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Wikispaces>genewardsmith **Imported revision 351859540 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 351866806 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-09 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-09 18:31:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>351866806</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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[[xenharmonic/huntington17|Seventeen note chromatic scale]] | [[xenharmonic/huntington17|Seventeen note chromatic scale]] | ||
= | =Pepperoni= | ||
Subgroup: 2. | Subgroup: 2.3.11/7.13/7 | ||
Commas: | Commas: 352/351, 364/363 | ||
Sval name: | Sval name: 5&12 | ||
Related temperament: [[xenharmonic/ | 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]]: ~ | [[Lp tuning|POL2 generator]]: ~3/2 = 703.856 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 3/2; 352/351 364/363] | ||
Gencom map: [<1 0 | Gencom map: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|] | ||
Map: [<1 0 | Map: [<1 0 7 12|, <0 1 -4 -7|] | ||
EDOs: | EDOs: 5, 7, 12, 17, 29, 46, 75, 104, 196, 271, 595bcd | ||
[[Lp tuning#L2 tuning|L2 error]]: | [[Lp tuning#L2 tuning|L2 error]]: 0.9282 cents | ||
[[image: | [[image:pepperoni_271edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/pepperoni7|Seven note albitonic scale]] | ||
[[xenharmonic/pepperoni12|Twelve note chromatic scale]] | |||
[[xenharmonic/ | |||
= | =Penta= | ||
Subgroup: 2. | Subgroup: 2.9.7.11 | ||
Commas: | Commas: 896/891, 26411/26244 | ||
Svalname: 8&11 | |||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~9/7 = 438.465 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 9/7; 896/891 26411/26244] | ||
Gencom map: [<1 | Gencom map: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|] | ||
Map: [<1 0 | Map: [<1 0 -1 6|, <0 5 6 -4|] | ||
EDOs: | EDOs: 8, 11, 30, 41, 52 | ||
[[Lp tuning#L2 tuning|L2 error]]: | [[Lp tuning#L2 tuning|L2 error]]: 0.9531 cents | ||
[[ | [[xenharmonic/penta5|Five note haplotonic scale]] | ||
[[xenharmonic/penta9|Nine note albitonic scale]] | |||
[[xenharmonic/ | [[xenharmonic/penta13|Thirteen chromatic note scale]] | ||
[[xenharmonic/ | [[xenharmonic/penta17|Seventeen note mega chromatic scale]] | ||
=Marveltri= | =Marveltri= | ||
| Line 307: | Line 304: | ||
[[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] | [[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] | ||
= | =Bossier= | ||
Subgroup: 2. | Subgroup: 2.7.11.13 | ||
Commas: | Commas: 1573/1568, 15488/15379 | ||
Sval name: | Sval name: 3&17 | ||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~14/11 = 421.309 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 14/11; 1573/1568 15488/15379] | ||
Gencom map: [<1 | Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|] | ||
Map: [<1 0 | Map: [<1 0 1 3|, <0 8 7 2|] | ||
EDOs: | EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd | ||
[[Lp tuning#L2 tuning|L2 error]]: 0. | [[Lp tuning#L2 tuning|L2 error]]: 0.9904 cents | ||
[[image: | [[image:bossier_225edo.jpg]] | ||
[[xenharmonic/ | [[xenharmonic/bossier8|Eight note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/bossier11|Eleven note chromatic scale]] | ||
[[xenharmonic/bossier14|Fourteen note mega chromatic scale]] | |||
[[xenharmonic/ | |||
=Shoe= | =Shoe= | ||
| Line 386: | Line 364: | ||
[[xenharmonic/guanyintet13|Thirteen note chromatic scale]] | [[xenharmonic/guanyintet13|Thirteen note chromatic scale]] | ||
=Garibaldi= | =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]]: 1.364 cents | |||
[[image:xenharmonic/roulette_37edo.jpg]] | |||
[[xenharmonic/roulette6|roulette6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] | |||
[[xenharmonic/roulette7|roulette7]] - seven note [[xenharmonic/albitonic scale|albitonic scale]] | |||
[[xenharmonic/roulette13|roulette13]] - thirteen note [[xenharmonic/chromatic scale|chromatic scale]] | |||
[[xenharmonic/roulette19|roulette19]] - nineteen note [[xenharmonic/mega chromatic scale|mega chromatic scale]] | |||
=Garibaldi= | |||
Group: 2.3.5.7 | Group: 2.3.5.7 | ||
Commas: 225/224, 3125/3087 | Commas: 225/224, 3125/3087 | ||
| Line 405: | Line 405: | ||
[[xenharmonic/garibaldi17|Seventeen note chromatic scale]] | [[xenharmonic/garibaldi17|Seventeen note chromatic scale]] | ||
=Baldy= | =Radon= | ||
Subgroup: 2.9.5.7.13 | Subgroup: 2.3.7.11 | ||
Commas: 896/891, 1029/1024 | |||
Sval name: 5&36 | |||
Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] | |||
[[Lp tuning|POL2 generator]]: ~8/7 = 234.381 | |||
[[Gencom]]: [2 8/7; 896/891 1029/1024] | |||
Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|] | |||
Map: [<1 1 3 6|, <0 3 -1 -13|] | |||
EDOs: 5, 36, 41, 87, 128 | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.454 cents | |||
[[image:radon_128edo.jpg]] | |||
[[xenharmonic/radon5|Five note haplotonic scale]] | |||
[[xenharmonic/radon11|Eleven note albitonic scale]] | |||
[[xenharmonic/radon16|Sixteen note chromatic scale]] | |||
=Baldy= | |||
Subgroup: 2.9.5.7.13 | |||
Commas: 225/224, 325/324, 640/637 | Commas: 225/224, 325/324, 640/637 | ||
Sval name: 6&35 | Sval name: 6&35 | ||
| Line 426: | Line 447: | ||
[[xenharmonic/baldy17|baldy17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | [[xenharmonic/baldy17|baldy17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | ||
= | =Photia= | ||
Subgroup: 2. | Subgroup: 2.3.5.17.19 | ||
Commas: | Commas: 171/170, 256/255, 324/323 | ||
Sval name: | Sval name: 12&41 | ||
Related temperament: [[xenharmonic/Schismatic family|schismatic]] | |||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~3/2 = 701.470 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 3/2; 171/170 256/255 324/323] | ||
Gencom map: [<1 0 0 0 | Gencom map: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|] | ||
Map: [<1 0 | Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|] | ||
EDOs: 17, | EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d | ||
[[Lp tuning#L2 tuning|L2 error]]: | [[Lp tuning#L2 tuning|L2 error]]: 1.520 cents | ||
[[image: | [[image:photia_65edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/photia7|Seven note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/photia12|Twelve note chromatic scale]] | ||
= | =Mabila= | ||
Subgroup: 2. | Subgroup: 2.5.7 | ||
Comma: 1071875/1048576 | |||
Sval name: | Sval name: 7&9 | ||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~175/128 = 527.236 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 175/128; 1071875/1048576] | ||
Gencom map: [<1 1 | Gencom map: [<1 0 1 5}, <0, 0, 3, -5|] | ||
Map: [<1 1 | Map: [<1 1 5|, <0 3 -5|] | ||
EDOs: | EDOs: 7, 9, 16, 25, 41, 66, 305bc | ||
[[Lp tuning#L2 tuning|L2 error]]: 1. | [[Lp tuning#L2 tuning|L2 error]]: 1.546 cents | ||
[[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]] | ||
=Myna= | =Silver= | ||
Group: 2.3.5.7 | Subgroup: 2.5.7.13.17 | ||
Commas: 170/169, 640/637, 5525/5488 | |||
Sval name: 10&27 | |||
[[Lp tuning|POL2 generator]]: ~13/8 = 842.711 | |||
[[Gencom]]: [2 13/8; 170/169 640/637 5525/5488] | |||
Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|] | |||
Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] | |||
EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, 178e, 309cde, [[xenharmonic/487edo|487bcdee]] | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.557 cents | |||
[[image:silver_487edo.jpg]] | |||
[[xenharmonic/silver7|silver7]] -seven note [[xenharmonic/haplotonic scale|haplotonic scale]] | |||
[[xenharmonic/silver10|silver10]] - ten note [[xenharmonic/albitonic scale|albitonic scale]] | |||
[[xenharmonic/silver17|silver17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] | |||
=Myna= | |||
Group: 2.3.5.7 | |||
Commas: 126/125, 1728/1715 | Commas: 126/125, 1728/1715 | ||
Val name: 4&27 | Val name: 4&27 | ||
| Line 487: | Line 527: | ||
[[xenharmonic/myna15|Fifteen note chromatic scale]] | [[xenharmonic/myna15|Fifteen note chromatic scale]] | ||
= | =Meantone= | ||
Group: 2.3.5.7 | |||
Commas: | Commas: 81/80, 126/125 | ||
Val name: 12&19 | |||
[[Lp tuning|POL2 generator]]: ~3/2 = 696.495 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 3/2; 81/80 126/125] | ||
Gencom map: [<1 1 0 -3|, <0 1 4 10|] | |||
[ | Map: [<1 0 -4 -13|, <0 1 4 10|] | ||
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 2.763 cents | ||
[[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 | |||
[[Lp tuning|POL2 generator]]: ~6/5 = 311.154 | |||
[[Gencom]]: [2 6/5; 126/125] | |||
Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|] | |||
[[ | Map: [<1 0 -1|, <0 1 3|] | ||
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.680 cents | |||
[[xenharmonic/ | [[xenharmonic/starlingtet4|Four note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/starlingtet7|Seven note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/starlingtet11|Eleven note chromatic scale]] | ||
= | =Indium= | ||
Subgroup: 2.5/3.7/3.11/3 | |||
Commas: | Commas: 3025/3024, 3125/3087 | ||
Sval name: 8&33 | |||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~12/11 = 147.010 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 12/11; 3025/3024 3125/3087] | ||
Gencom map: [<1 1 | Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|] | ||
Map: [<1 0 | Map: [<1 0 0 2|, <0 6 10 -1|] | ||
EDOs: | EDOs: 33, 41, 49, 57, 106, 204, 253 | ||
[[Lp tuning#L2 tuning|L2 error]]: | [[Lp tuning#L2 tuning|L2 error]]: 1.741 cents | ||
[[image: | [[image:indium_253edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/indium8|Eight note albitonic scale]] | ||
[[xenharmonic/indium17|Seventeen note chromatic scale]] | |||
[[xenharmonic/ | |||
= | ==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 | |||
[[Lp tuning|POL2 generator]]: ~5/4 = 380.696 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 5/4; 100/99 225/224 245/243] | ||
[ | Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | ||
[ | |||
Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] | |||
EDOs: 19, 22, 41, 104, 145 | |||
