Chromatic pairs
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-03-08 17:13:08 UTC.
- The original revision id was 208590298.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[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]. ==Greeley== Subgroup: 2.5/3.7/3.11/3 Commas: 121/120, 126/125 POTE generator: ~11/10 = 156.055 Map: [<1 1 2 2|, <0 -2 -6 -1|] EDOs: 8, 15, 23, 77, 100 [[greeley8|Eight note albitonic scale]] [[greeley15|Fifteen note chromatic scale]] ==Pepperoni== Subgroup: 2.3.11/7.13/7 Commas: 352/351, 364/363 Related temperament: [[Margo Schulter]]'s [[Pepper temperament|pepper temperament]] POTE generator: ~3/2 = 704.052 Map: [<1 0 7 12|, <0 1 -4 -7|] EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271 [[pepperoni7|Seven note albitonic scale]] [[pepperoni12|Twelve note chromatic scale]] ==Bridgetown== Subgroup: 2.3.11/5.13/5 Commas: 352/351, 676/675 Related temperament: [[The Archipelago|barabdos]] POTE generator: ~15/13 = 248.285 Map: [<1 0 -6 -1|, <0 2 9 3|] EDOs: 5, 9, 14, 19, 24, 29 [[bridgetown9|Nine note albitonic scale]] [[bridgetown14|Fourteen note chromatic scale]] ==Radon== Subgroup: 2.3.7.11 Commas: 896/891, 1029/1024 Related temperament: [[Gamelismic clan|Rodan]] POTE generator: ~8/7 = 234.381 Map: [<1 1 3 6|, <0 3 -1 -13|] EDOs: 5, 36, 41, 87, 128 [[radon5|Five note haplotonic scale]] [[radon11|Eleven note albitonic scale]] [[radon16|Sixteen note chromatic scale]] ==Skwares== Subgroup: 2.3.7.11 Commas: 99/98, 243/242 Related temperament: [[Meantone family|squares]] POTE generator: ~9/7 = 425.244 Map: [<1 3 6 7|, <0 -4 -9 -10|] EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 [[skwares8|Eight note albitonic scale]] [[skwares11|Eleven note mega albitonic scale]] [[skwares14|Fourteen note chromatic scale]] ==Hemif== Subgroup: 2.3.7.11.13 Commas: 144/143, 243/242, 364/363 Related temperament: [[Breedsmic temperaments|Hemififths]] POTE generator: ~11/9 = 351.691 Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] EDOs: 7, 10, 17, 24, 41, 58 [[hemif7|Seven note haplotonic scale]] [[hemif10|Ten note albitonic scale]] [[hemif17|Seventeen note chromatic scale]] ==Supra== Subgroup: 2.3.7.11 Commas: 64/63, 99/98 Related temperament: [[Archytas clan|superpyth]] POTE generator: ~3/2 = 707.192 Map: [<1 0 6 13|, <0 1 -2 -6|] EDOs: 5, 7, 12, 17, 22, 39, 56 [[supra7|Seven note albitonic scale]] [[supra12|Twelve note chromatic scale]] ==Mohaha== Subgroup: 2.3.5.11 Commas: 81/80, 121/120 Related temperament: [[Meantone family|mohajira]] POTE generator: ~11/9 = 348.094 Map: [<1 1 0 2|, <0 2 8 5|] EDOs: 7, 10, 17, 24, 31, 131 [[mohaha7|Seven note albitonic scale]] [[mohaha10|Ten note chromatic scale]] ==Cata== Subgroup: 2.3.5.13 Commas: 325/324, 625/624 Related temperament: [[Kleismic family|catakleismic]] POTE generator: ~6/5 = 317.076 Map: [<1 0 1 0|, <0 6 5 14|] EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246 [[cata7|Seven note albitonic scale]] [[cata11|Eleven note mega albitonic scale]] [[cata15|Fifteen note chromatic scale]] [[cata19|Nineteen note mega chromatic scale]] ==Nestoria== Subgroup: 2.3.5.19 Commas: 361/360, 513/512 Related temperament: [[Schismatic family|schismatic]] POTE generator: ~3/2 = 701.746 Map: [<1 0 15 9], <0 1 -8 -3|] EDOs: 7, 12, 17, 29, 41, 53, 118, 171 [[nestoria7|Seven note albitonic scale]] [[nestoria12|Twelve note chromatic scale]] ==Photia== Subgroup 2.3.5.17.19 Commas: 171/170, 256/255, 324/323 Related temperament: [[Schismatic family|schismatic]] POTE generator: ~3/2 = 701.470 Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|] EDOs: 7, 12, 17, 29, 41, 53, 65 [[photia7|Seven note albitonic scale]] [[photia12|Twelve