Porcupine family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 468004376 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 519361368 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-08-22 21:51:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>519361368</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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---- | ---- | ||
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. | 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. | ||
valid range: [150.000, 171.429] (8 to 7) | |||
nice range: [157.821, 166.015] | |||
strict range: [157.821, 166.015] | |||
[[POTE tuning|POTE generator]]: 163.950 | [[POTE tuning|POTE generator]]: 163.950 | ||
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Commas: 250/243, 64/63 | Commas: 250/243, 64/63 | ||
valid range: [160.000, 163.636] (15 to 22) | |||
nice range: [157.821, 166.015] | |||
strict range: [160.000, 163.636] | |||
[[POTE tuning|POTE generator]]: ~10/9 = 162.880 | [[POTE tuning|POTE generator]]: ~10/9 = 162.880 | ||
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==11-limit== | ==11-limit== | ||
Commas: 55/54, 64/63, 100/99 | Commas: 55/54, 64/63, 100/99 | ||
valid range: [160.000, 163.636] (15 to 22) | |||
nice range: [150.637, 182.404] | |||
strict range: [160.000, 163.636] | |||
POTE generator: ~10/9 = 162.747 | POTE generator: ~10/9 = 162.747 | ||
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==13-limit== | ==13-limit== | ||
Commas: 40/39, 55/54, 64/63, 66/65 | Commas: 40/39, 55/54, 64/63, 66/65 | ||
valid range: [160.000, 163.636] (15 to 22f) | |||
nice range: [138.573, 182.404] | |||
strict range: [160.000, 163.636] | |||
POTE generator: ~10/9 = 162.708 | POTE generator: ~10/9 = 162.708 | ||
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See also: [[The Biosphere]] | See also: [[The Biosphere]] | ||
Commas: 55/54, 64/63, 91/90, 100/99 | Commas: 55/54, 64/63, 91/90, 100/99 | ||
valid range: [160.000, 162.162] (15 to 37) | |||
nice range: [150.637, 182.404] | |||
strict range: [160.000, 162.162] | |||
POTE generator: ~10/9 = 162.277 | POTE generator: ~10/9 = 162.277 | ||
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<!-- ws:end:WikiTextTocRule:91 --><hr /> | <!-- ws:end:WikiTextTocRule:91 --><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 /> | 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 /> | |||
valid range: [150.000, 171.429] (8 to 7)<br /> | |||
nice range: [157.821, 166.015]<br /> | |||
strict range: [157.821, 166.015]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> | ||
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<br /> | <br /> | ||
Commas: 250/243, 64/63<br /> | Commas: 250/243, 64/63<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22)<br /> | |||
nice range: [157.821, 166.015]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Porcupine-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | <!-- 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 /> | Commas: 55/54, 64/63, 100/99<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22)<br /> | |||
nice range: [150.637, 182.404]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.747<br /> | POTE generator: ~10/9 = 162.747<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
Commas: 40/39, 55/54, 64/63, 66/65<br /> | Commas: 40/39, 55/54, 64/63, 66/65<br /> | ||
<br /> | |||
valid range: [160.000, 163.636] (15 to 22f)<br /> | |||
nice range: [138.573, 182.404]<br /> | |||
strict range: [160.000, 163.636]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.708<br /> | POTE generator: ~10/9 = 162.708<br /> | ||
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See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> | See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> | ||
Commas: 55/54, 64/63, 91/90, 100/99<br /> | Commas: 55/54, 64/63, 91/90, 100/99<br /> | ||
<br /> | |||
valid range: [160.000, 162.162] (15 to 37)<br /> | |||
nice range: [150.637, 182.404]<br /> | |||
strict range: [160.000, 162.162]<br /> | |||
<br /> | <br /> | ||
POTE generator: ~10/9 = 162.277<br /> | POTE generator: ~10/9 = 162.277<br /> | ||
Revision as of 21:51, 22 August 2014
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 2014-08-22 21:51:50 UTC.
- The original revision id was 519361368.
