Chromatic pairs: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 350962506 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 350979052 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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> | ||
| Line 73: | Line 73: | ||
[[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: --> | |||
<!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052942?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;11052942&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> | |||
</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | |||
<hr /> | |||
<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 /> | |||
<!-- ws:start:WikiTextLocalImageRule:187:&lt;img src=&quot;/file/view/terrain_3558edo.png/284858244/terrain_3558edo.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/terrain_3558edo.png/284858244/terrain_3558edo.png" alt="terrain_3558edo.png" title="terrain_3558edo.png" /><!-- ws:end:WikiTextLocalImageRule:187 --><br /> | |||
<br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain9">Nine note albitonic scale</a><br /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain15">Fifteen note chromatic scale</a><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:5:&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> | ||
Revision as of 19:54, 6 July 2012
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-07-06 19:54:27 UTC.
- The original revision id was 350979052.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc|flat]] [[media type="custom" key="11052942"]] ---- =Definitions= By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with [[xenharmonic/Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give. =Terrain= Subgroup: 2.9/5.9/7 Commas: 250047/250000 Sval name: 6&21 Related temperament: [[xenharmonic/Minortonic family#Domain|domain]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.0169 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]] =Tridec= Subgroup: 2.7/5.11/5.13/5 Commas: 847/845, 1001/1000 Sval name: 5&8 [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.0955 [[image:tridec_235edo.png]] [[xenharmonic/Tridec8|Eight note albitonic scale]] [[xenharmonic/Tridec13|Thirteen note chromatic scale]] =Petrtri= Subgroup: 2.11/5.13/5 Comma: 2200/2197 Svalname: 3&5 [[Lp tuning|POL2 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, 211, 240, 269, 298, 327, 356, 385, 741c, 1126c [[Lp tuning#L2 tuning|L2 error]]: 0.1745 cents [[image:petrtri_385edo.png]] [[xenharmonic/petrtri5|Five note haplotonic scale]] [[xenharmonic/petrtri8|Eight note albitonic 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= Subgroup: 2.3.5.19 Commas: 361/360, 513/512 Sval name: 12&29 Related temperament: [[xenharmonic/Schismatic family|schismatic]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.2438 cents [[image:nestoria_171edo.png]] [[xenharmonic/nestoria7|Seven note albitonic scale]] [[xenharmonic/nestoria12|Twelve note chromatic scale]] [[xenharmonic/nestoria17|Seventeen note mega chromatic scale]] =Bridgetown= Subgroup: 2.3.11/5.13/5 Commas: 352/351, 676/675 Sval name: 5&24 Related temperament: [[xenharmonic/The Archipelago|barabados]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.3920 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]] =Orgone= Subgroup: 2.7.11 Commas: 65536/65219 Svals: 4&7 Related temperament: [[Gamelismic clan#superkleismic|superkleismic]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.4197 cents [[image:orgone_308edo.jpg]] [[xenharmonic/orgone7|Seven note albitonic scale]] [[xenharmonic/orgone11|Eleven note chromatic scale]] [[xenharmonic/orgone15|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]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.4936 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]] =Marveltwintri= Subgroup: 2.5/3.13/9 Comma: 325/324 Svalname: 3&4 [[Lp tuning|POL2 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, 185, 219, 253, 287b, 321b [[Lp tuning#L2 tuning|L2 error]]: 0.5154 cents [[image:marveltwintri_321edo.png]] [[xenharmonic/marveltwintri7|Seven note albitonic scale]] [[xenharmonic/marveltwintri11|Eleven note chromatic scale]] [[xenharmonic/marveltwintri15|Fifteen note mega chromatic scale]] =Huntington= Subgroup: 2.5.7.13 Commas: 640/637, 10985/10976 Sval name: 10&27 [[Lp tuning|POL2 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, 400 [[Lp tuning#L2 tuning|L2 error]]: 0.5409 cents [[image:huntington_400edo.jpg]] [[xenharmonic/huntington7|Seven note haplotonic scale]] [[xenharmonic/huntington10|Ten note albitonic scale]] [[xenharmonic/huntington17|Seventeen note chromatic scale]] =Slendric= Subgroup: 2.3.7 Comma: 1029/1024 Sval name: 5&21 [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.6357 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]] =Photia= Subgroup: 2.3.5.17.19 Commas: 171/170, 256/255, 324/323 Sval name: 12&41 Related temperament: [[xenharmonic/Schismatic family|schismatic]] [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.6436 cents [[image:photia_65edo.png]] [[xenharmonic/photia7|Seven note albitonic scale]] [[xenharmonic/photia12|Twelve note chromatic scale]] =Neutraltet= Subgroup: 2.3.11 Commas: 243/242 Svalname: 7&17 [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.6714 cents [[image:neutraltet_380edo.png]] [[xenharmonic/neutraltet7|Seven note albitonic scale]] [[xenharmonic/neutraltet10|Ten note chromatic scale]] [[xenharmonic/neutraltet17|Seventeen note mega 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]] [[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 