[[Lp tuning#L2 tuning|L2 error]]: 2.741 cents | |||
[[ | [[image:xenharmonic/magic_145edo.jpg]] | ||
[[ | [[xenharmonic/magic7|Seven note haplotonic scale]] | ||
[[xenharmonic/magic10|Ten note albitonic scale]] | |||
[[xenharmonic/magic13|Thirteen note chromatic scale]] | |||
[[xenharmonic/magic16|Sixteen note mega chromatic scale]] | |||
==Music== | |||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]////</span> [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] | |||
[[ | |||
=Gariberttet= | |||
Subgroup: 2.5/3.7/3.13/11 | |||
Commas: 275/273, 847/845 | |||
Svalname: 4&29 | |||
[[ | [[Lp tuning|POL2 generator]]: ~13/11 = 293.679 | ||
[[Gencom]]: [2 13/11; 275/273 847/845] | |||
Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|] | |||
Map: [<1 0 0 0|, <0 3 5 1|] | |||
EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.694 cents | |||
[[ | [[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]] | |||
[[Lp tuning|POL2 generator]]: ~11/9 = 351.691 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 11/9; 144/143 243/242 364/363] | ||
Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] | |||
[ | Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | ||
EDOs: 7, 10, 17, 24, 41, 58 | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.756 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]] | |||
[[ | [[Lp tuning|POL2 generator]]: ~9/7 = 425.244 | ||
[[Gencom]]: [2 9/7; 99/98 243/242] | |||
Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|] | |||
[ | Map: [<1 3 6 7|, <0 -4 -9 -10|] | ||
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 2.457 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: 126/125, 245/243 | |||
Val name: 19&27 | |||
[[Lp tuning|POL2 generator]]: ~9/7 = 443.383 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 9/7; 126/125 245/243] | ||
Gencom map: [<1 -1 -1 -2|, <0 7 9 13|] | |||
[ | Map: [<1 6 8 11|, <0 -7 -9 -13|] | ||
EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 2.647 cents | ||
[[image:xenharmonic/sensi_46edo.jpg]] | |||
[[ | [[xenharmonic/sensi5|Five note haplotonic scale]] | ||
[[xenharmonic/sensi8|Eight note albitonic scale]] | |||
[[xenharmonic/sensi11|Eleven note mega albitonic scale]] | |||
[[xenharmonic/sensi19|Nineteen note chromatic scale]] | |||
=Greeley= | |||
Subgroup: 2.5/3.7/3.11/3 | |||
Commas: 121/120, 126/125 | |||
[[Lp tuning|POL2 generator]]: ~11/10 = 155.776 | |||
Related temperament: [[Porcupine family#Opossum|Opossum]] | |||
[[Gencom]]: [2 11/10; 121/120 126/125] | |||
Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|] | |||
[[ | Map: [<1 1 2 2|, <0 -2 -6 -1|] | ||
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd | |||
[[Lp tuning#L2 tuning|L2 error]]: 2.313 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 | |||
[[Lp tuning|POL2 generator]]: ~13/10 = 453.242 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 13/10; 121/120 169/168 275/273] | ||
Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|] | |||
[ | Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] | ||
EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde, | |||
[[Lp tuning#L2 tuning|L2 error]]: 2.577 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 | |||
[[ | [[Lp tuning|POL2 generator]]: ~7/6 = 271.426 | ||
[[ | [[Gencom]]: [2 7/6; 99/98 121/120 176/175] | ||
[ | Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|] | ||
Map: [<1 0 3 1 3|, <0 7 -3 8 2|] | |||
< | EDOs: 9, 22, 31, 53, 84e | ||
[[Lp tuning#L2 tuning|L2 error]]: 2.574 cents | |||
[[image:xenharmonic/orwell_84edo.png]] | |||
[[ | [[xenharmonic/orwell5|Five note haplotonic scale]] | ||
[[xenharmonic/orwell9|Nine note albitonic scale]] | |||
[[xenharmonic/orwell13|Thirteen note chromatic scale]] | |||
=Magicaltet= | |||
Group: 2.5/3.7.11 | |||
Commas: 100/99, 385/384 | |||
Related temperaments: 4&7&15, magic | |||
[[Lp tuning|POL2 generator]]: ~6/5 = 322.659 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 6/5; 100/99 385/384] | ||
Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|] | |||
[ | Map: [<1 0 5 2|, <0 1 -3 2|] | ||
[[ | EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd | ||
[[Lp tuning#L2 tuning|L2 error]]: 2.696 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 | |||
[[ | [[Lp tuning|POL2 generator]]: ~9/7 = 440.902 | ||
[[Gencom]]: [2 9/7; 245/243] | |||
Gencom map: [<1 0 0 0|, <0 0 2 -1|] | |||
[[ | Map: [<1 0 0|, <0 2 1|] | ||
EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.421 cents | |||
[[xenharmonic/ | [[xenharmonic/sentry5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/sentry8|Eight note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/sentry11|Eleven note note chromatic scale]] | ||
= | =Mothwelltri= | ||
Group: 2. | Group: 2.7/3.11 | ||
Comma: 99/98 | |||
Svalname: 1&4 | |||
Related temperament: Orwell | |||
[[Lp tuning|POL2 generator]]: ~6 | [[Lp tuning|POL2 generator]]: ~7/6 = 273.174 | ||
[[Gencom]]: [2 6 | [[Gencom]]: [2 7/6; 99/98] | ||
Gencom map: [<1 -1/2 1/2 | Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|] | ||
Map: [<1 0 | Map: [<1 0 1|, <0 1 2|] | ||
EDOs: | EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc | ||
[[Lp tuning#L2 tuning|L2 error]]: 2. | [[Lp tuning#L2 tuning|L2 error]]: 2.380 cents | ||
[[xenharmonic/ | [[xenharmonic/mothwelltri5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/mothwelltri9|Nine note albitonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/mothwelltri13|Thirteen note chromatic scale]] | ||
= | =Lovecraft= | ||
Group: 2. | Group: 2.11.13 | ||
Commas: | Commas: 1352/1331 | ||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~13/11 = 279.318 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 13/11; 1352/1331] | ||
Gencom map: [<1 0 0 0|, <0 0 2 | Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|] | ||
Map: [<1 | Map: [<1 1 0|, <0 2 3|] | ||
EDOS: 13, 30, 43, 73, 116b | |||
[[Lp tuning#L2 tuning|L2 error]]: | [[Lp tuning#L2 tuning|L2 error]]: 2.070 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 | |||
[[ | [[Lp tuning|POL2 generator]]: ~13/12 = 139.990 | ||
[[Gencom]]: [2 13/12; 78/77 99/98 144/143] | |||
Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] | |||
[[xenharmonic/ | Map: [<1 1 2 3 3|, <0 5 7 4 6|] | ||
[[xenharmonic/ | EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] | ||
[[xenharmonic/ | [[Lp tuning#L2 tuning|L2 error]]: 4.292 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]] | |||
[[Lp tuning|POL2 generator]]: ~11/9 = 348.094 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 11/9; 81/80 121/120] | ||
Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|] | |||
[ | Map: [<1 1 0 2|, <0 2 8 5|] | ||
EDOs: 24, 31, 69d, 100d, 131bd | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 3.113 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 | |||
[[ | [[Lp tuning|POL2 generator]]: ~11/9 = 348.916 | ||
[[ | [[Gencom]]: [2 11/9; 66/65 81/80 121/120] | ||
Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|] | |||
[ | |||
Map: [<1 1 0 2 4|, <0 2 8 5 -1|] | |||
EDOs: 17c, 24, 31, 55, 86de, 141cde | |||
[[Lp tuning#L2 tuning|L2 error]]: 4.829 cents | |||
=Stacks= | |||
Subgroup: 2.9.15.7.11.13 | |||
Commas: 100/99, 105/104, 144/143, 196/195 | |||
Svalname: 11&30 | |||
[[ | [[Lp tuning|POL2 generator]]: ~9/7 = 439.146 | ||
[[Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195] | |||
Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] | |||
[[ | Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] | ||
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef | |||
[[Lp tuning#L2 tuning|L2 error]]: 3.772 cents | |||
[[xenharmonic/ | [[xenharmonic/stacks5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[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]] | |||
= | [[Lp tuning|POL2 generator]]: ~9/8 = 193.937 | ||
[[ | [[Gencom]]: [2 9/8; 81/80 99/98 126/125] | ||
Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|] | |||
Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] | |||
EDOs: 25, 31, 68b, 99b | |||
[[Lp tuning#L2 tuning|L2 error]]: 3.218 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]] | |||
[[ | [[Lp tuning|POL2 generator]]: ~9/8 = 192.500 | ||
[[Gencom]]: [2 9/8; 45/44 56/55 81/80] | |||
Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|] | |||
[ | Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] | ||
EDOs: 6, 7, 13, 19, 25, 31, 56, 81 | |||
[[Lp tuning#L2 tuning|L2 error]]: 8.680 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 | |||
[[Lp tuning|POL2 generator]]: ~11/8 = 540.099 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 11/8; 343/338 847/832] | ||
[ | Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|] | ||
[[ | |||
Map: [<1 1 3 1|, <0 4 1 6|] | |||
EDOs: 5, 7, 9, 11, 20 | |||
[[Lp tuning#L2 tuning|L2 error]]: 3.141 cents | |||
[[image: | [[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]] | |||
[[ | [[Lp tuning|POL2 generator]]: ~3/2 = 707.192 | ||
[[Gencom]]: [2 3/2; 64/63 99/98] | |||
Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|] | |||
[[ | Map: [<1 0 6 13|, <0 1 -2 -6|] | ||
EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c | |||
[[Lp tuning#L2 tuning|L2 error]]: 4.421 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 | |||
[[ | [[Lp tuning|POL2 generator]]: ~3/2 = 706.137 | ||
[[Gencom]]: [2 3/2; 64/63 78/77 99/98] | |||
Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|] | |||
[[ | Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] | ||
EDOs: 5, 7, 12, 17 | |||
[[Lp tuning#L2 tuning|L2 error]]: 5.132 cents | |||
==Machine== | |||
Subgroup: 2.9.7.11 | |||
= | |||
Subgroup: 2. | |||
Commas: 64/63, 99/98 | Commas: 64/63, 99/98 | ||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~9/8 = 214.384 | ||
[[Gencom]]: [2 | [[Gencom]]: [2 9/8; 64/63 99/98] | ||
Gencom map: [<1 | Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] | ||
Map: [<1 0 6 13|, <0 1 - | Map: [<1 0 6 13|, <0 1 -1 -3|] | ||
EDOs: 5, | EDOs: 5, 6, 11, 17, 28 | ||
[[Lp tuning#L2 tuning|L2 error]]: 4.421 cents | [[Lp tuning#L2 tuning|L2 error]]: 4.421 cents | ||
