Porcupine family: Difference between revisions

Revision as of 17:50, 22 August 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author clumma and made on 2011-08-22 17:50:52 UTC.

The original revision id was 247768633.

The revision comment was: manually adding Gene's changes (no undo in wikispaces?)

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc|flat]]
----
The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10_9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.

[[POTE tuning|POTE generator]]: 163.950

Map: [<1 2 3|, <0 -3 -5|]

EDOs: [[15edo|15]], [[22edo|22]], [[161edo|161]], [[183edo|183]]

==Seven limit children== 
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. That means [[64_63|64/63]], the [[Archyta's comma]], for [[Porcupine family#Porcupine|porcupine]], [[36_35|36/35]], the [[septimal quarter tone]], for [[Porcupine family#Hystrix|hystrix]], [[50_49|50/49]], the [[jubilisma]], for [[Porcupine family#Hedgehog|hedgehog]], and [[49_48|49/48]], the [[slendro diesis]], for [[Porcupine family#Nautilus|nautilus]].

=Porcupine= 
Porcupine, with wedgie <<3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to [[7_4|7/4]]. For this to work you need a small minor tone such as [[22edo]] provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.

Commas: 250/243, 64/63

[[POTE tuning|POTE generator]]: ~10/9 = 162.880

Map: [<1 2 3 2|, <0 -3 -5 6|]
EDOs: 22, [[59edo|59]], [[81edo|81]], [[140edo|140]]

==11-limit== 
Commas: 55/54, 64/63, 100/99

POTE generator: ~10/9 = 162.747

Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|]
EDOs: [[7edo|7]], 15, 22, [[37edo|37]], 59
Badness: 0.0217

=Hystrix= 
Hystrix, with wedgie <<3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.

Commas: 36/35, 160/147

[[POTE tuning|POTE generator]]: 158.868

Map: [<1 2 3 3|, <0 -3 -5 -1|]

EDOs: 15, 68

=Hedgehog= 

See //[[Hedgehog]]//

=Nautilus=
Commas: 49/48, 250/243

Pote generator: ~21/20 = 82.505

Map: [<1 2 3 3|, <0 -6 -10 -3|]
Wedgie: <<6 10 3 2 -12 -21||
EDOs: [[14edo|14]], 15, [[29edo|29]], [[44edo|44]], [[73edo|73]], [[160edo|160]]

==11-limit==
Commas: 49/48, 55/54, 245/242

POTE generator: ~21/20 = 82.504

Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]
EDOs: 14, 15, 29, 44, 73, 160

==13-limit==
Commas: 49/48, 55/54, 91/90, 100/99

POTE generator: ~21/20 = 62.530

Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]
EDOs: 14, 15, 29, 44, 73, 160

=Ammonite=
Commas: 250/243, 686/675

POTE generator: ~9/7 = 454.448

Map: [<1 5 8 10|, <0 -9 -15 -19|]
Wedgie: <<9 15 19 3 5 2||
EDOs: 29, 37, 66
Badness: 0.1077

11-limit
Commas: 55/54, 100/99, 686/675

POTE generator: ~9/7 = 454.512

Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|]
EDOs: 29, 37, 66
Badness: 0.0457

13-limit
Commas: 55/54, 91/90, 100/99, 169/168

POTE generator: ~13/10 = 454.429

Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|]
EDOs: 29, 37, 66
Badness: 0.0272 

=Porky=
Commas: 225/224, 250/243

POTE generator: ~10/9 = 164.412

Map: [<1 2 3 5|, <0 -3 -5 -16|]
Wedgie: <<3 5 16 1 17 23||
EDOS: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0544

==11-limit==
Commas: 55/54, 100/99, 225/224

POTE generator: ~10/9 = 164.552

Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]
EDOs: 7, 8, 15, 22, 29, 51, 73
Badness: 0.0273

Original HTML content:

<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:22:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: -->
<!-- ws:end:WikiTextTocRule:34 --><hr />
The 5-limit parent comma for the porcupine family is 250/243, the maximal <a class="wiki_link" href="/diesis">diesis</a> or porcupine comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. This tells us the <a class="wiki_link" href="/generator">generator</a> is a minor whole tone, the <a class="wiki_link" href="/10_9">10/9</a> interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br />
<br />
Map: [&lt;1 2 3|, &lt;0 -3 -5|]<br />
<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/161edo">161</a>, <a class="wiki_link" href="/183edo">183</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
 The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. That means <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Archyta%27s%20comma">Archyta's comma</a>, for <a class="wiki_link" href="/Porcupine%20family#Porcupine">porcupine</a>, <a class="wiki_link" href="/36_35">36/35</a>, the <a class="wiki_link" href="/septimal%20quarter%20tone">septimal quarter tone</a>, for <a class="wiki_link" href="/Porcupine%20family#Hystrix">hystrix</a>, <a class="wiki_link" href="/50_49">50/49</a>, the <a class="wiki_link" href="/jubilisma">jubilisma</a>, for <a class="wiki_link" href="/Porcupine%20family#Hedgehog">hedgehog</a>, and <a class="wiki_link" href="/49_48">49/48</a>, the <a class="wiki_link" href="/slendro%20diesis">slendro diesis</a>, for <a class="wiki_link" href="/Porcupine%20family#Nautilus">nautilus</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1>
 Porcupine, with wedgie &lt;&lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to <a class="wiki_link" href="/7_4">7/4</a>. For this to work you need a small minor tone such as <a class="wiki_link" href="/22edo">22edo</a> provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.<br />
<br />
Commas: 250/243, 64/63<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br />
<br />
Map: [&lt;1 2 3 2|, &lt;0 -3 -5 6|]<br />
EDOs: 22, <a class="wiki_link" href="/59edo">59</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/140edo">140</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
 Commas: 55/54, 64/63, 100/99<br />
<br />
POTE generator: ~10/9 = 162.747<br />
<br />
Map: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]<br />
EDOs: <a class="wiki_link" href="/7edo">7</a>, 15, 22, <a class="wiki_link" href="/37edo">37</a>, 59<br />
Badness: 0.0217<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hystrix</h1>
 Hystrix, with wedgie &lt;&lt;3 5 1 1 -7 -12||, provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried <a class="wiki_link" href="/15edo">15edo</a>. They can try the even sharper fifth of hystrix in <a class="wiki_link" href="/68edo">68edo</a> and see how that suits.<br />
<br />
Commas: 36/35, 160/147<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.868<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]<br />
<br />
EDOs: 15, 68<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hedgehog</h1>
 <br />
See <em><a class="wiki_link" href="/Hedgehog">Hedgehog</a></em><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:10 -->Nautilus</h1>
Commas: 49/48, 250/243<br />
<br />
Pote generator: ~21/20 = 82.505<br />
<br />
Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]<br />
Wedgie: &lt;&lt;6 10 3 2 -12 -21||<br />
EDOs: <a class="wiki_link" href="/14edo">14</a>, 15, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/44edo">44</a>, <a class="wiki_link" href="/73edo">73</a>, <a class="wiki_link" href="/160edo">160</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2>
Commas: 49/48, 55/54, 245/242<br />
<br />
POTE generator: ~21/20 = 82.504<br />
<br />
Map: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]<br />
EDOs: 14, 15, 29, 44, 73, 160<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2>
Commas: 49/48, 55/54, 91/90, 100/99<br />
<br />
POTE generator: ~21/20 = 62.530<br />
<br />
Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]<br />
EDOs: 14, 15, 29, 44, 73, 160<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:16 -->Ammonite</h1>
Commas: 250/243, 686/675<br />
<br />
POTE generator: ~9/7 = 454.448<br />
<br />
Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]<br />
Wedgie: &lt;&lt;9 15 19 3 5 2||<br />
EDOs: 29, 37, 66<br />
Badness: 0.1077<br />
<br />
11-limit<br />
Commas: 55/54, 100/99, 686/675<br />
<br />
POTE generator: ~9/7 = 454.512<br />
<br />
Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]<br />
EDOs: 29, 37, 66<br />
Badness: 0.0457<br />
<br />
13-limit<br />
Commas: 55/54, 91/90, 100/99, 169/168<br />
<br />
POTE generator: ~13/10 = 454.429<br />
<br />
Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]<br />
EDOs: 29, 37, 66<br />
Badness: 0.0272 <br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:18 -->Porky</h1>
Commas: 225/224, 250/243<br />
<br />
POTE generator: ~10/9 = 164.412<br />
<br />
Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]<br />
Wedgie: &lt;&lt;3 5 16 1 17 23||<br />
EDOS: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0544<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2>
Commas: 55/54, 100/99, 225/224<br />
<br />
POTE generator: ~10/9 = 164.552<br />
<br />
Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]<br />
EDOs: 7, 8, 15, 22, 29, 51, 73<br />
Badness: 0.0273</body></html>

