Porcupine
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<span style="display: block; text-align: right;">Other languages: [[xenharmonie/Porcupine|Deutsch]] </span> **Porcupine** is a [[Regular Temperaments|linear temperament]] in the [[porcupine family]] that tempers out 250/243, the porcupine [[Comma|comma]], and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-[[Harmonic Limit|limit]], 7-limit, or 11-limit temperament, or a 2.3.5.11 [[Subgroup temperaments|subgroup temperament]]. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy. The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to [[12edo]], and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales. [[image:porcupine.png width="560" height="293"]] ==Interval chain== Main article: [[Porcupine intervals]] ||~ Generators ||~ Cents ||~ Ratios ||~ Ups and Downs notation ||~ Generators ||~ 2/1 inverse ||~ Ratios ||~ Ups and Downs notation || ||= 0 ||> 0.00 ||= 1/1 ||= P1 ||= 0 ||> 1200.00 ||= 2/1 ||= P8 || ||= 1 ||> 162.75 ||= 12/11~11/10~10/9 ||= vM2 = ^^m2 ||= -1 ||> 1037.25 ||= 9/5~20/11~11/6 ||= ^m7 = vvM7 || ||= 2 ||> 325.50 ||= 6/5~11/9 ||= ^m3 = vvM3 ||= -2 ||> 874.50 ||= 18/11~5/3 ||= vM6 = ^^m6 || ||= 3 ||> 488.25 ||= 4/3 ||= P4 ||= -3 ||> 711.75 ||= 3/2 ||= P5 || ||= 4 ||> 651.00 ||= 16/11~22/15 ||= vP5 = ^^d5 ||= -4 ||> 549.00 ||= 15/11~11/8 ||= ^P4 = vvA4 || ||= 5 ||> 813.75 ||= 8/5 ||= ^m6 = vvM6 ||= -5 ||> 386.25 ||= 5/4 ||= vM3 = ^^m3 || ||= 6 ||> 976.50 ||= 7/4~16/9 ||= m7 ||= -6 ||> 223.50 ||= 9/8~8/7 ||= M2 || ||= 7 ||> 1139.25 ||= 48/25~160/81 ||= vP8 = ^^d8 ||= -7 ||> 60.75 ||= 81/80~25/24 ||= ^P1 = vvA1 || ||= 8 ||> 102.00 ||= 16/15~21/20 ||= ^m2 = vvM2 ||= -8 ||> 1098.00 ||= 40/21~15/8 ||= vM7 = ^^m7 || ||= 9 ||> 264.75 ||= 7/6 ||= m3 ||= -9 ||> 935.25 ||= 12/7 ||= M6 || ||= 10 ||> 427.50 ||= 14/11 ||= vP4 = ^^d4 ||= -10 ||> 772.50 ||= 11/7 ||= ^P5 = vvA5 || ||= 11 ||> 590.25 ||= 7/5 ||= ^d5 = vvP5 ||= -11 ||> 609.75 ||= 10/7 ||= vA4 = ^^P4 || ||= 12 ||> 753.00 ||= 14/9 ||= m6 ||= -12 ||> 447.00 ||= 9/7 ||= M3 || The specific tuning shown is the full 11-limit [[POTE tuning]], but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents ([[15edo]]) and as large as 165.5 cents ([[29edo]]). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.) 12/11, 11/10, and 10/9 are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find. The 11/9 interval, usually considered a "neutral third", is in porcupine identical to the 6/5 "minor third". This means that the 27/20 "acute fourth" of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone). The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from <50 to 80 cents in general, represents both 25/24 and 81/80. [[media type="custom" key="11980245"]] ==Spectrum of Porcupine Tunings by Eigenmonzos== ||~ Eigenmonzo ||~ Neutral Second ||~ || || 13/12 || 138.573 || || 13/11 || 144.605 || || 12/11 || 150.637 || || 13/10 || 151.405 || || 6/5 || 157.821 || || 15/13 || 158.710 || || 18/13 || 159.154 || || 2\15 || 160.000 || || 8/7 || 161.471 || || 14/11 || 161.751 || || 7/5 || 162.047 || || 5\37 || 162.162 || || 11/8 || 162.171 13- and 15-limit minimax || || 8\59 || 162.712 || || 5/4 || 162.737 5-limit minimax || || 15/14 || 162.897 || || 7/6 || 162.986 || || 3\22 || 163.636 || || 9/7 || 163.743 7- 9- and 11-limit minimax || || 16/15 || 163.966 || || 7\51 || 164.706 || || 11/10 || 165.004 || || 4\29 || 165.517 || || 15/11 || 165.762 || || 4/3 || 166.015 || || 14/13 || 166.037 || || 11/9 || 173.704 || || 16/13 || 179.736 || || 10/9 || 182.404 || [8/5 12/7] eigenmonzos: [[porcupinewoo15]] [[porcupinewoo22]] ===Spectrum of Porcupinefish Tunings=== || 12/11 || 150.637 || || 6/5 || 157.821 || || 2\15 || 