Chromatic pairs: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2013-11-~~25 15~~:56:48 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-26 19:02:10 UTC</tt>.<br>

: The original revision id was <tt>~~472181902~~</tt>.<br>

: The original revision id was <tt>472562740</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>

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=Definitions=

By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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 [[Tp tuning|T2 error]], which is an appropriate error measure for subgroups as well as full p-limit groups.

By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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 [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full p-limit groups.

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<h1 id="toc0"><a name="Definitions"></a>Definitions</h1>

By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 <a class="wiki_link" href="/Tp%20tuning">T2 error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<br />

By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 <a class="wiki_link" href="/Tp%20tuning#T2 tuning">RMS error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<br />

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<h1 id="toc1"><a name="Terrain"></a>Terrain</h1>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2013-11-25 15:56:48 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-26 19:02:10 UTC</tt>.<br>
-: The original revision id was <tt>472181902</tt>.<br>
+: The original revision id was <tt>472562740</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>
@@ Line 11: / Line 11: @@
 =Definitions=
-By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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 [[Tp tuning|T2 error]], which is an appropriate error measure for subgroups as well as full p-limit groups.
+By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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 [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full p-limit groups.
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-  By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; in some rank two temperament (which may often be a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 &lt;a class="wiki_link" href="/Tp%20tuning"&gt;T2 error&lt;/a&gt;, which is an appropriate error measure for subgroups as well as full p-limit groups.&lt;br /&gt;
+  By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; in some rank two temperament (which may often be a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/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 &lt;a class="wiki_link" href="/Tp%20tuning#T2 tuning"&gt;RMS error&lt;/a&gt;, which is an appropriate error measure for subgroups as well as full p-limit groups.&lt;br /&gt;
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