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, 47, 69 [[Lp tuning#L2 tuning|L2 error]]: 0.8159 cents [[xenharmonic/marveltri7|Seven note albitonic scale]] [[xenharmonic/marveltri10|Ten note chromatic scale]] [[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] =Pepperoni= Subgroup: 2.3.11/7.13/7 Commas: 352/351, 364/363 Sval name: 5&12 Related temperament: The [[xenharmonic/Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name. [[Lp tuning|POL2 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, 75, 196, 271 [[Lp tuning#L2 tuning|L2 error]]: 0.8488 cents [[image:pepperoni_271edo.png]] [[xenharmonic/pepperoni7|Seven note albitonic scale]] [[xenharmonic/pepperoni12|Twelve note chromatic scale]] =Penta= Subgroup: 2.9.7.11 Commas: 896/891, 26411/26244 Svalname: 8&11 [[Lp tuning|POL2 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 [[Lp tuning#L2 tuning|L2 error]]: 0.9130 cents [[xenharmonic/penta5|Five note haplotonic scale]] [[xenharmonic/penta9|Nine note albitonic scale]] [[xenharmonic/penta13|Thirteen chromatic note scale]] [[xenharmonic/penta17|Seventeen note mega chromatic scale]] =Shoe= Subgroup: 2.5.7.11.13 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 Related temperaments: guanyin, orwell [[Lp tuning|POL2 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, 227bc, 316bcd [[Lp tuning#L2 tuning|L2 error]]: 1.043 cents [[xenharmonic/guanyintet5|Five note haplotonic scale]] [[xenharmonic/guanyintet9|Nine note albitonic scale]] [[xenharmonic/guanyintet13|Thirteen note chromatic scale]] =Baldy= Subgroup: 2.9.5.7.13 Commas: 225/224, 325/324, 640/637 Sval name: 6&35 Related temperament: [[xenharmonic/Schismatic family|Garibaldi]] POTE generator: ~9/8 = 204.090 [[Gencom]]: Gencom map: Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|] EDOs: 6, 11, 17, 23, 29, 35, 41, [[xenharmonic/47edo|47]], 100, [[xenharmonic/147edo|147]] Error: 2.617 cents [[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]] =Bossier= Subgroup: 2.7.11.13 Commas: 1573/1568, 15488/15379 Sval name: 3&17 POTE generator: ~14/11 = 421.309 [[Gencom]]: Gencom map: Map: [<1 0 1 3|, <0 8 7 2|] EDOs: 17, 20, 37, 57, 94, 225 Error: 2.665 cents [[image:bossier_225edo.jpg]] [[xenharmonic/bossier8|Eight note albitonic scale]] [[xenharmonic/bossier11|Eleven note chromatic scale]] [[xenharmonic/bossier14|Fourteen note mega chromatic scale]] =Radon= Subgroup: 2.3.7.11 Commas: 896/891, 1029/1024 Sval name: 5&36 Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] POTE generator: ~8/7 = 234.381 [[Gencom]]: Gencom map: Map: [<1 1 3 6|, <0 3 -1 -13|] EDOs: 5, 36, 41, 87, 128 Error: 2.925 cents [[image:radon_128edo.jpg]] [[xenharmonic/radon5|Five note haplotonic scale]] [[xenharmonic/radon11|Eleven note albitonic scale]] [[xenharmonic/radon16|Sixteen note chromatic scale]] =Myna= Group: 2.3.5.7 Commas: 126/125, 1728/1715 Val name: 4&27 POTE generator: ~6/5 = 310.146 [[Gencom]]: Gencom map: Map: [<1 9 9 8|, <0 -10 -9 -7|] EDOs: 4, 27, 31, 58, 89 Error: 3.310 cents [[image:myna_89edo.jpg]] [[xenharmonic/myna7|Seven note haplotonic scale]] [[xenharmonic/myna11|Eleven note albitonic scale]] [[xenharmonic/myna15|Fifteen note chromatic scale]] =Silver= Subgroup: 2.5.7.13.17 Commas: 170/169, 640/637, 5525/5488 Sval name: 10&27 POTE generator: ~13/8 = 842.711 [[Gencom]]: Gencom map: Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, [[xenharmonic/487edo|487]] Error: 3.437 [[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]] =Mabila= Subgroup: 2.5.7 Comma: 1071875/1048576 Sval name: 7&9 POTE generator: ~175/128 = 527.236 [[Gencom]]: Gencom map: Map: [<1 1 5|, <0 3 -5|] EDOs: 7, 9, 16, 25, 41, 66 Error: 3.560 [[image:mabila_66edo.jpg]] [[xenharmonic/mabila7|Seven note haplotonic scale]] [[xenharmonic/mabila9|Nine note albitonic scale]] [[xenharmonic/mabila16|Sixteen note chromatic scale]] =Meantone= Group: 2.3.5.7 Commas: 81/80, 126/125 Val name: 12&19 POTE generator: 696.495 [[Gencom]]: Gencom map: Map: [<1 0 -4 -13|, <0 1 4 10|] EDOs: 5, 7, 12, 19, 31, 81, 112, 143 Error: 3.585 [[image:meantone_31edo.jpg]] [[xenharmonic/meantone5|Five note haplotonic scale]] [[xenharmonic/meantone7|Seven note albitonic scale]] [[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: ~6/5 = 311.213 [[Gencom]]: Gencom map: Map: [<1 0 -1|, <0 1 3|] EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b 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 [[Gencom]]: Gencom map: Map: [<1 0 0 2|, <0 6 10 -1|] EDOs: 33, 41, 49, 57, 106, 204, 253 Error: 3.968 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]] =Magic= Group: 2.3.5.7.11 Commas: 100/99, 225/224, 245/243 Val name: 19&22 POTE generator: ~5/4 = 380.696 [[Gencom]]: Gencom map: Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] EDOs: 19, 22, 41, 104, 145 Error: 4.489 [[image:xenharmonic/magic_145edo.jpg]] [[xenharmonic/magic7|Seven note haplotonic scale]] [[xenharmonic/magic10|Ten note albitonic scale]] [[xenharmonic/magic13|Thirteen note chromatic scale]] [[xenharmonic/magic16|Sixteen note mega chromatic scale]] ==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]] =Gariberttet= Subgroup: 2.5/3.7/3.13/11 Commas: 275/273, 847/845 Svalname: 4&29 POTE generator: ~13/11 = 292.418 [[Gencom]]: Gencom map: Map: [<1 0 0 0|, <0 3 5 1|] EDOs: 29, 33, 37, 41, 78 Error: 4.473 [[xenharmonic/gariberttet5|Five note haplotonic scale]] [[xenharmonic/gariberttet9|Nine note albitonic scale]] [[xenharmonic/gariberttet13|Thirteen note chromatic scale]] =Hemif= Subgroup: 2.3.7.11.13 Commas: 144/143, 243/242, 364/363 Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]] POTE generator: ~11/9 = 351.691 [[Gencom]]: Gencom map: Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] EDOs: 7, 10, 17, 24, 41, 58 Error: 4.867 cents [[image:hemif_58edo.jpg]] [[xenharmonic/hemif7|Seven note haplotonic scale]] [[xenharmonic/hemif10|Ten note albitonic scale]] [[xenharmonic/hemif17|Seventeen note chromatic scale]] =Skwares= Subgroup: 2.3.7.11 Commas: 99/98, 243/242 Related temperament: [[xenharmonic/Meantone family|squares]] POTE generator: ~9/7 = 425.244 [[Gencom]]: Gencom map: Map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 Error: 4.942 cents [[image:skwares_206edo.png]] [[xenharmonic/skwares8|Eight note albitonic scale]] [[xenharmonic/skwares11|Eleven note mega albitonic scale]] [[xenharmonic/skwares14|Fourteen note chromatic scale]] =Sensi= Group: 2.3.5.7 Commas: 126/126, 245/243 Val name: 19&27 POTE generator: ~9/7 = 443.383 [[Gencom]]: Gencom map: Map: [<1 6 8 11|, <0 -7 -9 -13|] EDOs: 5, 8, 11, 19, 27, 46 Error: 5.019 [[image:xenharmonic/sensi_46edo.jpg]] [[xenharmonic/sensi5|Five note haplotonic scale]] [[xenharmonic/sensi8|Eight note albitonic scale]] [[xenharmonic/sensi11|Eleven note mega albitonic scale]] [[xenharmonic/sensi19|Nineteen note chromatic scale]] =Greeley= Subgroup: 2.5/3.7/3.11/3 Commas: 121/120, 126/125 POTE generator: ~11/10 = 156.055 Related temperament: [[Porcupine family#Opossum|Opossum]] [[Gencom]]: Gencom map: Map: [<1 1 2 2|, <0 -2 -6 -1|] EDOs: 8, 15, 23, 77, 100 Error: 5.404 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 POTE generator: ~13/10 = 453.190 [[Gencom]]: Gencom map: Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] EDOs: 5, 8, 13, 21, 29, 37, 45 Error: 5.433 cents [[image:semidim_770edo.png]] [[xenharmonic/semidim8|Eight note albitonic scale]] [[xenharmonic/semidim13|Thirteen note chromatic scale]] =Orwell= Group: 2.3.5.7.11 Commas: 99/98, 121/120, 176/175 Val name: 9&22 POTE generator: ~7/6 = 271.426 [[Gencom]]: Gencom map: Map: [<1 0 3 1 3|, <0 7 -3 8 2|] EDOs: 9, 22, 31, 53, 84 Error: 5.584 [[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, magic POTE generator: ~6/5 = 319.424 [[Gencom]]: Gencom map: Map: [<1 0 5 2|, <0 1 -3 2|] EDOs: 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd 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 [[Gencom]]: Gencom map: Map: [<1 0 0|, <0 2 1|] EDOs: 8, 11, 30, 41, 52, 145b, 197bc 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 [[Gencom]]: Gencom map: Map: [<1 0 1|, <0 1 2|] EDOs: 9, 40, 49c, 58c, 67c, 76c 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 [[Gencom]]: Gencom map: Map: [<1 1 0|, <0 2 3|] EDOS: 13, 30, 43, 73, 116b 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]] =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 map: Map: [<1 1 2 3 3|, <0 5 7 4 6|] EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] Error: 6.361 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]] =Mohaha= Subgroup: 2.3.5.11 Commas: 81/80, 121/120 Related temperament: [[xenharmonic/Meantone family|mohajira]] POTE generator: ~11/9 = 348.094 [[Gencom]]: Gencom map: Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 24, 31, 69d, 100d, 131bd 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: ~11/9 = 348.916 [[Gencom]]: Gencom map: Map: [<1 1 0 2 4|, <0 2 8 5 -1|] EDOs: 17c, 24, 31, 55, 86de, 141cde 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 [[Gencom]]: Gencom map: Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] EDOs: 11, 30, 41 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 Commas: 81/80, 99/98, 126/125 Related temperament: [[xenharmonic/Meantone family|meantone]] POTE generator: ~9/8 = 193.937 [[Gencom]]: Gencom map: Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] EDOs: 25, 31, 68b, 99b 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 [[Gencom]]: Gencom map: Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] EDOs: 6, 7, 13, 19, 25, 31, 56, 81 Error: 20.338 cents [[image:leantone_81edo.png]] [[xenharmonic/leantone6|Six note haplotonic scale]] [[xenharmonic/leantone7|Seven note albitonic scale]] [[xenharmonic/leantone13|Thirteen note chromatic scale]] =Score= Subgroup: 2.7.11.13 Commas: 343/338, 847/832 POTE generator: ~11/8 = 540.099 [[Gencom]]: Gencom map: Map: [<1 1 3 1|, <0 4 1 6|] EDOs: 5, 7, 9, 11, 20 Error: 8.052 cents [[image:xenharmonic/score_20edo.jpg]] [[xenharmonic/score5|Five note haplotonic scale]] [[xenharmonic/score7|Seven note albitonic scale]] [[xenharmonic/score9|Nine note mega albitonic scale]] [[xenharmonic/score11|Eleven note chromatic scale]] =Supra= Subgroup: 2.3.7.11 Commas: 64/63, 99/98 Related temperament: [[xenharmonic/suprapyth|suprapyth]] POTE generator: ~3/2 = 707.192 [[Gencom]]: Gencom map: Map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c Error: 9.795 cents [[image:supra_56edo.png]] [[xenharmonic/supra7|Seven note albitonic scale]] [[xenharmonic/supra12|Twelve note chromatic scale]] ==Supraphon== Subgroup: 2.3.7.11.13 Commas: 64/63, 78/77, 99/98 POTE generator: ~3/2 = 706.137 [[Gencom]]: Gencom map: Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] EDOs: 5, 7, 12, 17 Error: 10.534 cents ==Machine== Subgroup: 2.9.7.11 Commas: 64/63, 99/98 POTE generator: ~9/8 = 214.384 [[Gencom]]: Gencom map: 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: ~8/7 = 214.095 [[Gencom]]: Gencom map: Map: [<2 0 11 12|, <0 1 -1 -1|] EDOS: 4, 6, 10, 16, 22, 28 Error: 11.508 cents [[image:antikythera_28edo.png]] [[xenharmonic/antikythera6|Six note haplotonic scale]] [[xenharmonic/antikythera10|Ten note albitonic scale]] [[xenharmonic/antikythera16|Sixteen note chromatic scale]] =Deutone= Subgroup: 2.9.5.7.13 Commas: 65/64, 81/80, 