Porcupine family: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-26 16:18:53 UTC</tt>.<br>

The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;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: [&lt;1 2 3|, &lt;0 -3 -5|]

EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]

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 &lt;&lt;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: [&lt;1 2 3 2|, &lt;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: [&lt;1 2 3 2 4|, &lt;0 -3 -5 6 -4|]

EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]]

Badness: 0.0217

POTE generator: ~10/9 = 162.708

Map: [&lt;1 2 3 2 4 4|, &lt;0 -3 -5 6 -4 -2|]

Badness: 0.0213

==Porcupinefish==  

See also: [[The Biosphere]]

Commas: 55/54, 64/63, 91/90, 100/99

POTE generator: ~10/9 = 162.277

Map: [&lt;1 2 3 2 4 6|, &lt;0 -3 -5 6 -4 -17|]

EDOs: 15, 22, 37, 59, 96b

&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;

Commas: 55/54, 64/63, 65/63, 100/99

POTE generator: ~10/9 = 163.688

Map: [&lt;1 2 3 2 4 3|, &lt;0 -3 -5 6 -4 5|]

=Hystrix=  

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 [[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: [&lt;1 2 3 3|, &lt;0 -3 -5 -1|]

EDOs: 10d, 12, 13d, 15

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.

Commas: 50/49, 245/243

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

Map: [&lt;2 1 1 2|, &lt;0 3 5 5|]

EDOs: 22, [[146edo|146]]

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

Commas: 50/49, 55/54, 65/63, 99/98

POTE generator: ~9/7 = 435.861

Map: [&lt;2 1 1 2 4 3|, &lt;0 3 5 5 4 6|]

==Urchin==

Commas: 40/39, 50/49, 55/54, 66/65

POTE generator: ~9/7 = 437.078

Map: [&lt;2 1 1 2 4 6|, &lt;0 3 5 5 4 2|]

EDOs: 14c, 22f

Badness: 0.0252

==Hedgepig==

Commas: 50/49, 245/243, 385/384

POTE generator: ~9/7 = 435.425

Map: [&lt;2 1 1 2 12|, &lt;0 3 5 5 -7|]

Badness: 0.0684

[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.

Commas: 49/48, 250/243

Pote generator: ~21/20 = 82.505

Map: [&lt;1 2 3 3|, &lt;0 -6 -10 -3|]

Wedgie: &lt;&lt;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: [&lt;1 2 3 3 4|, &lt;0 -6 -10 -3 -8|]

==13-limit==  

POTE generator: ~21/20 = 62.530

Map: [&lt;1 2 3 3 4 5|, &lt;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]]

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

==11-limit==

Commas: 55/54, 100/99, 686/675

POTE generator: ~9/7 = 454.512

Badness: 0.0457

==13-limit==  

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

Commas: 250/243, 1728/1715

POTE generator: ~36/35 = 54.384

Map: [&lt;1 2 3 3|, &lt;0 -9 -15 -4|]

Wedgie: &lt;&lt;9 15 4 3 -19 -33||

EDOs: 22

Badness: 0.115

==11-limit==

Commas: 55/54, 100/99, 5324/5145

POTE generator: ~36/35 = 54.376

Badness: 0.0513

==13-limit==

Commas: 55/54, 65/63, 100/99, 352/343

POTE generator: ~36/35 = 54.665

Map: [&lt;1 2 3 3 4 4|, &lt;0 -9 -15 -4 -12 -7|]

=Porky=  

Commas: 225/224, 250/243

POTE generator: ~10/9 = 164.412

Map: [&lt;1 2 3 5|, &lt;0 -3 -5 -16|]

Wedgie: &lt;&lt;3 5 16 1 17 23||

EDOS: 7, 8, 15, 22, 29, 51, 73

Commas: 55/54, 100/99, 225/224

POTE generator: ~10/9 = 164.552

Map: [&lt;1 2 3 5 4|, &lt;0 -3 -5 -16 -4|]

EDOs: 7, 8, 15, 22, 29, 51, 73

Commas: 250/243, 525/512

POTE generator: ~10/9 = 166.041

Map: [&lt;1 2 3 1|, &lt;0 -3 -5 13|]

Wedgie: &lt;&lt;3 5 -13 1 -29 -44||

EDOs: 7, 29, 65c, 94cd

Badness: 0.1183

==11-limit==

Commas: 55/54, 100/99, 525/512

POTE generator: ~10/9 = 165.981

Map: [&lt;1 2 3 1 4|, &lt;0 -3 -5 13 -4|]

EDOs: 7, 29, 65ce, 94cde

Badness: 0.0497

Commas: 55/54, 65/64, 100/99, 105/104

POTE generator: ~10/9 = 165.974

Map: [&lt;1 2 3 1 4 3|, &lt;0 -3 -5 13 -4 5|]

EDOs: 7, 29, 65cef, 94cdef

Badness: 0.0302</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:54:&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:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Porcupine"&gt;Porcupine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Hystrix"&gt;Hystrix&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Hedgehog"&gt;Hedgehog&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Nautilus"&gt;Nautilus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Ammonite"&gt;Ammonite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Ceratitid"&gt;Ceratitid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Porky"&gt;Porky&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Coendou"&gt;Coendou&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;