[[image: | [[image:machine_28edo.png]] | ||
[[xenharmonic/ | [[xenharmonic/machine5|Five note haplotonic scale]] | ||
[[xenharmonic/ | [[xenharmonic/machine6|Six note albitonic scale]] | ||
[[xenharmonic/machine11|Eleven note chromatic scale]] | |||
= | =Antikythera= | ||
Subgroup: 2. | Subgroup: 2.9.5.7 | ||
Commas: 64/63 | Commas: 50/49, 64/63 | ||
Related temperament: [[xenharmonic/pajara|pajara]] | |||
[[Lp tuning|POL2 generator]]: ~ | [[Lp tuning|POL2 generator]]: ~8/7 = 214.095 | ||
[[Gencom]]: [ | [[Gencom]]: [7/5 8/7; 50/49 64/63] | ||
Gencom map: [< | Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|] | ||
Map: [< | Map: [<2 0 11 12|, <0 1 -1 -1|] | ||
EDOS: 4, 6, 10, 16, 22, 28 | |||
[[Lp tuning#L2 tuning|L2 error]]: 5. | [[Lp tuning#L2 tuning|L2 error]]: 5.145 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]] | |||
[[Lp tuning|POL2 generator]]: ~9/8 = 191.059 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 9/8; 65/64 81/80 91/90] | ||
Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|] | |||
[ | Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] | ||
EDOs: 6, 7, 13, 19, 25e, 44de | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 4.906 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 | |||
[[Lp tuning|POL2 generator]]: ~7/6 = 250.385 | |||
[[Lp | |||
[[ | [[Gencom]]: [2 7/6; 49/48] | ||
Gencom map: [<1 2 0 3}, <0 -2 0 -1|] | |||
[ | Map: [<1 0 2|, <0 2 1|] | ||
EDOs: 5, 9, 14, 19, 24, 67c, 91c | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 5.046 cents | ||
[[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]] | |||
[[Lp tuning|POL2 generator]]: ~8/7 = 228.275 | |||
[[Lp | |||
[[ | [[Gencom]]: [5/4 8/7; 56/55 128/125] | ||
Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|] | |||
[ | Map: [<3 7 0 2|, <0 0 1 1|] | ||
EDOs: 3, 6, 9, 15, 21 | |||
[[ | [[Lp tuning#L2 tuning|L2 error]]: 5.415 cents | ||
[[image:augment_21edo.png]] | |||
[[ | [[xenharmonic/augment6|Six note haplotonic scale]] | ||
[[xenharmonic/augment9|Nine note albitonic scale]] | |||
[[ | [[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="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Neutraltet">Neutraltet</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <a href="#Penta">Penta</a><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --> | <a href="#Starlingtet">Starlingtet</a><!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --> | <a href="#Gariberttet">Gariberttet</a><!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --><!-- ws:end:WikiTextTocRule:163 --><!-- ws:start:WikiTextTocRule:164: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:164 --><!-- ws:start:WikiTextTocRule:165: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:165 --><!-- ws:start:WikiTextTocRule:166: --> | <a href="#Magicaltet">Magicaltet</a><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --> | <a href="#Sentry">Sentry</a><!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --> | <a href="#Mothwelltri">Mothwelltri</a><!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --> | <a href="#Lovecraft">Lovecraft</a><!-- ws:end:WikiTextTocRule:169 --><!-- ws:start:WikiTextTocRule:170: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:170 --><!-- ws:start:WikiTextTocRule:171: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --> | <a href="#Stacks">Stacks</a><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --> | <a href="#Semaphore">Semaphore</a><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --> | |||
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<!-- 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 <a class="wiki_link" href="/Lp%20tuning">POL2 error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<br /> | |||
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<!-- 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 /> | |||
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<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~10/9 = 182.461<br /> | |||
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<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 /> | |||
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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 /> | |||
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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 /> | |||
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< | <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 /> | |||
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<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Petrtri"></a><!-- ws:end:WikiTextHeadingRule:5 -->Petrtri</h1> | |||
Subgroup: 2.11/5.13/5<br /> | |||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Petrtri"></a><!-- ws:end:WikiTextHeadingRule:5 -->Petrtri</h1> | |||
Subgroup: 2.11/5.13/5<br /> | |||
Comma: 2200/2197<br /> | Comma: 2200/2197<br /> | ||
Svalname: 3&amp;5<br /> | Svalname: 3&amp;5<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/huntington17">Seventeen note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc14"><a name=" | <!-- ws:start:WikiTextHeadingRule:29:&lt;h1&gt; --><h1 id="toc14"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:29 -->Pepperoni</h1> | ||
Subgroup: 2. | Subgroup: 2.3.11/7.13/7<br /> | ||
Commas: | Commas: 352/351, 364/363<br /> | ||
Sval name: | Sval name: 5&amp;12<br /> | ||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | 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 /> | ||
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<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 703.856<br /> | ||
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<a class="wiki_link" href="/Gencom">Gencom</a>: [2 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 352/351 364/363]<br /> | ||
Gencom map: [&lt;1 0 | 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 | Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br /> | ||
EDOs: | EDOs: 5, 7, 12, 17, 29, 46, 75, 104, 196, 271, 595bcd<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9282 cents<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | <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 /> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | |||
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<!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name=" | <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name="Penta"></a><!-- ws:end:WikiTextHeadingRule:31 -->Penta</h1> | ||
Subgroup: 2. | Subgroup: 2.9.7.11<br /> | ||
Commas: | Commas: 896/891, 26411/26244<br /> | ||
Svalname: 8&amp;11<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <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 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 896/891 26411/26244]<br /> | ||
Gencom map: [&lt;1 | Gencom map: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 | Map: [&lt;1 0 -1 6|, &lt;0 5 6 -4|]<br /> | ||
EDOs: | EDOs: 8, 11, 30, 41, 52<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9531 cents<br /> | ||
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< | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta5">Five note haplotonic scale</a><br /> | ||
<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/ | <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/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta17">Seventeen note mega chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:33:&lt;h1&gt; --><h1 id="toc16"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:33 -->Marveltri</h1> | <!-- ws:start:WikiTextHeadingRule:33:&lt;h1&gt; --><h1 id="toc16"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:33 -->Marveltri</h1> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri13">Thirteen note mega chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/marveltri13">Thirteen note mega chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc17"><a name=" | <!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc17"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:35 -->Bossier</h1> | ||
Subgroup: 2. | Subgroup: 2.7.11.13<br /> | ||
Commas: | Commas: 1573/1568, 15488/15379<br /> | ||
Sval name: | Sval name: 3&amp;17<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~14/11 = 421.309<br /> | ||
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<a class="wiki_link" href="/Gencom">Gencom</a>: [2 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 14/11; 1573/1568 15488/15379]<br /> | ||
Gencom map: [&lt;1 | Gencom map: [&lt;1 0 0 0 1 3|, &lt;0 0 0 8 7 2|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 | Map: [&lt;1 0 1 3|, &lt;0 8 7 2|]<br /> | ||
EDOs: | EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0. | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9904 cents<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | <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/ | <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 /> | |||
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<!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc18"><a name=" | <!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc18"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:37 -->Shoe</h1> | ||
Subgroup: 2. | Subgroup: 2.5.7.11.13<br /> | ||
Commas: | Commas: 176/175, 640/637, 847/845<br /> | ||
Sval name: 16&amp;21<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <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 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 176/175 640/637 847/845]<br /> | ||
Gencom map: [&lt;1 | 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, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce<br /> | |||
Map: [&lt;1 1 3 1 2|, &lt;0 7 -1 13 9|]<br /> | |||
EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.331 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.331 cents<br /> | ||
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<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/shoe5">shoe5</a> - five note mini <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> | ||