91/90 Related temperament: [[xenharmonic/Meantone family|meanpop]] POTE generator: ~9/8 = 191.059 [[Gencom]]: Gencom map: Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] EDOs: 6, 7, 13, 19, 25, 44, 69 Error: 12.145 cents [[image:deutone_44edo.png]] [[xenharmonic/deutone6|Six note haplotonic scale]] [[xenharmonic/deutone7|seven note albitonic scale]] [[xenharmonic/deutone13|Thirteen note chromatic scale]] =Semaphore= Subgroup: 2.3.7 Comma: 49/48 POTE generator: ~7/6 = 250.385 [[Gencom]]: Gencom map: Map: [<1 0 2|, <0 2 1|] EDOs: 5, 9, 14, 19, 24 Error: 12.428 [[image:semaphore_24edo.png]] [[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 map: Map: [<3 7 0 2|, <0 0 1 1|] EDOs: 3, 6, 9, 15, 21 Error: 12.830 cents [[image:augment_21edo.png]] [[xenharmonic/augment6|Six note haplotonic scale]] [[xenharmonic/augment9|Nine note albitonic scale]] [[xenharmonic/augment12|Twelve note chromatic scale]]
Original HTML content:
<html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:123:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- 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: --> <!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextMediaRule:0:<img src="http://www.wikispaces.com/site/embedthumbnail/custom/11052942?h=0&w=0" class="WikiMedia WikiMediaCustom" id="wikitext@@media@@type=&quot;custom&quot; key=&quot;11052942&quot;" title="Custom Media"/> --><script type="text/javascript" src="http://mediaplayer.yahoo.com/js"> </script><!-- ws:end:WikiTextMediaRule:0 --><br /> <hr /> <br /> <!-- ws:start:WikiTextHeadingRule:1:<h1> --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definitions</h1> By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Just%20intonation%20subgroups">subgroup temperament</a>) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:3:<h1> --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1> Subgroup: 2.9/5.9/7<br /> Commas: 250047/250000<br /> Sval name: 6&21<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortonic%20family#Domain">domain</a><br /> <br /> <a class="wiki_link" href="/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: [<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="/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 /> <!-- ws:start:WikiTextLocalImageRule:187:<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:187 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/terrain15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:5:<h1> --><h1 id="toc2"><a name="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&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: [<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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.0955<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:188:<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: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:<h1> --><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&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: [<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, 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:<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: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 /> <!-- ws:start:WikiTextHeadingRule:9:<h1> --><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&29<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.2419<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:190:<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:190 --><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: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="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.2438 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:191:<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:191 --><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="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&24<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barabados</a><br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.3920 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:192:<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:192 --><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:15:<h2> --><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 /> <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:17:<h1> --><h1 id="toc8"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:17 -->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="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4197 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:193:<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:193 --><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:19:<h1> --><h1 id="toc9"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:19 -->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="/Lp%20tuning">POL2 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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4936 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:194:<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: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 /> <!