Ragismic microtemperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2012-04-20 00:23:16 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-20 00:36:24 UTC</tt>.<br>

: The original revision id was <tt>~~322984716~~</tt>.<br>

: The original revision id was <tt>322987966</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>

Line 423:

EDOs: 190, 224, 414, 638, 1052c, 1690bc

Badness: 0.1760

==11-limit==

Commas: 3025/3024, 4375/4374, 1265625/1261568

POTE generator: ~448/405 = 176.806

Map: [<2 7 7 23 19|, <0 -13 -8 -59 -41|]

EDOs: 190, 224, 414, 638, 1052c

Badness: 0.0410

==13-limit==

Commas: 625/624, 729/728, 1575/1573, 2200/2197

POTE generator: ~448/405 = 176.804

Map: [<2 7 7 23 19 13|, <0 -13 -8 -59 -41 =19|]

EDOs: 190, 224, 414, 638, 1690bc, 2328bcde

Badness: 0.0226

=Nearly Micro=

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Badness: 0.0152</pre></div>

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<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-

<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:

<br />

<h1 id="toc0"><a name="Ennealimmal"></a>Ennealimmal</h1>

Line 1,123:

Line 1,143:

Badness: 0.1760<br />

<br />

<h1 id="~~toc44~~"><a name="Nearly Micro"></a>Nearly Micro</h1>

<h2 id="toc44"><a name="Quatracot-11-limit"></a>11-limit</h2>

Commas: 3025/3024, 4375/4374, 1265625/1261568<br />

<br />

POTE generator: ~448/405 = 176.806<br />

<br />

Map: [&lt;2 7 7 23 19|, &lt;0 -13 -8 -59 -41|]<br />

EDOs: 190, 224, 414, 638, 1052c<br />

Badness: 0.0410<br />

<br />

<h2 id="toc45"><a name="Quatracot-13-limit"></a>13-limit</h2>

Commas: 625/624, 729/728, 1575/1573, 2200/2197<br />

<br />

POTE generator: ~448/405 = 176.804<br />

<br />

Map: [&lt;2 7 7 23 19 13|, &lt;0 -13 -8 -59 -41 =19|]<br />

EDOs: 190, 224, 414, 638, 1690bc, 2328bcde<br />

Badness: 0.0226<br />

<br />

<h1 id="toc46"><a name="Nearly Micro"></a>Nearly Micro</h1>

<br />

<h1 id="~~toc45~~"><a name="Octoid"></a>Octoid</h1>

<h1 id="toc47"><a name="Octoid"></a>Octoid</h1>

Commas: 4375/4374, 16875/16807<br />

<br />

Line 1,135:

Line 1,173:

Badness: 0.0427<br />

<br />

<h2 id="~~toc46~~"><a name="Octoid-11-limit"></a>11-limit</h2>

<h2 id="toc48"><a name="Octoid-11-limit"></a>11-limit</h2>

Commas: 540/539, 1375/1372, 4000/3993<br />

<br />

Line 1,144:

Line 1,182:

Badness: 0.0141<br />

<br />

<h2 id="~~toc47~~"><a name="Octoid-13-limit"></a>13-limit</h2>

<h2 id="toc49"><a name="Octoid-13-limit"></a>13-limit</h2>

Commas: 540/539, 1375/1372, 4000/3993, 625/624<br />

<br />

Line 1,153:

Line 1,191:

Badness: 0.0153<br />

<br />

<h2 id="~~toc48~~"><a name="Octoid-Music"></a>Music</h2>

<h2 id="toc50"><a name="Octoid-Music"></a>Music</h2>

<a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow">http://www.archive.org/details/Dreyfus</a><br />

<a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow">http://www.archive.org/details/Dreyfus</a><br />

<br />

<h2 id="~~toc49~~"><a name="Octoid-Octopus"></a>Octopus</h2>

<h2 id="toc51"><a name="Octoid-Octopus"></a>Octopus</h2>

Commas: 169/168, 325/324, 364/363, 540/539<br />

<br />

Line 1,166:

Line 1,204:

Badness: 0.0217<br />

<br />

<h1 id="~~toc50~~"><a name="Amity"></a>Amity</h1>

<h1 id="toc52"><a name="Amity"></a>Amity</h1>

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;53 temperament, or by its wedgie, &lt;&lt;5 13 -17 9 -41 -76||. <a class="wiki_link" href="/99edo">99edo</a> 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.<br />