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<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 /> | <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:39:&lt;h1&gt; --><h1 id="toc19"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:39 -->Guanyintet</h1> | ||
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 1,470: | Line 1,448: | ||
<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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:43:&lt;h1&gt; --><h1 id="toc21"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:43 -->Garibaldi</h1> | <!-- ws:start:WikiTextHeadingRule:41:&lt;h1&gt; --><h1 id="toc20"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:41 -->Roulette</h1> | ||
Group: 2.3.5.7<br /> | Subgroup: 2.5.7.11.13<br /> | ||
Commas: 225/224, 3125/3087<br /> | Commas: 176/175, 1375/1372, 640/637<br /> | ||
Val name: 12&amp;29<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 /> | |||
<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: [&lt;1 0 2 2 2 5|, &lt;0 0 2 5 9 -8|]<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>: 1.364 cents<br /> | |||
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<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 /> | |||
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<!-- ws:start:WikiTextHeadingRule:43:&lt;h1&gt; --><h1 id="toc21"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:43 -->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 /> | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 702.085<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/garibaldi17">Seventeen note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:45:&lt;h1&gt; --><h1 id="toc22"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:45:&lt;h1&gt; --><h1 id="toc22"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:45 -->Radon</h1> | ||
Subgroup: 2.9.5.7.13<br /> | Subgroup: 2.3.7.11<br /> | ||
Commas: 225/224, 325/324, 640/637<br /> | Commas: 896/891, 1029/1024<br /> | ||
Sval name: 6&amp;35<br /> | Sval name: 5&amp;36<br /> | ||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gamelismic%20clan">Rodan</a><br /> | |||
<br /> | |||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 234.381<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 896/891 1029/1024]<br /> | |||
Gencom map: [&lt;1 1 0 3 6|, &lt;0 3 0 -1 -13|]<br /> | |||
<br /> | |||
Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br /> | |||
EDOs: 5, 36, 41, 87, 128<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.454 cents<br /> | |||
<br /> | |||
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<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:47:&lt;h1&gt; --><h1 id="toc23"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:47 -->Baldy</h1> | |||
Subgroup: 2.9.5.7.13<br /> | |||
Commas: 225/224, 325/324, 640/637<br /> | |||
Sval name: 6&amp;35<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br /> | Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br /> | ||
<br /> | <br /> | ||
| Line 1,504: | Line 1,525: | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.469 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.469 cents<br /> | ||
<br /> | <br /> | ||
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<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/baldy6">baldy6</a> - six note <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haplotonic%20scale">haplotonic scale</a><br /> | ||
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<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 /> | <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:49:&lt;h1&gt; --><h1 id="toc24"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:49 -->Photia</h1> | ||
Subgroup: 2. | Subgroup: 2.3.5.17.19<br /> | ||
Commas: | Commas: 171/170, 256/255, 324/323<br /> | ||
Sval name: | 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="/Lp%20tuning">POL2 generator</a>: ~ | <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 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 171/170 256/255 324/323]<br /> | ||
Gencom map: [&lt;1 0 0 0 | Gencom map: [&lt;1 1 7 0 0 0 0 6|, &lt;0 1 -8 0 0 0 7 -3|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 0 | Map: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]<br /> | ||
EDOs: 17, | EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.520 cents<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | <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/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia12">Twelve note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:51:&lt;h1&gt; --><h1 id="toc25"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:51 -->Mabila</h1> | ||
Subgroup: 2. | Subgroup: 2.5.7<br /> | ||
Comma: 1071875/1048576<br /> | |||
Sval name: | Sval name: 7&amp;9<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~175/128 = 527.236<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 175/128; 1071875/1048576]<br /> | ||
Gencom map: [&lt;1 1 | Gencom map: [&lt;1 0 1 5}, &lt;0, 0, 3, -5|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 1 | Map: [&lt;1 1 5|, &lt;0 3 -5|]<br /> | ||
EDOs: | EDOs: 7, 9, 16, 25, 41, 66, 305bc<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1. | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.546 cents<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | <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/ | <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/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/mabila16">Sixteen note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:53:&lt;h1&gt; --><h1 id="toc26"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:53 -->Silver</h1> | ||
Subgroup: 2.5.7.13.17<br /> | |||
Commas: | Commas: 170/169, 640/637, 5525/5488<br /> | ||
Sval name: 10&amp;27<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/8 = 842.711<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/8; 170/169 640/637 5525/5488]<br /> | ||
Gencom map: [&lt;1 - | Gencom map: [&lt;1 0 -4 0 0 3 9|, &lt;0 0 9 4 0 1 -7|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br /> | |||
Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br /> | |||
EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, 178e, 309cde, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487bcdee</a><br /> | EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, 178e, 309cde, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487bcdee</a><br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.557 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.557 cents<br /> | ||
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<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 /> | <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:55:&lt;h1&gt; --><h1 id="toc27"><a name=" | <!-- ws:start:WikiTextHeadingRule:55:&lt;h1&gt; --><h1 id="toc27"><a name="Myna"></a><!-- ws:end:WikiTextHeadingRule:55 -->Myna</h1> | ||
Group: 2.3.5.7<br /> | |||
Commas: 126/125, 1728/1715<br /> | |||
Val name: 4&amp;27<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~ | <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 310.146<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 | <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125 1728/1715]<br /> | ||
Gencom map: [&lt;1 0 1 | Gencom map: [&lt;1 -1 0 1|,&lt;0 10 9 7|]<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 | Map: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]<br /> | ||
EDOs: | EDOs: 4, 27, 31, 58, 89, 236c, 325cd<br /> | ||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1. | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.903 cents<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/ | <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/ | <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/ | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/myna15">Fifteen note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:57:&lt;h1&gt; --><h1 id="toc28"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:57 -->Meantone</h1> | <!-- ws:start:WikiTextHeadingRule:57:&lt;h1&gt; --><h1 id="toc28"><a name="Meantone"></a><!-- ws:end:WikiTextHeadingRule:57 -->Meantone</h1> | ||
Revision as of 18:31, 9 July 2012
IMPORTED REVISION FROM WIKISPACES
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[[toc|flat]] [[media type="custom" key="11052942"]] ---- =Definitions= By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing [[Lp tuning|POL2 error]], which is an appropriate error measure for subgroups as well as full p-limit groups. =Terrain= Subgroup: 2.9/5.9/7 Commas: 250047/250000 Sval name: 6&21 Related temperament: [[xenharmonic/Minortonic family#Domain|domain]] [[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]] =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, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c [[Lp tuning#L2 tuning|L2 error]]: 0.1835 cents [[image:petrtri_385edo.png]] [[xenharmonic/petrtri5|Five note haplotonic scale]] [[xenharmonic/petrtri8|Eight note albitonic scale]] [[xenharmonic/petrtri13|Thirteen 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, 953bc [[Lp tuning#L2 tuning|L2 error]]: 0.3950 cents [[image:tridec_235edo.png]] [[xenharmonic/Tridec8|Eight note albitonic scale]] [[xenharmonic/Tridec13|Thirteen note chromatic scale]] =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, 475bc, 783bc [[Lp tuning#L2 tuning|L2 error]]: 0.4222 cents [[image:orgone_308edo.jpg]] [[xenharmonic/orgone7|Seven note albitonic scale]] [[xenharmonic/orgone11|Eleven note chromatic scale]] [[xenharmonic/orgone15|Fifteen note mega 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, 460d, 631d [[Lp tuning#L2 tuning|L2 error]]: 0.4987 cents [[image:nestoria_171edo.png]] [[xenharmonic/nestoria7|Seven note albitonic scale]] [[xenharmonic/nestoria12|Twelve note chromatic scale]] [[xenharmonic/nestoria17|Seventeen 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, 53, 87, 140, 185, 219, 253, 