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>2011-02-~~23 23~~:29:56 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-12 13:42:15 UTC</tt>.<br>

: The original revision id was <tt>~~204558584~~</tt>.<br>

: The original revision id was <tt>209868590</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>

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EDOs: 19, 152, 171, 665, 836, 1007, 2185

Badness: 0.0110

~~==Mitonic==~~

As a 5-limit temperament, mitonic is a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17>. Flipping that gives the 5-limit wedgie <<17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.

However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. The wedgie is now <<17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.

~~Commas: 4375/4374, 2100875/2097152~~

~~POTE generator: ~10/9 = 182.458~~

~~Map: [<1 16 32 -15|, <0 -17 -35 21|]~~

~~EDOs: 7, 13, 33, 46, 125, 171~~

~~Badness: 0.0252~~

==Abigail==

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Badness: 0.0110<br />

<br />

<h2 id="toc6"><a name="x-~~Mitonic~~"></a>Mitonic</h2>

<h2 id="toc6"><a name="x-Abigail"></a>Abigail</h2>

As a 5-limit temperament, mitonic is a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&gt;. Flipping that gives the 5-limit wedgie &lt;&lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.<br />

~~<br />~~

However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in <a class="wiki_link" href="/171edo">171edo</a>. The wedgie is now &lt;&lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.<br />

~~<br />~~

~~Commas: 4375/4374, 2100875/2097152<br />~~

~~<br />~~

~~POTE generator: ~10/9 = 182.458<br />~~

~~<br />~~

~~Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]<br />~~

~~EDOs: 7, 13, 33, 46, 125, 171<br />~~

~~Badness: 0.0252<br />~~

~~<br />~~

<h2 id="toc7"><a name="x-Abigail"></a>Abigail</h2>

Commas: 4375/4374, 2147483648/2144153025<br />

<br />

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Badness: 0.0370<br />

<br />

<h3 id="~~toc8~~"><a name="x-Abigail-11-limit"></a>11-limit</h3>

<h3 id="toc7"><a name="x-Abigail-11-limit"></a>11-limit</h3>

Comma: 3025/3024, 4375/4374, 20614528/20588575<br />

<br />

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Badness: 0.0129<br />

<br />

<h3 id="~~toc9~~"><a name="x-Abigail-13-limit"></a>13-limit</h3>

<h3 id="toc8"><a name="x-Abigail-13-limit"></a>13-limit</h3>

Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095<br />

<br />

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Badness: 0.00886<br />

<br />

<h1 id="~~toc10~~"><a name="Nearly Micro"></a>Nearly Micro</h1>

<h1 id="toc9"><a name="Nearly Micro"></a>Nearly Micro</h1>

<br />

<h2 id="~~toc11~~"><a name="Nearly Micro-Octoid"></a>Octoid</h2>

<h2 id="toc10"><a name="Nearly Micro-Octoid"></a>Octoid</h2>

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

<br />

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Badness: 0.0427<br />

<br />

<h3 id="~~toc12~~"><a name="Nearly Micro-Octoid-11-limit"></a>11-limit</h3>

<h3 id="toc11"><a name="Nearly Micro-Octoid-11-limit"></a>11-limit</h3>

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

<br />

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Badness: 0.0141<br />

<br />

<h3 id="~~toc13~~"><a name="Nearly Micro-Octoid-13-limit"></a>13-limit</h3>

<h3 id="toc12"><a name="Nearly Micro-Octoid-13-limit"></a>13-limit</h3>

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

<br />

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Badness: 0.0153<br />

<br />

<h2 id="~~toc14~~"><a name="Nearly Micro-Amity"></a>Amity</h2>

<h2 id="toc13"><a name="Nearly Micro-Amity"></a>Amity</h2>

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 />

<h3 id="~~toc15~~"><a name="Nearly Micro-Amity-5-limit"></a>5-limit</h3>

<h3 id="toc14"><a name="Nearly Micro-Amity-5-limit"></a>5-limit</h3>

Comma: 1600000/1594323<br />

<br />

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Badness: 0.0220<br />

<br />

<h3 id="~~toc16~~"><a name="Nearly Micro-Amity-7-limit"></a>7-limit</h3>

<h3 id="toc15"><a name="Nearly Micro-Amity-7-limit"></a>7-limit</h3>

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

<br />

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Badness: 0.0236<br />

<br />

<h3 id="~~toc17~~"><a name="Nearly Micro-Amity-Hemiamity"></a>Hemiamity</h3>

<h3 id="toc16"><a name="Nearly Micro-Amity-Hemiamity"></a>Hemiamity</h3>

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

<br />

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

<br />

<h2 id="~~toc18~~"><a name="Nearly Micro-Parakleismic"></a>Parakleismic</h2>

<h2 id="toc17"><a name="Nearly Micro-Parakleismic"></a>Parakleismic</h2>

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 />

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Badness: 0.0433<br />

<br />

<h3 id="~~toc19~~"><a name="Nearly Micro-Parakleismic-7-limit"></a>7-limit</h3>

<h3 id="toc18"><a name="Nearly Micro-Parakleismic-7-limit"></a>7-limit</h3>

Commas: 3136/3125, 5475/4374<br />

<br />

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Badness: 0.0274<br />

<br />

<h3 id="~~toc20~~"><a name="Nearly Micro-Parakleismic-11-limit"></a>11-limit</h3>

