Porcupine: Difference between revisions
Wikispaces>hstraub **Imported revision 615953235 - 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:hstraub|hstraub]] and made on <tt>2017- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-09-09 08:22:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>617421575</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 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.) | 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. | 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. | ||
|| [[media type="file" key="OtonalPentad_JI.mp3"]] || [[media type="file" key="OtonalPentad_22edo.mp3"]] || [[media type="file" key="OtonalPentad_29edo.mp3"]] || | |||
|| 8:9:10:11:12 chord, in just intonation || Porcupine-tempered8:9:10:11:12 chord, in [[22edo]] || Porcupine-tempered 8:9:10:11:12 chord, in [[29edo]] || | |||
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 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. | 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. | ||
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Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in <a class="wiki_link" href="/22edo">22edo</a>)<br /> | Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in <a class="wiki_link" href="/22edo">22edo</a>)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:677:&lt;img src=&quot;/file/view/porcupine.png/615923469/porcupine.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/porcupine.png/615923469/porcupine.png" alt="porcupine.png" title="porcupine.png" /><!-- ws:end:WikiTextLocalImageRule:677 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc0"><a name="x-Interval chain"></a><!-- ws:end:WikiTextHeadingRule:5 -->Interval chain</h2> | ||
Main article: <a class="wiki_link" href="/Porcupine%20intervals">Porcupine intervals</a><br /> | Main article: <a class="wiki_link" href="/Porcupine%20intervals">Porcupine intervals</a><br /> | ||
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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 /> | 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 /> | 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 /> | ||
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<td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/OtonalPentad_JI.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;OtonalPentad_JI.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FOtonalPentad_JI.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | |||
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<td><!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/OtonalPentad_22edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;OtonalPentad_22edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FOtonalPentad_22edo.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:2 --><br /> | |||
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<td><!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/OtonalPentad_29edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;OtonalPentad_29edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FOtonalPentad_29edo.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | |||
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<td>8:9:10:11:12 chord, in just intonation<br /> | |||
</td> | |||
<td>Porcupine-tempered8:9:10:11:12 chord, in <a class="wiki_link" href="/22edo">22edo</a><br /> | |||
</td> | |||
<td>Porcupine-tempered 8:9:10:11:12 chord, in <a class="wiki_link" href="/29edo">29edo</a><br /> | |||
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The 11/9 interval, usually considered a &quot;neutral third&quot;, is in porcupine identical to the 6/5 &quot;minor third&quot;. This means that the 27/20 &quot;acute fourth&quot; of the JI diatonic scale is equivalent to 11/8 (rather than becoming 4/3 as in meantone).<br /> | The 11/9 interval, usually considered a &quot;neutral third&quot;, is in porcupine identical to the 6/5 &quot;minor third&quot;. This means that the 27/20 &quot;acute fourth&quot; 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 &lt;50 to 80 cents in general, represents both 25/24 and 81/80.<br /> | The characteristic small interval of porcupine, which is 60.75 cents in this tuning but can range from &lt;50 to 80 cents in general, represents both 25/24 and 81/80.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc1"><a name="x-Spectrum of Porcupine Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:7 -->Spectrum of Porcupine Tunings by Eigenmonzos</h2> | ||
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[8/5 12/7] eigenmonzos: <a class="wiki_link" href="/porcupinewoo15">porcupinewoo15</a> <a class="wiki_link" href="/porcupinewoo22">porcupinewoo22</a><br /> | [8/5 12/7] eigenmonzos: <a class="wiki_link" href="/porcupinewoo15">porcupinewoo15</a> <a class="wiki_link" href="/porcupinewoo22">porcupinewoo22</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h3&gt; --><h3 id="toc2"><a name="x-Spectrum of Porcupine Tunings by Eigenmonzos-Spectrum of Porcupinefish Tunings"></a><!-- ws:end:WikiTextHeadingRule:9 -->Spectrum of Porcupinefish Tunings</h3> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc3"><a name="x-History"></a><!-- ws:end:WikiTextHeadingRule:11 -->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 /> | 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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc4"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:13 -->See also</h2> | ||
<a class="wiki_link" href="/Chords%20of%20porcupine">Chords of porcupine</a><br /> | <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%20Notation">Porcupine Notation</a><br /> | ||
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<a class="wiki_link" href="/Porcupine%20Album%20Project">Porcupine Album Project</a><br /> | <a class="wiki_link" href="/Porcupine%20Album%20Project">Porcupine Album Project</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h2&gt; --><h2 id="toc5"><a name="x-Musical examples"></a><!-- ws:end:WikiTextHeadingRule:15 -->Musical examples</h2> | ||
<ul><li>&quot;<a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow">Mizarian Porcupine Overture</a>&quot;, Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>&quot;<a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a>&quot;, Paul Erlich, <a class="wiki_link" href="/22edo">22edo</a> (at least the beginning part is in porcupine).</li><li>&quot;<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>&quot;, Gene Ward Smith and Modest Mussorgsky, <a class="wiki_link" href="/22edo">22edo</a>.</li><li>&quot;<a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow">being a</a>&quot;, 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: | <ul><li>&quot;<a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/home#TOC-Mizarian-music" rel="nofollow">Mizarian Porcupine Overture</a>&quot;, Herman Miller, 1999. (15edo, namesake of the temperament)</li><li>&quot;<a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a>&quot;, Paul Erlich, <a class="wiki_link" href="/22edo">22edo</a> (at least the beginning part is in porcupine).</li><li>&quot;<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>&quot;, Gene Ward Smith and Modest Mussorgsky, <a class="wiki_link" href="/22edo">22edo</a>.</li><li>&quot;<a class="wiki_link_ext" href="http://soundclick.com/share.cfm?id=8839060" rel="nofollow">being a</a>&quot;, 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:17:&lt;h2&gt; --><h2 id="toc6"><a name="x-Images"></a><!-- ws:end:WikiTextHeadingRule:17 -->Images</h2> | ||
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