&lt;!-- ws:end:WikiTextTocRule:82 --&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;

Map: [&amp;lt;1 2 3|, &amp;lt;0 -3 -5|]&lt;br /&gt;

EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/95edo"&gt;95c&lt;/a&gt;, &lt;a class="wiki_link" href="/117edo"&gt;117bc&lt;/a&gt;, &lt;a class="wiki_link" href="/139edo"&gt;139bc&lt;/a&gt;, &lt;a class="wiki_link" href="/161edo"&gt;161bc&lt;/a&gt;, &lt;a class="wiki_link" href="/183edo"&gt;183bc&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;

The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. That means &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Archyta%27s%20comma"&gt;Archyta's comma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Porcupine"&gt;porcupine&lt;/a&gt;, &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20quarter%20tone"&gt;septimal quarter tone&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hystrix"&gt;hystrix&lt;/a&gt;, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, the &lt;a class="wiki_link" href="/jubilisma"&gt;jubilisma&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, and &lt;a class="wiki_link" href="/49_48"&gt;49/48&lt;/a&gt;, the &lt;a class="wiki_link" href="/slendro%20diesis"&gt;slendro diesis&lt;/a&gt;, for &lt;a class="wiki_link" href="/Porcupine%20family#Nautilus"&gt;nautilus&lt;/a&gt;.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Porcupine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Porcupine&lt;/h1&gt;

&lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;, with wedgie &amp;lt;&amp;lt;3 5 -6 1 -18 -28||, uses six of its minor tone generator steps to get to &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. For this to work you need a small minor tone such as &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 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.&lt;br /&gt;

Commas: 250/243, 64/63&lt;br /&gt;

&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 162.880&lt;br /&gt;

&lt;br /&gt;

Map: [&amp;lt;1 2 3 2|, &amp;lt;0 -3 -5 6|]&lt;br /&gt;

EDOs: 22, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81bd&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140bd&lt;/a&gt;&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Porcupine-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;

Commas: 55/54, 64/63, 100/99&lt;br /&gt;

POTE generator: ~10/9 = 162.747&lt;br /&gt;

Map: [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]&lt;br /&gt;

EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, 15, 22, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/59edo"&gt;59&lt;/a&gt;&lt;br /&gt;

Badness: 0.0217&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Porcupine-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;

Commas: 40/39, 55/54, 64/63, 66/65&lt;br /&gt;

POTE generator: ~10/9 = 162.708&lt;br /&gt;

Map: [&amp;lt;1 2 3 2 4 4|, &amp;lt;0 -3 -5 6 -4 -2|]&lt;br /&gt;

EDOs: 7, 15, 22f, 37f&lt;br /&gt;

Badness: 0.0213&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine-Porcupinefish"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porcupinefish&lt;/h2&gt;

See also: &lt;a class="wiki_link" href="/The%20Biosphere"&gt;The Biosphere&lt;/a&gt;&lt;br /&gt;

Commas: 55/54, 64/63, 91/90, 100/99&lt;br /&gt;

POTE generator: ~10/9 = 162.277&lt;br /&gt;

Map: [&amp;lt;1 2 3 2 4 6|, &amp;lt;0 -3 -5 6 -4 -17|]&lt;br /&gt;

EDOs: 15, 22, 37, 59, 96b&lt;br /&gt;

&lt;span style="background-color: #ffffff;"&gt;Badness: 0.0253&lt;/span&gt;&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="Porcupine-Porkpie"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Porkpie&lt;/h2&gt;

Commas: 55/54, 64/63, 65/63, 100/99&lt;br /&gt;

POTE generator: ~10/9 = 163.688&lt;br /&gt;

&lt;br /&gt;

Map: [&amp;lt;1 2 3 2 4 3|, &amp;lt;0 -3 -5 6 -4 5|]&lt;br /&gt;

EDOs: 7, 15f, 22&lt;br /&gt;

Badness: 0.0260&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Hystrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Hystrix&lt;/h1&gt;

Hystrix, with wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;. They can try the even sharper fifth of hystrix in &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; and see how that suits.&lt;br /&gt;

Commas: 36/35, 160/147&lt;br /&gt;

&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 158.868&lt;br /&gt;

Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -1|]&lt;br /&gt;

EDOs: 10d, 12, 13d, 15&lt;br /&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Hedgehog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hedgehog&lt;/h1&gt;

Hedgehog, with wedgie &amp;lt;&amp;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 &amp;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.&lt;br /&gt;

Commas: 50/49, 245/243&lt;br /&gt;

&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 435.648&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;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Hedgehog-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;

Commas: 50/49, 55/54, 99/98&lt;br /&gt;

POTE generator: ~9/7 = 435.386&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;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hedgehog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;

Map: [&amp;lt;1 2 3 1 4 3|, &amp;lt;0 -3 -5 13 -4 5|]&lt;br /&gt;