- 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. valid range: [150.000, 171.429] (8 to 7) nice range: [157.821, 166.015] strict range: [157.821, 166.015] [[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]] Badness: 0.0308 ==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 [[64_63|Archytas 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 valid range: [160.000, 163.636] (15 to 22) nice range: [157.821, 166.015] strict range: [160.000, 163.636] [[POTE tuning|POTE generator]]: ~10/9 = 162.880 7- and 9-limit minimax eigenmonzo: 9/7 Map: [<1 2 3 2|, <0 -3 -5 6|] EDOs: 22, [[59edo|59]], [[81edo|81bd]], [[140edo|140bd]] Badness: 0.0411 ==11-limit== Commas: 55/54, 64/63, 100/99 valid range: [160.000, 163.636] (15 to 22) nice range: [150.637, 182.404] strict range: [160.000, 163.636] POTE generator: ~10/9 = 162.747 11-limit minimax eigenmonzo: 9/7 Map: [<1 2 3 2 4|, <0 -3 -5 6 -4|] EDOs: [[7edo|7]], 15, 22, [[37edo|37]], [[59edo|59]] Badness: 0.0217 ==13-limit== Commas: 40/39, 55/54, 64/63, 66/65 valid range: [160.000, 163.636] (15 to 22f) nice range: [138.573, 182.404] strict range: [160.000, 163.636] POTE generator: ~10/9 = 162.708 13- and 15-limit minimax eigenmonzo: 11/8 Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|] EDOs: 7, 15, 22f, 37f Badness: 0.0213 ==Porcupinefish== See also: [[The Biosphere]] Commas: 55/54, 64/63, 91/90, 100/99 valid range: [160.000, 162.162] (15 to 37) nice range: [150.637, 182.404] strict range: [160.000, 162.162] POTE generator: ~10/9 = 162.277 13- and 15-limit minimax eigenmonzo: 13/11 Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|] EDOs: 15, 22, 37, 59, 96b <span style="background-color: #ffffff;">Badness: 0.0253</span> Badness: 0.0253 ==Pourcup== Commas: 55/54, 64/63, 100/99, 196/195 POTE generator: ~10/9 = 162.482 13- and 15-limit minimax eigenmonzo: 13/7 Map: [<1 2 3 2 4 1|, <0 -3 -5 6 -4 20|] EDOs: 15f, 22f, 37 Badness: 0.0351 ==Porkpie== Commas: 55/54, 64/63, 65/63, 100/99 POTE generator: ~10/9 = 163.688 13- and 15-limit minimax eigenmonzo: 9/7 Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|] EDOs: 7, 15f, 22 Badness: 0.0260 =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 7- and 9-limit minimax eigenmonzo: 5/4 Map: [<1 2 3 3|, <0 -3 -5 -1|] EDOs: 10d, 12, 13d, 15 Badness: 0.0449 =Porky= Commas: 225/224, 250/243 POTE generator: ~10/9 = 164.412 7- and 9-limit minimax eigenmonzo: 7/5 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 11-limit minimax eigenmonzo: 7/5 Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|] EDOs: 7, 8, 15, 22, 29, 51, 73 Badness: 0.0273 ==13-limit== Commas: 55/54, 65/64, 91/90, 100/99 POTE generator: ~10/9 = 164.953 Map: [<1 2 3 5 4 3|, <0 -3 -5 -16 -4 5|] EDOs: 22, 29, 51f, 80cdef Badness: 0.0265 =Coendou= Commas: 250/243, 525/512 POTE generator: ~10/9 = 166.041 7- and 9-limit minimax eigenmonzo: 3/2 Map: [<1 2 3 1|, <0 -3 -5 13|] Wedgie: <<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 11-limit minimax eigenmonzo: 3/2 Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|] EDOs: 7, 29, 65ce, 94cde Badness: 0.0497 ==13-limit== Commas: 55/54, 65/64, 100/99, 105/104 POTE generator: ~10/9 = 165.974 13- and 15-limit minimax eigenmonzo: 3/2 Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|] EDOs: 7, 29, 65cef, 94cdef Badness: 0.0302 =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 ==13-limit== Commas: 50/49, 55/54, 65/63, 99/98 POTE generator: ~9/7 = 435.861 Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|] EDOs: 14cf, 22 Badness: 0.0215 ==Urchin== Commas: 40/39, 50/49, 55/54, 66/65 POTE generator: ~9/7 = 437.078 Map: [<2 1 1 2 4 6|, <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: [<2 1 1 2 12|, <0 3 5 5 -7|] EDOs: 22, 80c, 102cd, 124cd Badness: 0.0684 ===Music=== [[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo. =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 Badness: 0.0223 ==Belauensis== Commas: 40/39, 49/48, 55/54, 66/65 POTE generator: ~21/20 = ~14/13 = 81.759 Map: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|] EDOs: 14c, 15, 29f, 44df Badness: 0.0298 [[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 =Ceratitid= Commas: 250/243, 1728/1715 POTE generator: ~36/35 = 54.384 Map: [<1 2 3 3|, <0 -9 -15 -4|] Wedgie: <<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 Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|] EDOs: 22 Badness: 0.0513 ==13-limit== Commas: 55/54, 65/63, 100/99, 352/343 POTE generator: ~36/35 = 54.665 Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|] EDOs: 22 Badness: 0.0447
