 2.3.7.11.13 | ||
Commas: | Commas: 144/143, 243/242, 364/363 | ||
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]] | |||
POTE generator: ~ | POTE generator: ~11/9 = 351.691 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | ||
EDOs: | EDOs: 7, 10, 17, 24, 41, 58 | ||
Error: | Error: 4.867 cents | ||
[[image: | [[image:hemif_58edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/hemif7|Seven note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/hemif10|Ten note albitonic scale]] | ||
[[xenharmonic/hemif17|Seventeen note chromatic scale]] | |||
= | =Skwares= | ||
Subgroup: 2.3.7.11 | |||
Commas: 99/98, 243/242 | |||
Related temperament: [[xenharmonic/Meantone family|squares]] | |||
POTE generator: ~9/7 = 425.244 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 3 6 7|, <0 -4 -9 -10|] | ||
EDOs: | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 | ||
Error: 4. | Error: 4.942 cents | ||
[[image: | [[image:skwares_206edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/skwares8|Eight note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/skwares11|Eleven note mega albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/skwares14|Fourteen note chromatic scale]] | ||
= | =Sensi= | ||
Group: 2.3.5.7 | |||
Commas: 126/126, 245/243 | |||
Val name: 19&27 | |||
POTE generator: ~9/7 = 443.383 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 6 8 11|, <0 -7 -9 -13|] | ||
EDOs: | EDOs: 5, 8, 11, 19, 27, 46 | ||
Error: | Error: 5.019 | ||
[[xenharmonic/ | [[image:xenharmonic/sensi_46edo.jpg]] | ||
[[xenharmonic/sensi5|Five note haplotonic scale]] | |||
[[xenharmonic/sensi8|Eight note albitonic scale]] | |||
[[xenharmonic/sensi11|Eleven note mega albitonic scale]] | |||
[[xenharmonic/sensi19|Nineteen note chromatic scale]] | |||
=Greeley= | |||
Subgroup: 2.5/3.7/3.11/3 | |||
Commas: 121/120, 126/125 | |||
POTE generator: ~11/10 = 156.055 | |||
Related temperament: [[Porcupine family#Opossum|Opossum]] | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 1 | Map: [<1 1 2 2|, <0 -2 -6 -1|] | ||
EDOs: | EDOs: 8, 15, 23, 77, 100 | ||
Error: | Error: 5.404 cents | ||
[[image: | [[image:greeley_100edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/greeley8|Eight note albitonic scale]] | ||
[[xenharmonic/greeley15|Fifteen note chromatic scale]] | |||
[[xenharmonic/ | |||
= | ==Music== | ||
Subgroup: 2.3.7.11 | <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 | ||
Commas: | |||
=Semidim= | |||
Subgroup: 2.5/3.7/3.11/3.13/3 | |||
Commas: 121/120, 169/168, 275/273 | |||
Sval name: 8&29 | |||
POTE generator: ~ | POTE generator: ~13/10 = 453.190 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 3 | Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] | ||
EDOs: 5, 8, | EDOs: 5, 8, 13, 21, 29, 37, 45 | ||
Error: | Error: 5.433 cents | ||
[[image: | [[image:semidim_770edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/semidim8|Eight note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/semidim13|Thirteen note chromatic scale]] | ||
= | =Orwell= | ||
Group: 2.3.5.7 | Group: 2.3.5.7.11 | ||
Commas: | Commas: 99/98, 121/120, 176/175 | ||
Val name: | Val name: 9&22 | ||
POTE generator: ~ | POTE generator: ~7/6 = 271.426 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 3 1 3|, <0 7 -3 8 2|] | ||
EDOs: | EDOs: 9, 22, 31, 53, 84 | ||
Error: 5. | Error: 5.584 | ||
[[image:xenharmonic/ | [[image:xenharmonic/orwell_84edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/orwell5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/orwell9|Nine note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/orwell13|Thirteen note chromatic scale]] | ||
= | =Magicaltet= | ||
Group: 2.5/3.7.11 | |||
Commas: | Commas: 100/99, 385/384 | ||
Related temperaments: 4&7&15, magic | |||
POTE generator: ~6/5 = 319.424 | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 5 2|, <0 1 -3 2|] | ||
EDOs: | EDOs: 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd | ||
Error: 5. | Error: 5.720 cents | ||
[[ | [[xenharmonic/magicaltet7|Seven note albitonic scale]] | ||
[[xenharmonic/magicaltet11|Eleven note chromatic scale]] | |||
[[xenharmonic/magicaltet15|Fifteen note mega scale]] | |||
=Sentry= | |||
