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Ragismic microtemperaments: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 299526228 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 299583232 - 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>2012-02-07 20:28:20 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-08 00:35:22 UTC</tt>.<br>
: The original revision id was <tt>299526228</tt>.<br>
: The original revision id was <tt>299583232</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: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214
EDOs: 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214
Badness: 0.0108
Badness: 0.0108
==Semisupermajor==
Commas: 3025/3024, 4375/4374, 35156250/35153041
POTE generator: ~9/7 = 435.082
Map: [&lt;2 30 38 60 41|, &lt;0 -37 -46 -75 -47|]
EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf
Badness: 0.0128


=Enneadecal=  
=Enneadecal=  
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</pre></div>
</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
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&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&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:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&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:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Abigail-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Abigail-13-limit"&gt;13-limit&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: 1em;"&gt;&lt;a href="#Semidimi"&gt;Semidimi&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Brahmagupta"&gt;Brahmagupta&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&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:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amity"&gt;Amity&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amity-Hitchcock"&gt;Hitchcock&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Parakleismic"&gt;Parakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&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:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&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:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&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:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&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:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Parkleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&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:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Paradigmic"&gt;Paradigmic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Parkleismic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Paradigmic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Parakleismic-Paradigmic"&gt;Paradigmic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semiparakleismic"&gt;Semiparakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Parakleismic-Paradigmic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quincy"&gt;Quincy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Semiparakleismic"&gt;Semiparakleismic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quincy"&gt;Quincy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Quincy-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&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;
&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:148 --&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;
&lt;br /&gt;
&lt;br /&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;
&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;
Line 624: Line 634:
Badness: 0.0108&lt;br /&gt;
Badness: 0.0108&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Enneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Enneadecal&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Supermajor-Semisupermajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Semisupermajor&lt;/h2&gt;
Commas: 3025/3024, 4375/4374, 35156250/35153041&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~9/7 = 435.082&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 30 38 60 41|, &amp;lt;0 -37 -46 -75 -47|]&lt;br /&gt;
EDOs: 80, 342, 764, 1106, 1448, 2554, 4002f, 6556cf&lt;br /&gt;
Badness: 0.0128&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Enneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Enneadecal&lt;/h1&gt;
  Enndedecal temperament tempers out the enneadeca, |-14 -19 19&amp;gt;, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; up to just ones. &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; is a good tuning for either the 5 or 7 limits, and &lt;a class="wiki_link" href="/494edo"&gt;494edo&lt;/a&gt; shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use &lt;a class="wiki_link" href="/665edo"&gt;665edo&lt;/a&gt; for a tuning.&lt;br /&gt;
  Enndedecal temperament tempers out the enneadeca, |-14 -19 19&amp;gt;, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; up to just ones. &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; is a good tuning for either the 5 or 7 limits, and &lt;a class="wiki_link" href="/494edo"&gt;494edo&lt;/a&gt; shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use &lt;a class="wiki_link" href="/665edo"&gt;665edo&lt;/a&gt; for a tuning.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 636: Line 655:
Badness: 0.0110&lt;br /&gt;
Badness: 0.0110&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Deca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Deca&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Deca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Deca&lt;/h1&gt;
  Commas: 4375/4374, 165288374272/164794921875&lt;br /&gt;
  Commas: 4375/4374, 165288374272/164794921875&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 645: Line 664:
Badness: 0.0806&lt;br /&gt;
Badness: 0.0806&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Deca-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Deca-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
  Commas: 3025/3024, 4375/4374, 422576/421875&lt;br /&gt;
  Commas: 3025/3024, 4375/4374, 422576/421875&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 654: Line 673:
Badness: 0.0243&lt;br /&gt;
Badness: 0.0243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Deca-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Deca-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
  Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374&lt;br /&gt;
  Commas: 1001/1000, 3025/3024, 4225/4224, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 663: Line 682:
Badness: 0.0168&lt;br /&gt;
Badness: 0.0168&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Mitonic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Mitonic&lt;/h1&gt;
  Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
  Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 672: Line 691:
Badness: 0.0252&lt;br /&gt;
Badness: 0.0252&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Abigail&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Abigail&lt;/h1&gt;
  Commas: 4375/4374, 2147483648/2144153025&lt;br /&gt;
  Commas: 4375/4374, 2147483648/2144153025&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 682: Line 701:
Badness: 0.0370&lt;br /&gt;
Badness: 0.0370&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
  Comma: 3025/3024, 4375/4374, 20614528/20588575&lt;br /&gt;
  Comma: 3025/3024, 4375/4374, 20614528/20588575&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 691: Line 710:
Badness: 0.0129&lt;br /&gt;
Badness: 0.0129&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
  Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095&lt;br /&gt;
  Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 700: Line 719:
Badness: 0.00886&lt;br /&gt;
Badness: 0.00886&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Semidimi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Semidimi&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Semidimi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Semidimi&lt;/h1&gt;
Commas: 4375/4374, 3955078125/3954653486&lt;br /&gt;
Commas: 4375/4374, 3955078125/3954653486&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 710: Line 729:
Badness: 0.0151&lt;br /&gt;
Badness: 0.0151&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Brahmagupta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Brahmagupta&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Brahmagupta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Brahmagupta&lt;/h1&gt;
Commas: 4375/4374, 70368744177664/70338939985125&lt;br /&gt;
Commas: 4375/4374, 70368744177664/70338939985125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 720: Line 739:
Badness: 0.0291&lt;br /&gt;
Badness: 0.0291&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Brahmagupta-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Brahmagupta-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
Commas: 4000/3993, 4375/4374, 131072/130977&lt;br /&gt;
Commas: 4000/3993, 4375/4374, 131072/130977&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 729: Line 748:
Badness: 0.0522&lt;br /&gt;
Badness: 0.0522&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Nearly Micro&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Nearly Micro&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Octoid&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Octoid&lt;/h1&gt;
  Commas: 4375/4374, 16875/16807&lt;br /&gt;
  Commas: 4375/4374, 16875/16807&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 741: Line 760:
Badness: 0.0427&lt;br /&gt;
Badness: 0.0427&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
  Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
  Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 750: Line 769:
Badness: 0.0141&lt;br /&gt;
Badness: 0.0141&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
  Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
  Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 759: Line 778:
Badness: 0.0153&lt;br /&gt;
Badness: 0.0153&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Music&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Music&lt;/h2&gt;
&lt;!-- ws:start:WikiTextUrlRule:553: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:553 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextUrlRule:564: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:564 --&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;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Amity&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Amity&lt;/h1&gt;
  The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;amp;53 temperament, or by its wedgie, &amp;lt;&amp;lt;5 13 -17 9 -41 -76||. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.&lt;br /&gt;
  The generator for amity temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, 5120/5103 and 6144/6125. It can also be described as the 46&amp;amp;53 temperament, or by its wedgie, &amp;lt;&amp;lt;5 13 -17 9 -41 -76||. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is a good tuning for amity, with generator 28/99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.&lt;br /&gt;
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;5-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;5-limit&lt;/h2&gt;
  Comma: 1600000/1594323&lt;br /&gt;
  Comma: 1600000/1594323&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 777: Line 796:
Badness: 0.0220&lt;br /&gt;
Badness: 0.0220&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;7-limit&lt;/h2&gt;
  Commas: 4375/4374, 5120/5103&lt;br /&gt;
  Commas: 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 787: Line 806:
Badness: 0.0236&lt;br /&gt;
Badness: 0.0236&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 796: Line 815:
Badness: 0.0315&lt;br /&gt;
Badness: 0.0315&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Hitchcock&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Hitchcock&lt;/h2&gt;
  Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
  Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 805: Line 824:
Badness: 0.0352&lt;br /&gt;
Badness: 0.0352&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Hemiamity&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Hemiamity&lt;/h2&gt;
  Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
  Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 813: Line 832:
EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Parakleismic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc36"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;Parakleismic&lt;/h1&gt;
  In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&amp;gt;, with the &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &amp;lt;&amp;lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &amp;lt;&amp;lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; may be preferred, but in the 11-limit it is best to stick with 118.&lt;br /&gt;
  In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&amp;gt;, with the &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt; tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &amp;lt;&amp;lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &amp;lt;&amp;lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; may be preferred, but in the 11-limit it is best to stick with 118.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 824: Line 843:
Badness: 0.0433&lt;br /&gt;
Badness: 0.0433&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;7-limit&lt;/h2&gt;
  Commas: 3136/3125, 4375/4374&lt;br /&gt;
  Commas: 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 833: Line 852:
Badness: 0.0274&lt;br /&gt;
Badness: 0.0274&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&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="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
  Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
  Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 842: Line 861:
Badness: 0.0497&lt;br /&gt;
Badness: 0.0497&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Parkleismic&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;Parkleismic&lt;/h2&gt;
Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 851: Line 870:
Badness: 0.0559&lt;br /&gt;
Badness: 0.0559&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc39"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc40"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 860: Line 879:
Badness: 0.0366&lt;br /&gt;
Badness: 0.0366&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Paradigmic&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Paradigmic&lt;/h2&gt;
Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 869: Line 888:
Badness: 0.0417&lt;br /&gt;
Badness: 0.0417&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc41"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc42"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;13-limit&lt;/h3&gt;
Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 878: Line 897:
Badness: 0.0358&lt;br /&gt;
Badness: 0.0358&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;Semiparakleismic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Semiparakleismic&lt;/h1&gt;
Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 887: Line 906:
Badness: 0.0342&lt;br /&gt;
Badness: 0.0342&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Quincy&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc44"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;Quincy&lt;/h1&gt;
  Commas: 4375/4374, 823543/819200&lt;br /&gt;
  Commas: 4375/4374, 823543/819200&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 896: Line 915:
Badness: 0.0797&lt;br /&gt;
Badness: 0.0797&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&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;
&lt;br /&gt;
&lt;br /&gt;
Line 905: Line 924:
Badness: 0.0309&lt;br /&gt;
Badness: 0.0309&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&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;
&lt;br /&gt;
&lt;br /&gt;
Line 914: Line 933:
Badness: 0.0239&lt;br /&gt;
Badness: 0.0239&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;17-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&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;
&lt;br /&gt;
&lt;br /&gt;
Line 923: Line 942:
Badness: 0.0147&lt;br /&gt;
Badness: 0.0147&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&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;
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