Original HTML content:
<html><head><title>Porcupine family</title></head><body><!-- ws:start:WikiTextTocRule:60:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Porcupine">Porcupine</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Hystrix">Hystrix</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Porky">Porky</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Coendou">Coendou</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#Hedgehog">Hedgehog</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Nautilus">Nautilus</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Ammonite">Ammonite</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Ceratitid">Ceratitid</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> <!-- ws:end:WikiTextTocRule:91 --><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>, and flipping that yields <<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 /> valid range: [150.000, 171.429] (8 to 7)<br /> nice range: [157.821, 166.015]<br /> strict range: [157.821, 166.015]<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 163.950<br /> <br /> Map: [<1 2 3|, <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 /> Badness: 0.0308<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><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="/64_63">Archytas 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:<h1> --><h1 id="toc1"><a name="Porcupine"></a><!-- ws:end:WikiTextHeadingRule:2 -->Porcupine</h1> <a class="wiki_link" href="/Porcupine">Porcupine</a>, with wedgie <<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 /> valid range: [160.000, 163.636] (15 to 22)<br /> nice range: [157.821, 166.015]<br /> strict range: [160.000, 163.636]<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 162.880<br /> 7- and 9-limit minimax eigenmonzo: 9/7<br /> <br /> Map: [<1 2 3 2|, <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 /> Badness: 0.0411<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><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 /> valid range: [160.000, 163.636] (15 to 22)<br /> nice range: [150.637, 182.404]<br /> strict range: [160.000, 163.636]<br /> <br /> POTE generator: ~10/9 = 162.747<br /> 11-limit minimax eigenmonzo: 9/7<br /> <br /> Map: [<1 2 3 2 4|, <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:<h2> --><h2 id="toc3"><a name="Porcupine-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 40/39, 55/54, 64/63, 66/65<br /> <br /> valid range: [160.000, 163.636] (15 to 22f)<br /> nice range: [138.573, 182.404]<br /> strict range: [160.000, 163.636]<br /> <br /> POTE generator: ~10/9 = 162.708<br /> 13- and 15-limit minimax eigenmonzo: 11/8<br /> <br /> Map: [<1 2 3 2 4 4|, <0 -3 -5 6 -4 -2|]<br /> EDOs: 7, 15, 22f, 37f<br /> Badness: 0.0213<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Porcupine-Porcupinefish"></a><!-- ws:end:WikiTextHeadingRule:8 -->Porcupinefish</h2> See also: <a class="wiki_link" href="/The%20Biosphere">The Biosphere</a><br /> Commas: 55/54, 64/63, 91/90, 100/99<br /> <br /> valid range: [160.000, 162.162] (15 to 37)<br /> nice range: [150.637, 182.404]<br /> strict range: [160.000, 162.162]<br /> <br /> POTE generator: ~10/9 = 162.277<br /> 13- and 15-limit minimax eigenmonzo: 13/11<br /> <br /> Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]<br /> EDOs: 15, 22, 37, 59, 96b<br /> <span style="background-color: #ffffff;">Badness: 0.0253</span><br /> Badness: 0.0253<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Porcupine-Pourcup"></a><!