Pajara: Difference between revisions
Wikispaces>genewardsmith **Imported revision 246567081 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 246585785 - 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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-17 19:18:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>246585785</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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===10-note (proper)=== | ===10-note (proper)=== | ||
See [[2L 8s]]. | See [[2L 8s]]. | ||
The true MOS is called the "symmetric" decatonic scale, because it repeats exactly at the half-octave, so the symmetric scale starting from 7/5~10/7 is the same as the symmetric scale starting from 1/1. | |||
The near-MOS, LsssLsssss, in which only the 5-step interval violates the "no more than 2 intervals per class" rule, is called the "pentachordal" decatonic, because it consists of two identical "pentachords" plus a split 9/8~8/7 whole tone to complete the octave. | |||
===12-note (proper)=== | ===12-note (proper)=== | ||
See [[10L 2s]].</pre></div> | See [[10L 2s]]. | ||
==References== | |||
* Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [[http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]]</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>pajara</title></head><body>Pajara (pronounced with the J as in &quot;jar&quot;) is a temperament with a half-octave period that represents both 7/5 and 10/7, so 50/49 is tempered out and it is in the <a class="wiki_link" href="/jubilismic%20clan">jubilismic clan</a>. The generator is in the neighborhood of 105-110 cents, so that period + generator represents 3/2. Period minus 2 generators is 5/4, which, if you work it out, implies that 2048/2025 is tempered out, so pajara is also in the <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>. Finally, two 4/3s (or a 2/1 minus two generators) represents 7/4 as well as 16/9, so 64/63 is tempered out and pajara is in the <a class="wiki_link" href="/Archytas%20clan">Archytas clan</a>. Tempering out any two of these commas (among others) produces the unique temperament, pajara.<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>pajara</title></head><body>Pajara (pronounced with the J as in &quot;jar&quot;) is a temperament with a half-octave period that represents both 7/5 and 10/7, so 50/49 is tempered out and it is in the <a class="wiki_link" href="/jubilismic%20clan">jubilismic clan</a>. The generator is in the neighborhood of 105-110 cents, so that period + generator represents 3/2. Period minus 2 generators is 5/4, which, if you work it out, implies that 2048/2025 is tempered out, so pajara is also in the <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>. Finally, two 4/3s (or a 2/1 minus two generators) represents 7/4 as well as 16/9, so 64/63 is tempered out and pajara is in the <a class="wiki_link" href="/Archytas%20clan">Archytas clan</a>. Tempering out any two of these commas (among others) produces the unique temperament, pajara.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-MOSes-10-note (proper)"></a><!-- ws:end:WikiTextHeadingRule:10 -->10-note (proper)</h3> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-MOSes-10-note (proper)"></a><!-- ws:end:WikiTextHeadingRule:10 -->10-note (proper)</h3> | ||
See <a class="wiki_link" href="/2L%208s">2L 8s</a>.<br /> | See <a class="wiki_link" href="/2L%208s">2L 8s</a>.<br /> | ||
The true MOS is called the &quot;symmetric&quot; decatonic scale, because it repeats exactly at the half-octave, so the symmetric scale starting from 7/5~10/7 is the same as the symmetric scale starting from 1/1.<br /> | |||
The near-MOS, LsssLsssss, in which only the 5-step interval violates the &quot;no more than 2 intervals per class&quot; rule, is called the &quot;pentachordal&quot; decatonic, because it consists of two identical &quot;pentachords&quot; plus a split 9/8~8/7 whole tone to complete the octave.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-MOSes-12-note (proper)"></a><!-- ws:end:WikiTextHeadingRule:12 -->12-note (proper)</h3> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-MOSes-12-note (proper)"></a><!-- ws:end:WikiTextHeadingRule:12 -->12-note (proper)</h3> | ||
See <a class="wiki_link" href="/10L%202s">10L 2s</a>.</body></html></pre></div> | See <a class="wiki_link" href="/10L%202s">10L 2s</a>.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-References"></a><!-- ws:end:WikiTextHeadingRule:14 -->References</h2> | |||
<ul><li>Erlich, Paul. &quot;Tuning, Tonality and 22-Tone Temperament.&quot; Xenharmonicon 17, 1998. <a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf" rel="nofollow">http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf</a></li></ul></body></html></pre></div> | |||