<h3 id="toc19"><a name="Nearly Micro-Parakleismic-11-limit"></a>11-limit</h3>

Commas: 385/384, 3136/3125, 4375/4374<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>2011-02-23 23:29:56 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-12 13:42:15 UTC</tt>.<br>
-: The original revision id was <tt>204558584</tt>.<br>
+: The original revision id was <tt>209868590</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 73: / Line 73: @@
 EDOs: 19, 152, 171, 665, 836, 1007, 2185
 Badness: 0.0110
-==Mitonic==
-As a 5-limit temperament, mitonic is a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&gt;. Flipping that gives the 5-limit wedgie &lt;&lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.
-However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. The wedgie is now &lt;&lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.
-Commas: 4375/4374, 2100875/2097152
-POTE generator: ~10/9 = 182.458
-Map: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
-EDOs: 7, 13, 33, 46, 125, 171
-Badness: 0.0252
 ==Abigail==
@@ Line 273: / Line 260: @@
 Badness: 0.0110&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Mitonic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Abigail&lt;/h2&gt;
-As a 5-limit temperament, mitonic is a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&amp;gt;. Flipping that gives the 5-limit wedgie &amp;lt;&amp;lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.&lt;br /&gt;
-&lt;br /&gt;
-However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;. The wedgie is now &amp;lt;&amp;lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 4375/4374, 2100875/2097152&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/9 = 182.458&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 16 32 -15|, &amp;lt;0 -17 -35 21|]&lt;br /&gt;
-EDOs: 7, 13, 33, 46, 125, 171&lt;br /&gt;
-Badness: 0.0252&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Abigail"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Abigail&lt;/h2&gt;
 Commas: 4375/4374, 2147483648/2144153025&lt;br /&gt;
 &lt;br /&gt;
@@ Line 296: / Line 270: @@
 Badness: 0.0370&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Abigail-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h3&gt;
 Comma: 3025/3024, 4375/4374, 20614528/20588575&lt;br /&gt;
 &lt;br /&gt;
@@ Line 305: / Line 279: @@
 Badness: 0.0129&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Abigail-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
 Commas: 1716/1715, 2080/2079, 3025/3024, 4096/4095&lt;br /&gt;
 &lt;br /&gt;
@@ Line 314: / Line 288: @@
 Badness: 0.00886&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Nearly Micro&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Nearly Micro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Nearly Micro&lt;/h1&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Nearly Micro-Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Octoid&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Nearly Micro-Octoid"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Octoid&lt;/h2&gt;
 Commas: 4375/4374, 16875/16807&lt;br /&gt;
 &lt;br /&gt;
@@ Line 326: / Line 300: @@
 Badness: 0.0427&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Nearly Micro-Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Nearly Micro-Octoid-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h3&gt;
 Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
@@ Line 335: / Line 309: @@
 Badness: 0.0141&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Nearly Micro-Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Nearly Micro-Octoid-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&gt;
 Commas: 540/539, 1375/1372, 4000/3993, 625/624&lt;br /&gt;
 &lt;br /&gt;
@@ Line 344: / Line 318: @@
 Badness: 0.0153&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Nearly Micro-Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Amity&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Nearly Micro-Amity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Amity&lt;/h2&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:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Nearly Micro-Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;5-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Nearly Micro-Amity-5-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;5-limit&lt;/h3&gt;
 Comma: 1600000/1594323&lt;br /&gt;
 &lt;br /&gt;
@@ Line 358: / Line 332: @@
 Badness: 0.0220&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Nearly Micro-Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;7-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Nearly Micro-Amity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;7-limit&lt;/h3&gt;
 Commas: 4375/4374, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
@@ Line 367: / Line 341: @@
 Badness: 0.0236&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="Nearly Micro-Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Hemiamity&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Nearly Micro-Amity-Hemiamity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Hemiamity&lt;/h3&gt;
 Commas: 4375/4374, 5120/5103, 3025/3024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 375: / Line 349: @@
 EDOs: 14, 46, 106, 152, 350&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Nearly Micro-Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Parakleismic&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Nearly Micro-Parakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Parakleismic&lt;/h2&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 386: / Line 360: @@
 Badness: 0.0433&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Nearly Micro-Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;7-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Nearly Micro-Parakleismic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;7-limit&lt;/h3&gt;
 Commas: 3136/3125, 5475/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 395: / Line 369: @@
 Badness: 0.0274&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="Nearly Micro-Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Nearly Micro-Parakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h3&gt;
 Commas: 385/384, 3136/3125, 4375/4374&lt;br /&gt;
 &lt;br /&gt;