-- ws:start:WikiTextHeadingRule:21:<h1> --><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&4<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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, 185, 219, 253, 287b, 321b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.5154 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:195:<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:195 --><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:23:<h1> --><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&27<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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, 400<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.5409 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:196:<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:196 --><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:25:<h1> --><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&21<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6357 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:197:<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:197 --><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:27:<h2> --><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 /> <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:29:<h1> --><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&41<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6436 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:198:<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:198 --><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:31:<h1> --><h1 id="toc15"><a name="Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:31 -->Neutraltet</h1> Subgroup: 2.3.11<br /> Commas: 243/242<br /> Svalname: 7&17<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6714 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:199:<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:199 --><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:33:<h1> --><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&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="/Lp%20tuning">POL2 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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6943 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:200:<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:200 --><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:35:<h1> --><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&13<br /> Related temperaments: marvel, 22&47, magic<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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, 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 /> <!-- 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="/Lp%20tuning">POL2 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, 75, 196, 271<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.8488 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:201:<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:201 --><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="Penta"></a><!-- ws:end:WikiTextHeadingRule:39 -->Penta</h1> Subgroup: 2.9.7.11<br /> Commas: 896/891, 26411/26244<br /> Svalname: 8&11<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9130 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/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 /> <!-- ws:start:WikiTextHeadingRule:41:<h1> --><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&21<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 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<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.035<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:202:<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:202 --><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:43:<h1> --><h1 id="toc21"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:43 -->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="/Lp%20tuning">POL2 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, 227bc, 316bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.043 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:45:<h1> --><h1 id="toc22"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:45 -->Baldy</h1> Subgroup: 2.9.5.7.13<br /> Commas: 225/224, 325/324, 640/637<br /> Sval name: 6&35<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br /> <br /> POTE generator: ~9/8 = 204.090<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]<br /> EDOs: 6, 11, 17, 23, 29, 35, 41, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 100, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/147edo">147</a><br /> Error: 2.617 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:203:<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:203 --><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:47:<h1> --><h1 id="toc23"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:47 -->Bossier</h1> Subgroup: 2.7.11.13<br /> Commas: 1573/1568, 15488/15379<br /> Sval name: 3&17<br /> <br /> POTE generator: ~14/11 = 421.309<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 1 3|, <0 8 7 2|]<br /> EDOs: 17, 20, 37, 57, 94, 225<br /> Error: 2.665 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:204:<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:204 --><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:49:<h1> --><h1 id="toc24"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:49 -->Radon</h1> Subgroup: 2.3.7.11<br /> Commas: 896/891, 1029/1024<br /> Sval name: 5&36<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gamelismic%20clan">Rodan</a><br /> <br /> POTE generator: ~8/7 = 234.381<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> Error: 2.925 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:205:<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:205 --><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:51:<h1> --><h1 id="toc25"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:51 -->Myna</h1> Group: 2.3.5.7<br /> Commas: 