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Wikispaces>genewardsmith **Imported revision 209682360 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 209682780 - 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 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 13:59:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>209682780</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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<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;white-space: pre-wrap ! important" class="old-revision-html">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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. | <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;white-space: pre-wrap ! important" class="old-revision-html">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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. | ||
[[toc|flat]] | |||
=Terrain= | =Terrain= | ||
Subgroup: 2.9/5.9/7 | Subgroup: 2.9/5.9/7 | ||
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<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>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 &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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it.<br /> | <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>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 &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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1> | <!-- ws:start:WikiTextTocRule:40:&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:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | ||
<!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1> | |||
Subgroup: 2.9/5.9/7<br /> | Subgroup: 2.9/5.9/7<br /> | ||
Commas: 250047/250000<br /> | Commas: 250047/250000<br /> | ||
Revision as of 13:59, 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 13:59:08 UTC.
- The original revision id was 209682780.
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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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it. [[toc|flat]] =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]] =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: 0.611 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: 1.512 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: 0.735 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: 0.8489 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: 1.036 cents [[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 Error: 1.363 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: 1.469 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: 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]] =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: 3.218 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: 8.680 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: 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 =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: 3.846 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: 5.414 cents [[supra7|Seven note albitonic scale]] [[supra12|Twelve 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: 6.632 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: 7.555 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 TE error; since this is a weighted measure, subgroups which emphasize the higher primes will get a lower error rating because of it.<br /> <br /> <!-- ws:start:WikiTextTocRule:40:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> <!-- ws:end:WikiTextTocRule:61 --><!-- 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 /> <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:<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: 0.611 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: 1.512 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: 0.735 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: 0.8489 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: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: 1.036 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="Roulette"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: 1.363 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:14:<h1> --><h1 id="toc7"><a name="Baldy"></a><!-- ws:end:WikiTextHeadingRule:14 -->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: 1.469 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:16:<h1> --><h1 id="toc8"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:16 -->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: 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:18:<h1> --><h1 id="toc9"><a name="Radon"></a><!-- ws:end:WikiTextHeadingRule:18 -->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: 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:20:<h1> --><h1 id="toc10"><a name="Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:20 -->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: 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:22:<h1> --><h1 id="toc11"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:22 -->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: 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:24:<h1> --><h1 id="toc12"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:24 -->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: 3.218 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:26:<h2> --><h2 id="toc13"><a name="Tutone-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 /> Error: 8.680 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:28:<h1> --><h1 id="toc14"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:28 -->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: 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:30:<h2> --><h2 id="toc15"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:30 -->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: 4.829 cents<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:32 -->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: 3.846 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:34:<h1> --><h1 id="toc17"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:34 -->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: 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:36:<h1> --><h1 id="toc18"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:36 -->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: 6.632 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:38:<h1> --><h1 id="toc19"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:38 -->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: 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></body></html>