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Ragismic microtemperaments: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 287843888 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 288766025 - 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>2011-12-21 01:14:41 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-29 15:50:37 UTC</tt>.<br>
: The original revision id was <tt>287843888</tt>.<br>
: The original revision id was <tt>288766025</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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Map: [&lt;1 5 6 12 20|, &lt;0 -13 -14 -35 -63|]
Map: [&lt;1 5 6 12 20|, &lt;0 -13 -14 -35 -63|]
EDOs: 15, 19, 80, 179
EDOs: 80, 179, 259cd
Badness: 0.0559
Badness: 0.0559


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EDOs: 15, 19, 80, 179
EDOs: 15, 19, 80, 179
Badness: 0.0366
Badness: 0.0366
==Paradigmic=
Commas: 540/539, 896/891, 3136/3125
POTE generator: ~6/5 = 315.096
Map: [&lt;1 5 6 12 -1|, &lt;0 -13 -14 -35 17|]
EDOs: 19, 80, 99e, 179e
Badness: 0.0417
===13-limit===
Commas: 169/168, 325/324, 540/539, 832/825
POTE generator: ~6/5 = 315.080
Map: [&lt;1 5 6 12 -1 10|, &lt;0 -13 -14 -35 17 -24|]
EDOs: 19, 80, 99e, 179e
Badness: 0.0358


=Quincy=  
=Quincy=  
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Badness: 0.0152</pre></div>
Badness: 0.0152</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ragismic microtemperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:80:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ennealimmal"&gt;Ennealimmal&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-13 limit hemiennealimmal"&gt;13 limit hemiennealimmal&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ennealimmal-13 limit hemiennealimmal"&gt;13 limit hemiennealimmal&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Ennealimmal-Semiennealimmal-13 limit semiennealimmal"&gt;13 limit semiennealimmal&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octoid-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Parkleismic"&gt;Parkleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Parkleismic"&gt;Parkleismic&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#x=Paradigmic--13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:121 --&gt;The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&amp;gt;, 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 &amp;quot;relatively&amp;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 complexity, with the same caveat about &amp;quot;relatively&amp;quot;; however 27/25 is the period for ennealimmal.&lt;br /&gt;
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&lt;!-- ws:end:WikiTextTocRule:127 --&gt;The ragisma is 4375/4374 with a monzo of |-1 -7 4 1&amp;gt;, 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 &amp;quot;relatively&amp;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 complexity, with the same caveat about &amp;quot;relatively&amp;quot;; however 27/25 is the period for ennealimmal.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ennealimmal&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ennealimmal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ennealimmal&lt;/h1&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Music&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Music&lt;/h2&gt;
&lt;!-- ws:start:WikiTextUrlRule:461:http://www.archive.org/details/Dreyfus --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow"&gt;http://www.archive.org/details/Dreyfus&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:461 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:484:http://www.archive.org/details/Dreyfus --&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow"&gt;http://www.archive.org/details/Dreyfus&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:484 --&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
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Line 713: Line 734:
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Map: [&amp;lt;1 5 6 12 20|, &amp;lt;0 -13 -14 -35 -63|]&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 20|, &amp;lt;0 -13 -14 -35 -63|]&lt;br /&gt;
EDOs: 15, 19, 80, 179&lt;br /&gt;
EDOs: 80, 179, 259cd&lt;br /&gt;
Badness: 0.0559&lt;br /&gt;
Badness: 0.0559&lt;br /&gt;
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Line 725: Line 746:
Badness: 0.0366&lt;br /&gt;
Badness: 0.0366&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Quincy&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="x=Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;=Paradigmic&lt;/h1&gt;
Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.096&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 -1|, &amp;lt;0 -13 -14 -35 17|]&lt;br /&gt;
EDOs: 19, 80, 99e, 179e&lt;br /&gt;
Badness: 0.0417&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc36"&gt;&lt;a name="x=Paradigmic--13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 315.080&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 6 12 -1 10|, &amp;lt;0 -13 -14 -35 17 -24|]&lt;br /&gt;
EDOs: 19, 80, 99e, 179e&lt;br /&gt;
Badness: 0.0358&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Quincy&lt;/h1&gt;
  Commas: 4375/4374, 823543/819200&lt;br /&gt;
  Commas: 4375/4374, 823543/819200&lt;br /&gt;
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Line 734: Line 774:
Badness: 0.0797&lt;br /&gt;
Badness: 0.0797&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
  Commas: 441/440, 4000/3993, 41503/41472&lt;br /&gt;
  Commas: 441/440, 4000/3993, 41503/41472&lt;br /&gt;
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Line 743: Line 783:
Badness: 0.0309&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h2&gt;
  Commas: 364/363, 441/440, 676/675, 4375/4374&lt;br /&gt;
  Commas: 364/363, 441/440, 676/675, 4375/4374&lt;br /&gt;
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Line 752: Line 792:
Badness: 0.0239&lt;br /&gt;
Badness: 0.0239&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;17-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;17-limit&lt;/h2&gt;
  Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155&lt;br /&gt;
  Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155&lt;br /&gt;
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Line 761: Line 801:
Badness: 0.0147&lt;br /&gt;
Badness: 0.0147&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;19-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;19-limit&lt;/h2&gt;
  Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600&lt;br /&gt;
  Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600&lt;br /&gt;
&lt;br /&gt;
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