160.000 || || 18/13 || 160.307 || || 15/13 || 160.860 || || 8/7 || 161.471 || || 13/12 || 161.531 || || 14/11 || 161.751 || || 7/5 || 162.047 || || 14/13 || 162.100 || || 13/10 || 162.149 || || 5\37 || 162.162 || || 11/8 || 162.171 || || 16/13 || 162.322 || || 13/11 || 162.368 13- and 15-limit minimax || || 8\59 || 162.712 || || 5/4 || 162.737 || || 15/14 || 162.897 || || 7/6 || 162.986 || || 3\22 || 163.636 || || 9/7 || 163.743 || || 16/15 || 163.966 || || 7\51 || 164.706 || || 11/10 || 165.004 || || 4\29 || 165.517 || || 15/11 || 165.762 || || 4/3 || 166.015 || || 11/9 || 173.704 || || 10/9 || 182.404 || ==History== Porcupine temperament/scales were discovered by [[Dave Keenan]], but didn't have a name until [[Herman Miller]] mentioned that his Mizarian Porcupine Overture in 15-tET had a section that pumps the 250:243 comma. Although this music did not use a Porcupine MOS or MODMOS (which would have 7 or 8 notes), the name was adopted for such scales as well, once the essentially one-to-one relationship between vanishing commas and sequences of DE scales was fully evident. It was clear that even though Herman's piece was in 15, 22 was a porcupine tuning par excellence, and that was an interesting development in itself. ==See also== [[Chords of porcupine]] [[Porcupine Notation]] [[Porcupine modes]] [[Porcupine Album Project]] ==Musical examples== * "[[http://sites.google.com/site/teamouse/home#TOC-Mizarian-music|Mizarian Porcupine Overture]]", Herman Miller, 1999. (15edo, namesake of the temperament) * "[[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095|Glassic]]", Paul Erlich, [[22edo]] (at least the beginning part is in porcupine). * "<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]//</span></span>", Gene Ward Smith and Modest Mussorgsky, [[22edo]]. * "[[http://soundclick.com/share.cfm?id=8839060|being a]]", Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8]. * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3|Playing Gently with Miller's Porcupine]]//</span></span>, [[Chris Vaisvil]] * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3|15 Porcupines in India]]//</span></span>, Sarangi, Tambura and Sitar improvisation by [[Chris Vaisvil]] * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3|15 Quills]]//</span></span> piano solo by Chris Vaisvil * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3|Prickly Side of Love]]//</span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil * <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link">//[[http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3|Porcupine Organ Composition]]//</span> by [[Chris Vaisvil]] * //[[file:xenharmonic/AmongOtherThings2.mp3|Among Other Things 2]]// by Petr Pařízek * //[[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3|Porcupine Comma Pump]]//, by Jake Freivald * [[@http://www.youtube.com/watch?v=DSao0Yg3Tck|Life on Mars]] by Omega9 ==Images== [[image:porcupine8.jpg]]
Original HTML content:
<html><head><title>Porcupine</title></head><body><span style="display: block; text-align: right;">Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/Porcupine">Deutsch</a><br />
</span><br />
<strong>Porcupine</strong> is a <a class="wiki_link" href="/Regular%20Temperaments">linear temperament</a> in the <a class="wiki_link" href="/porcupine%20family">porcupine family</a> that tempers out 250/243, the porcupine <a class="wiki_link" href="/Comma">comma</a>, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-<a class="wiki_link" href="/Harmonic%20Limit">limit</a>, 7-limit, or 11-limit temperament, or a 2.3.5.11 <a class="wiki_link" href="/Subgroup%20temperaments">subgroup temperament</a>. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.<br />
