Chromatic pairs: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 211872328 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 211876668 - 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>2011-03-18 16: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-18 16:30:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>211876668</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 195: | Line 195: | ||
Map: [<1 3 6 7|, <0 -4 -9 -10|] | Map: [<1 3 6 7|, <0 -4 -9 -10|] | ||
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 | ||
Error: | Error: 4.942 cents | ||
[[skwares8|Eight note albitonic scale]] | [[skwares8|Eight note albitonic scale]] | ||
| Line 210: | Line 210: | ||
Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] | Map: [<1 0 -4 -13 -25|, <0 1 2 5 9|] | ||
EDOs: 6, 7, 13, 19, 25, 31, 99 | EDOs: 6, 7, 13, 19, 25, 31, 99 | ||
Error: | Error: 7.047 cents | ||
[[tutone6|Six note haplotonic scale]] | [[tutone6|Six note haplotonic scale]] | ||
| Line 225: | Line 225: | ||
Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] | Map: [<1 0 -4 -13 -6|, <0 1 2 5 3|] | ||
EDOs: 6, 7, 13, 19, 25, 31, 56, 81 | EDOs: 6, 7, 13, 19, 25, 31, 56, 81 | ||
Error: | Error: 20.338 cents | ||
[[leantone6|Six note haplotonic scale]] | [[leantone6|Six note haplotonic scale]] | ||
| Line 240: | Line 240: | ||
Map: [<1 1 0 2|, <0 2 8 5|] | Map: [<1 1 0 2|, <0 2 8 5|] | ||
EDOs: 7, 10, 17, 24, 31, 131 | EDOs: 7, 10, 17, 24, 31, 131 | ||
Error: | Error: 6.733 cents | ||
[[mohaha7|Seven note albitonic scale]] | [[mohaha7|Seven note albitonic scale]] | ||
| Line 253: | Line 253: | ||
Map: [<1 1 0 2 4|, <0 2 8 5 -1|] | Map: [<1 1 0 2 4|, <0 2 8 5 -1|] | ||
EDOs: 7, 10, 17, 24, 31, 55 | EDOs: 7, 10, 17, 24, 31, 55 | ||
Error: | Error: 9.556 cents | ||
=Score= | =Score= | ||
| Line 263: | Line 263: | ||
Map: [<1 1 3 1|, <0 4 1 6|] | Map: [<1 1 3 1|, <0 4 1 6|] | ||
EDOs: 5, 7, 9, 11, 20 | EDOs: 5, 7, 9, 11, 20 | ||
Error: | Error: 8.052 cents | ||
[[score5|Five note haplotonic scale]] | [[score5|Five note haplotonic scale]] | ||
| Line 279: | Line 279: | ||
Map: [<1 0 6 13|, <0 1 -2 -6|] | Map: [<1 0 6 13|, <0 1 -2 -6|] | ||
EDOs: 5, 7, 12, 17, 22, 39, 56 | EDOs: 5, 7, 12, 17, 22, 39, 56 | ||
Error: | Error: 9.795 cents | ||
[[supra7|Seven note albitonic scale]] | [[supra7|Seven note albitonic scale]] | ||
| Line 292: | Line 292: | ||
Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] | Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] | ||
EDOs: 5, 7, 12, 17 | EDOs: 5, 7, 12, 17 | ||
Error: | Error: 10.534 cents | ||
==Machine== | ==Machine== | ||
| Line 302: | Line 302: | ||
Map: [<1 0 6 13|, <0 1 -1 -3|] | Map: [<1 0 6 13|, <0 1 -1 -3|] | ||
EDOs: 5, 6, 11, 17, 28 | EDOs: 5, 6, 11, 17, 28 | ||
Error: | Error: 10.100 cents | ||
[[machine5|Five note haplotonic scale]] | [[machine5|Five note haplotonic scale]] | ||
| Line 317: | Line 317: | ||
Map: [<3 7 0 2|, <0 0 1 1|] | Map: [<3 7 0 2|, <0 0 1 1|] | ||
EDOs: 3, 6, 9, 15, 21 | EDOs: 3, 6, 9, 15, 21 | ||
Error: | Error: 12.830 cents | ||
[[augment6|Six note haplotonic scale]] | [[augment6|Six note haplotonic scale]] | ||
| Line 331: | Line 331: | ||
Map: [<1 1 2 2|, <0 -2 -6 -1|] | Map: [<1 1 2 2|, <0 -2 -6 -1|] | ||
EDOs: 8, 15, 23, 77, 100 | EDOs: 8, 15, 23, 77, 100 | ||
Error: | Error: 5.404 cents | ||
[[greeley8|Eight note albitonic scale]] | [[greeley8|Eight note albitonic scale]] | ||
| Line 526: | Line 526: | ||
Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br /> | Map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br /> | ||
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br /> | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206<br /> | ||
Error: | Error: 4.942 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/skwares8">Eight note albitonic scale</a><br /> | <a class="wiki_link" href="/skwares8">Eight note albitonic scale</a><br /> | ||
| Line 541: | Line 541: | ||
Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 2 5 9|]<br /> | Map: [&lt;1 0 -4 -13 -25|, &lt;0 1 2 5 9|]<br /> | ||