Group: 2.5/3.9/7 | |||
Commas: 245/243 | |||
Svalname: 3&5 | |||
Related temperaments: sensi | |||
POTE generator: ~9/7 = 438.574 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 0 0|, <0 2 1|] | ||
EDOs: | EDOs: 8, 11, 30, 41, 52, 145b, 197bc | ||
Error: 5. | Error: 5.793 cents | ||
[[ | [[xenharmonic/sentry5|Five note haplotonic scale]] | ||
[[xenharmonic/sentry8|Eight note albitonic scale]] | |||
[[xenharmonic/sentry11|Eleven note note chromatic scale]] | |||
=Mothwelltri= | |||
Group: 2.7/3.11 | |||
Comma: 99/98 | |||
Svalname: 1&4 | |||
Related temperament: Orwell | |||
POTE generator:~7/6 = 268.508 | |||
POTE generator: ~7/6 = | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 1|, <0 1 2|] | ||
EDOs: 9, | EDOs: 9, 40, 49c, 58c, 67c, 76c | ||
Error: | Error: 6.119 cents | ||
[[ | [[xenharmonic/mothwelltri5|Five note haplotonic scale]] | ||
[[xenharmonic/mothwelltri9|Nine note albitonic scale]] | |||
[[xenharmonic/mothwelltri13|Thirteen note chromatic scale]] | |||
=Lovecraft= | |||
Group: 2.11.13 | |||
POTE generator: ~13/11 = 279.318 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 1 0|, <0 2 3|] | ||
EDOS: 13, 30, 43, 73, 116b | |||
Error: | Error: 6.026 cents | ||
[[ | [[image:lovecraft_116edo.png]] | ||
[[xenharmonic/lovecraft5|Five note haplotonic scale]] | |||
[[xenharmonic/lovecraft9|Nine note albitonic scale]] | |||
[[xenharmonic/lovecraft13|Thirteen note chromatic scale]] | |||
POTE generator: ~ | =Bleu= | ||
Group: 2.3.7.11.13 | |||
Commas: 78/77, 99/98, 144/143 | |||
Sval name: 9&17 | |||
POTE generator: ~13/12 = 139.990 | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 1 2 3 3|, <0 5 7 4 6|] | ||
EDOs: | EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] | ||
Error: | Error: 6.361 cents | ||
[[image:blue_60edo.png]] | |||
[[xenharmonic/ | [[xenharmonic/bleu8|bleu8]] - Eight note [[xenharmonic/haplotonic scale|haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/bleu9|bleu9]] - Nine note [[xenharmonic/albitonic scale|albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/bleu17|bleu17]] - Seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | ||
= | =Mohaha= | ||
Subgroup: 2.3.5.11 | |||
Commas: 81/80, 121/120 | |||
Related temperament: [[xenharmonic/Meantone family|mohajira]] | |||
Related temperament: | |||
POTE generator:~ | POTE generator: ~11/9 = 348.094 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 1 0 2|, <0 2 8 5|] | ||
EDOs: | EDOs: 24, 31, 69d, 100d, 131bd | ||
Error: 6. | Error: 6.733 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]] | |||
[[ | |||
= | ==Mohoho== | ||
Subgroup: 2.3.5.11.13 | |||
Commas: 66/65, 81/80, 121/120 | |||
POTE generator: ~ | POTE generator: ~11/9 = 348.916 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 1 0|, <0 2 | Map: [<1 1 0 2 4|, <0 2 8 5 -1|] | ||
EDOs: 17c, 24, 31, 55, 86de, 141cde | |||
Error: | Error: 9.556 cents | ||
=Stacks= | |||
Subgroup: 2.9.15.7.11.13 | |||
Commas: 100/99, 105/104, 144/143, 196/195 | |||
Svalname: 11&30 | |||
POTE generator: ~9/7 = 438.977 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 1 2 | Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] | ||
EDOs: | EDOs: 11, 30, 41 | ||
Error: 6. | Error: 6.947 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]] | |||
=Tutone= | |||
Subgroup: 2.9.5.7.11 | |||
[[xenharmonic/ | Commas: 81/80, 99/98, 126/125 | ||
Related temperament: [[xenharmonic/Meantone family|meantone]] | |||
POTE generator: ~9/8 = 193.937 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [< | Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] | ||
EDOs: | EDOs: 25, 31, 68b, 99b | ||
Error: | Error: 7.047 cents | ||
[[ | [[xenharmonic/tutone6|Six note haplotonic scale]] | ||
[[xenharmonic/tutone7|Seven note albitonic scale]] | |||
[[xenharmonic/tutone13|Thirteen note chromatic scale]] | |||
[[ | [[image:tutone_99edo.png]] | ||
= | =Leantone= | ||
Subgroup: 2.9.5.7.11 | |||
Commas: 45/44, 56/55, 81/80 | |||
Related temperament: [[meanenneadecal]] | |||
POTE generator: ~9/8 = 192.500 | |||
POTE generator: ~ | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [< | Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] | ||
EDOs: | EDOs: 6, 7, 13, 19, 25, 31, 56, 81 | ||