<br />
The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to <a class="wiki_link" href="/12edo">12edo</a>, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.<br />
<br />
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<br />
<!-- ws:start:WikiTextHeadingRule:1:<h2> --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:1 -->Interval chain</h2>
Main article: <a class="wiki_link" href="/Porcupine%20intervals">Porcupine intervals</a><br />
<table class="wiki_table">
<tr>
<th>Generators<br />
</th>
<th>Cents<br />
</th>
<th>Ratios<br />
</th>
<th>Ups and Downs<br />
notation<br />
</th>
<th>Generators<br />
</th>
<th>2/1 inverse<br />
</th>
<th>Ratios<br />
</th>
<th>Ups and Downs<br />
notation<br />
</th>
</tr>
<tr>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: right;">0.00<br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td style="text-align: center;">P1<br />
</td>
<td style="text-align: center;">0<br />
</td>
<td style="text-align: right;">1200.00<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
<td style="text-align: center;">P8<br />
</td>
</tr>
<tr>
<td style="text-align: center;">1<br />
</td>
<td style="text-align: right;">162.75<br />
</td>
<td style="text-align: center;">12/11~11/10~10/9<br />
</td>
<td style="text-align: center;">vM2 = ^^m2<br />
</td>
<td style="text-align: center;">-1<br />
</td>
<td style="text-align: right;">1037.25<br />
</td>
<td style="text-align: center;">9/5~20/11~11/6<br />
</td>
<td style="text-align: center;">^m7 = vvM7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2<br />
</td>
<td style="text-align: right;">325.50<br />
</td>
<td style="text-align: center;">6/5~11/9<br />
</td>
<td style="text-align: center;">^m3 = vvM3<br />
</td>
<td style="text-align: center;">-2<br />
</td>
<td style="text-align: right;">874.50<br />
</td>
<td style="text-align: center;">18/11~5/3<br />
</td>
<td style="text-align: center;">vM6 = ^^m6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3<br />
</td>
<td style="text-align: right;">488.25<br />
</td>
<td style="text-align: center;">4/3<br />
</td>
<td style="text-align: center;">P4<br />
</td>
<td style="text-align: center;">-3<br />
</td>
<td style="text-align: right;">711.75<br />
</td>
<td style="text-align: center;">3/2<br />
</td>
<td style="text-align: center;">P5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4<br />
</td>
<td style="text-align: right;">651.00<br />
</td>
<td style="text-align: center;">16/11~22/15<br />
</td>
<td style="text-align: center;">vP5 = ^^d5<br />
</td>
<td style="text-align: center;">-4<br />
</td>
<td style="text-align: right;">549.00<br />
</td>
<td style="text-align: center;">15/11~11/8<br />
</td>
<td style="text-align: center;">^P4 = vvA4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5<br />
</td>
<td style="text-align: right;">813.75<br />
</td>
<td style="text-align: center;">8/5<br />
</td>
<td style="text-align: center;">^m6 = vvM6<br />
</td>
<td style="text-align: center;">-5<br />
</td>
<td style="text-align: right;">386.25<br />
</td>
<td style="text-align: center;">5/4<br />
</td>
<td style="text-align: center;">vM3 = ^^m3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">6<br />
</td>
<td style="text-align: right;">976.50<br />
</td>
<td style="text-align: center;">7/4~16/9<br />
</td>
<td style="text-align: center;">m7<br />
</td>
<td style="text-align: center;">-6<br />
</td>
<td style="text-align: right;">223.50<br />
</td>
<td style="text-align: center;">9/8~8/7<br />
</td>
<td style="text-align: center;">M2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">7<br />
</td>
<td style="text-align: right;">1139.25<br />