287b, 321b [[Lp tuning#L2 tuning|L2 error]]: 0.5985 cents [[image:marveltwintri_321edo.png]] [[xenharmonic/marveltwintri7|Seven note albitonic scale]] [[xenharmonic/marveltwintri11|Eleven note chromatic scale]] [[xenharmonic/marveltwintri15|Fifteen note mega chromatic scale]] =Cata= Subgroup: 2.3.5.13 Commas: 325/324, 625/624 Sval name: 15&19 Related temperament: [[xenharmonic/Kleismic family|catakleismic]] [[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]]: 0.6001 cents [[image:xenharmonic/cata_246edo2.jpg]] [[xenharmonic/cata7|Seven note albitonic scale]] [[xenharmonic/cata11|Eleven note mega albitonic scale]] [[xenharmonic/cata15|Fifteen note chromatic scale]] [[xenharmonic/cata19|Nineteen note mega chromatic scale]] =Bridgetown= Subgroup: 2.3.11/5.13/5 Commas: 352/351, 676/675 Sval name: 5&24 Related 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, 169, 198, 227, 256, 285, 314 [[Lp tuning#L2 tuning|L2 error]]: 0.6154 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]] =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]]: 0.6403 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]] =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]]: 0.6756 cents [[image:neutraltet_380edo.png]] [[xenharmonic/neutraltet7|Seven note albitonic scale]] [[xenharmonic/neutraltet10|Ten note chromatic scale]] [[xenharmonic/neutraltet17|Seventeen 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, 279cd, 400cd [[Lp tuning#L2 tuning|L2 error]]: 0.8455 cents [[image:huntington_400edo.jpg]] [[xenharmonic/huntington7|Seven note haplotonic scale]] [[xenharmonic/huntington10|Ten note albitonic scale]] [[xenharmonic/huntington17|Seventeen note chromatic scale]] =Pepperoni= Subgroup: 2.3.11/7.13/7 Commas: 352/351, 364/363 Sval name: 5&12 Related temperament: The [[xenharmonic/Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name. [[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, 104, 196, 271, 595bcd [[Lp tuning#L2 tuning|L2 error]]: 0.9282 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]]: 0.9531 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]] =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, 25, 47, 69, 72, 97, 122, 269bc, 660bc [[Lp tuning#L2 tuning|L2 error]]: 0.9602 cents [[xenharmonic/marveltri7|Seven note albitonic scale]] [[xenharmonic/marveltri10|Ten note chromatic scale]] [[xenharmonic/marveltri13|Thirteen note mega chromatic scale]] =Bossier= Subgroup: 2.7.11.13 Commas: 1573/1568, 15488/15379 Sval name: 3&17 [[Lp tuning|POL2 generator]]: ~14/11 = 421.309 [[Gencom]]: [2 14/11; 1573/1568 15488/15379] Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|] Map: [<1 0 1 3|, <0 8 7 2|] EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd [[Lp tuning#L2 tuning|L2 error]]: 0.9904 cents [[image:bossier_225edo.jpg]] [[xenharmonic/bossier8|Eight note albitonic scale]] [[xenharmonic/bossier11|Eleven note chromatic scale]] [[xenharmonic/bossier14|Fourteen 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, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce [[Lp tuning#L2 tuning|L2 error]]: 1.331 cents [[image:xenharmonic/shoe_37edo.jpg]] [[xenharmonic/shoe5|shoe5]] - five note mini [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/shoe6|shoe6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/shoe11|shoe11]] - eleven note note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/shoe16|shoe16]] - sixteen note [[xenharmonic/chromatic scale|chromatic scale]] =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, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd [[Lp tuning#L2 tuning|L2 error]]: 1.348 cents [[xenharmonic/guanyintet5|Five note haplotonic scale]] [[xenharmonic/guanyintet9|Nine note albitonic scale]] [[xenharmonic/guanyintet13|Thirteen note 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]]: 1.364 cents [[image:xenharmonic/roulette_37edo.jpg]] [[xenharmonic/roulette6|roulette6]] - six note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/roulette7|roulette7]] - seven note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/roulette13|roulette13]] - thirteen note [[xenharmonic/chromatic scale|chromatic scale]] [[xenharmonic/roulette19|roulette19]] - nineteen note [[xenharmonic/mega chromatic scale|mega chromatic scale]] =Garibaldi= Group: 2.3.5.7 Commas: 225/224, 3125/3087 Val name: 12&29 [[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, 241c [[Lp tuning#L2 tuning|L2 error]]: 1.451 cents [[image:garibaldi_94edo.png]] [[xenharmonic/garibaldi12|Twelve note albitonic scale]] [[xenharmonic/garibaldi17|Seventeen note chromatic scale]] =Radon= Subgroup: 2.3.7.11 Commas: 896/891, 1029/1024 Sval name: 5&36 Related temperament: [[xenharmonic/Gamelismic clan|Rodan]] [[Lp tuning|POL2 generator]]: ~8/7 = 234.381 [[Gencom]]: [2 8/7; 896/891 1029/1024] Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|] Map: [<1 1 3 6|, <0 3 -1 -13|] EDOs: 5, 36, 41, 87, 128 [[Lp tuning#L2 tuning|L2 error]]: 1.454 cents [[image:radon_128edo.jpg]] [[xenharmonic/radon5|Five note haplotonic scale]] [[xenharmonic/radon11|Eleven note albitonic scale]] [[xenharmonic/radon16|Sixteen 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]] [[Lp tuning|POL2 generator]]: ~9/8 = 204.090 [[Gencom]]: [2 9/8; 225/224 325/324 640/637] Gencom map: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|] Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|] EDOs: 6, 11, 17, 23, 29, 35, 41, [[xenharmonic/47edo|47]], 100, [[xenharmonic/147edo|147]], 488cd, 635cd [[Lp tuning#L2 tuning|L2 error]]: 1.469 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]] =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, 142d, 207d, 272d [[Lp tuning#L2 tuning|L2 error]]: 1.520 cents [[image:photia_65edo.png]] [[xenharmonic/photia7|Seven note albitonic scale]] [[xenharmonic/photia12|Twelve note chromatic scale]] =Mabila= Subgroup: 2.5.7 Comma: 1071875/1048576 Sval name: 7&9 [[Lp tuning|POL2 generator]]: ~175/128 = 527.236 [[Gencom]]: [2 175/128; 1071875/1048576] Gencom map: [<1 0 1 5}, <0, 0, 3, -5|] Map: [<1 1 5|, <0 3 -5|] EDOs: 7, 9, 16, 25, 41, 66, 305bc [[Lp tuning#L2 tuning|L2 error]]: 1.546 cents [[image:mabila_66edo.jpg]] [[xenharmonic/mabila7|Seven note haplotonic scale]] [[xenharmonic/mabila9|Nine note albitonic scale]] [[xenharmonic/mabila16|Sixteen note chromatic scale]] =Silver= Subgroup: 2.5.7.13.17 Commas: 170/169, 640/637, 5525/5488 Sval name: 10&27 [[Lp tuning|POL2 generator]]: ~13/8 = 842.711 [[Gencom]]: [2 13/8; 170/169 640/637 5525/5488] Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|] Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] EDOs: 7, 10, 17, 27, 37, [[xenharmonic/47edo|47]], 84, 131, 178e, 309cde, [[xenharmonic/487edo|487bcdee]] [[Lp tuning#L2 tuning|L2 error]]: 1.557 cents [[image:silver_487edo.jpg]] [[xenharmonic/silver7|silver7]] -seven note [[xenharmonic/haplotonic scale|haplotonic scale]] [[xenharmonic/silver10|silver10]] - ten note [[xenharmonic/albitonic scale|albitonic scale]] [[xenharmonic/silver17|silver17]] - seventeen note [[xenharmonic/chromatic scale|chromatic scale]] =Myna= Group: 2.3.5.7 Commas: 126/125, 1728/1715 Val name: 4&27 [[Lp tuning|POL2 generator]]: ~6/5 = 310.146 [[Gencom]]: [2 6/5; 126/125 1728/1715] Gencom map: [<1 -1 0 1|,<0 10 9 7|] Map: [<1 9 9 8|, <0 -10 -9 -7|] EDOs: 4, 27, 31, 58, 89, 236c, 325cd [[Lp tuning#L2 tuning|L2 error]]: 1.903 cents [[image:myna_89edo.jpg]] [[xenharmonic/myna7|Seven note haplotonic scale]] [[xenharmonic/myna11|Eleven note albitonic scale]] [[xenharmonic/myna15|Fifteen note chromatic scale]] =Meantone= Group: 2.3.5.7 Commas: 81/80, 126/125 Val name: 12&19 [[Lp tuning|POL2 generator]]: ~3/2 = 696.495 [[Gencom]]: [2 3/2; 81/80 126/125] Gencom map: [<1 1 0 -3|, <0 1 4 10|] Map: [<1 0 -4 -13|, <0 1 4 10|] EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b [[Lp tuning#L2 tuning|L2 error]]: 2.763 cents [[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 [[Lp tuning|POL2 generator]]: ~6/5 = 311.154 [[Gencom]]: [2 6/5; 126/125] Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|] Map: [<1 0 -1|, <0 1 3|] EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b [[Lp tuning#L2 tuning|L2 error]]: 1.680 cents [[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 [[Lp tuning|POL2 generator]]: ~12/11 = 147.010 [[Gencom]]: [2 12/11; 3025/3024 3125/3087] Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|] Map: [<1 0 0 2|, <0 6 10 -1|] EDOs: 33, 41, 49, 57, 106, 204, 253 [[Lp tuning#L2 tuning|L2 error]]: 1.741 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 [[Lp tuning|POL2 generator]]: ~5/4 = 380.696 [[Gencom]]: [2 5/4; 100/99 225/224 245/243] Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|] Map: [<1 0 2 -1 6|, <0 5 1 12 -8|] EDOs: 19, 22, 41, 104, 145 [[Lp tuning#L2 tuning|L2 error]]: 2.741 cents [[image:xenharmonic/magic_145edo.jpg]] [[xenharmonic/magic7|Seven note haplotonic scale]] [[xenharmonic/magic10|Ten note albitonic scale]] [[xenharmonic/magic13|Thirteen note chromatic scale]] [[xenharmonic/magic16|Sixteen note mega chromatic scale]] ==Music== <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">////[[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3|Chromatic piece in magic 16]]////</span> [[@http://www.chrisvaisvil.com/|Chris Vaisvil]] =Gariberttet= Subgroup: 2.5/3.7/3.13/11 Commas: 275/273, 847/845 Svalname: 4&29 [[Lp tuning|POL2 generator]]: ~13/11 = 293.679 [[Gencom]]: [2 13/11; 275/273 847/845] Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|] Map: [<1 0 0 0|, <0 3 5 1|] EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd [[Lp tuning#L2 tuning|L2 error]]: 1.694 cents [[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]] [[Lp tuning|POL2 generator]]: ~11/9 = 351.691 [[Gencom]]: [2 11/9; 144/143 243/242 364/363] Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] EDOs: 7, 10, 17, 24, 41, 58 [[Lp tuning#L2 tuning|L2 error]]: 1.756 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]] [[Lp tuning|POL2 generator]]: ~9/7 = 425.244 [[Gencom]]: [2 9/7; 99/98 