Error: | Error: 20.338 cents | ||
[[image:leantone_81edo.png]] | |||
= | [[xenharmonic/leantone6|Six note haplotonic scale]] | ||
Subgroup: 2 | [[xenharmonic/leantone7|Seven note albitonic scale]] | ||
Commas: | [[xenharmonic/leantone13|Thirteen note chromatic scale]] | ||
=Score= | |||
Subgroup: 2.7.11.13 | |||
Commas: 343/338, 847/832 | |||
POTE generator: ~ | POTE generator: ~11/8 = 540.099 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 | Map: [<1 1 3 1|, <0 4 1 6|] | ||
EDOs: 11, | EDOs: 5, 7, 9, 11, 20 | ||
Error: | Error: 8.052 cents | ||
[[xenharmonic/ | [[image:xenharmonic/score_20edo.jpg]] | ||
= | [[xenharmonic/score5|Five note haplotonic scale]] | ||
Subgroup: 2. | [[xenharmonic/score7|Seven note albitonic scale]] | ||
Commas: | [[xenharmonic/score9|Nine note mega albitonic scale]] | ||
Related temperament: [[xenharmonic/ | [[xenharmonic/score11|Eleven note chromatic scale]] | ||
=Supra= | |||
Subgroup: 2.3.7.11 | |||
Commas: 64/63, 99/98 | |||
Related temperament: [[xenharmonic/suprapyth|suprapyth]] | |||
POTE generator: ~ | POTE generator: ~3/2 = 707.192 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 6 13|, <0 1 -2 -6|] | ||
EDOs: | EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c | ||
Error: | Error: 9.795 cents | ||
[[ | [[image:supra_56edo.png]] | ||
[[ | [[xenharmonic/supra7|Seven note albitonic scale]] | ||
[[xenharmonic/supra12|Twelve note chromatic scale]] | |||
= | ==Supraphon== | ||
Subgroup: 2. | Subgroup: 2.3.7.11.13 | ||
Commas: | Commas: 64/63, 78/77, 99/98 | ||
POTE generator: ~ | POTE generator: ~3/2 = 706.137 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] | ||
EDOs: | EDOs: 5, 7, 12, 17 | ||
Error: | Error: 10.534 cents | ||
==Machine== | |||
Subgroup: 2.9.7.11 | |||
Commas: 64/63, 99/98 | |||
POTE generator: ~9/8 = 214.384 | |||
= | [[Gencom]]: | ||
Subgroup: 2. | Gencom map: | ||
Commas: | |||
Map: [<1 0 6 13|, <0 1 -1 -3|] | |||
EDOs: 5, 6, 11, 17, 28 | |||
Error: 10.100 cents | |||
[[image:machine_28edo.png]] | |||
[[xenharmonic/machine5|Five note haplotonic scale]] | |||
[[xenharmonic/machine6|Six note albitonic scale]] | |||
[[xenharmonic/machine11|Eleven note chromatic scale]] | |||
=Antikythera= | |||
Subgroup: 2.9.5.7 | |||
Commas: 50/49, 64/63 | |||
Related temperament: [[xenharmonic/pajara|pajara]] | |||
POTE generator: ~ | POTE generator: ~8/7 = 214.095 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [< | Map: [<2 0 11 12|, <0 1 -1 -1|] | ||
EDOS: 4, 6, 10, 16, 22, 28 | |||
Error: | Error: 11.508 cents | ||
[[image: | [[image:antikythera_28edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/antikythera6|Six note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/antikythera10|Ten note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/antikythera16|Sixteen note chromatic scale]] | ||
= | =Deutone= | ||
Subgroup: 2. | Subgroup: 2.9.5.7.13 | ||
Commas: 64/ | Commas: 65/64, 81/80, 91/90 | ||
Related temperament: [[xenharmonic/ | Related temperament: [[xenharmonic/Meantone family|meanpop]] | ||
POTE generator: ~ | POTE generator: ~9/8 = 191.059 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] | ||
EDOs: | EDOs: 6, 7, 13, 19, 25, 44, 69 | ||
Error: | Error: 12.145 cents | ||
[[image: | [[image:deutone_44edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/deutone6|Six note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/deutone7|seven note albitonic scale]] | ||
[[xenharmonic/deutone13|Thirteen note chromatic scale]] | |||
= | =Semaphore= | ||
Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
Comma: 49/48 | |||
POTE generator: ~ | POTE generator: ~7/6 = 250.385 | ||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [<1 0 | Map: [<1 0 2|, <0 2 1|] | ||
EDOs: 5, | EDOs: 5, 9, 14, 19, 24 | ||
Error: | Error: 12.428 | ||
[[image:semaphore_24edo.png]] | |||
POTE generator: ~ | [[xenharmonic/semiphore5|Five note haplotonic scale]] | ||
[[xenharmonic/semiphore9|Nine note albitonic scale]] | |||
[[xenharmonic/semiphore14|Fourteen note chromatic scale]] | |||
=Augment= | |||
Subgroup: 2.5.7.11 | |||
Commas: 56/55, 128/125 | |||
Related temperament: [[xenharmonic/Augmented family|augmented]] | |||
POTE generator: ~8/7 = 228.275 | |||
