Pajara: Difference between revisions
Wikispaces>genewardsmith **Imported revision 378863856 - Original comment: ** |
Wikispaces>hstraub **Imported revision 445081770 - 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:hstraub|hstraub]] and made on <tt>2013-08-16 05:55:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>445081770</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">Pajara (pronounced with the J as in "jar") 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 [[jubilismic clan]]. 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 [[diaschismic family]]. 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 [[Archytas clan]]. Tempering out any two of these commas (among others) produces the unique temperament, pajara. | <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"><span style="display: block; text-align: right;">Other languages: [[xenharmonie/Pajara|Deutsch]] | ||
</span> | |||
Pajara (pronounced with the J as in "jar") 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 [[jubilismic clan]]. 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 [[diaschismic family]]. 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 [[Archytas clan]]. Tempering out any two of these commas (among others) produces the unique temperament, pajara. | |||
The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by [[Paul Erlich]] and [[Gene Ward Smith]]. They are often thought of as subsets of [[22edo]], without much loss of generality and accuracy. | The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by [[Paul Erlich]] and [[Gene Ward Smith]]. They are often thought of as subsets of [[22edo]], without much loss of generality and accuracy. | ||
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See [[10L 2s]]. | See [[10L 2s]]. | ||
==Spectrum of Pajara Tunings by Eigenmonzos== | ==Spectrum of Pajara Tunings by Eigenmonzos== | ||
||~ Eigenmonzo ||~ Fifth || | ||~ Eigenmonzo ||~ Fifth || | ||
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* Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [[http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]] | * Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [[http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]] | ||
=Music= | =Music= | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]] and | [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]] and | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Sonatina.mp3|12-22hexachordal Sonatina]] both by [[Joel Grant Taylor]], in the hexachordal dodecatonic MODMOS. | [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Sonatina.mp3|12-22hexachordal Sonatina]] both by [[Joel Grant Taylor]], in the hexachordal dodecatonic MODMOS. | ||
[[http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3|Smoke Filled Bar]] by [[http://chrisvaisvil.com/?p=2403|Chris Vaisvil]], also in 12-22h.</pre></div> | [[http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3|Smoke Filled Bar]] by [[http://chrisvaisvil.com/?p=2403|Chris Vaisvil]], also in 12-22h.</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><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/Pajara">Deutsch</a><br /> | ||
</span><br /> | |||
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 /> | |||
<br /> | <br /> | ||
The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> and <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a>. They are often thought of as subsets of <a class="wiki_link" href="/22edo">22edo</a>, without much loss of generality and accuracy.<br /> | The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> and <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a>. They are often thought of as subsets of <a class="wiki_link" href="/22edo">22edo</a>, without much loss of generality and accuracy.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Spectrum of Pajara Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:14 -->Spectrum of Pajara Tunings by Eigenmonzos</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Spectrum of Pajara Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:14 -->Spectrum of Pajara Tunings by Eigenmonzos</h2> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
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<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><br /> | <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><br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:18 -->Music</h1> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:18 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a> and<br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a> and<br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Sonatina.mp3" rel="nofollow">12-22hexachordal Sonatina</a> both by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a>, in the hexachordal dodecatonic MODMOS.<br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Sonatina.mp3" rel="nofollow">12-22hexachordal Sonatina</a> both by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a>, in the hexachordal dodecatonic MODMOS.<br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3" rel="nofollow">Smoke Filled Bar</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2403" rel="nofollow">Chris Vaisvil</a>, also in 12-22h.</body></html></pre></div> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3" rel="nofollow">Smoke Filled Bar</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2403" rel="nofollow">Chris Vaisvil</a>, also in 12-22h.</body></html></pre></div> | ||