Chromatic pairs: Difference between revisions
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 /> | ||
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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 /> | |||
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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 = 701.470<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; 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 /> | ||
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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 /> | ||
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<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 /> | ||
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<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 /> | ||
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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 /> | ||
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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 /> | |||
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<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 /> | ||
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<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 /> | ||
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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 /> | |||
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<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 /> | ||
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<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 /> | ||
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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> | ||