[[Gencom]]: | [[Gencom]]: | ||
Gencom map: | Gencom map: | ||
Map: [< | Map: [<3 7 0 2|, <0 0 1 1|] | ||
EDOs: | EDOs: 3, 6, 9, 15, 21 | ||
Error: | Error: 12.830 cents | ||
[[image: | [[image:augment_21edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/augment6|Six note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/augment9|Nine note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/augment12|Twelve note chromatic scale]]</pre></div> | ||
<h4>Original HTML content:</h4> | |||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:123:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --> | <a href="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <a href="#Neutraltet">Neutraltet</a><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --> | <a href="#Penta">Penta</a><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --> | <a href="#Starlingtet">Starlingtet</a><!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --> | <a href="#Gariberttet">Gariberttet</a><!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --> | <a href="#Magicaltet">Magicaltet</a><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --> | <a href="#Sentry">Sentry</a><!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --> | <a href="#Mothwelltri">Mothwelltri</a><!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --> | <a href="#Lovecraft">Lovecraft</a><!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --> | <a href="#Stacks">Stacks</a><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --> | <a href="#Semaphore">Semaphore</a><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --> | |||
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</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | |||
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<br /> | |||
<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><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 &quot;albitonic&quot; from the Latin word for &quot;white&quot;. Also included at times are &quot;haplotonic&quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><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&amp;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="/Lp%20tuning">POL2 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: [&lt;3 10/9 -7/9 2/9|, &lt;0 -2/3 -1/3 2/3|]<br /> | |||
<br /> | |||
Map: [&lt;3 0 -4|, &lt;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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.0169 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 /> | |||
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<br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain9">Nine note albitonic scale</a><br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain15">Fifteen note chromatic scale</a><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:5 -->Tridec</h1> | |||
Subgroup: 2.7/5.11/5.13/5<br /> | |||
Commas: 847/845, 1001/1000<br /> | |||
Sval name: 5&amp;8<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Lp%20tuning">POL2 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: [&lt;1 0 -3/4 5/4 -3/4 1/4|, &lt;0 0 0 -4 3 1|]<br /> | |||
<br /> | |||
= | Map: [&lt;1 2 0 1|, &lt;0 -4 3 1|]<br /> | ||
EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.0955<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:188:&lt;img src=&quot;/file/view/tridec_235edo.png/284860428/tridec_235edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/tridec_235edo.png/284860428/tridec_235edo.png" alt="tridec_235edo.png" title="tridec_235edo.png" /><!-- ws:end:WikiTextLocalImageRule:188 --><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:7:&lt;h1&gt; --><h1 id="toc3"><a name="Petrtri"></a><!-- ws:end:WikiTextHeadingRule:7 -->Petrtri</h1> | |||
Subgroup: 2.11/5.13/5<br /> | |||
Comma: 2200/2197<br /> | |||
Svalname: 3&amp;5<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/10 = 455.012<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/10; 2200/2197]<br /> | |||
Gencom map: [&lt;1 0 -1/3 0 -1/3 2/3|, &lt;0 0 -4/3 0 5/3 -1/3|]<br /> | |||
<br /> | |||
Map: [&lt;1 0 1|, &lt;0 3 1|]<br /> | |||