</td>
<td style="text-align: center;">48/25~160/81<br />
</td>
<td style="text-align: center;">vP8 = ^^d8<br />
</td>
<td style="text-align: center;">-7<br />
</td>
<td style="text-align: right;">60.75<br />
</td>
<td style="text-align: center;">81/80~25/24<br />
</td>
<td style="text-align: center;">^P1 = vvA1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">8<br />
</td>
<td style="text-align: right;">102.00<br />
</td>
<td style="text-align: center;">16/15~21/20<br />
</td>
<td style="text-align: center;">^m2 = vvM2<br />
</td>
<td style="text-align: center;">-8<br />
</td>
<td style="text-align: right;">1098.00<br />
</td>
<td style="text-align: center;">40/21~15/8<br />
</td>
<td style="text-align: center;">vM7 = ^^m7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">9<br />
</td>
<td style="text-align: right;">264.75<br />
</td>
<td style="text-align: center;">7/6<br />
</td>
<td style="text-align: center;">m3<br />
</td>
<td style="text-align: center;">-9<br />
</td>
<td style="text-align: right;">935.25<br />
</td>
<td style="text-align: center;">12/7<br />
</td>
<td style="text-align: center;">M6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">10<br />
</td>
<td style="text-align: right;">427.50<br />
</td>
<td style="text-align: center;">14/11<br />
</td>
<td style="text-align: center;">vP4 = ^^d4<br />
</td>
<td style="text-align: center;">-10<br />
</td>
<td style="text-align: right;">772.50<br />
</td>
<td style="text-align: center;">11/7<br />
</td>
<td style="text-align: center;">^P5 = vvA5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">11<br />
</td>
<td style="text-align: right;">590.25<br />
</td>
<td style="text-align: center;">7/5<br />
</td>
<td style="text-align: center;">^d5 = vvP5<br />
</td>
<td style="text-align: center;">-11<br />
</td>
<td style="text-align: right;">609.75<br />
</td>
<td style="text-align: center;">10/7<br />
</td>
<td style="text-align: center;">vA4 = ^^P4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">12<br />
</td>
<td style="text-align: right;">753.00<br />
</td>
<td style="text-align: center;">14/9<br />
</td>
<td style="text-align: center;">m6<br />
</td>
<td style="text-align: center;">-12<br />
</td>
<td style="text-align: right;">447.00<br />
</td>
<td style="text-align: center;">9/7<br />
</td>
<td style="text-align: center;">M3<br />
</td>
</tr>
</table>
The specific tuning shown is the full 11-limit <a class="wiki_link" href="/POTE%20tuning">POTE tuning</a>, but of course there is a range of acceptible porcupine tunings that includes generators as small as 160 cents (<a class="wiki_link" href="/15edo">15edo</a>) and as large as 165.5 cents (<a class="wiki_link" href="/29edo">29edo</a>). (However, the 29edo patent val does not support 11-limit porcupine proper, not annihilating 64/63.)<br />
12/11, 11/10, and 10/9 are all represented by the same interval, the generator. This makes chords such as 8:9:10:11:12 exceptionally common and easy to find.<br />
The 11/9 interval, usually considered a "neutral third", is in porcupine identical to the 6/5 "minor third". This means that the 27/20 "acute fourth" of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone).<br />
The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from <50 to 80 cents in general, represents both 25/24 and 81/80.<br />
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<!-- ws:start:WikiTextHeadingRule:3:<h2> --><h2 id="toc1"><a name="x-Spectrum of Porcupine Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:3 -->Spectrum of Porcupine Tunings by Eigenmonzos</h2>
<table class="wiki_table">
<tr>
<th>Eigenmonzo<br />
</th>
<th>Neutral Second<br />
