Porcupine family: Difference between revisions

Revision as of 19:17, 28 December 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 genewardsmith and made on 2011-12-28 19:17:58 UTC.

The original revision id was 288691764.

The revision comment was:

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]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]

==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|81bd]], [[140edo|140bd]]

==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]], [[59edo|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: 10d, 12, 13d, 15

=Hedgehog= 
Hedgehog, with wedgie <<6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the <146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.

Commas: 50/49, 245/243

[[POTE tuning|POTE generator]]: ~9/7 = 435.648

Map: [<2 1 1 2|, <0 3 5 5|]
Wedgie: <<6 10 10 2 -1 -5||
EDOs: 22, [[146edo|146]]
Badness: 0.0440

==11-limit==
Commas: 50/49, 55/54, 99/98

POTE generator: ~9/7 = 435.386

Map: [<2 1 1 2 4|, <0 3 5 5 4|]
EDOs: 14c, 22, 58ce, 80ce, 102cde
Badness: 0.0231

=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: 10, 15, 19, [[29edo|29]], [[102edo|102cd]]

==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: 10e, 14c, 15, 19, 22d, 29, 102cde

==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: 10e, 15f, 17d, 19, 22d, 29, 102cde

[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3|Nautilus Reverie]] by [[IgliashonJones|Igliashon Calvin Jones-Coolidge]]
=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:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: -->
<!-- ws:end:WikiTextTocRule:43 --><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="/95edo">95c</a>, <a class="wiki_link" href="/117edo">117bc</a>, <a class="wiki_link" href="/139edo">139bc</a>, <a class="wiki_link" href="/161edo">161bc</a>, <a class="wiki_link" href="/183edo">183bc</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">81bd</a>, <a class="wiki_link" href="/140edo">140bd</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>, <a class="wiki_link" href="/59edo">59</a><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: 10d, 12, 13d, 15<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hedgehog</h1>
 Hedgehog, with wedgie &lt;&lt;6 10 10 2 -1 -5||, has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. 22et provides the obvious tuning, but if you are looking for an alternative, you could try the &lt;146 232 338 411| val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14 note MOS gives scope for harmony while stopping well short of 22.<br />
<br />
Commas: 50/49, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 435.648<br />
<br />
Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]<br />
Wedgie: &lt;&lt;6 10 10 2 -1 -5||<br />
EDOs: 22, <a class="wiki_link" href="/146edo">146</a><br />
Badness: 0.0440<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Hedgehog-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2>
Commas: 50/49, 55/54, 99/98<br />
<br />
POTE generator: ~9/7 = 435.386<br />
<br />
Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]<br />
EDOs: 14c, 22, 58ce, 80ce, 102cde<br />
Badness: 0.0231<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: 10, 15, 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/102edo">102cd</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->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: 10e, 14c, 15, 19, 22d, 29, 102cde<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->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: 10e, 15f, 17d, 19, 22d, 29, 102cde<br />
<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow">Nautilus Reverie</a> by <a class="wiki_link" href="/IgliashonJones">Igliashon Calvin Jones-Coolidge</a><br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2>
 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 />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h2>
 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:24:&lt;h1&gt; --><h1 id="toc12"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:24 -->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:26:&lt;h2&gt; --><h2 id="toc13"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->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:keenanpepper|keenanpepper]] and made on <tt>2011-11-19 19:25:36 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-28 19:17:58 UTC</tt>.<br>
-: The original revision id was <tt>277281722</tt>.<br>
+: The original revision id was <tt>288691764</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 54: / Line 54: @@
 Commas: 50/49, 245/243
-[[POTE tuning|POTE generator]]: 164.352
+[[POTE tuning|POTE generator]]: ~9/7 = 435.648
 Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]
 Wedgie: &lt;&lt;6 10 10 2 -1 -5||
 EDOs: 22, [[146edo|146]]
+Badness: 0.0440
+==11-limit==
+Commas: 50/49, 55/54, 99/98
+POTE generator: ~9/7 = 435.386
+Map: [&lt;2 1 1 2 4|, &lt;0 3 5 5 4|]
+EDOs: 14c, 22, 58ce, 80ce, 102cde
+Badness: 0.0231
 =Nautilus=
@@ Line 133: / Line 143: @@
 Badness: 0.0273</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-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:26:&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:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&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;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&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:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&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:28:&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:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:43 --&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 181: / Line 191: @@
 Commas: 50/49, 245/243&lt;br /&gt;
 &lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 164.352&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;2 1 1 2|, &amp;lt;0 3 5 5|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;6 10 10 2 -1 -5||&lt;br /&gt;
 EDOs: 22, &lt;a class="wiki_link" href="/146edo"&gt;146&lt;/a&gt;&lt;br /&gt;
+Badness: 0.0440&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
+Commas: 50/49, 55/54, 99/98&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~9/7 = 435.386&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 1 1 2 4|, &amp;lt;0 3 5 5 4|]&lt;br /&gt;
+EDOs: 14c, 22, 58ce, 80ce, 102cde&lt;br /&gt;
+Badness: 0.0231&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Nautilus&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Nautilus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Nautilus&lt;/h1&gt;
   Commas: 49/48, 250/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 196: / Line 216: @@
 EDOs: 10, 15, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102cd&lt;/a&gt;&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="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Nautilus-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
   Commas: 49/48, 55/54, 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 204: / Line 224: @@
 EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde&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="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Nautilus-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
   Commas: 49/48, 55/54, 91/90, 100/99&lt;br /&gt;
 &lt;br /&gt;
@@ Line 213: / Line 233: @@
 &lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/NautilusReverie.mp3" rel="nofollow"&gt;Nautilus Reverie&lt;/a&gt; by &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&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;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Ammonite"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Ammonite&lt;/h1&gt;
   Commas: 250/243, 686/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 223: / Line 243: @@
 Badness: 0.1077&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="Ammonite-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="Ammonite-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
   Commas: 55/54, 100/99, 686/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 232: / Line 252: @@
 Badness: 0.0457&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Ammonite-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
   Commas: 55/54, 91/90, 100/99, 169/168&lt;br /&gt;
 &lt;br /&gt;
@@ Line 241: / Line 261: @@
 Badness: 0.0272&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Porky&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Porky"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Porky&lt;/h1&gt;
   Commas: 225/224, 250/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 251: / Line 271: @@
 Badness: 0.0544&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Porky-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&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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