EDOs: 6, 7, 13, 19, 25, 31, 99<br /> | EDOs: 6, 7, 13, 19, 25, 31, 99<br /> | ||
Error: | Error: 7.047 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/tutone6">Six note haplotonic scale</a><br /> | <a class="wiki_link" href="/tutone6">Six note haplotonic scale</a><br /> | ||
| Line 556: | Line 556: | ||
Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]<br /> | Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]<br /> | ||
EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> | EDOs: 6, 7, 13, 19, 25, 31, 56, 81<br /> | ||
Error: | Error: 20.338 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/leantone6">Six note haplotonic scale</a><br /> | <a class="wiki_link" href="/leantone6">Six note haplotonic scale</a><br /> | ||
| Line 571: | Line 571: | ||
Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br /> | Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br /> | ||
EDOs: 7, 10, 17, 24, 31, 131<br /> | EDOs: 7, 10, 17, 24, 31, 131<br /> | ||
Error: | Error: 6.733 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/mohaha7">Seven note albitonic scale</a><br /> | <a class="wiki_link" href="/mohaha7">Seven note albitonic scale</a><br /> | ||
| Line 584: | Line 584: | ||
Map: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]<br /> | Map: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]<br /> | ||
EDOs: 7, 10, 17, 24, 31, 55<br /> | EDOs: 7, 10, 17, 24, 31, 55<br /> | ||
Error: | Error: 9.556 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:34 -->Score</h1> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:34 -->Score</h1> | ||
| Line 594: | Line 594: | ||
Map: [&lt;1 1 3 1|, &lt;0 4 1 6|]<br /> | Map: [&lt;1 1 3 1|, &lt;0 4 1 6|]<br /> | ||
EDOs: 5, 7, 9, 11, 20<br /> | EDOs: 5, 7, 9, 11, 20<br /> | ||
Error: | Error: 8.052 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/score5">Five note haplotonic scale</a><br /> | <a class="wiki_link" href="/score5">Five note haplotonic scale</a><br /> | ||
| Line 610: | Line 610: | ||
Map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]<br /> | Map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]<br /> | ||
EDOs: 5, 7, 12, 17, 22, 39, 56<br /> | EDOs: 5, 7, 12, 17, 22, 39, 56<br /> | ||
Error: | Error: 9.795 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/supra7">Seven note albitonic scale</a><br /> | <a class="wiki_link" href="/supra7">Seven note albitonic scale</a><br /> | ||
| Line 623: | Line 623: | ||
Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]<br /> | Map: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]<br /> | ||
EDOs: 5, 7, 12, 17<br /> | EDOs: 5, 7, 12, 17<br /> | ||
Error: | Error: 10.534 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:40 -->Machine</h2> | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:40 -->Machine</h2> | ||
| Line 633: | Line 633: | ||
Map: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br /> | Map: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br /> | ||
EDOs: 5, 6, 11, 17, 28<br /> | EDOs: 5, 6, 11, 17, 28<br /> | ||
Error: | Error: 10.100 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/machine5">Five note haplotonic scale</a><br /> | <a class="wiki_link" href="/machine5">Five note haplotonic scale</a><br /> | ||
| Line 648: | Line 648: | ||
Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]<br /> | Map: [&lt;3 7 0 2|, &lt;0 0 1 1|]<br /> | ||
EDOs: 3, 6, 9, 15, 21<br /> | EDOs: 3, 6, 9, 15, 21<br /> | ||
Error: | Error: 12.830 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/augment6">Six note haplotonic scale</a><br /> | <a class="wiki_link" href="/augment6">Six note haplotonic scale</a><br /> | ||
| Line 662: | Line 662: | ||
Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]<br /> | Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]<br /> | ||
EDOs: 8, 15, 23, 77, 100<br /> | EDOs: 8, 15, 23, 77, 100<br /> | ||
Error: | Error: 5.404 cents<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br /> | <a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br /> | ||