<br />

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.<br />

<br />

<h2 id="~~toc51~~"><a name="Amity-5-limit"></a>5-limit</h2>

<h2 id="toc53"><a name="Amity-5-limit"></a>5-limit</h2>

Comma: 1600000/1594323<br />

<br />

Line 1,180:

Line 1,218:

Badness: 0.0220<br />

<br />

<h2 id="~~toc52~~"><a name="Amity-7-limit"></a>7-limit</h2>

<h2 id="toc54"><a name="Amity-7-limit"></a>7-limit</h2>

Commas: 4375/4374, 5120/5103<br />

<br />

Line 1,190:

Line 1,228:

Badness: 0.0236<br />

<br />

<h2 id="~~toc53~~"><a name="Amity-11-limit"></a>11-limit</h2>

<h2 id="toc55"><a name="Amity-11-limit"></a>11-limit</h2>

Commas: 540/539, 4375/4374, 5120/5103<br />

<br />

Line 1,199:

Line 1,237:

Badness: 0.0315<br />

<br />

<h2 id="~~toc54~~"><a name="Amity-Hitchcock"></a>Hitchcock</h2>

<h2 id="toc56"><a name="Amity-Hitchcock"></a>Hitchcock</h2>

Commas: 121/120, 176/175, 2200/2187<br />

<br />

Line 1,208:

Line 1,246:

Badness: 0.0352<br />

<br />

<h2 id="~~toc55~~"><a name="Amity-Hemiamity"></a>Hemiamity</h2>

<h2 id="toc57"><a name="Amity-Hemiamity"></a>Hemiamity</h2>

Commas: 4375/4374, 5120/5103, 3025/3024<br />

<br />

Line 1,216:

Line 1,254:

EDOs: 14, 46, 106, 152, 350<br />

<br />

<h1 id="~~toc56~~"><a name="Parakleismic"></a>Parakleismic</h1>

<h1 id="toc58"><a name="Parakleismic"></a>Parakleismic</h1>

In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> 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 &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br />

<br />

Line 1,227:

Line 1,265:

Badness: 0.0433<br />

<br />

<h2 id="~~toc57~~"><a name="Parakleismic-7-limit"></a>7-limit</h2>

<h2 id="toc59"><a name="Parakleismic-7-limit"></a>7-limit</h2>

Commas: 3136/3125, 4375/4374<br />

<br />

Line 1,236:

Line 1,274:

Badness: 0.0274<br />

<br />

<h2 id="~~toc58~~"><a name="Parakleismic-11-limit"></a>11-limit</h2>

<h2 id="toc60"><a name="Parakleismic-11-limit"></a>11-limit</h2>

Commas: 385/384, 3136/3125, 4375/4374<br />

<br />

Line 1,245:

Line 1,283:

Badness: 0.0497<br />

<br />

<h2 id="~~toc59~~"><a name="Parakleismic-Parkleismic"></a>Parkleismic</h2>

<h2 id="toc61"><a name="Parakleismic-Parkleismic"></a>Parkleismic</h2>

Commas: 176/175, 1375/1372, 2200/2187<br />

<br />

Line 1,254:

Line 1,292:

Badness: 0.0559<br />

<br />

<h3 id="~~toc60~~"><a name="Parakleismic-Parkleismic-13-limit"></a>13-limit</h3>

<h3 id="toc62"><a name="Parakleismic-Parkleismic-13-limit"></a>13-limit</h3>

Commas: 169/168, 176/175, 325/324, 1375/1372<br />

<br />

Line 1,263:

Line 1,301:

Badness: 0.0366<br />

<br />

<h2 id="~~toc61~~"><a name="Parakleismic-Paradigmic"></a>Paradigmic</h2>

<h2 id="toc63"><a name="Parakleismic-Paradigmic"></a>Paradigmic</h2>

Commas: 540/539, 896/891, 3136/3125<br />

<br />

Line 1,272:

Line 1,310:

Badness: 0.0417<br />

<br />

<h3 id="~~toc62~~"><a name="Parakleismic-Paradigmic-13-limit"></a>13-limit</h3>

<h3 id="toc64"><a name="Parakleismic-Paradigmic-13-limit"></a>13-limit</h3>

Commas: 169/168, 325/324, 540/539, 832/825<br />

<br />

Line 1,281:

Line 1,319:

Badness: 0.0358<br />

<br />

<h1 id="~~toc63~~"><a name="Semiparakleismic"></a>Semiparakleismic</h1>

<h1 id="toc65"><a name="Semiparakleismic"></a>Semiparakleismic</h1>

Commas: 3025/3024, 3136/3125, 4375/4374<br />

<br />

Line 1,290:

Line 1,328:

Badness: 0.0342<br />

<br />

<h1 id="~~toc64~~"><a name="Quincy"></a>Quincy</h1>

<h1 id="toc66"><a name="Quincy"></a>Quincy</h1>

Commas: 4375/4374, 823543/819200<br />

<br />

Line 1,299:

Line 1,337:

Badness: 0.0797<br />

<br />

<h2 id="~~toc65~~"><a name="Quincy-11-limit"></a>11-limit</h2>

<h2 id="toc67"><a name="Quincy-11-limit"></a>11-limit</h2>

Commas: 441/440, 4000/3993, 41503/41472<br />

<br />

Line 1,308:

Line 1,346:

Badness: 0.0309<br />

<br />

<h2 id="~~toc66~~"><a name="Quincy-13-limit"></a>13-limit</h2>

<h2 id="toc68"><a name="Quincy-13-limit"></a>13-limit</h2>

Commas: 364/363, 441/440, 676/675, 4375/4374<br />

<br />

Line 1,317:

Line 1,355:

Badness: 0.0239<br />

<br />

<h2 id="~~toc67~~"><a name="Quincy-17-limit"></a>17-limit</h2>

<h2 id="toc69"><a name="Quincy-17-limit"></a>17-limit</h2>

Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br />

<br />

Line 1,326:

Line 1,364:

Badness: 0.0147<br />

<br />

<h2 id="~~toc68~~"><a name="Quincy-19-limit"></a>19-limit</h2>

<h2 id="toc70"><a name="Quincy-19-limit"></a>19-limit</h2>

Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br />

<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-04-20 00:23:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-20 00:36:24 UTC</tt>.<br>
-: The original revision id was <tt>322984716</tt>.<br>
+: The original revision id was <tt>322987966</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>
@@ Line 423: / Line 423: @@
 EDOs: 190, 224, 414, 638, 1052c, 1690bc
 Badness: 0.1760
+==11-limit==
+Commas: 3025/3024, 4375/4374, 1265625/1261568
+POTE generator: ~448/405 = 176.806
+Map: [&lt;2 7 7 23 19|, &lt;0 -13 -8 -59 -41|]
+EDOs: 190, 224, 414, 638, 1052c
+Badness: 0.0410
+==13-limit==
+Commas: 625/624, 729/728, 1575/1573, 2200/2197
+POTE generator: ~448/405 = 176.804
+Map: [&lt;2 7 7 23 19 13|, &lt;0 -13 -8 -59 -41 =19|]
+EDOs: 190, 224, 414, 638, 1690bc, 2328bcde
+Badness: 0.0226
 =Nearly Micro=
@@ Line 636: / Line 654: @@
 Badness: 0.0152</pre></div>
 <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-
+<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:
 &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;
@@ Line 1,123: / Line 1,143: @@
 Badness: 0.1760&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc44"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;Nearly Micro&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Quatracot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
+Commas: 3025/3024, 4375/4374, 1265625/1261568&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~448/405 = 176.806&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 7 7 23 19|, &amp;lt;0 -13 -8 -59 -41|]&lt;br /&gt;
+EDOs: 190, 224, 414, 638, 1052c&lt;br /&gt;
+Badness: 0.0410&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="Quatracot-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
+Commas: 625/624, 729/728, 1575/1573, 2200/2197&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~448/405 = 176.804&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 7 7 23 19 13|, &amp;lt;0 -13 -8 -59 -41 =19|]&lt;br /&gt;
+EDOs: 190, 224, 414, 638, 1690bc, 2328bcde&lt;br /&gt;
+Badness: 0.0226&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc46"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;Nearly Micro&lt;/h1&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc45"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;Octoid&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc47"&gt;&lt;a name="Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;Octoid&lt;/h1&gt;
   Commas: 4375/4374, 16875/16807&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,135: / Line 1,173: @@
 Badness: 0.0427&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="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;11-limit&lt;/h2&gt;
   Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,144: / Line 1,182: @@
 Badness: 0.0141&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;13-limit&lt;/h2&gt;
   Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,153: / Line 1,191: @@
 Badness: 0.0153&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Music&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Octoid-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;Music&lt;/h2&gt;
-  &lt;!-- ws:start:WikiTextUrlRule:787: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:787 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextUrlRule:809: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:809 --&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;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Octoid-Octopus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;Octopus&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Octoid-Octopus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;Octopus&lt;/h2&gt;
   Commas: 169/168, 325/324, 364/363, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,166: / Line 1,204: @@
 Badness: 0.0217&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc50"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;Amity&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc52"&gt;&lt;a name="Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&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;
 &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;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;5-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;5-limit&lt;/h2&gt;
   Comma: 1600000/1594323&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,180: / Line 1,218: @@
 Badness: 0.0220&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;7-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc54"&gt;&lt;a name="Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;7-limit&lt;/h2&gt;
   Commas: 4375/4374, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,190: / Line 1,228: @@
 Badness: 0.0236&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Amity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;11-limit&lt;/h2&gt;
   Commas: 540/539, 4375/4374, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,199: / Line 1,237: @@
 Badness: 0.0315&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc54"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;Hitchcock&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc56"&gt;&lt;a name="Amity-Hitchcock"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;Hitchcock&lt;/h2&gt;
   Commas: 121/120, 176/175, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,208: / Line 1,246: @@
 Badness: 0.0352&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;Hemiamity&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc57"&gt;&lt;a name="Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;Hemiamity&lt;/h2&gt;
   Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,216: / Line 1,254: @@
 EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc56"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;Parakleismic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc58"&gt;&lt;a name="Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&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;
 &lt;br /&gt;
@@ Line 1,227: / Line 1,265: @@
 Badness: 0.0433&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc57"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;7-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc59"&gt;&lt;a name="Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;7-limit&lt;/h2&gt;
   Commas: 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,236: / Line 1,274: @@
 Badness: 0.0274&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc58"&gt;&lt;a name="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc60"&gt;&lt;a name="Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;11-limit&lt;/h2&gt;
   Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,245: / Line 1,283: @@
 Badness: 0.0497&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc59"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;Parkleismic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc61"&gt;&lt;a name="Parakleismic-Parkleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;Parkleismic&lt;/h2&gt;
   Commas: 176/175, 1375/1372, 2200/2187&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,254: / Line 1,292: @@
 Badness: 0.0559&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc60"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc62"&gt;&lt;a name="Parakleismic-Parkleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;13-limit&lt;/h3&gt;
   Commas: 169/168, 176/175, 325/324, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,263: / Line 1,301: @@
 Badness: 0.0366&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc61"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;Paradigmic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc63"&gt;&lt;a name="Parakleismic-Paradigmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;Paradigmic&lt;/h2&gt;
   Commas: 540/539, 896/891, 3136/3125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,272: / Line 1,310: @@
 Badness: 0.0417&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc62"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc64"&gt;&lt;a name="Parakleismic-Paradigmic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;13-limit&lt;/h3&gt;
   Commas: 169/168, 325/324, 540/539, 832/825&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,281: / Line 1,319: @@
 Badness: 0.0358&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc63"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;Semiparakleismic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc65"&gt;&lt;a name="Semiparakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;Semiparakleismic&lt;/h1&gt;
   Commas: 3025/3024, 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,290: / Line 1,328: @@
 Badness: 0.0342&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc64"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;Quincy&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc66"&gt;&lt;a name="Quincy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;Quincy&lt;/h1&gt;
   Commas: 4375/4374, 823543/819200&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,299: / Line 1,337: @@
 Badness: 0.0797&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc65"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc67"&gt;&lt;a name="Quincy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;11-limit&lt;/h2&gt;
   Commas: 441/440, 4000/3993, 41503/41472&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,308: / Line 1,346: @@
 Badness: 0.0309&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc66"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:136:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc68"&gt;&lt;a name="Quincy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:136 --&gt;13-limit&lt;/h2&gt;
   Commas: 364/363, 441/440, 676/675, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,317: / Line 1,355: @@
 Badness: 0.0239&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc67"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:138:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc69"&gt;&lt;a name="Quincy-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:138 --&gt;17-limit&lt;/h2&gt;
   Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,326: / Line 1,364: @@
 Badness: 0.0147&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:136:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc68"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:136 --&gt;19-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:140:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc70"&gt;&lt;a name="Quincy-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:140 --&gt;19-limit&lt;/h2&gt;
   Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600&lt;br /&gt;
 &lt;br /&gt;