243/242] Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|] Map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd [[Lp tuning#L2 tuning|L2 error]]: 2.457 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: 126/125, 245/243 Val name: 19&27 [[Lp tuning|POL2 generator]]: ~9/7 = 443.383 [[Gencom]]: [2 9/7; 126/125 245/243] Gencom map: [<1 -1 -1 -2|, <0 7 9 13|] Map: [<1 6 8 11|, <0 -7 -9 -13|] EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd [[Lp tuning#L2 tuning|L2 error]]: 2.647 cents [[image:xenharmonic/sensi_46edo.jpg]] [[xenharmonic/sensi5|Five note haplotonic scale]] [[xenharmonic/sensi8|Eight note albitonic scale]] [[xenharmonic/sensi11|Eleven note mega albitonic scale]] [[xenharmonic/sensi19|Nineteen note chromatic scale]] =Greeley= Subgroup: 2.5/3.7/3.11/3 Commas: 121/120, 126/125 [[Lp tuning|POL2 generator]]: ~11/10 = 155.776 Related temperament: [[Porcupine family#Opossum|Opossum]] [[Gencom]]: [2 11/10; 121/120 126/125] Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|] Map: [<1 1 2 2|, <0 -2 -6 -1|] EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd [[Lp tuning#L2 tuning|L2 error]]: 2.313 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 [[Lp tuning|POL2 generator]]: ~13/10 = 453.242 [[Gencom]]: [2 13/10; 121/120 169/168 275/273] Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|] Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|] EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde, [[Lp tuning#L2 tuning|L2 error]]: 2.577 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 [[Lp tuning|POL2 generator]]: ~7/6 = 271.426 [[Gencom]]: [2 7/6; 99/98 121/120 176/175] Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|] Map: [<1 0 3 1 3|, <0 7 -3 8 2|] EDOs: 9, 22, 31, 53, 84e [[Lp tuning#L2 tuning|L2 error]]: 2.574 cents [[image:xenharmonic/orwell_84edo.png]] [[xenharmonic/orwell5|Five note haplotonic scale]] [[xenharmonic/orwell9|Nine note albitonic scale]] [[xenharmonic/orwell13|Thirteen note chromatic scale]] =Magicaltet= Group: 2.5/3.7.11 Commas: 100/99, 385/384 Related temperaments: 4&7&15, magic [[Lp tuning|POL2 generator]]: ~6/5 = 322.659 [[Gencom]]: [2 6/5; 100/99 385/384] Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|] Map: [<1 0 5 2|, <0 1 -3 2|] EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd [[Lp tuning#L2 tuning|L2 error]]: 2.696 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 [[Lp tuning|POL2 generator]]: ~9/7 = 440.902 [[Gencom]]: [2 9/7; 245/243] Gencom map: [<1 0 0 0|, <0 0 2 -1|] Map: [<1 0 0|, <0 2 1|] EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc [[Lp tuning#L2 tuning|L2 error]]: 1.421 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 [[Lp tuning|POL2 generator]]: ~7/6 = 273.174 [[Gencom]]: [2 7/6; 99/98] Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|] Map: [<1 0 1|, <0 1 2|] EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc [[Lp tuning#L2 tuning|L2 error]]: 2.380 cents [[xenharmonic/mothwelltri5|Five note haplotonic scale]] [[xenharmonic/mothwelltri9|Nine note albitonic scale]] [[xenharmonic/mothwelltri13|Thirteen note chromatic scale]] =Lovecraft= Group: 2.11.13 Commas: 1352/1331 [[Lp tuning|POL2 generator]]: ~13/11 = 279.318 [[Gencom]]: [2 13/11; 1352/1331] Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|] Map: [<1 1 0|, <0 2 3|] EDOS: 13, 30, 43, 73, 116b [[Lp tuning#L2 tuning|L2 error]]: 2.070 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 [[Lp tuning|POL2 generator]]: ~13/12 = 139.990 [[Gencom]]: [2 13/12; 78/77 99/98 144/143] Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] Map: [<1 1 2 3 3|, <0 5 7 4 6|] EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]] [[Lp tuning#L2 tuning|L2 error]]: 4.292 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]] [[Lp tuning|POL2 generator]]: ~11/9 = 348.094 [[Gencom]]: [2 11/9; 81/80 121/120] Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|] Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 24, 31, 69d, 100d, 131bd [[Lp tuning#L2 tuning|L2 error]]: 3.113 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 [[Lp tuning|POL2 generator]]: ~11/9 = 348.916 [[Gencom]]: [2 11/9; 66/65 81/80 121/120] Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|] Map: [<1 1 0 2 4|, <0 2 8 5 -1|] EDOs: 17c, 24, 31, 55, 86de, 141cde [[Lp tuning#L2 tuning|L2 error]]: 4.829 cents =Stacks= Subgroup: 2.9.15.7.11.13 Commas: 100/99, 105/104, 144/143, 196/195 Svalname: 11&30 [[Lp tuning|POL2 generator]]: ~9/7 = 439.146 [[Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195] Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef [[Lp tuning#L2 tuning|L2 error]]: 3.772 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]] [[Lp tuning|POL2 generator]]: ~9/8 = 193.937 [[Gencom]]: [2 9/8; 81/80 99/98 126/125] Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|] Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] EDOs: 25, 31, 68b, 99b [[Lp tuning#L2 tuning|L2 error]]: 3.218 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]] [[Lp tuning|POL2 generator]]: ~9/8 = 192.500 [[Gencom]]: [2 9/8; 45/44 56/55 81/80] Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|] Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] EDOs: 6, 7, 13, 19, 25, 31, 56, 81 [[Lp tuning#L2 tuning|L2 error]]: 8.680 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 [[Lp tuning|POL2 generator]]: ~11/8 = 540.099 [[Gencom]]: [2 11/8; 343/338 847/832] Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|] Map: [<1 1 3 1|, <0 4 1 6|] EDOs: 5, 7, 9, 11, 20 [[Lp tuning#L2 tuning|L2 error]]: 3.141 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]] [[Lp tuning|POL2 generator]]: ~3/2 = 707.192 [[Gencom]]: [2 3/2; 64/63 99/98] Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|] Map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c [[Lp tuning#L2 tuning|L2 error]]: 4.421 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 [[Lp tuning|POL2 generator]]: ~3/2 = 706.137 [[Gencom]]: [2 3/2; 64/63 78/77 99/98] Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|] Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] EDOs: 5, 7, 12, 17 [[Lp tuning#L2 tuning|L2 error]]: 5.132 cents ==Machine== Subgroup: 2.9.7.11 Commas: 64/63, 99/98 [[Lp tuning|POL2 generator]]: ~9/8 = 214.384 [[Gencom]]: [2 9/8; 64/63 99/98] Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] Map: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 [[Lp tuning#L2 tuning|L2 error]]: 4.421 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]] [[Lp tuning|POL2 generator]]: ~8/7 = 214.095 [[Gencom]]: [7/5 8/7; 50/49 64/63] Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|] Map: [<2 0 11 12|, <0 1 -1 -1|] EDOS: 4, 6, 10, 16, 22, 28 [[Lp tuning#L2 tuning|L2 error]]: 5.145 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]] [[Lp tuning|POL2 generator]]: ~9/8 = 191.059 [[Gencom]]: [2 9/8; 65/64 81/80 91/90] Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|] Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|] EDOs: 6, 7, 13, 19, 25e, 44de [[Lp tuning#L2 tuning|L2 error]]: 4.906 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 [[Lp tuning|POL2 generator]]: ~7/6 = 250.385 [[Gencom]]: [2 7/6; 49/48] Gencom map: [<1 2 0 3}, <0 -2 0 -1|] Map: [<1 0 2|, <0 2 1|] EDOs: 5, 9, 14, 19, 24, 67c, 91c [[Lp tuning#L2 tuning|L2 error]]: 5.046 cents [[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]] [[Lp tuning|POL2 generator]]: ~8/7 = 228.275 [[Gencom]]: [5/4 8/7; 56/55 128/125] Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|] Map: [<3 7 0 2|, <0 0 1 1|] EDOs: 3, 6, 9, 15, 21 [[Lp tuning#L2 tuning|L2 error]]: 5.415 cents [[image:augment_21edo.png]] [[xenharmonic/augment6|Six note haplotonic scale]] [[xenharmonic/augment9|Nine note albitonic scale]] [[xenharmonic/augment12|Twelve note chromatic scale]]
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<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="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --> | <a href="#Neutraltet">Neutraltet</a><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <a href="#Penta">Penta</a><!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --> | <a href="#Myna">Myna</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 <a class="wiki_link" href="/Lp%20tuning">POL2 error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:3:<h1> --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1> Subgroup: 2.9/5.9/7<br /> Commas: 250047/250000<br /> Sval name: 6&21<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Minortonic%20family#Domain">domain</a><br /> <br /> <a class="wiki_link" href="/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="Petrtri"></a><!-- ws:end:WikiTextHeadingRule:5 -->Petrtri</h1> Subgroup: 2.11/5.13/5<br /> Comma: 2200/2197<br /> Svalname: 3&5<br /> <br /> <a class="wiki_link" href="/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, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.1835 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:188:<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:188 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/petrtri13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:7:<h1> --><h1 id="toc3"><a name="Tridec"></a><!-- ws:end:WikiTextHeadingRule:7 -->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, 953bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.3950 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:189:<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:189 --><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:9:<h1> --><h1 id="toc4"><a name="Orgone"></a><!-- ws:end:WikiTextHeadingRule:9 -->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, 475bc, 783bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4222 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:190:<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:190 --><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: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, 460d, 631d<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.4987 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="Marveltwintri"></a><!