EDOs: 21, 29, 211, 240, 269, 298, 327, 356, 385, 741c, 1126c<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.1745 cents<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:189:&lt;img src=&quot;/file/view/petrtri_385edo.png/284586314/petrtri_385edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/petrtri_385edo.png/284586314/petrtri_385edo.png" alt="petrtri_385edo.png" title="petrtri_385edo.png" /><!-- ws:end:WikiTextLocalImageRule:189 --><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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:9 -->Garibaldi</h1> | ||
Group: 2.3.5.7<br /> | |||
Commas: 225/224, 3125/3087<br /> | |||
Val name: 12&amp;29<br /> | |||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 702.085<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 225/224 3125/3087]<br /> | ||
Gencom map: [&lt;1 1 7 11], &lt;0 1 -8 -14|]<br /> | |||
<br /> | <br /> | ||
< | Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]<br /> | ||
EDOs: 7, 12, 17, 29, 41, 53, 94<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.2419<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule:190:&lt;img src=&quot;/file/view/garibaldi_94edo.png/284865722/garibaldi_94edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/garibaldi_94edo.png/284865722/garibaldi_94edo.png" alt="garibaldi_94edo.png" title="garibaldi_94edo.png" /><!-- ws:end:WikiTextLocalImageRule:190 --><br /> | |||
< | |||
<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 /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><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&amp;29<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 701.746<br /> | ||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 361/360 513/512]<br /> | ||
Gencom map: [&lt;1 1 7 0 0 0 0 6|, &lt;0 1 -8 0 0 0 0 -3|]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning"> | Map: [&lt;1 0 15 9|, &lt;0 1 -8 -3|]<br /> | ||
EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.2438 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:191:&lt;img src=&quot;/file/view/nestoria_171edo.png/284862598/nestoria_171edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/nestoria_171edo.png/284862598/nestoria_171edo.png" alt="nestoria_171edo.png" title="nestoria_171edo.png" /><!-- ws:end:WikiTextLocalImageRule:191 --><br /> | ||
<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="/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nestoria17">Seventeen note mega chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:13 -->Bridgetown</h1> | ||
Subgroup: 2.3.11/5.13/5<br /> | |||
Commas: 352/351, 676/675<br /> | |||
Sval name: 5&amp;24<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barabados</a><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~15/13 = 248.399<br /> | ||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 15/13; 352/351 676/675]<br /> | ||
Gencom map: [&lt;1 2 -5/3 0 4/3 1/3|, &lt;0 -2 4 0 -5 1|]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning"> | Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br /> | ||
EDOs: 5, 9, 14, 19, 24, 29<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.3920 cents<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:192:&lt;img src=&quot;/file/view/bridgetown_29edo.png/284859430/bridgetown_29edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/bridgetown_29edo.png/284859430/bridgetown_29edo.png" alt="bridgetown_29edo.png" title="bridgetown_29edo.png" /><!-- ws:end:WikiTextLocalImageRule:192 --><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:15:&lt;h2&gt; --><h2 id="toc7"><a name="Bridgetown-Music"></a><!-- ws:end:WikiTextHeadingRule:15 -->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 /> | |||
<a class=" | <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 /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:17 -->Orgone</h1> | ||
Subgroup: 2.7.11<br /> | |||
Commas: 65536/65219<br /> | |||
Svals: 4&amp;7<br /> | |||
Related temperament: <a class="wiki_link" href="/Gamelismic%20clan#superkleismic">superkleismic</a><br /> | |||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~77/64 = 323.372<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 77/64; 65536/65219]<br /> | ||
Gencom map: [&lt;1 0 0 2 4|, &lt;0 0 0 3 -2|]<br /> | |||
< | |||
<br /> | <br /> | ||