-- ws:end:WikiTextHeadingRule:10 -->Pourcup</h2> Commas: 55/54, 64/63, 100/99, 196/195<br /> <br /> POTE generator: ~10/9 = 162.482<br /> 13- and 15-limit minimax eigenmonzo: 13/7<br /> <br /> Map: [<1 2 3 2 4 1|, <0 -3 -5 6 -4 20|]<br /> EDOs: 15f, 22f, 37<br /> Badness: 0.0351<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Porcupine-Porkpie"></a><!-- ws:end:WikiTextHeadingRule:12 -->Porkpie</h2> Commas: 55/54, 64/63, 65/63, 100/99<br /> <br /> POTE generator: ~10/9 = 163.688<br /> 13- and 15-limit minimax eigenmonzo: 9/7<br /> <br /> Map: [<1 2 3 2 4 3|, <0 -3 -5 6 -4 5|]<br /> EDOs: 7, 15f, 22<br /> Badness: 0.0260<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Hystrix"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hystrix</h1> 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 <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 /> 7- and 9-limit minimax eigenmonzo: 5/4<br /> <br /> Map: [<1 2 3 3|, <0 -3 -5 -1|]<br /> <br /> EDOs: 10d, 12, 13d, 15<br /> Badness: 0.0449<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="Porky"></a><!-- ws:end:WikiTextHeadingRule:16 -->Porky</h1> Commas: 225/224, 250/243<br /> <br /> POTE generator: ~10/9 = 164.412<br /> 7- and 9-limit minimax eigenmonzo: 7/5<br /> <br /> Map: [<1 2 3 5|, <0 -3 -5 -16|]<br /> Wedgie: <<3 5 16 1 17 23||<br /> EDOS: 7, 8, 15, 22, 29, 51, 73<br /> Badness: 0.0544<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Porky-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> Commas: 55/54, 100/99, 225/224<br /> <br /> POTE generator: ~10/9 = 164.552<br /> 11-limit minimax eigenmonzo: 7/5<br /> <br /> Map: [<1 2 3 5 4|, <0 -3 -5 -16 -4|]<br /> EDOs: 7, 8, 15, 22, 29, 51, 73<br /> Badness: 0.0273<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Porky-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2> Commas: 55/54, 65/64, 91/90, 100/99 <br /> <br /> POTE generator: ~10/9 = 164.953<br /> <br /> Map: [<1 2 3 5 4 3|, <0 -3 -5 -16 -4 5|]<br /> EDOs: 22, 29, 51f, 80cdef<br /> Badness: 0.0265<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="Coendou"></a><!-- ws:end:WikiTextHeadingRule:22 -->Coendou</h1> Commas: 250/243, 525/512<br /> <br /> POTE generator: ~10/9 = 166.041<br /> 7- and 9-limit minimax eigenmonzo: 3/2<br /> <br /> Map: [<1 2 3 1|, <0 -3 -5 13|]<br /> Wedgie: <<3 5 -13 1 -29 -44||<br /> EDOs: 7, 29, 65c, 94cd<br /> Badness: 0.1183<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="Coendou-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> Commas: 55/54, 100/99, 525/512<br /> <br /> POTE generator: ~10/9 = 165.981<br /> 11-limit minimax eigenmonzo: 3/2 <br /> <br /> Map: [<1 2 3 1 4|, <0 -3 -5 13 -4|]<br /> EDOs: 7, 29, 65ce, 94cde<br /> Badness: 0.0497<br /> <br /> <!-- ws:start:WikiTextHeadingRule:26:<h2> --><h2 id="toc13"><a name="Coendou-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> Commas: 55/54, 65/64, 100/99, 105/104<br /> <br /> POTE generator: ~10/9 = 165.974<br /> 13- and 15-limit minimax eigenmonzo: 3/2<br /> <br /> Map: [<1 2 3 1 4 3|, <0 -3 -5 13 -4 5|]<br /> EDOs: 7, 29, 65cef, 94cdef<br /> Badness: 0.0302<br /> <br /> <!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="Hedgehog"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hedgehog</h1> 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.<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: [<2 1 1 2|, <0 3 5 5|]<br /> Wedgie: <<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:30:<h2> --><h2 id="toc15"><a name="Hedgehog-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> Commas: 50/49, 55/54, 99/98<br /> <br /> POTE generator: ~9/7 = 435.386<br /> <br /> Map: [<2 1 1 2 4|, <0 3 5 5 4|]<br /> EDOs: 14c, 22, 58ce, 80ce, 102cde<br /> Badness: 0.0231<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><h2 id="toc16"><a name="Hedgehog-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> Commas: 50/49, 55/54, 65/63, 99/98<br /> <br /> POTE generator: ~9/7 = 435.861<br /> <br /> Map: [<2 1 1 2 4 3|, <0 3 5 5 4 6|]<br /> EDOs: 14cf, 22<br /> Badness: 0.0215<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Hedgehog-Urchin"></a><!