note chromatic scale]] ==Baldy== Subgroup: 2.9.5.7.13 Commas: 225/224, 325/325, 640/637 Related temperament: [[Schismatic family|Garibaldi]] POTE generator: ~9/8 = 204.090 Map: [<1 0 15 25 -8|, <0 1 -4 -7 10|] EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147 [[baldy6|Six note haplotonic scale]] [[baldy11|Eleven note albitonic scale]] [[baldy17|Seventeen note chromatic scale]] ==Tutone== Subgroup: 2.9.5.7.11 Commas: 81/80, 99/98, 126/125 Related temperament: [[Meantone family|meantone]] POTE generator: ~9/8 = 193.937 Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] EDOs: 6, 7, 13, 19, 25, 31, 99 [[tutone6|Six note haplotonic scale]] [[tutone7|Seven note albitonic scale]] [[tutone13|Thirteen note chromatic scale]] ==Leantone== Subgroup: 2.9.5.7.11 Commas: 45/44, 56/55, 81/80 Related temperament: [[Meantone family|flattone]] POTE generator: ~9/8 = 192.500 Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] EDOs: 6, 7, 13, 19, 25, 31, 56, 81 [[leantone6|Six note haplotonic scale]] [[leantone7|Seven note albitonic scale]] [[leantone13|Thirteen note chromatic scale]] ==Augment== Subgroup: 2.5.7.11 Commas: 56/55, 128/125 Related temperament: [[Augmented family|augmented]] POTE generator: ~8/7 Map: [<3 7 9 11|, <0 0 -1 -1|] EDOs: 3, 6, 9, 15, 21 [[augment6|Six note haplotonic scale]] [[augment9|Nine note albitonic scale]] [[augment12|Twelve note chromatic scale]] ==Roulette== Subgroup: 2.5.7.11.13 Commas: 176/175, 1375/1372, 640/637 Related temperament: [[Wuerschmidt family|Hemiwuerschmidt]] POTE generator: ~28/25 = 194.594 Map: [<1 0 -3 -7 -13|, <0 2 5 9 -8|] EDOs: 6, 7, 13, 19, 25, 31, 37 [[roulette6|Six note haplotonic scale]] [[roulette7|Seven note albitonic scale]] [[roulette13|Thirteen note chromatic scale]] [[roulette19|Nineteen note mega chromatic scale]] ==Huntington== Subgroup: 2.5.7.13 Commas: 640/637, 10985/10976 POTE generator: ~16/13 = 357.002 Map: [<1 5 4 4|, <0 -9 -4 -1|] EDOs: 7, 10, 17, 27, 37, 84, 121, 400 [[huntington7|Seven note haplotonic scale]] [[huntington10|Ten note albitonic scale]] [[huntington17|Seventeen note chromatic scale]]
Original HTML content:
<html><head><title>Chromatic pairs</title></head><body>By a <em>chromatic pair</em> is meant a pair of MOS in some rank two temperament (which may often be a <a class="wiki_link" href="/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].<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:0 -->Greeley</h2> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 121/120, 126/125<br /> <br /> POTE generator: ~11/10 = 156.055<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 77, 100<br /> <br /> <a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pepperoni</h2> Subgroup: 2.3.11/7.13/7<br /> Commas: 352/351, 364/363<br /> Related temperament: <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>'s <a class="wiki_link" href="/Pepper%20temperament">pepper temperament</a><br /> <br /> POTE generator: ~3/2 = 704.052<br /> <br /> Map: [<1 0 7 12|, <0 1 -4 -7|]<br /> EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br /> <br /> <a class="wiki_link" href="/pepperoni7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:4 -->Bridgetown</h2> Subgroup: 2.3.11/5.13/5<br /> Commas: 352/351, 676/675<br /> Related temperament: <a class="wiki_link" href="/The%20Archipelago">barabdos</a><br /> <br /> POTE generator: ~15/13 = 248.285<br /> <br /> Map: [<1 0 -6 -1|, <0 2 9 3|]<br /> EDOs: 5, 9, 14, 19, 24, 29<br /> <br /> <a class="wiki_link" href="/bridgetown9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Radon"></a><!