Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 203306588 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 203610024 - 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>2011-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-21 02:15:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>203610024</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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===11-limit=== | ===11-limit=== | ||
Commas: 540/539, 1375/1372, 4000/3993 | Commas: 540/539, 1375/1372, 4000/3993 | ||
POTE generator: ~7/5 = 583.692 | |||
Map: Map: [<8 1 3 3 16|, <0 3 4 5 3|] | |||
EDOs: 72, 152, 224 | |||
Badness: 0.0141 | |||
===13-limit=== | ===13-limit=== | ||
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EDOs: 19, 80, 99, 217, 316, 415 | EDOs: 19, 80, 99, 217, 316, 415 | ||
Badness: 0.0274 | Badness: 0.0274 | ||
</pre></div> | |||
===11-limit=== | |||
Commas: 385/384, 3136/3125, 4375/4374 | |||
POTE generator: ~6/5 = 315.251 | |||
Map: [<1 5 6 12 -6|, <0 -13 -14 -35 36|] | |||
EDOs: 19, 99, 118 | |||
Badness: 0.0497</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>Ragismic microtemperaments</title></head><body>The ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<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>Ragismic microtemperaments</title></head><body>The ragisma is 4375/4374, the smallest 7-limit superparticular ratio. Since (10/9)^4 = 4375/4374 * 32/21, the minor tone 10/9 tends to be an interval of relatively low complexity in temperaments tempering out the ragisma, though when looking at microtemperaments the word &quot;relatively&quot; should be emphasized. Even so mitonic uses it as a generator, which ennealimmal and enneadecal can do also, and amity reaches it in three generators. We also have 7/6 = 4375/4374 * (27/25)^2, so 27/25 also tends to relatively low cmplexity, with the same caveat about &quot;relatively&quot;; however 27/25 is the period for ennealimmal.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Nearly Micro-Octoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Nearly Micro-Octoid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h3> | ||
Commas: 540/539, 1375/1372, 4000/3993<br /> | Commas: 540/539, 1375/1372, 4000/3993<br /> | ||
<br /> | |||
POTE generator: ~7/5 = 583.692<br /> | |||
<br /> | |||
Map: Map: [&lt;8 1 3 3 16|, &lt;0 3 4 5 3|]<br /> | |||
EDOs: 72, 152, 224<br /> | |||
Badness: 0.0141<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Nearly Micro-Octoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h3> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Nearly Micro-Octoid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h3> | ||
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Map: [&lt;1 5 6 12|, &lt;0 -13 -14 -35|]<br /> | Map: [&lt;1 5 6 12|, &lt;0 -13 -14 -35|]<br /> | ||
EDOs: 19, 80, 99, 217, 316, 415<br /> | EDOs: 19, 80, 99, 217, 316, 415<br /> | ||
Badness: 0.0274</body></html></pre></div> | Badness: 0.0274<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h3&gt; --><h3 id="toc20"><a name="Nearly Micro-Parakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h3> | |||
Commas: 385/384, 3136/3125, 4375/4374<br /> | |||
<br /> | |||
POTE generator: ~6/5 = 315.251<br /> | |||
<br /> | |||
Map: [&lt;1 5 6 12 -6|, &lt;0 -13 -14 -35 36|]<br /> | |||
EDOs: 19, 99, 118<br /> | |||
Badness: 0.0497</body></html></pre></div> | |||