Superpyth: Difference between revisions
Wikispaces>genewardsmith **Imported revision 342882370 - Original comment: ** |
Wikispaces>hstraub **Imported revision 586573087 - 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>2016-07-05 04:39:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>586573087</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">[[toc|flat]] | <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;">[[xenharmonie/Superpyth|Deutsch]] | ||
</span> | |||
[[toc|flat]] | |||
**Superpyth**, a member of the [[Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[meantone]] and [[12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [[@http://en.wikipedia.org/wiki/Plastic_number|plastic number]]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth. | **Superpyth**, a member of the [[Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[meantone]] and [[12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [[@http://en.wikipedia.org/wiki/Plastic_number|plastic number]]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth. | ||
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See [[5L 7s]]. The boundary of propriety is [[17edo]]. | See [[5L 7s]]. The boundary of propriety is [[17edo]]. | ||
=Music= | =Music= | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22studyPentUp4thsMstr.mp3|12of22studyPentUp4thsMstr]] | [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22studyPentUp4thsMstr.mp3|12of22studyPentUp4thsMstr]] | ||
[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22gamelan1b.mp3|12of22gamelan1b]] | [[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22gamelan1b.mp3|12of22gamelan1b]] | ||
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By [[Joel Grant Taylor]], all in Superpyth[12] in 22edo tuning.</pre></div> | By [[Joel Grant Taylor]], all in Superpyth[12] in 22edo tuning.</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>Superpyth</title></head><body><!-- ws:start:WikiTextTocRule:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Suprapyth">Suprapyth</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <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>Superpyth</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Superpyth">Deutsch</a><br /> | ||
<!-- ws:end:WikiTextTocRule:43 --> | </span><br /> | ||
<strong>Superpyth</strong>, a member of the <a class="wiki_link" href="/Archytas%20clan">Archytas clan</a>, has 4/3 as a generator, and the Archytas comma 64/63 is <a class="wiki_link" href="/tempering%20out">tempered out</a>, so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/12edo">12edo</a>, with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Plastic_number" rel="nofollow" target="_blank">plastic number</a>has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.<br /> | <!-- ws:start:WikiTextTocRule:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Suprapyth">Suprapyth</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule:43 --><strong>Superpyth</strong>, a member of the <a class="wiki_link" href="/Archytas%20clan">Archytas clan</a>, has 4/3 as a generator, and the Archytas comma 64/63 is <a class="wiki_link" href="/tempering%20out">tempered out</a>, so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for <a class="wiki_link" href="/meantone">meantone</a> and <a class="wiki_link" href="/12edo">12edo</a>, with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Plastic_number" rel="nofollow" target="_blank">plastic number</a>has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.<br /> | |||
<br /> | <br /> | ||
If the 5th harmonic is used at all, it is mapped to -9 generators, so C-D# is 5/4. So superpyth is &quot;the opposite of&quot; septimal meantone in several different ways: meantone has 4/3 tempered wide so that intervals of 5 are simple and intervals of 7 are complex, while superpyth has 4/3 tempered narrow so that intervals of 7 are simple while intervals of 5 are complex.<br /> | If the 5th harmonic is used at all, it is mapped to -9 generators, so C-D# is 5/4. So superpyth is &quot;the opposite of&quot; septimal meantone in several different ways: meantone has 4/3 tempered wide so that intervals of 5 are simple and intervals of 7 are complex, while superpyth has 4/3 tempered narrow so that intervals of 7 are simple while intervals of 5 are complex.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:26 -->Music</h1> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:26 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22studyPentUp4thsMstr.mp3" rel="nofollow">12of22studyPentUp4thsMstr</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22studyPentUp4thsMstr.mp3" rel="nofollow">12of22studyPentUp4thsMstr</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22gamelan1b.mp3" rel="nofollow">12of22gamelan1b</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22gamelan1b.mp3" rel="nofollow">12of22gamelan1b</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study3.mp3" rel="nofollow">12of22study3 (children's story)</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study3.mp3" rel="nofollow">12of22study3 (children's story)</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study7.mp3" rel="nofollow">12of22study7</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study7.mp3" rel="nofollow">12of22study7</a><br /> | ||
By <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a>, all in Superpyth[12] in 22edo tuning.</body></html></pre></div> | By <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a>, all in Superpyth[12] in 22edo tuning.</body></html></pre></div> | ||