-- ws:end:WikiTextHeadingRule:6 -->Radon</h2> Subgroup: 2.3.7.11<br /> Commas: 896/891, 1029/1024<br /> Related temperament: <a class="wiki_link" href="/Gamelismic%20clan">Rodan</a><br /> <br /> POTE generator: ~8/7 = 234.381<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> <br /> <a class="wiki_link" href="/radon5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="/radon11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-Skwares"></a><!-- ws:end:WikiTextHeadingRule:8 -->Skwares</h2> Subgroup: 2.3.7.11<br /> Commas: 99/98, 243/242<br /> Related temperament: <a class="wiki_link" href="/Meantone%20family">squares</a><br /> <br /> POTE generator: ~9/7 = 425.244<br /> <br /> Map: [<1 3 6 7|, <0 -4 -9 -10|]<br /> EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br /> <br /> <a class="wiki_link" href="/skwares8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="/skwares11">Eleven note mega albitonic scale</a><br /> <a class="wiki_link" href="/skwares14">Fourteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-Hemif"></a><!-- ws:end:WikiTextHeadingRule:10 -->Hemif</h2> Subgroup: 2.3.7.11.13<br /> Commas: 144/143, 243/242, 364/363<br /> Related temperament: <a class="wiki_link" href="/Breedsmic%20temperaments">Hemififths</a><br /> <br /> POTE generator: ~11/9 = 351.691<br /> <br /> Map: [<1 1 -1 2 4|, <0 2 13 5 -1|]<br /> EDOs: 7, 10, 17, 24, 41, 58<br /> <br /> <a class="wiki_link" href="/hemif7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="/hemif10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="/hemif17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:12 -->Supra</h2> Subgroup: 2.3.7.11<br /> Commas: 64/63, 99/98<br /> Related temperament: <a class="wiki_link" href="/Archytas%20clan">superpyth</a><br /> <br /> POTE generator: ~3/2 = 707.192<br /> <br /> Map: [<1 0 6 13|, <0 1 -2 -6|]<br /> EDOs: 5, 7, 12, 17, 22, 39, 56<br /> <br /> <a class="wiki_link" href="/supra7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/supra12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:14 -->Mohaha</h2> Subgroup: 2.3.5.11<br /> Commas: 81/80, 121/120<br /> Related temperament: <a class="wiki_link" href="/Meantone%20family">mohajira</a><br /> <br /> POTE generator: ~11/9 = 348.094<br /> <br /> Map: [<1 1 0 2|, <0 2 8 5|]<br /> EDOs: 7, 10, 17, 24, 31, 131<br /> <br /> <a class="wiki_link" href="/mohaha7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:16 -->Cata</h2> Subgroup: 2.3.5.13<br /> Commas: 325/324, 625/624<br /> Related temperament: <a class="wiki_link" href="/Kleismic%20family">catakleismic</a><br /> <br /> POTE generator: ~6/5 = 317.076<br /> <br /> Map: [<1 0 1 0|, <0 6 5 14|]<br /> EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246<br /> <br /> <a class="wiki_link" href="/cata7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/cata11">Eleven note mega albitonic scale</a><br /> <a class="wiki_link" href="/cata15">Fifteen note chromatic scale</a><br /> <a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x-Nestoria"></a><!-- ws:end:WikiTextHeadingRule:18 -->Nestoria</h2> Subgroup: 2.3.5.19<br /> Commas: 361/360, 513/512<br /> Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br /> <br /> POTE generator: ~3/2 = 701.746<br /> <br /> Map: [<1 0 15 9], <0 1 -8 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 118, 171<br /> <br /> <a class="wiki_link" href="/nestoria7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="x-Photia"></a><!-- ws:end:WikiTextHeadingRule:20 -->Photia</h2> Subgroup 2.3.5.17.19<br /> Commas: 171/170, 256/255, 324/323<br /> Related temperament: <a class="wiki_link" href="/Schismatic%20family">schismatic</a><br /> <br /> POTE generator: ~3/2 = 701.470<br /> <br /> Map: [<1 0 15 -7 9|, <0 1 -8 7 -3|]<br /> EDOs: 7, 12, 17, 29, 41, 53, 65<br /> <br /> <a class="wiki_link" href="/photia7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="x-Baldy"></a><!