Superpyth: Difference between revisions
Wikispaces>genewardsmith **Imported revision 268529912 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 319886746 - 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-12 13:13:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>319886746</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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EDOs: 5, 17, 22, 27, 49 | EDOs: 5, 17, 22, 27, 49 | ||
Badness: 0.0323 | Badness: 0.0323 | ||
==11-limit== | |||
Commas: 64/63, 100/99, 245/243 | |||
POTE generator: ~3/2 = 710.175 | |||
Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|] | |||
EDOs: 22, 27e, 49 | |||
Badness: 0.0250 | |||
==13-limit== | |||
Commas: 64/63, 78/77, 91/90, 100/99 | |||
POTE generator: ~3/2 = 710.479 | |||
Map: [<1 0 -12 6 -22 -17|, <0 1 9 -2 16 13|] | |||
EDOs: 22, 27e, 49, 76bcde | |||
Badness: 0.0247 | |||
=Suprapyth= | =Suprapyth= | ||
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See [[5L 2s]]. In contrast to the meantone diatonic scale, the superpyth diatonic is slightly improper. | See [[5L 2s]]. In contrast to the meantone diatonic scale, the superpyth diatonic is slightly improper. | ||
===12-note (LsLsLssLsLss, borderline improper)=== | ===12-note (LsLsLssLsLss, borderline improper)=== | ||
See [[5L 7s]]. The boundary of propriety is [[17edo]]. | See [[5L 7s]]. The boundary of propriety is [[17edo]].</pre></div> | ||
</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: | <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:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Suprapyth">Suprapyth</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- 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: | <!-- ws:end:WikiTextTocRule:40 --><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).<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).<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0323<br /> | Badness: 0.0323<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Superpyth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> | ||
Commas: 64/63, 100/99, 245/243<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 710.175<br /> | |||
<br /> | |||
Map: [&lt;1 0 -12 6 -22|, &lt;0 1 9 -2 16|]<br /> | |||
EDOs: 22, 27e, 49<br /> | |||
Badness: 0.0250<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Superpyth-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> | |||
Commas: 64/63, 78/77, 91/90, 100/99<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 710.479<br /> | |||
<br /> | |||
Map: [&lt;1 0 -12 6 -22 -17|, &lt;0 1 9 -2 16 13|]<br /> | |||
EDOs: 22, 27e, 49, 76bcde<br /> | |||
Badness: 0.0247<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Suprapyth"></a><!-- ws:end:WikiTextHeadingRule:6 -->Suprapyth</h1> | |||
Commas: 55/54, 64/63, 99/98<br /> | Commas: 55/54, 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0328<br /> | Badness: 0.0328<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Suprapyth-Interval chains"></a><!-- ws:end:WikiTextHeadingRule:8 -->Interval chains</h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Suprapyth-Interval chains-Basic superpyth (2.3.7)"></a><!-- ws:end:WikiTextHeadingRule:10 -->Basic superpyth (2.3.7)</h3> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Suprapyth-Interval chains-Full 7-limit superpyth"></a><!-- ws:end:WikiTextHeadingRule:12 -->Full 7-limit superpyth</h3> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Suprapyth-Interval chains-Supra (2.3.7.11)"></a><!-- ws:end:WikiTextHeadingRule:14 -->Supra (2.3.7.11)</h3> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Suprapyth-Interval chains-Full 11-limit suprapyth"></a><!-- ws:end:WikiTextHeadingRule:16 -->Full 11-limit suprapyth</h3> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Suprapyth-MOSes"></a><!-- ws:end:WikiTextHeadingRule:18 -->MOSes</h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="Suprapyth-MOSes-5-note (LsLss, proper)"></a><!-- ws:end:WikiTextHeadingRule:20 -->5-note (LsLss, proper)</h3> | ||
See <a class="wiki_link" href="/2L%203s">2L 3s</a>.<br /> | See <a class="wiki_link" href="/2L%203s">2L 3s</a>.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Suprapyth-MOSes-7-note (LLLsLLs, improper)"></a><!-- ws:end:WikiTextHeadingRule:22 -->7-note (LLLsLLs, improper)</h3> | ||
See <a class="wiki_link" href="/5L%202s">5L 2s</a>. In contrast to the meantone diatonic scale, the superpyth diatonic is slightly improper.<br /> | See <a class="wiki_link" href="/5L%202s">5L 2s</a>. In contrast to the meantone diatonic scale, the superpyth diatonic is slightly improper.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Suprapyth-MOSes-12-note (LsLsLssLsLss, borderline improper)"></a><!-- ws:end:WikiTextHeadingRule:24 -->12-note (LsLsLssLsLss, borderline improper)</h3> | ||
See <a class="wiki_link" href="/5L%207s">5L 7s</a>. The boundary of propriety is <a class="wiki_link" href="/17edo">17edo</a>.</body></html></pre></div> | See <a class="wiki_link" href="/5L%207s">5L 7s</a>. The boundary of propriety is <a class="wiki_link" href="/17edo">17edo</a>.</body></html></pre></div> | ||