126/125, 1728/1715<br /> Val name: 4&27<br /> <br /> POTE generator: ~6/5 = 310.146<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 9 9 8|, <0 -10 -9 -7|]<br /> EDOs: 4, 27, 31, 58, 89<br /> Error: 3.310 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:206:<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:206 --><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:53:<h1> --><h1 id="toc26"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:53 -->Silver</h1> Subgroup: 2.5.7.13.17<br /> Commas: 170/169, 640/637, 5525/5488<br /> Sval name: 10&27<br /> <br /> POTE generator: ~13/8 = 842.711<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]<br /> EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487</a><br /> Error: 3.437<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:207:<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:207 --><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:55:<h1> --><h1 id="toc27"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:55 -->Mabila</h1> Subgroup: 2.5.7<br /> Comma: 1071875/1048576<br /> Sval name: 7&9<br /> <br /> POTE generator: ~175/128 = 527.236<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 5|, <0 3 -5|]<br /> EDOs: 7, 9, 16, 25, 41, 66<br /> Error: 3.560<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:208:<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:208 --><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:57:<h1> --><h1 id="toc28"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:57 -->Meantone</h1> Group: 2.3.5.7<br /> Commas: 81/80, 126/125<br /> Val name: 12&19<br /> <br /> POTE generator: 696.495<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 -4 -13|, <0 1 4 10|]<br /> EDOs: 5, 7, 12, 19, 31, 81, 112, 143<br /> Error: 3.585<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:209:<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:209 --><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:59:<h1> --><h1 id="toc29"><a name="Starlingtet"></a><!-- ws:end:WikiTextHeadingRule:59 -->Starlingtet</h1> Group: 2.5/3.7/3<br /> Comma: 126/125<br /> Svalname: 4&15<br /> Related temperaments: starling; becomes myna<br /> POTE generator: ~6/5 = 311.213<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 -1|, <0 1 3|]<br /> EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br /> Error: 311.213<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:61:<h1> --><h1 id="toc30"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:61 -->Indium</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 3025/3024, 3125/3087<br /> Sval name: 8&33<br /> <br /> POTE generator: ~12/11 = 147.159<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 0 2|, <0 6 10 -1|]<br /> EDOs: 33, 41, 49, 57, 106, 204, 253<br /> Error: 3.968 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:210:<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:210 --><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:63:<h2> --><h2 id="toc31"><a name="Indium-Music"></a><!-- ws:end:WikiTextHeadingRule:63 -->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:65:<h1> --><h1 id="toc32"><a name="Magic"></a><!-- ws:end:WikiTextHeadingRule:65 -->Magic</h1> Group: 2.3.5.7.11<br /> Commas: 100/99, 225/224, 245/243<br /> Val name: 19&22<br /> <br /> POTE generator: ~5/4 = 380.696<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> EDOs: 19, 22, 41, 104, 145<br /> Error: 4.489<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:211:<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:211 --><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:67:<h2> --><h2 id="toc33"><a name="Magic-Music"></a><!-- ws:end:WikiTextHeadingRule:67 -->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:69:<h1> --><h1 id="toc34"><a name="Gariberttet"></a><!-- ws:end:WikiTextHeadingRule:69 -->Gariberttet</h1> Subgroup: 2.5/3.7/3.13/11<br /> Commas: 275/273, 847/845<br /> Svalname: 4&29<br /> <br /> POTE generator: ~13/11 = 292.418<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 0 0|, <0 3 5 1|]<br /> EDOs: 29, 33, 37, 41, 78<br /> Error: 4.473<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:71:<h1> --><h1 id="toc35"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:71 -->Hemif</h1> Subgroup: 2.3.7.11.13<br /> Commas: 144/143, 243/242, 364/363<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a><br /> <br /> POTE generator: ~11/9 = 351.691<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> Error: 4.867 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:212:<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:212 --><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:73:<h1> --><h1 id="toc36"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:73 -->Skwares</h1> Subgroup: 2.3.7.11<br /> Commas: 99/98, 243/242<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">squares</a><br /> <br /> POTE generator: ~9/7 = 425.244<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br /> Error: 4.942 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:213:<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:213 --><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:75:<h1> --><h1 id="toc37"><a name="Sensi"></a><!