</th>
<th><br />
</th>
</tr>
<tr>
<td>13/12<br />
</td>
<td>138.573<br />
</td>
</tr>
<tr>
<td>13/11<br />
</td>
<td>144.605<br />
</td>
</tr>
<tr>
<td>12/11<br />
</td>
<td>150.637<br />
</td>
</tr>
<tr>
<td>13/10<br />
</td>
<td>151.405<br />
</td>
</tr>
<tr>
<td>6/5<br />
</td>
<td>157.821<br />
</td>
</tr>
<tr>
<td>15/13<br />
</td>
<td>158.710<br />
</td>
</tr>
<tr>
<td>18/13<br />
</td>
<td>159.154<br />
</td>
</tr>
<tr>
<td>2\15<br />
</td>
<td>160.000<br />
</td>
</tr>
<tr>
<td>8/7<br />
</td>
<td>161.471<br />
</td>
</tr>
<tr>
<td>14/11<br />
</td>
<td>161.751<br />
</td>
</tr>
<tr>
<td>7/5<br />
</td>
<td>162.047<br />
</td>
</tr>
<tr>
<td>5\37<br />
</td>
<td>162.162<br />
</td>
</tr>
<tr>
<td>11/8<br />
</td>
<td>162.171 13- and 15-limit minimax<br />
</td>
</tr>
<tr>
<td>8\59<br />
</td>
<td>162.712<br />
</td>
</tr>
<tr>
<td>5/4<br />
</td>
<td>162.737 5-limit minimax<br />
</td>
</tr>
<tr>
<td>15/14<br />
</td>
<td>162.897<br />
</td>
</tr>
<tr>
<td>7/6<br />
</td>
<td>162.986<br />
</td>
</tr>
<tr>
<td>3\22<br />
</td>
<td>163.636<br />
</td>
</tr>
<tr>
<td>9/7<br />
</td>
<td>163.743 7- 9- and 11-limit minimax<br />
</td>
</tr>
<tr>
<td>16/15<br />
</td>
<td>163.966<br />
</td>
</tr>
<tr>
<td>7\51<br />
</td>
<td>164.706<br />
</td>
</tr>
<tr>
<td>11/10<br />
</td>
<td>165.004<br />
</td>
</tr>
<tr>
<td>4\29<br />
</td>
<td>165.517<br />
</td>
</tr>
<tr>
<td>15/11<br />
</td>
<td>165.762<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>166.015<br />
</td>
</tr>
<tr>
<td>14/13<br />
</td>
<td>166.037<br />
</td>
</tr>
<tr>
<td>11/9<br />
</td>
<td>173.704<br />
</td>
</tr>
<tr>
<td>16/13<br />
</td>
<td>179.736<br />
</td>
</tr>
<tr>
<td>10/9<br />
</td>
<td>182.404<br />
</td>
</tr>
</table>
[8/5 12/7] eigenmonzos: <a class="wiki_link" href="/porcupinewoo15">porcupinewoo15</a> <a class="wiki_link" href="/porcupinewoo22">porcupinewoo22</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:<h3> --><h3 id="toc2"><a name="x-Spectrum of Porcupine Tunings by Eigenmonzos-Spectrum of Porcupinefish Tunings"></a><!-- ws:end:WikiTextHeadingRule:5 -->Spectrum of Porcupinefish Tunings</h3>
<table class="wiki_table">
<tr>
<td>12/11<br />
</td>
<td>150.637<br />
</td>
</tr>
<tr>
<td>6/5<br />
</td>
<td>157.821<br />
</td>
</tr>
<tr>
<td>2\15<br />
</td>
<td>160.000<br />
</td>
</tr>
<tr>
<td>18/13<br />
</td>
<td>160.307<br />
</td>
</tr>
<tr>
<td>15/13<br />
</td>
<td>160.860<br />
</td>
</tr>
<tr>
<td>8/7<br />
</td>
<td>161.471<br />
</td>
</tr>
<tr>
<td>13/12<br />
</td>
<td>161.531<br />
</td>
</tr>
<tr>
<td>14/11<br />
</td>
<td>161.751<br />
</td>
</tr>
<tr>
<td>7/5<br />
</td>
<td>162.047<br />
</td>
</tr>
<tr>
<td>14/13<br />
</td>
<td>162.100<br />
</td>
</tr>
<tr>
<td>13/10<br />
</td>
<td>162.149<br />
</td>
</tr>
<tr>
<td>5\37<br />
</td>
<td>162.162<br />
</td>
</tr>
<tr>
<td>11/8<br />
</td>
<td>162.171<br />
</td>
</tr>
<tr>
<td>16/13<br />
</td>
<td>162.322<br />
</td>
</tr>
<tr>
<td>13/11<br />
</td>
<td>162.368 13- and 15-limit minimax<br />
</td>
</tr>
<tr>
<td>8\59<br />
</td>
<td>162.712<br />
</td>
</tr>
<tr>
<td>5/4<br />
</td>
<td>162.737<br />
</td>
</tr>
<tr>
<td>15/14<br />
</td>
<td>162.897<br />
</td>
</tr>
<tr>
<td>7/6<br />
</td>
<td>162.986<br />
</td>
</tr>
<tr>
<td>3\22<br />
</td>
<td>163.636<br />
</td>
</tr>
<tr>
<td>9/7<br />
</td>
<td>163.743<br />
</td>
</tr>
<tr>
<td>16/15<br />
</td>
<td>163.966<br />
</td>
</tr>
<tr>
<td>7\51<br />
</td>
<td>164.706<br />
</td>
</tr>
<tr>
<td>11/10<br />
</td>
<td>165.004<br />
</td>
</tr>
<tr>
<td>4\29<br />
</td>
<td>165.517<br />
</td>
</tr>
<tr>
<td>15/11<br />
</td>
<td>165.762<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>166.015<br />