Map: [&lt;1 2 4|, &lt;0 3 -2|]<br /> | |||
EDOs: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4197 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:193:&lt;img src=&quot;/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_308edo.jpg/270849182/orgone_308edo.jpg" alt="orgone_308edo.jpg" title="orgone_308edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:193 --><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:19 -->Cata</h1> | |||
Subgroup: 2.3.5.13<br /> | |||
<a class="wiki_link" href="/ | Commas: 325/324, 625/624<br /> | ||
Sval name: 15&amp;19<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kleismic%20family">catakleismic</a><br /> | |||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 317.076<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 325/324 625/624]<br /> | ||
Gencom map: [&lt;1 0 1 0 0 0|, &lt;0 6 5 0 0 14|]<br /> | |||
< | |||
<br /> | <br /> | ||
Map: [&lt;1 0 1 0|, &lt;0 6 5 14|]<br /> | |||
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4936 cents<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <!-- ws:start:WikiTextLocalImageRule:194:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/cata_246edo2.jpg/270809448/cata_246edo2.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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:194 --><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 /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc10"><a name="Marveltwintri"></a><!-- ws:end:WikiTextHeadingRule:21 -->Marveltwintri</h1> | ||
Subgroup: 2.5/3.13/9<br /> | |||
Comma: 325/324<br /> | |||
Svalname: 3&amp;4<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 317.139<br /> | |||
<a class="wiki_link" href="/Lp%20tuning | |||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 325/324]<br /> | ||
Gencom map: [&lt;1 -1/6 5/6 0 0 -1/3|, &lt;0 -1/2 -3/2 0 0 1|]<br /> | |||
<br /> | <br /> | ||
< | Map: [&lt;1 0 2|, &lt;0 1 -2|]<br /> | ||
<a class="wiki_link" href=" | EDOs: 11, 15, 19, 34, 185, 219, 253, 287b, 321b<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.5154 cents<br /> | |||
<br /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextLocalImageRule:195:&lt;img src=&quot;/file/view/marveltwintri_321edo.png/284588650/marveltwintri_321edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/marveltwintri_321edo.png/284588650/marveltwintri_321edo.png" alt="marveltwintri_321edo.png" title="marveltwintri_321edo.png" /><!-- ws:end:WikiTextLocalImageRule:195 --><br /> | ||
<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 /> | |||
<a class="wiki_link" href="/ | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc11"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:23 -->Huntington</h1> | ||
Subgroup: 2.5.7.13<br /> | |||
Commas: 640/637, 10985/10976<br /> | |||
Sval name: 10&amp;27<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~16/13 = 357.002<br /> | |||
<a class="wiki_link" href="/Lp%20tuning | |||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 16/13; 640/637 10985/10976]<br /> | ||
Gencom map: [&lt;1 0 5 4 0 4|, &lt;0 0 -9 -4 0 -1|]<br /> | |||
<br /> | <br /> | ||
< | Map: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]<br /> | ||
EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br /> | |||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.5409 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextLocalImageRule:196:&lt;img src=&quot;/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/huntington_400edo.jpg/271195682/huntington_400edo.jpg" alt="huntington_400edo.jpg" title="huntington_400edo.jpg" /><!-- ws:end:WikiTextLocalImageRule:196 --><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:25:&lt;h1&gt; --><h1 id="toc12"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:25 -->Slendric</h1> | ||
Subgroup: 2.3.7<br /> | |||
Comma: 1029/1024<br /> | |||
Sval name: 5&amp;21<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 233.688<br /> | |||
<a class="wiki_link" href="/Lp%20tuning | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 1029/1024]<br /> | |||
<a class="wiki_link" href=" | Gencom map: [&lt;1 1 0 3|, &lt;0 3 0 -1|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 1 3|, &lt;0 3 -1|]<br /> | |||
EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6357 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:197:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/slendric_190edo.jpg/270813524/slendric_190edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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:197 --><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:27:&lt;h2&gt; --><h2 id="toc13"><a name="Slendric-Music"></a><!-- ws:end:WikiTextHeadingRule:27 -->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 /> | |||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc14"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:29 -->Photia</h1> | ||
Subgroup: 2.3.5.17.19<br /> | |||
Commas: 171/170, 256/255, 324/323<br /> | |||
Sval name: 12&amp;41<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 701.470<br /> | ||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 171/170 256/255 324/323]<br /> | ||
Gencom map: [&lt;1 1 7 0 0 0 0 6|, &lt;0 1 -8 0 0 0 7 -3|]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning"> | Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br /> | ||
EDOs: 7, 12, 17, 29, 41, 53, 65<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6436 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:198:&lt;img src=&quot;/file/view/photia_65edo.png/284863542/photia_65edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/photia_65edo.png/284863542/photia_65edo.png" alt="photia_65edo.png" title="photia_65edo.png" /><!-- ws:end:WikiTextLocalImageRule:198 --><br /> | ||
<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 /> | |||
<a class="wiki_link" href="/ | |||
<br /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name="Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:31 -->Neutraltet</h1> | ||
Subgroup: 2.3.11<br /> | |||
Commas: 243/242<br /> | |||
Svalname: 7&amp;17<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 350.525<br /> | ||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 243/242]<br /> | ||
Gencom map: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning"> | Map: [&lt;1 1 2|, &lt;0 2 5|]<br /> | ||
EDOs: 7, 17, 24, 65, 89, 202, 291, 380<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6714 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:199:&lt;img src=&quot;/file/view/neutraltet_380edo.png/284587504/neutraltet_380edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/neutraltet_380edo.png/284587504/neutraltet_380edo.png" alt="neutraltet_380edo.png" title="neutraltet_380edo.png" /><!-- ws:end:WikiTextLocalImageRule:199 --><br /> | ||
<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="/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start: | <!-- ws:start:WikiTextHeadingRule:33:&lt;h1&gt; --><h1 id="toc16"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:33 -->Roulette</h1> | ||
Subgroup: 2.5.7.11.13<br /> | |||
Commas: 176/175, 1375/1372, 640/637<br /> | |||
Sval name: 6&amp;25<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/W%C3%BCrschmidt%20family">Hemiwürschmidt</a><br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~28/25 = 194.594<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 28/25; 176/175 1375/1372 640/637]<br /> | |||
Gencom map: [&lt;1 0 2 2 2 5|, &lt;0 0 2 5 9 -8|]<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -3 -7 13|, &lt;0 2 5 9 -8|]<br /> | |||
EDOs: 6, 7, 13, 19, 25, 31, 37<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6943 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:200:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/roulette_37edo.jpg/270817184/roulette_37edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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:200 --><br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc17"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:35 -->Marveltri</h1> | |||
Subgroup: 2.5.9/7<br /> | |||
< | Comma: 225/224<br /> | ||
Sval name: 3&amp;13<br /> | |||
Related temperaments: marvel, 22&amp;47, magic<br /> | |||
<br /> | <br /> | ||
< | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~5/4 = 383.638<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 225/224]<br /> | ||
