Chromatic pairs: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 209616254 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 209619832 - 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>2011-03-11 11: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 11:09:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>209619832</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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EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 | EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206 | ||
Error: 3.009 cents | Error: 3.009 cents | ||
[[skwares8|Eight note albitonic scale]] | [[skwares8|Eight note albitonic scale]] | ||
[[skwares11|Eleven note mega albitonic scale]] | [[skwares11|Eleven note mega albitonic scale]] | ||
[[skwares14|Fourteen note chromatic scale]] | [[skwares14|Fourteen 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: 3.813 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: 4.829 cents | |||
==Supra== | ==Supra== | ||
| Line 104: | Line 129: | ||
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: 5.414 | Error: 5.414 cents | ||
[[supra7|Seven note albitonic scale]] | [[supra7|Seven note albitonic scale]] | ||
| Line 121: | Line 146: | ||
[[greeley8|Eight note albitonic scale]] | [[greeley8|Eight note albitonic scale]] | ||
[[greeley15|Fifteen note chromatic scale]] | [[greeley15|Fifteen note chromatic scale]] | ||
==Cata== | ==Cata== | ||
| Line 368: | Line 371: | ||
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: 3.009 cents<br /> | Error: 3.009 cents<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 /> | ||
<a class="wiki_link" href="/skwares11">Eleven note mega 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 /> | <a class="wiki_link" href="/skwares14">Fourteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br /> | |||
EDOs: 7, 10, 17, 24, 31, 131<br /> | |||
Error: 3.813 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:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:14 -->Mohoho</h3> | |||
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: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]<br /> | |||
EDOs: 7, 10, 17, 24, 31, 55<br /> | |||
Error: 4.829 cents<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:16 -->Supra</h2> | |||
Subgroup: 2.3.7.11<br /> | Subgroup: 2.3.7.11<br /> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<br /> | ||
| Line 381: | Line 409: | ||
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: 5.414<br /> | Error: 5.414 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 /> | ||
<a class="wiki_link" href="/supra12">Twelve note chromatic scale</a><br /> | <a class="wiki_link" href="/supra12">Twelve note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:18 -->Greeley</h2> | ||
Subgroup: 2.5/3.7/3.11/3<br /> | Subgroup: 2.5/3.7/3.11/3<br /> | ||
Commas: 121/120, 126/125<br /> | Commas: 121/120, 126/125<br /> | ||
| Line 398: | Line 426: | ||
<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><br /> | <a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:20 -->Cata</h2> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:20 -->Cata</h2> | ||
Revision as of 11:09, 11 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 2011-03-11 11:09:31 UTC.
- The original revision id was 209619832.
- 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]. ==Terrain== Subgroup: 2.9/5.9/7 Commas: 250047/250000 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: 0.0859 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]] ==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: 0.8489 cents [[bridgetown9|Nine note albitonic scale]] [[bridgetown14|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 Error: 1.756 [[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: 1.781 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: 2.155 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: 3.009 cents [[skwares8|Eight note albitonic scale]] [[skwares11|Eleven note mega albitonic scale]] [[skwares14|Fourteen 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: 3.813 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: 4.829 cents ==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: 5.414 cents [[supra7|Seven note albitonic scale]] [[supra12|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: 7.555 cents [[greeley8|Eight note albitonic scale]] [[greeley15|Fifteen 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]] ==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]] ==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]] ==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 [[score5|Five note haplotonic scale]] [[score7|Seven note albitonic scale]] [[score9|Nine note mega albitonic scale]] [[score11|Eleven 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-Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h2> Subgroup: 2.9/5.9/7<br /> Commas: 250047/250000<br /> <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: 0.0859 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:<h2> --><h2 id="toc1"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 /> Error: 0.8489 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:4:<h2> --><h2 id="toc2"><a name="x-Hemif"></a><!-- ws:end:WikiTextHeadingRule:4 -->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 /> Error: 1.756<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: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 /> Error: 1.781 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:8:<h2> --><h2 id="toc4"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:8 -->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 /> Error: 2.155 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:10:<h2> --><h2 id="toc5"><a name="x-Skwares"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 /> Error: 3.009 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:12:<h2> --><h2 id="toc6"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:12 -->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 /> Error: 3.813 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:14:<h3> --><h3 id="toc7"><a name="x-Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:14 -->Mohoho</h3> 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: 4.829 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:16 -->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 /> Error: 5.414 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:18:<h2> --><h2 id="toc9"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 /> Error: 7.555 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><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:<h2> --><h2 id="toc11"><a name="x-Nestoria"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:<h2> --><h2 id="toc12"><a name="x-Photia"></a><!-- ws:end:WikiTextHeadingRule:24 -->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:26:<h2> --><h2 id="toc13"><a name="x-Baldy"></a><!-- ws:end:WikiTextHeadingRule:26 -->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:28:<h2> --><h2 id="toc14"><a name="x-Tutone"></a><!-- ws:end:WikiTextHeadingRule:28 -->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:30:<h2> --><h2 id="toc15"><a name="x-Leantone"></a><!-- ws:end:WikiTextHeadingRule:30 -->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:32:<h2> --><h2 id="toc16"><a name="x-Augment"></a><!-- ws:end:WikiTextHeadingRule:32 -->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:34:<h2> --><h2 id="toc17"><a name="x-Huntington"></a><!-- ws:end:WikiTextHeadingRule:34 -->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><br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="x-Roulette"></a><!-- ws:end:WikiTextHeadingRule:36 -->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:38:<h2> --><h2 id="toc19"><a name="x-Score"></a><!-- ws:end:WikiTextHeadingRule:38 -->Score</h2> 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 /> <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></body></html>