-- ws:end:WikiTextHeadingRule:13 -->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, 53, 87, 140, 185, 219, 253, 287b, 321b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.5985 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:192:<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:192 --><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:15:<h1> --><h1 id="toc7"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:15 -->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>: 0.6001 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:193:<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:193 --><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:17:<h1> --><h1 id="toc8"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:17 -->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, 169, 198, 227, 256, 285, 314<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6154 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:194:<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:194 --><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:19:<h2> --><h2 id="toc9"><a name="Bridgetown-Music"></a><!-- ws:end:WikiTextHeadingRule:19 -->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:21:<h1> --><h1 id="toc10"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:21 -->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>: 0.6403 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:195:<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:195 --><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:23:<h2> --><h2 id="toc11"><a name="Slendric-Music"></a><!-- ws:end:WikiTextHeadingRule:23 -->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:25:<h1> --><h1 id="toc12"><a name="Neutraltet"></a><!-- ws:end:WikiTextHeadingRule:25 -->Neutraltet</h1> Subgroup: 2.3.11<br /> Commas: 243/242<br /> Svalname: 7&17<br /> <br /> <a class="wiki_link" href="/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>: 0.6756 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:196:<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:196 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10">Ten note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:27:<h1> --><h1 id="toc13"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:27 -->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, 279cd, 400cd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.8455 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:197:<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:197 --><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:29:<h1> --><h1 id="toc14"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:29 -->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, 104, 196, 271, 595bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9282 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:198:<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:198 --><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:31:<h1> --><h1 id="toc15"><a name="Penta"></a><!-- ws:end:WikiTextHeadingRule:31 -->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>: 0.9531 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:33:<h1> --><h1 id="toc16"><a name="Marveltri"></a><!-- ws:end:WikiTextHeadingRule:33 -->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, 25, 47, 69, 72, 97, 122, 269bc, 660bc <br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9602 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:35:<h1> --><h1 id="toc17"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:35 -->Bossier</h1> Subgroup: 2.7.11.13<br /> Commas: 1573/1568, 15488/15379<br /> Sval name: 3&17<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~14/11 = 421.309<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 14/11; 1573/1568 15488/15379]<br /> Gencom map: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]<br /> <br /> Map: [<1 0 1 3|, <0 8 7 2|]<br /> EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9904 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:199:<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:199 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bossier14">Fourteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:37:<h1> --><h1 id="toc18"><a name="Shoe"></a><!-- ws:end:WikiTextHeadingRule:37 -->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, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.331 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:200:<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:200 --><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:39:<h1> --><h1 id="toc19"><a name="Guanyintet"></a><!-- ws:end:WikiTextHeadingRule:39 -->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, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.348 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:41:<h1> --><h1 id="toc20"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:41 -->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>: 1.364 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:201:<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:201 --><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:43:<h1> --><h1 id="toc21"><a name="Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:43 -->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, 241c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.451 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:202:<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:202 --><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:45:<h1> --><h1 id="toc22"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:45 -->Radon</h1> Subgroup: 2.3.7.11<br /> Commas: 896/891, 1029/1024<br /> Sval name: 5&36<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gamelismic%20clan">Rodan</a><br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 234.381<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 896/891 1029/1024]<br /> Gencom map: [<1 1 0 3 6|, <0 3 0 -1 -13|]<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.454 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:203:<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:203 --><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:47:<h1> --><h1 id="toc23"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:47 -->Baldy</h1> Subgroup: 2.9.5.7.13<br /> Commas: 225/224, 325/324, 640/637<br /> Sval name: 6&35<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">Garibaldi</a><br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/8 = 204.090<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 225/224 325/324 640/637]<br /> Gencom map: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]<br /> <br /> Map: [<1 0 15 25 -28|, <0 1 -4 -7 10|]<br /> EDOs: 6, 11, 17, 23, 29, 35, 41, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 100, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/147edo">147</a>, 488cd, 635cd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.469 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:204:<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:204 --><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:49:<h1> --><h1 id="toc24"><a name="Photia"></a><!-- ws:end:WikiTextHeadingRule:49 -->Photia</h1> Subgroup: 2.3.5.17.19<br /> Commas: 171/170, 256/255, 324/323<br /> Sval name: 12&41<br /> Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Schismatic%20family">schismatic</a><br /> <br /> <a class="wiki_link" href="/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, 142d, 207d, 272d<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.520 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:205:<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:205 --><br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/photia12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:51:<h1> --><h1 id="toc25"><a name="Mabila"></a><!-- ws:end:WikiTextHeadingRule:51 -->Mabila</h1> Subgroup: 2.5.7<br /> Comma: 1071875/1048576<br /> Sval name: 7&9<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~175/128 = 527.236<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 175/128; 1071875/1048576]<br /> Gencom map: [<1 0 1 5}, <0, 0, 3, -5|]<br /> <br /> Map: [<1 1 5|, <0 3 -5|]<br /> EDOs: 7, 9, 16, 25, 41, 66, 305bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.546 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:206:<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:206 --><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: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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/8 = 842.711<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/8; 170/169 640/637 5525/5488]<br /> Gencom map: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]<br /> <br /> Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|]<br /> EDOs: 7, 10, 17, 27, 37, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo">47</a>, 84, 131, 178e, 309cde, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/487edo">487bcdee</a><br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.557 cents<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="Myna"></a><!