-- ws:end:WikiTextHeadingRule:22 -->Baldy</h2> Subgroup: 2.9.5.7.13<br /> Commas: 225/224, 325/325, 640/637<br /> Related temperament: <a class="wiki_link" href="/Schismatic%20family">Garibaldi</a><br /> <br /> POTE generator: ~9/8 = 204.090<br /> <br /> Map: [<1 0 15 25 -8|, <0 1 -4 -7 10|]<br /> EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147<br /> <br /> <a class="wiki_link" href="/baldy6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/baldy11">Eleven note albitonic scale</a><br /> <a class="wiki_link" href="/baldy17">Seventeen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="x-Tutone"></a><!-- ws:end:WikiTextHeadingRule:24 -->Tutone</h2> Subgroup: 2.9.5.7.11<br /> Commas: 81/80, 99/98, 126/125<br /> Related temperament: <a class="wiki_link" href="/Meantone%20family">meantone</a><br /> <br /> POTE generator: ~9/8 = 193.937<br /> <br /> Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 99<br /> <br /> <a class="wiki_link" href="/tutone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/tutone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="x-Leantone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Leantone</h2> Subgroup: 2.9.5.7.11<br /> Commas: 45/44, 56/55, 81/80<br /> Related temperament: <a class="wiki_link" href="/Meantone%20family">flattone</a><br /> <br /> POTE generator: ~9/8 = 192.500<br /> <br /> Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> <br /> <a class="wiki_link" href="/leantone6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/leantone7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/leantone13">Thirteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h2> --><h2 id="toc14"><a name="x-Augment"></a><!-- ws:end:WikiTextHeadingRule:28 -->Augment</h2> Subgroup: 2.5.7.11<br /> Commas: 56/55, 128/125<br /> Related temperament: <a class="wiki_link" href="/Augmented%20family">augmented</a><br /> <br /> POTE generator: ~8/7<br /> <br /> Map: [<3 7 9 11|, <0 0 -1 -1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> <br /> <a class="wiki_link" href="/augment6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/augment9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="/augment12">Twelve note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h2> --><h2 id="toc15"><a name="x-Roulette"></a><!-- ws:end:WikiTextHeadingRule:30 -->Roulette</h2> Subgroup: 2.5.7.11.13<br /> Commas: 176/175, 1375/1372, 640/637<br /> Related temperament: <a class="wiki_link" href="/Wuerschmidt%20family">Hemiwuerschmidt</a><br /> <br /> POTE generator: ~28/25 = 194.594<br /> <br /> Map: [<1 0 -3 -7 -13|, <0 2 5 9 -8|]<br /> EDOs: 6, 7, 13, 19, 25, 31, 37<br /> <br /> <a class="wiki_link" href="/roulette6">Six note haplotonic scale</a><br /> <a class="wiki_link" href="/roulette7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/roulette13">Thirteen note chromatic scale</a><br /> <a class="wiki_link" href="/roulette19">Nineteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="x-Huntington"></a><!-- ws:end:WikiTextHeadingRule:32 -->Huntington</h2> Subgroup: 2.5.7.13<br /> Commas: 640/637, 10985/10976<br /> <br /> POTE generator: ~16/13 = 357.002<br /> <br /> Map: [<1 5 4 4|, <0 -9 -4 -1|]<br /> EDOs: 7, 10, 17, 27, 37, 84, 121, 400<br /> <br /> <a class="wiki_link" href="/huntington7">Seven note haplotonic scale</a><br /> <a class="wiki_link" href="/huntington10">Ten note albitonic scale</a><br /> <a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a></body></html>