</td>
</tr>
<tr>
<td>11/9<br />
</td>
<td>173.704<br />
</td>
</tr>
<tr>
<td>10/9<br />
</td>
<td>182.404<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:7:<h2> --><h2 id="toc3"><a name="x-History"></a><!-- ws:end:WikiTextHeadingRule:7 -->History</h2>
Porcupine temperament/scales were discovered by <a class="wiki_link" href="/Dave%20Keenan">Dave Keenan</a>, but didn't have a name until <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a> mentioned that his Mizarian Porcupine Overture in 15-tET had a section that pumps the 250:243 comma. Although this music did not use a Porcupine MOS or MODMOS (which would have 7 or 8 notes), the name was adopted for such scales as well, once the essentially one-to-one relationship between vanishing commas and sequences of DE scales was fully evident. It was clear that even though Herman's piece was in 15, 22 was a porcupine tuning par excellence, and that was an interesting development in itself.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:9:<h2> --><h2 id="toc4"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:9 -->See also</h2>
<a class="wiki_link" href="/Chords%20of%20porcupine">Chords of porcupine</a><br />
<a class="wiki_link" href="/Porcupine%20Notation">Porcupine Notation</a><br />
<a class="wiki_link" href="/Porcupine%20modes">Porcupine modes</a><br />
<a class="wiki_link" href="/Porcupine%20Album%20Project">Porcupine Album Project</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:11:<h2> --><h2 id="toc5"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:11 -->Musical examples</h2>
<ul><li>"<a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow">Mizarian Porcupine Overture</a>", Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>"<a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a>", Paul Erlich, <a class="wiki_link" href="/22edo">22edo</a> (at least the beginning part is in porcupine).</li><li>"<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a></em></span></span>", Gene Ward Smith and Modest Mussorgsky, <a class="wiki_link" href="/22edo">22edo</a>.</li><li>"<a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow">being a</a>", Andrew Heathwaite, 2010, 22edo, mode 3 1 3 3 3 3 3 3 of Porcupine[8].</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3" rel="nofollow">Playing Gently with Miller's Porcupine</a></em></span></span>, <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3" rel="nofollow">15 Porcupines in India</a></em></span></span>, Sarangi, Tambura and Sitar improvisation by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3" rel="nofollow">15 Quills</a></em></span></span> piano solo by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3" rel="nofollow">Prickly Side of Love</a></em></span></span> - rock band in Porcupine Temperament with vocals by Chris Vaisvil</li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/15-ET/daily20120102-porcupine-organ.mp3" rel="nofollow">Porcupine Organ Composition</a></em></span> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li><li><em><a href="http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/AmongOtherThings2.mp3/319978024/AmongOtherThings2.mp3');">Among Other Things 2</a></em> by Petr Pařízek</li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/porcupine-comma-pump.mp3" rel="nofollow">Porcupine Comma Pump</a></em>, by Jake Freivald</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=DSao0Yg3Tck" rel="nofollow" target="_blank">Life on Mars</a> by Omega9</li></ul><!-- ws:start:WikiTextHeadingRule:13:<h2> --><h2 id="toc6"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:13 -->Images</h2>
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