Chromatic pairs: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 242936411 - Original comment: **
Wikispaces>hstraub
**Imported revision 245007527 - 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>2011-07-26 15:15:03 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-09 07:35:11 UTC</tt>.<br>
: The original revision id was <tt>242936411</tt>.<br>
: The original revision id was <tt>245007527</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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=Definitions=
=Definitions=  
By a //chromatic pair// is meant a pair of [[MOSScales|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.
By a //chromatic pair// is meant a pair of [[MOSScales|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.


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Related temperament: [[Minortonic family#Domain|domain]]
Related temperament: [[Minortonic family#Domain|domain]]


POTE generator: ~10/9 = 182.462
[[POTE generator]]: ~10/9 = 182.462


Map: [&lt;3 0 -4|, &lt;0 1 2|]
Map: [&lt;3 0 -4|, &lt;0 1 2|]
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[[orwell13|Thirteen note chromatic scale]]
[[orwell13|Thirteen note chromatic scale]]


=Bleu=
=Bleu=  
Group: 2.3.7.11.13
Group: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Commas: 78/77, 99/98, 144/143
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definitions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Definitions&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Definitions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Definitions&lt;/h1&gt;
By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) 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 &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with &lt;a class="wiki_link" href="/Target%20tunings"&gt;tuning target&lt;/a&gt; the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.&lt;br /&gt;
By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) 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 &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with &lt;a class="wiki_link" href="/Target%20tunings"&gt;tuning target&lt;/a&gt; the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Terrain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Terrain&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Terrain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Terrain&lt;/h1&gt;
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Related temperament: &lt;a class="wiki_link" href="/Minortonic%20family#Domain"&gt;domain&lt;/a&gt;&lt;br /&gt;
Related temperament: &lt;a class="wiki_link" href="/Minortonic%20family#Domain"&gt;domain&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 182.462&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.462&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 0 -4|, &amp;lt;0 1 2|]&lt;br /&gt;
Map: [&amp;lt;3 0 -4|, &amp;lt;0 1 2|]&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Bleu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Bleu&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Bleu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Bleu&lt;/h1&gt;
Group: 2.3.7.11.13&lt;br /&gt;
Group: 2.3.7.11.13&lt;br /&gt;
Commas: 78/77, 99/98, 144/143&lt;br /&gt;
Commas: 78/77, 99/98, 144/143&lt;br /&gt;
Sval name: 9&amp;amp;17&lt;br /&gt;
Sval name: 9&amp;amp;17&lt;br /&gt;