Chromatic pairs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 209500308 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 209513684 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 01:44:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>209513684</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;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]. | <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]. | ||
==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 | |||
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]] | |||
==Greeley== | ==Greeley== | ||
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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].<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].<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><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: [&lt;3 0 -4|, &lt;0 1 2|]<br /> | |||
EDOs: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558<br /> | |||
<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:&lt;h2&gt; --><h2 id="toc1"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 276: | Line 304: | ||
<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: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pepperoni</h2> | ||
Subgroup: 2.3.11/7.13/7<br /> | Subgroup: 2.3.11/7.13/7<br /> | ||
Commas: 352/351, 364/363<br /> | Commas: 352/351, 364/363<br /> | ||
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<a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br /> | <a class="wiki_link" href="/pepperoni12">Twelve note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:6 -->Bridgetown</h2> | ||
Subgroup: 2.3.11/5.13/5<br /> | Subgroup: 2.3.11/5.13/5<br /> | ||
Commas: 352/351, 676/675<br /> | Commas: 352/351, 676/675<br /> | ||
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<a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br /> | <a class="wiki_link" href="/bridgetown14">Fourteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Radon"></a><!-- ws:end:WikiTextHeadingRule:8 -->Radon</h2> | ||
Subgroup: 2.3.7.11<br /> | Subgroup: 2.3.7.11<br /> | ||
Commas: 896/891, 1029/1024<br /> | Commas: 896/891, 1029/1024<br /> | ||
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<a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br /> | <a class="wiki_link" href="/radon16">Sixteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Skwares"></a><!-- ws:end:WikiTextHeadingRule:10 -->Skwares</h2> | ||
Subgroup: 2.3.7.11<br /> | Subgroup: 2.3.7.11<br /> | ||
Commas: 99/98, 243/242<br /> | Commas: 99/98, 243/242<br /> | ||
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<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: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Hemif"></a><!-- ws:end:WikiTextHeadingRule:12 -->Hemif</h2> | ||
Subgroup: 2.3.7.11.13<br /> | Subgroup: 2.3.7.11.13<br /> | ||
Commas: 144/143, 243/242, 364/363<br /> | Commas: 144/143, 243/242, 364/363<br /> | ||
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<a class="wiki_link" href="/hemif17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="/hemif17">Seventeen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Supra"></a><!-- ws:end:WikiTextHeadingRule:14 -->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 357: | Line 385: | ||
<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:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mohaha</h2> | ||
Subgroup: 2.3.5.11<br /> | Subgroup: 2.3.5.11<br /> | ||
Commas: 81/80, 121/120<br /> | Commas: 81/80, 121/120<br /> | ||
| Line 370: | Line 398: | ||
<a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br /> | <a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:18 -->Mohoho</h3> | ||
Subgroup: 3.3.5.11.13<br /> | Subgroup: 3.3.5.11.13<br /> | ||
Commas: 66/65, 81/80, 121/120<br /> | Commas: 66/65, 81/80, 121/120<br /> | ||
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EDOs: 7, 10, 17, 24, 31, 55<br /> | EDOs: 7, 10, 17, 24, 31, 55<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-Cata"></a><!-- ws:end:WikiTextHeadingRule:20 -->Cata</h2> | ||
Subgroup: 2.3.5.13<br /> | Subgroup: 2.3.5.13<br /> | ||
Commas: 325/324, 625/624<br /> | Commas: 325/324, 625/624<br /> | ||
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<a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br /> | <a class="wiki_link" href="/cata19">Nineteen note mega chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Nestoria"></a><!-- ws:end:WikiTextHeadingRule:22 -->Nestoria</h2> | ||
Subgroup: 2.3.5.19<br /> | Subgroup: 2.3.5.19<br /> | ||
Commas: 361/360, 513/512<br /> | Commas: 361/360, 513/512<br /> | ||
| Line 407: | Line 435: | ||
<a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br /> | <a class="wiki_link" href="/nestoria12">Twelve note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="x-Photia"></a><!-- ws:end:WikiTextHeadingRule:24 -->Photia</h2> | ||
Subgroup 2.3.5.17.19<br /> | Subgroup 2.3.5.17.19<br /> | ||
Commas: 171/170, 256/255, 324/323<br /> | Commas: 171/170, 256/255, 324/323<br /> | ||
| Line 420: | Line 448: | ||
<a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br /> | <a class="wiki_link" href="/photia12">Twelve note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x-Baldy"></a><!-- ws:end:WikiTextHeadingRule:26 -->Baldy</h2> | ||
Subgroup: 2.9.5.7.13<br /> | Subgroup: 2.9.5.7.13<br /> | ||
Commas: 225/224, 325/325, 640/637<br /> | Commas: 225/224, 325/325, 640/637<br /> | ||
| Line 434: | Line 462: | ||
<a class="wiki_link" href="/baldy17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="/baldy17">Seventeen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x-Tutone"></a><!-- ws:end:WikiTextHeadingRule:28 -->Tutone</h2> | ||
Subgroup: 2.9.5.7.11<br /> | Subgroup: 2.9.5.7.11<br /> | ||
Commas: 81/80, 99/98, 126/125<br /> | Commas: 81/80, 99/98, 126/125<br /> | ||
| Line 448: | Line 476: | ||
<a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br /> | <a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="x-Leantone"></a><!-- ws:end:WikiTextHeadingRule:30 -->Leantone</h2> | ||
Subgroup: 2.9.5.7.11<br /> | Subgroup: 2.9.5.7.11<br /> | ||
Commas: 45/44, 56/55, 81/80<br /> | Commas: 45/44, 56/55, 81/80<br /> | ||
| Line 462: | Line 490: | ||
<a class="wiki_link" href="/leantone13">Thirteen note chromatic scale</a><br /> | <a class="wiki_link" href="/leantone13">Thirteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x-Augment"></a><!-- ws:end:WikiTextHeadingRule:32 -->Augment</h2> | ||
Subgroup: 2.5.7.11<br /> | Subgroup: 2.5.7.11<br /> | ||
Commas: 56/55, 128/125<br /> | Commas: 56/55, 128/125<br /> | ||
| Line 476: | Line 504: | ||
<a class="wiki_link" href="/augment12">Twelve note chromatic scale</a><br /> | <a class="wiki_link" href="/augment12">Twelve note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x-Huntington"></a><!-- ws:end:WikiTextHeadingRule:34 -->Huntington</h2> | ||
Subgroup: 2.5.7.13<br /> | Subgroup: 2.5.7.13<br /> | ||
Commas: 640/637, 10985/10976<br /> | Commas: 640/637, 10985/10976<br /> | ||
| Line 489: | Line 517: | ||
<a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="/huntington17">Seventeen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="x-Roulette"></a><!-- ws:end:WikiTextHeadingRule:36 -->Roulette</h2> | ||
Subgroup: 2.5.7.11.13<br /> | Subgroup: 2.5.7.11.13<br /> | ||
Commas: 176/175, 1375/1372, 640/637<br /> | Commas: 176/175, 1375/1372, 640/637<br /> | ||
| Line 504: | Line 532: | ||
<a class="wiki_link" href="/roulette19">Nineteen note mega chromatic scale</a><br /> | <a class="wiki_link" href="/roulette19">Nineteen note mega chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="x-Score"></a><!-- ws:end:WikiTextHeadingRule:38 -->Score</h2> | ||
Subgroup: 2.7.11.13<br /> | Subgroup: 2.7.11.13<br /> | ||
Commas: 343/338, 847/832<br /> | Commas: 343/338, 847/832<br /> | ||