@@ 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:clumma|clumma]] and made on <tt>2011-08-22 17:48:06 UTC</tt>.<br>
+: This revision was by author [[User:clumma|clumma]] and made on <tt>2011-08-22 17:50:52 UTC</tt>.<br>
-: The original revision id was <tt>247768013</tt>.<br>
+: The original revision id was <tt>247768633</tt>.<br>
-: The revision comment was: <tt>Reverted to Aug 21, 2011 4:22 pm</tt><br>
+: The revision comment was: <tt>manually adding Gene's changes (no undo in wikispaces?)</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 77: / Line 77: @@
 Map: [&lt;1 2 3 3 4 5|, &lt;0 -6 -10 -3 -8 -19|]
 EDOs: 14, 15, 29, 44, 73, 160
+=Ammonite=
+Commas: 250/243, 686/675
+POTE generator: ~9/7 = 454.448
+Map: [&lt;1 5 8 10|, &lt;0 -9 -15 -19|]
+Wedgie: &lt;&lt;9 15 19 3 5 2||
+EDOs: 29, 37, 66
+Badness: 0.1077
+-limit
+Commas: 55/54, 100/99, 686/675
+POTE generator: ~9/7 = 454.512
+Map: [&lt;1 5 8 10 8|, &lt;0 -9 -15 -19 -12|]
+EDOs: 29, 37, 66
+Badness: 0.0457
+-limit
+Commas: 55/54, 91/90, 100/99, 169/168
+POTE generator: ~13/10 = 454.429
+Map: [&lt;1 5 8 10 8 9|, &lt;0 -9 -15 -19 -12 -14|]
+EDOs: 29, 37, 66
+Badness: 0.0272
 =Porky=
@@ Line 98: / Line 126: @@
 </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-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;
+<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;Porcupine family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:22:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;hr /&gt;
 The 5-limit parent comma for the porcupine family is 250/243, the maximal &lt;a class="wiki_link" href="/diesis"&gt;diesis&lt;/a&gt; or porcupine comma. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |1 -5 3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 5 1|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. This tells us the &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; is a minor whole tone, the &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3/22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 170: / Line 198: @@
 EDOs: 14, 15, 29, 44, 73, 160&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Porky&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Ammonite&lt;/h1&gt;
+Commas: 250/243, 686/675&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~9/7 = 454.448&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 5 8 10|, &amp;lt;0 -9 -15 -19|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;9 15 19 3 5 2||&lt;br /&gt;
+EDOs: 29, 37, 66&lt;br /&gt;
+Badness: 0.1077&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 55/54, 100/99, 686/675&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~9/7 = 454.512&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 5 8 10 8|, &amp;lt;0 -9 -15 -19 -12|]&lt;br /&gt;
+EDOs: 29, 37, 66&lt;br /&gt;
+Badness: 0.0457&lt;br /&gt;
+&lt;br /&gt;
+-limit&lt;br /&gt;
+Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~13/10 = 454.429&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 5 8 10 8 9|, &amp;lt;0 -9 -15 -19 -12 -14|]&lt;br /&gt;
+EDOs: 29, 37, 66&lt;br /&gt;
+Badness: 0.0272 &lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Porky&lt;/h1&gt;
 Commas: 225/224, 250/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 180: / Line 236: @@
 Badness: 0.0544&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
 Commas: 55/54, 100/99, 225/224&lt;br /&gt;
 &lt;br /&gt;

Porcupine family: Difference between revisions

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