<a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a></body></html></pre></div> | <a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a></body></html></pre></div> | ||
Revision as of 16:30, 18 March 2011
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 2011-03-18 16:30:48 UTC.
- The original revision id was 211876668.
- 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]. The pair temperaments are listed in order of increasing unweighted rms error with [[Target tunings|tuning target]] the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give. [[toc|flat]] =Terrain= Subgroup: 2.9/5.9/7 Commas: 250047/250000 Related temperament: [[Minortonic family#Domain|domain]] POTE generator: ~10/9 = 182.462 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 Error: 0.0443 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. [[terrain9|Nine note albitonic scale]] [[terrain15|Fifteen note 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 Error: 1.819 cents [[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 Error: 3.457 cents [[photia7|Seven note albitonic scale]] [[photia12|Twelve 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 Error: 0.9355 cents [[cata7|Seven note albitonic scale]] [[cata11|Eleven note mega albitonic scale]] [[cata15|Fifteen note chromatic scale]] [[cata19|Nineteen note mega 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 Error: 0.8996 cents [[bridgetown9|Nine note albitonic scale]] [[bridgetown14|Fourteen note 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 Error: 2.1001 cents [[huntington7|Seven note haplotonic scale]] [[huntington10|Ten note albitonic scale]] [[huntington17|Seventeen note chromatic scale]] =Bossier= Subgroup: 2.7.11.13 Commas: 1573/1569, 15488/15379 POTE generator: ~14/11 = 421.309 Map: [<1 0 1 3|, <0 8 7 2|] EDOs: 17, 20, 37, 57, 94, 225 Error: 2.665 cents [[bossier8|Eight note albitonic scale]] [[bossier11|Eleven note chromatic scale]] [[bossier14|Fourteen note mega 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 Error: 2.555 cents [[roulette6|Six note haplotonic scale]] [[roulette7|Seven note albitonic scale]] [[roulette13|Thirteen note chromatic scale]] [[roulette19|Nineteen note mega 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 Error: 2.617 cents [[baldy6|Six note haplotonic scale]] [[baldy11|Eleven note albitonic scale]] [[baldy17|Seventeen 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 Error: 4.867 cents [[hemif7|Seven note haplotonic scale]] [[hemif10|Ten note albitonic scale]] [[hemif17|Seventeen 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 Error: 2.925 cents [[radon5|Five note haplotonic scale]] [[radon11|Eleven note albitonic scale]] [[radon16|Sixteen 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 Error: 1.298 cents [[pepperoni7|Seven note albitonic scale]] [[pepperoni12|Twelve 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 Error: 4.942 cents [[skwares8|Eight note albitonic scale]] [[skwares11|Eleven note mega albitonic scale]] [[skwares14|Fourteen 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 Error: 7.047 cents [[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 Error: 20.338 cents [[leantone6|Six note haplotonic scale]] [[leantone7|Seven note albitonic scale]] [[leantone13|Thirteen 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 Error: 6.733 cents [[mohaha7|Seven note albitonic scale]] [[mohaha10|Ten note chromatic scale]] ==Mohoho== Subgroup: 2.3.5.11.13 Commas: 66/65, 81/80, 121/120 POTE generator: ~11/9 = 348.916 Map: [<1 1 0 2 4|, <0 2 8 5 -1|] EDOs: 7, 10, 17, 24, 31, 55 Error: 9.556 cents =Score= Subgroup: 2.7.11.13 Commas: 343/338, 847/832 POTE generator: ~11/8 = 540.099 Map: [<1 1 3 1|, <0 4 1 6|] EDOs: 5, 7, 9, 11, 20 Error: 8.052 cents [[score5|Five note haplotonic scale]] [[score7|Seven note albitonic scale]] [[score9|Nine note mega albitonic scale]] [[score11|Eleven 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 Error: 9.795 cents [[supra7|Seven note albitonic scale]] [[supra12|Twelve note chromatic scale]] ==Supraphon== Subgroup: 2.3.7.11.13 Commas: 64/63, 78/77, 99/98 POTE generator: ~3/2 = 706.137 Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|] EDOs: 5, 7, 12, 17 Error: 10.534 cents ==Machine== Subgroup: 2.9.7.11 Commas: 64/63, 99/98 POTE generator: ~9/8 = 214.384 Map: [<1 0 6 13|, <0 1 -1 -3|] EDOs: 5, 6, 11, 17, 28 Error: 10.100 cents [[machine5|Five note haplotonic scale]] [[machine6|Six note albitonic scale]] [[machine11|Eleven 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 0 2|, <0 0 1 1|] EDOs: 3, 6, 9, 15, 21 Error: 12.830 cents [[augment6|Six note haplotonic scale]] [[augment9|Nine note albitonic scale]] [[augment12|Twelve note chromatic scale]] =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 Error: 5.404 cents [[greeley8|Eight note albitonic scale]] [[greeley15|Fifteen 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]. The pair temperaments are listed in order of increasing unweighted rms error with <a class="wiki_link" href="/Target%20tunings">tuning target</a> the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.<br /> <br /> <!-- ws:start:WikiTextTocRule:46:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> <!-- ws:end:WikiTextTocRule:70 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1> Subgroup: 2.9/5.9/7<br /> Commas: 250047/250000<br /> Related temperament: <a class="wiki_link" href="/Minortonic%20family#Domain">domain</a><br /> POTE generator: ~10/9 = 182.462<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 /> Error: 0.0443 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 /> <a class="wiki_link" href="/terrain9">Nine note albitonic scale</a><br /> <a class="wiki_link" href="/terrain15">Fifteen note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Nestoria"></a><!-- ws:end:WikiTextHeadingRule:2 -->Nestoria</h1> 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 /> Error: 1.819 cents<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:4:<h2> --><h2 id="toc2"><a name="Nestoria-Photia"></a><!-- ws:end:WikiTextHeadingRule:4 -->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 /> Error: 3.457 cents<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:6:<h1> --><h1 id="toc3"><a name="Cata"></a><!-- ws:end:WikiTextHeadingRule:6 -->Cata</h1> 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 /> Error: 0.9355 cents<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:8:<h1> --><h1 id="toc4"><a name="Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:8 -->Bridgetown</h1> 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 /> Error: 0.8996 cents<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:10:<h1> --><h1 id="toc5"><a name="Huntington"></a><!-- ws:end:WikiTextHeadingRule:10 -->Huntington</h1> 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 /> Error: 2.1001 cents<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><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Bossier"></a><!-- ws:end:WikiTextHeadingRule:12 -->Bossier</h1> Subgroup: 2.7.11.13<br /> Commas: 1573/1569, 15488/15379<br /> <br /> POTE generator: ~14/11 = 421.309<br /> <br /> Map: [<1 0 1 3|, <0 8 7 2|]<br /> EDOs: 17, 20, 37, 57, 94, 225<br /> Error: 2.665 cents<br /> <br /> <a class="wiki_link" href="/bossier8">Eight note albitonic scale</a><br /> <a class="wiki_link" href="/bossier11">Eleven note chromatic scale</a><br /> <a class="wiki_link" href="/bossier14">Fourteen note mega chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Roulette"></a><!