-- ws:end:WikiTextHeadingRule:75 -->Sensi</h1> Group: 2.3.5.7<br /> Commas: 126/126, 245/243<br /> Val name: 19&27<br /> <br /> POTE generator: ~9/7 = 443.383<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 6 8 11|, <0 -7 -9 -13|]<br /> EDOs: 5, 8, 11, 19, 27, 46<br /> Error: 5.019<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:214:<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:214 --><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:77:<h1> --><h1 id="toc38"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:77 -->Greeley</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 121/120, 126/125<br /> <br /> POTE generator: ~11/10 = 156.055<br /> Related temperament: <a class="wiki_link" href="/Porcupine%20family#Opossum">Opossum</a><br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 77, 100<br /> Error: 5.404 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:215:<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:215 --><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:79:<h2> --><h2 id="toc39"><a name="Greeley-Music"></a><!-- ws:end:WikiTextHeadingRule:79 -->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:81:<h1> --><h1 id="toc40"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:81 -->Semidim</h1> Subgroup: 2.5/3.7/3.11/3.13/3<br /> Commas: 121/120, 169/168, 275/273<br /> Sval name: 8&29<br /> <br /> POTE generator: ~13/10 = 453.190<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]<br /> EDOs: 5, 8, 13, 21, 29, 37, 45<br /> Error: 5.433 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:216:<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:216 --><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:83:<h1> --><h1 id="toc41"><a name="Orwell"></a><!-- ws:end:WikiTextHeadingRule:83 -->Orwell</h1> Group: 2.3.5.7.11<br /> Commas: 99/98, 121/120, 176/175<br /> Val name: 9&22<br /> <br /> POTE generator: ~7/6 = 271.426<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> EDOs: 9, 22, 31, 53, 84<br /> Error: 5.584<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:217:<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:217 --><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:85:<h1> --><h1 id="toc42"><a name="Magicaltet"></a><!-- ws:end:WikiTextHeadingRule:85 -->Magicaltet</h1> Group: 2.5/3.7.11<br /> Commas: 100/99, 385/384<br /> Related temperaments: 4&7&15, magic<br /> <br /> POTE generator: ~6/5 = 319.424<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 5 2|, <0 1 -3 2|]<br /> EDOs: 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd<br /> Error: 5.720 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:87:<h1> --><h1 id="toc43"><a name="Sentry"></a><!-- ws:end:WikiTextHeadingRule:87 -->Sentry</h1> Group: 2.5/3.9/7<br /> Commas: 245/243<br /> Svalname: 3&5<br /> Related temperaments: sensi<br /> <br /> POTE generator: ~9/7 = 438.574<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 0|, <0 2 1|]<br /> EDOs: 8, 11, 30, 41, 52, 145b, 197bc<br /> Error: 5.793 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:89:<h1> --><h1 id="toc44"><a name="Mothwelltri"></a><!-- ws:end:WikiTextHeadingRule:89 -->Mothwelltri</h1> Group: 2.7/3.11<br /> Comma: 99/98<br /> Svalname: 1&4<br /> Related temperament: Orwell<br /> <br /> POTE generator:~7/6 = 268.508<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 1|, <0 1 2|]<br /> EDOs: 9, 40, 49c, 58c, 67c, 76c<br /> Error: 6.119 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:91:<h1> --><h1 id="toc45"><a name="Lovecraft"></a><!-- ws:end:WikiTextHeadingRule:91 -->Lovecraft</h1> Group: 2.11.13<br /> <br /> POTE generator: ~13/11 = 279.318<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 0|, <0 2 3|]<br /> EDOS: 13, 30, 43, 73, 116b<br /> Error: 6.026 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:218:<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:218 --><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:93:<h1> --><h1 id="toc46"><a name="Bleu"></a><!-- ws:end:WikiTextHeadingRule:93 -->Bleu</h1> Group: 2.3.7.11.13<br /> Commas: 78/77, 99/98, 144/143<br /> Sval name: 9&17<br /> <br /> POTE generator: ~13/12 = 139.990<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<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 /> Error: 6.361 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:219:<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:219 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu8">bleu8</a> - Eight note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu9">bleu9</a> - Nine note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/albitonic%20scale">albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bleu17">bleu17</a> - Seventeen note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/chromatic%20scale">chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:95:<h1> --><h1 id="toc47"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:95 -->Mohaha</h1> Subgroup: 2.3.5.11<br /> Commas: 81/80, 121/120<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">mohajira</a><br /> <br /> POTE generator: ~11/9 = 348.094<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 24, 31, 69d, 100d, 131bd<br /> Error: 6.733 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:220:<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:220 --><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:97:<h3> --><h3 id="toc48"><a name="Mohaha--Music"></a><!-- ws:end:WikiTextHeadingRule:97 -->Music</h3> <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:99:<h2> --><h2 id="toc49"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:99 -->Mohoho</h2> Subgroup: 2.3.5.11.13<br /> Commas: 66/65, 81/80, 121/120<br /> <br /> POTE generator: ~11/9 = 348.916<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 0 2 4|, <0 2 8 5 -1|]<br /> EDOs: 17c, 24, 31, 55, 86de, 141cde<br /> Error: 9.556 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:101:<h1> --><h1 id="toc50"><a name="Stacks"></a><!