Chromatic pairs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 212270648 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 214132852 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-03-25 22:57:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>214132852</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 196: | Line 196: | ||
[[radon11|Eleven note albitonic scale]] | [[radon11|Eleven note albitonic scale]] | ||
[[radon16|Sixteen note chromatic scale]] | [[radon16|Sixteen note chromatic scale]] | ||
=Silver= | |||
Subgroup: 2.5.7.13.17 | |||
Commas: 170/169, 640/637, 5525/5488 | |||
Sval name: 10&27 | |||
POTE generator: ~13/8 = 842.711 | |||
Map: [<1 5 4 4 2|, <0 -9 -4 -1 7|] | |||
EDOs: 7, 10, 17, 27, 37, 47, 84, 131 | |||
Error: 3.437 | |||
[[silver7|Seven note haplotonic scale]] | |||
[[silver10|Ten note albitonic scale]] | |||
[[silver17|Seventeen note chromatic scale]] | |||
=Indium= | =Indium= | ||
| Line 393: | Line 408: | ||
<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 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 /> | <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 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 /> | <br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:54:&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:54 --><!-- ws:start:WikiTextTocRule:55: --><a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Terrain</h1> | <!-- 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 /> | ||
| Line 582: | Line 597: | ||
<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:24:&lt;h1&gt; --><h1 id="toc12"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Silver"></a><!-- ws:end:WikiTextHeadingRule:24 -->Silver</h1> | ||
Subgroup: 2.5.7.13.17<br /> | |||
Commas: 170/169, 640/637, 5525/5488<br /> | |||
Sval name: 10&amp;27<br /> | |||
<br /> | |||
POTE generator: ~13/8 = 842.711<br /> | |||
<br /> | |||
Map: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]<br /> | |||
EDOs: 7, 10, 17, 27, 37, 47, 84, 131<br /> | |||
Error: 3.437<br /> | |||
<br /> | |||
<a class="wiki_link" href="/silver7">Seven note haplotonic scale</a><br /> | |||
<a class="wiki_link" href="/silver10">Ten note albitonic scale</a><br /> | |||
<a class="wiki_link" href="/silver17">Seventeen note chromatic scale</a><br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Indium"></a><!-- ws:end:WikiTextHeadingRule:26 -->Indium</h1> | |||
Subgroup: 2.5/3.7/3.11/3<br /> | Subgroup: 2.5/3.7/3.11/3<br /> | ||
Commas: 3025/3024, 3125/3087<br /> | Commas: 3025/3024, 3125/3087<br /> | ||
| Line 596: | Line 626: | ||
<a class="wiki_link" href="/indium17">Seventeen note chromatic scale</a><br /> | <a class="wiki_link" href="/indium17">Seventeen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Hemif"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemif</h1> | ||
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 /> | ||
| Line 611: | Line 641: | ||
<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:30:&lt;h1&gt; --><h1 id="toc15"><a name="Skwares"></a><!-- ws:end:WikiTextHeadingRule:30 -->Skwares</h1> | ||
Subgroup: 2.3.7.11<br /> | Subgroup: 2.3.7.11<br /> | ||
Commas: 99/98, 243/242<br /> | Commas: 99/98, 243/242<br /> | ||
| Line 626: | Line 656: | ||
<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:32:&lt;h1&gt; --><h1 id="toc16"><a name="Greeley"></a><!-- ws:end:WikiTextHeadingRule:32 -->Greeley</h1> | ||
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 639: | Line 669: | ||
<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:34:&lt;h1&gt; --><h1 id="toc17"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:34 -->Semidim</h1> | ||
Subgroup: 2.5/3.7/3.11/3.13/3<br /> | Subgroup: 2.5/3.7/3.11/3.13/3<br /> | ||
Commas: 121/120, 169/168, 275/273<br /> | Commas: 121/120, 169/168, 275/273<br /> | ||
| Line 653: | Line 683: | ||
<a class="wiki_link" href="/semidim13">Thirteen note chromatic scale</a><br /> | <a class="wiki_link" href="/semidim13">Thirteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Mohaha"></a><!-- ws:end:WikiTextHeadingRule:36 -->Mohaha</h1> | ||
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 667: | Line 697: | ||
<a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br /> | <a class="wiki_link" href="/mohaha10">Ten note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Mohaha-Mohoho"></a><!-- ws:end:WikiTextHeadingRule:38 -->Mohoho</h2> | ||
Subgroup: 2.3.5.11.13<br /> | Subgroup: 2.3.5.11.13<br /> | ||
Commas: 66/65, 81/80, 121/120<br /> | Commas: 66/65, 81/80, 121/120<br /> | ||
| Line 677: | Line 707: | ||
Error: 9.556 cents<br /> | Error: 9.556 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Tutone"></a><!-- ws:end:WikiTextHeadingRule:40 -->Tutone</h1> | ||
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 692: | Line 722: | ||
<a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br /> | <a class="wiki_link" href="/tutone13">Thirteen note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Tutone-Leantone"></a><!-- ws:end:WikiTextHeadingRule:42 -->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 707: | Line 737: | ||
<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:44:&lt;h1&gt; --><h1 id="toc22"><a name="Score"></a><!-- ws:end:WikiTextHeadingRule:44 -->Score</h1> | ||
Subgroup: 2.7.11.13<br /> | Subgroup: 2.7.11.13<br /> | ||
Commas: 343/338, 847/832<br /> | Commas: 343/338, 847/832<br /> | ||
| Line 722: | Line 752: | ||
<a class="wiki_link" href="/score11">Eleven note chromatic scale</a><br /> | <a class="wiki_link" href="/score11">Eleven note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Supra"></a><!-- ws:end:WikiTextHeadingRule:46 -->Supra</h1> | ||
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 736: | Line 766: | ||
<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:48:&lt;h2&gt; --><h2 id="toc24"><a name="Supra-Supraphon"></a><!-- ws:end:WikiTextHeadingRule:48 -->Supraphon</h2> | ||
Subgroup: 2.3.7.11.13<br /> | Subgroup: 2.3.7.11.13<br /> | ||
Commas: 64/63, 78/77, 99/98<br /> | Commas: 64/63, 78/77, 99/98<br /> | ||
| Line 746: | Line 776: | ||
Error: 10.534 cents<br /> | Error: 10.534 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Supra-Machine"></a><!-- ws:end:WikiTextHeadingRule:50 -->Machine</h2> | ||
Subgroup: 2.9.7.11<br /> | Subgroup: 2.9.7.11<br /> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<br /> | ||
| Line 760: | Line 790: | ||
<a class="wiki_link" href="/machine11">Eleven note chromatic scale</a><br /> | <a class="wiki_link" href="/machine11">Eleven note chromatic scale</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Augment"></a><!-- ws:end:WikiTextHeadingRule:52 -->Augment</h1> | ||
Subgroup: 2.5.7.11<br /> | Subgroup: 2.5.7.11<br /> | ||
Commas: 56/55, 128/125<br /> | Commas: 56/55, 128/125<br /> | ||