-- ws:end:WikiTextHeadingRule:14 -->Roulette</h1> 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 /> Error: 2.555 cents<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:16:<h1> --><h1 id="toc8"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:16 -->Baldy</h1> 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 /> Error: 2.617 cents<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:18:<h1> --><h1 id="toc9"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemif</h1> 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 /> Error: 4.867 cents<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:20:<h1> --><h1 id="toc10"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:20 -->Radon</h1> 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 /> Error: 2.925 cents<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:22:<h1> --><h1 id="toc11"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:22 -->Pepperoni</h1> 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 /> Error: 1.298 cents<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:24:<h1> --><h1 id="toc12"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:24 -->Skwares</h1> 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 /> Error: 4.942 cents<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:26:<h1> --><h1 id="toc13"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Tutone</h1> 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 /> Error: 7.047 cents<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:28:<h2> --><h2 id="toc14"><a name="Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:28 -->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 /> Error: 20.338 cents<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:30:<h1> --><h1 id="toc15"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:30 -->Mohaha</h1> 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 /> Error: 6.733 cents<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:32:<h2> --><h2 id="toc16"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:32 -->Mohoho</h2> Subgroup: 2.3.5.11.13<br /> Commas: 66/65, 81/80, 121/120<br /> <br /> POTE generator: ~11/9 = 348.916<br /> <br /> Map: [<1 1 0 2 4|, <0 2 8 5 -1|]<br /> EDOs: 7, 10, 17, 24, 31, 55<br /> Error: 9.556 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:34 -->Score</h1> Subgroup: 2.7.11.13<br /> Commas: 343/338, 847/832<br /> <br /> POTE generator: ~11/8 = 540.099<br /> <br /> Map: [<1 1 3 1|, <0 4 1 6|]<br /> EDOs: 5, 7, 9, 11, 20<br /> Error: 8.052 cents<br /> <br /> <a class="wiki_link" href="/score5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="/score7">Seven note albitonic scale</a><br /> <a class="wiki_link" href="/score9">Nine note mega albitonic scale</a><br /> <a class="wiki_link" href="/score11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:36 -->Supra</h1> 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 /> Error: 9.795 cents<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:38:<h2> --><h2 id="toc19"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:38 -->Supraphon</h2> Subgroup: 2.3.7.11.13<br /> Commas: 64/63, 78/77, 99/98<br /> <br /> POTE generator: ~3/2 = 706.137<br /> <br /> Map: [<1 0 6 13 18|, <0 1 -2 -6 -9|]<br /> EDOs: 5, 7, 12, 17<br /> Error: 10.534 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h2> --><h2 id="toc20"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:40 -->Machine</h2> Subgroup: 2.9.7.11<br /> Commas: 64/63, 99/98<br /> <br /> POTE generator: ~9/8 = 214.384<br /> <br /> Map: [<1 0 6 13|, <0 1 -1 -3|]<br /> EDOs: 5, 6, 11, 17, 28<br /> Error: 10.100 cents<br /> <br /> <a class="wiki_link" href="/machine5">Five note haplotonic scale</a><br /> <a class="wiki_link" href="/machine6">Six note albitonic scale</a><br /> <a class="wiki_link" href="/machine11">Eleven note chromatic scale</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:42 -->Augment</h1> 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 0 2|, <0 0 1 1|]<br /> EDOs: 3, 6, 9, 15, 21<br /> Error: 12.830 cents<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:44:<h1> --><h1 id="toc22"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:44 -->Greeley</h1> Subgroup: 2.5/3.7/3.11/3<br /> Commas: 121/120, 126/125<br /> <br /> POTE generator: ~11/10 = 156.055<br /> <br /> Map: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 77, 100<br /> Error: 5.404 cents<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></body></html>