-- ws:end:WikiTextHeadingRule:34 -->Urchin</h2> Commas: 40/39, 50/49, 55/54, 66/65<br /> <br /> POTE generator: ~9/7 = 437.078<br /> <br /> Map: [<2 1 1 2 4 6|, <0 3 5 5 4 2|]<br /> EDOs: 14c, 22f<br /> Badness: 0.0252<br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Hedgehog-Hedgepig"></a><!-- ws:end:WikiTextHeadingRule:36 -->Hedgepig</h2> Commas: 50/49, 245/243, 385/384<br /> <br /> POTE generator: ~9/7 = 435.425<br /> <br /> Map: [<2 1 1 2 12|, <0 3 5 5 -7|]<br /> EDOs: 22, 80c, 102cd, 124cd<br /> Badness: 0.0684<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h3> --><h3 id="toc19"><a name="Hedgehog-Hedgepig-Music"></a><!-- ws:end:WikiTextHeadingRule:38 -->Music</h3> <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h1> --><h1 id="toc20"><a name="Nautilus"></a><!-- ws:end:WikiTextHeadingRule:40 -->Nautilus</h1> Commas: 49/48, 250/243<br /> <br /> POTE generator: ~21/20 = 82.505<br /> <br /> Map: [<1 2 3 3|, <0 -6 -10 -3|]<br /> Wedgie: <<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:42:<h2> --><h2 id="toc21"><a name="Nautilus-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> Commas: 49/48, 55/54, 245/242<br /> <br /> POTE generator: ~21/20 = 82.504<br /> <br /> Map: [<1 2 3 3 4|, <0 -6 -10 -3 -8|]<br /> EDOs: 10e, 14c, 15, 19, 22d, 29, 102cde<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Nautilus-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> Commas: 49/48, 55/54, 91/90, 100/99<br /> <br /> POTE generator: ~21/20 = 62.530<br /> <br /> Map: [<1 2 3 3 4 5|, <0 -6 -10 -3 -8 -19|]<br /> EDOs: 10e, 15f, 17d, 19, 22d, 29, 102cde<br /> Badness: 0.0223<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h2> --><h2 id="toc23"><a name="Nautilus-Belauensis"></a><!-- ws:end:WikiTextHeadingRule:46 -->Belauensis</h2> Commas: 40/39, 49/48, 55/54, 66/65<br /> <br /> POTE generator: ~21/20 = ~14/13 = 81.759<br /> <br /> Map: [<1 2 3 3 4 4|, <0 -6 -10 -3 -8 -4|]<br /> EDOs: 14c, 15, 29f, 44df<br /> Badness: 0.0298<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:48:<h1> --><h1 id="toc24"><a name="Ammonite"></a><!-- ws:end:WikiTextHeadingRule:48 -->Ammonite</h1> Commas: 250/243, 686/675<br /> <br /> POTE generator: ~9/7 = 454.448<br /> <br /> Map: [<1 5 8 10|, <0 -9 -15 -19|]<br /> Wedgie: <<9 15 19 3 5 2||<br /> EDOs: 29, 37, 66<br /> Badness: 0.1077<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="Ammonite-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> Commas: 55/54, 100/99, 686/675<br /> <br /> POTE generator: ~9/7 = 454.512<br /> <br /> Map: [<1 5 8 10 8|, <0 -9 -15 -19 -12|]<br /> EDOs: 29, 37, 66<br /> Badness: 0.0457<br /> <br /> <!-- ws:start:WikiTextHeadingRule:52:<h2> --><h2 id="toc26"><a name="Ammonite-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> Commas: 55/54, 91/90, 100/99, 169/168<br /> <br /> POTE generator: ~13/10 = 454.429<br /> <br /> Map: [<1 5 8 10 8 9|, <0 -9 -15 -19 -12 -14|]<br /> EDOs: 29, 37, 66<br /> Badness: 0.0272<br /> <br /> <!-- ws:start:WikiTextHeadingRule:54:<h1> --><h1 id="toc27"><a name="Ceratitid"></a><!-- ws:end:WikiTextHeadingRule:54 -->Ceratitid</h1> Commas: 250/243, 1728/1715<br /> <br /> POTE generator: ~36/35 = 54.384<br /> <br /> Map: [<1 2 3 3|, <0 -9 -15 -4|]<br /> Wedgie: <<9 15 4 3 -19 -33||<br /> EDOs: 22<br /> Badness: 0.115<br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h2> --><h2 id="toc28"><a name="Ceratitid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2> Commas: 55/54, 100/99, 5324/5145<br /> <br /> POTE generator: ~36/35 = 54.376<br /> <br /> Map: [<1 2 3 3 4|, <0 -9 -15 -4 -12|]<br /> EDOs: 22<br /> Badness: 0.0513<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="Ceratitid-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2> Commas: 55/54, 65/63, 100/99, 352/343<br /> <br /> POTE generator: ~36/35 = 54.665<br /> <br /> Map: [<1 2 3 3 4 4|, <0 -9 -15 -4 -12 -7|]<br /> EDOs: 22<br /> Badness: 0.0447</body></html>