< | Gencom map: [&lt;1 2/5 2 -1/5|, &lt;0 -4/5 1 2/5|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 5|, &lt;0 1 -2|]<br /> | |||
EDOs: 12, 13, 16, 19, 22, 47, 69<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.8159 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 /> | <br /> | ||
<a class="wiki_link" href="/ | <!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><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&amp;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 /> | <br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 703.856<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 352/351 364/363]<br /> | |||
Gencom map: [&lt;1 1 0 -8/3 1/3 7/3|, &lt;0 1 0 11/3 -1/3 -10/3|]<br /> | |||
< | |||
<br /> | <br /> | ||
Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br /> | |||
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.8488 cents<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:201:&lt;img src=&quot;/file/view/pepperoni_271edo.png/284861296/pepperoni_271edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/pepperoni_271edo.png/284861296/pepperoni_271edo.png" alt="pepperoni_271edo.png" title="pepperoni_271edo.png" /><!-- ws:end:WikiTextLocalImageRule:201 --><br /> | ||
< | |||
<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 /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:39:&lt;h1&gt; --><h1 id="toc19"><a name="Penta"></a><!-- ws:end:WikiTextHeadingRule:39 -->Penta</h1> | ||
Subgroup: 2.9.7.11<br /> | |||
Commas: 896/891, 26411/26244<br /> | |||
Svalname: 8&amp;11<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 438.465<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 896/891 26411/26244]<br /> | |||
Gencom map: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]<br /> | |||
< | |||
<br /> | <br /> | ||
< | Map: [&lt;1 0 -1 6|, &lt;0 5 6 -4|]<br /> | ||
EDOs: 8, 11, 30, 41, 52<br /> | |||
<a class="wiki_link" href=" | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9130 cents<br /> | ||
<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/penta9">Nine note albitonic scale</a><br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta13">Thirteen chromatic note scale</a><br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta17">Seventeen note mega chromatic scale</a><br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:41:&lt;h1&gt; --><h1 id="toc20"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:41 -->Shoe</h1> | ||
Subgroup: 2.5.7.11.13<br /> | |||
Commas: 176/175, 640/637, 847/845<br /> | |||
Sval name: 16&amp;21<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 227.108<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 176/175 640/637 847/845]<br /> | |||
Gencom map: [&lt;1 0 1 3 1 2|, &lt;0 0 7 -1 13 9|]<br /> | |||
< | |||
<br /> | <br /> | ||
Map: [&lt;1 1 3 1 2|, &lt;0 7 -1 13 9|]<br /> | |||
EDOs: 16, 21, 37<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.035<br /> | |||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextLocalImageRule:202:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/shoe_37edo.jpg/270828948/shoe_37edo.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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:202 --><br /> | ||
< | |||
<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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:43:&lt;h1&gt; --><h1 id="toc21"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:43 -->Guanyintet</h1> | |||
<!-- ws:start:WikiTextHeadingRule: | |||
Subgroup: 2.5.7/3.11/3<br /> | Subgroup: 2.5.7/3.11/3<br /> | ||
Commas: 176/175, 540/539<br /> | Commas: 176/175, 540/539<br /> | ||
| Line 1,425: | Line 1,487: | ||
<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/guanyintet9">Nine note albitonic scale</a><br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet13">Thirteen note chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/guanyintet13">Thirteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:45:&lt;h1&gt; --><h1 id="toc22"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:45 -->Baldy</h1> | <!-- ws:start:WikiTextHeadingRule:45:&lt;h1&gt; --><h1 id="toc22"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:45 -->Baldy</h1> | ||