-- ws:end:WikiTextHeadingRule:101 -->Stacks</h1> Subgroup: 2.9.15.7.11.13<br /> Commas: 100/99, 105/104, 144/143, 196/195<br /> Svalname: 11&30<br /> <br /> POTE generator: ~9/7 = 438.977<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]<br /> EDOs: 11, 30, 41<br /> Error: 6.947 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:103:<h1> --><h1 id="toc51"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:103 -->Tutone</h1> Subgroup: 2.9.5.7.11<br /> Commas: 81/80, 99/98, 126/125<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meantone</a><br /> <br /> POTE generator: ~9/8 = 193.937<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]<br /> EDOs: 25, 31, 68b, 99b<br /> Error: 7.047 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tutone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextLocalImageRule:221:<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:221 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:105:<h1> --><h1 id="toc52"><a name="Leantone"></a><!-- ws:end:WikiTextHeadingRule:105 -->Leantone</h1> Subgroup: 2.9.5.7.11<br /> Commas: 45/44, 56/55, 81/80<br /> Related temperament: <a class="wiki_link" href="/meanenneadecal">meanenneadecal</a><br /> <br /> POTE generator: ~9/8 = 192.500<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> Error: 20.338 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:222:<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:222 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/leantone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:107:<h1> --><h1 id="toc53"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:107 -->Score</h1> Subgroup: 2.7.11.13<br /> Commas: 343/338, 847/832<br /> <br /> POTE generator: ~11/8 = 540.099<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 1 3 1|, <0 4 1 6|]<br /> EDOs: 5, 7, 9, 11, 20<br /> Error: 8.052 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:223:<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:223 --><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:109:<h1> --><h1 id="toc54"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:109 -->Supra</h1> Subgroup: 2.3.7.11<br /> Commas: 64/63, 99/98<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/suprapyth">suprapyth</a><br /> <br /> POTE generator: ~3/2 = 707.192<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c<br /> Error: 9.795 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:224:<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:224 --><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:111:<h2> --><h2 id="toc55"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:111 -->Supraphon</h2> Subgroup: 2.3.7.11.13<br /> Commas: 64/63, 78/77, 99/98<br /> <br /> POTE generator: ~3/2 = 706.137<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]<br /> EDOs: 5, 7, 12, 17<br /> Error: 10.534 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:113:<h2> --><h2 id="toc56"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:113 -->Machine</h2> Subgroup: 2.9.7.11<br /> Commas: 64/63, 99/98<br /> <br /> POTE generator: ~9/8 = 214.384<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> Error: 10.100 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:225:<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:225 --><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:115:<h1> --><h1 id="toc57"><a name="Antikythera"></a><!-- ws:end:WikiTextHeadingRule:115 -->Antikythera</h1> Subgroup: 2.9.5.7<br /> Commas: 50/49, 64/63<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/pajara">pajara</a><br /> <br /> POTE generator: ~8/7 = 214.095<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<2 0 11 12|, <0 1 -1 -1|]<br /> EDOS: 4, 6, 10, 16, 22, 28<br /> Error: 11.508 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:226:<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:226 --><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:117:<h1> --><h1 id="toc58"><a name="Deutone"></a><!-- ws:end:WikiTextHeadingRule:117 -->Deutone</h1> Subgroup: 2.9.5.7.13<br /> Commas: 65/64, 81/80, 91/90<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone%20family">meanpop</a><br /> <br /> POTE generator: ~9/8 = 191.059<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]<br /> EDOs: 6, 7, 13, 19, 25, 44, 69<br /> Error: 12.145 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:227:<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:227 --><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:119:<h1> --><h1 id="toc59"><a name="Semaphore"></a><!-- ws:end:WikiTextHeadingRule:119 -->Semaphore</h1> Subgroup: 2.3.7<br /> Comma: 49/48<br /> <br /> POTE generator: ~7/6 = 250.385<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<1 0 2|, <0 2 1|]<br /> EDOs: 5, 9, 14, 19, 24<br /> Error: 12.428<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:228:<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:228 --><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:121:<h1> --><h1 id="toc60"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:121 -->Augment</h1> Subgroup: 2.5.7.11<br /> Commas: 56/55, 128/125<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Augmented%20family">augmented</a><br /> <br /> POTE generator: ~8/7 = 228.275<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>:<br /> Gencom map:<br /> <br /> Map: [<3 7 0 2|, <0 0 1 1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> Error: 12.830 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:229:<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:229 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/augment12">Twelve note chromatic scale</a></body></html>