-- ws:end:WikiTextHeadingRule:55 -->Myna</h1> Group: 2.3.5.7<br /> Commas: 126/125, 1728/1715<br /> Val name: 4&27<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 310.146<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125 1728/1715]<br /> Gencom map: [<1 -1 0 1|,<0 10 9 7|]<br /> <br /> Map: [<1 9 9 8|, <0 -10 -9 -7|]<br /> EDOs: 4, 27, 31, 58, 89, 236c, 325cd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.903 cents<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:208:<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:208 --><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: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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 696.495<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 81/80 126/125]<br /> Gencom map: [<1 1 0 -3|, <0 1 4 10|]<br /> <br /> Map: [<1 0 -4 -13|, <0 1 4 10|]<br /> EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.763 cents<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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 311.154<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 126/125]<br /> Gencom map: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]<br /> <br /> Map: [<1 0 -1|, <0 1 3|]<br /> EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.680 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet4">Four note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/starlingtet11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule: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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~12/11 = 147.010<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 12/11; 3025/3024 3125/3087]<br /> Gencom map: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|]<br /> <br /> Map: [<1 0 0 2|, <0 6 10 -1|]<br /> EDOs: 33, 41, 49, 57, 106, 204, 253<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.741 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~5/4 = 380.696<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 5/4; 100/99 225/224 245/243]<br /> Gencom map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> <br /> Map: [<1 0 2 -1 6|, <0 5 1 12 -8|]<br /> EDOs: 19, 22, 41, 104, 145<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.741 cents<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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/11 = 293.679<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/11; 275/273 847/845]<br /> Gencom map: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|]<br /> <br /> Map: [<1 0 0 0|, <0 3 5 1|]<br /> EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.694 cents<br /> <br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/gariberttet13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule: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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 351.691<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br /> Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.756 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 425.244<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 99/98 243/242]<br /> Gencom map: [<1 3 0 6 7|, <0 -4 0 -9 -10|]<br /> <br /> Map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.457 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: 126/125, 245/243<br /> Val name: 19&27<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 443.383<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 126/125 245/243]<br /> Gencom map: [<1 -1 -1 -2|, <0 7 9 13|]<br /> <br /> Map: [<1 6 8 11|, <0 -7 -9 -13|]<br /> EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.647 cents<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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/10 = 155.776<br /> Related temperament: <a class="wiki_link" href="/Porcupine%20family#Opossum">Opossum</a><br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/10; 121/120 126/125]<br /> Gencom map: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.313 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/10 = 453.242<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/10; 121/120 169/168 275/273]<br /> Gencom map: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]<br /> <br /> Map: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]<br /> EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde, <br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.577 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~7/6 = 271.426<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 99/98 121/120 176/175]<br /> Gencom map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> <br /> Map: [<1 0 3 1 3|, <0 7 -3 8 2|]<br /> EDOs: 9, 22, 31, 53, 84e<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.574 cents<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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~6/5 = 322.659<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 6/5; 100/99 385/384]<br /> Gencom map: [<1 -1/2 1/2 2 4|, <0 1/2 -1/2 3 -2|]<br /> <br /> Map: [<1 0 5 2|, <0 1 -3 2|]<br /> EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.696 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 440.902<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 245/243]<br /> Gencom map: [<1 0 0 0|, <0 0 2 -1|]<br /> <br /> Map: [<1 0 0|, <0 2 1|]<br /> EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.421 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~7/6 = 273.174<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 99/98]<br /> Gencom map: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]<br /> <br /> Map: [<1 0 1|, <0 1 2|]<br /> EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.380 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 /> Commas: 1352/1331<br /> <br /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/11 = 279.318<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/11; 1352/1331]<br /> Gencom map: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]<br /> <br /> Map: [<1 1 0|, <0 2 3|]<br /> EDOS: 13, 30, 43, 73, 116b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.070 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~13/12 = 139.990<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/12; 78/77 99/98 144/143]<br /> Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]<br /> <br /> Map: [<1 1 2 3 3|, <0 5 7 4 6|]<br /> EDOs: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo">43</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo">60c</a><br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.292 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 348.094<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 81/80 121/120]<br /> Gencom map: [<1 1 0 0 2|, <[0 2 8 0 5|]<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 24, 31, 69d, 100d, 131bd<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.113 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 348.916<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 66/65 81/80 121/120]<br /> Gencom map: [<1 1 0 0 2 4|, <0 2 8 0 5 -1|]<br /> <br /> Map: [<1 1 0 2 4|, <0 2 8 5 -1|]<br /> EDOs: 17c, 24, 31, 55, 86de, 141cde<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.829 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 439.146<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/7; 100/99 105/104 144/143 196/195]<br /> Gencom map: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]<br /> <br /> Map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]<br /> EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.772 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/8 = 193.937<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 81/80 99/98 126/125]<br /> Gencom map: [<1 3/2 2 2 2|, <0 1/2 2 5 9|]<br /> <br /> Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]<br /> EDOs: 25, 31, 68b, 99b<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.218 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/8 = 192.500<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 45/44 56/55 81/80]<br /> Gencom map: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]<br /> <br /> Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 8.680 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/8 = 540.099<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/8; 343/338 847/832]<br /> Gencom map: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]<br /> <br /> Map: [<1 1 3 1|, <0 4 1 6|]<br /> EDOs: 5, 7, 9, 11, 20<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.141 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 707.192<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 64/63 99/98]<br /> Gencom map: [<1 1 0 4 7|, <0 1 0 -2 -6|]<br /> <br /> Map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 706.137<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 3/2; 64/63 78/77 99/98]<br /> Gencom map: [<1 1 0 4 7 9|, <0 1 0 -2 -6 -9|]<br /> <br /> Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]<br /> EDOs: 5, 7, 12, 17<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.132 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/8 = 214.384<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 64/63 99/98]<br /> Gencom map: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]<br /> <br /> Map: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 214.095<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [7/5 8/7; 50/49 64/63]<br /> Gencom map: [<2 3 5 6|, <0 1/2 -1 -1|]<br /> <br /> Map: [<2 0 11 12|, <0 1 -1 -1|]<br /> EDOS: 4, 6, 10, 16, 22, 28<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.145 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/8 = 191.059<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 9/8; 65/64 81/80 91/90]<br /> Gencom map: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]<br /> <br /> Map: [<1 0 -4 -13 10|, <0 1 2 5 -2|]<br /> EDOs: 6, 7, 13, 19, 25e, 44de<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.906 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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~7/6 = 250.385<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [2 7/6; 49/48]<br /> Gencom map: [<1 2 0 3}, <0 -2 0 -1|]<br /> <br /> Map: [<1 0 2|, <0 2 1|]<br /> EDOs: 5, 9, 14, 19, 24, 67c, 91c<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.046 cents<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 /> <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 228.275<br /> <br /> <a class="wiki_link" href="/Gencom">Gencom</a>: [5/4 8/7; 56/55 128/125]<br /> Gencom map: [<3 0 7 9 11|, <0 0 0 -1 -1|]<br /> <br /> Map: [<3 7 0 2|, <0 0 1 1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 5.415 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>