Porcupine notation: Difference between revisions
Wikispaces>TallKite **Imported revision 630868519 - Original comment: ** |
Wikispaces>TallKite **Imported revision 630868567 - 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:TallKite|TallKite]] and made on <tt>2018-07-11 19: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-07-11 19:34:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>630868567</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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=<span class="commentBody">Kite Giedraitis's approach </span>= | =<span class="commentBody">Kite Giedraitis's approach </span>= | ||
<span class="commentBody"> Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen]] is (P8, P4/3). </span>[[xenharmonic/Ups and Downs Notation|Ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]]<span class="commentBody"> can be used. The generator is vM2, and the enharmonic is v</span><span style="vertical-align: super;">3</span><span class="commentBody">A1 (C^</span><span style="vertical-align: super;">3</span><span class="commentBody"> = C#). The genchain is </span> | <span class="commentBody"> Porcupine divides the perfect 4th into 3 equal steps, thus its [[pergen]] is (P8, P4/3). </span>[[xenharmonic/Ups and Downs Notation|Ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]]<span class="commentBody"> can be used. The generator is vM2, and the enharmonic is v</span><span style="vertical-align: super;">3</span><span class="commentBody">A1 (C^</span><span style="vertical-align: super;">3</span><span class="commentBody"> = C#). The alternate generator is G - E = ^^m2. The genchain is </span> | ||
<span class="commentBody">...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - __**P1**__ - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...</span> | <span class="commentBody">...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - __**P1**__ - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...</span> | ||
<span class="commentBody">In C, this would be </span> | <span class="commentBody">In C, this would be </span> | ||
<span class="commentBody">...C^ - D - Ev - F^ - G - Av - Bb^ - __**C**__ - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...</span> | <span class="commentBody">...C^ - D - Ev - F^ - G - Av - Bb^ - __**C**__ - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...</span> | ||
<span class="commentBody">Unlike the other proposals here, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.</span> | |||
<span class="commentBody">Porcupine[8] in A is A Bv C</span>^ D Ev F^ G Av A. Porcupine[7] would omit Av. | |||
<span class="commentBody">Example comma pump, with brackets indicating an enharmonic equivalence:</span> | <span class="commentBody">Example comma pump, with brackets indicating an enharmonic equivalence:</span> | ||
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Some diagrams by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> to illustrate:<br /> | Some diagrams by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> to illustrate:<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:9:&lt;img src=&quot;/file/view/porcupine%20spectrum%20with%20letter%20names.png/353430856/499x462/porcupine%20spectrum%20with%20letter%20names.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 462px; width: 499px;&quot; /&gt; --><img src="/file/view/porcupine%20spectrum%20with%20letter%20names.png/353430856/499x462/porcupine%20spectrum%20with%20letter%20names.png" alt="porcupine spectrum with letter names.png" title="porcupine spectrum with letter names.png" style="height: 462px; width: 499px;" /><!-- ws:end:WikiTextLocalImageRule:9 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:10:&lt;img src=&quot;/file/view/porcupine%20circles%2022edo.png/353430910/499x462/porcupine%20circles%2022edo.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 462px; width: 499px;&quot; /&gt; --><img src="/file/view/porcupine%20circles%2022edo.png/353430910/499x462/porcupine%20circles%2022edo.png" alt="porcupine circles 22edo.png" title="porcupine circles 22edo.png" style="height: 462px; width: 499px;" /><!-- ws:end:WikiTextLocalImageRule:10 --><br /> | ||
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<span class="messageBody"><!-- ws:start:WikiTextLocalImageRule: | <span class="messageBody"><!-- ws:start:WikiTextLocalImageRule:11:&lt;img src=&quot;/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /><!-- ws:end:WikiTextLocalImageRule:11 --></span><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Kite Giedraitis's approach"></a><!-- ws:end:WikiTextHeadingRule:4 --><span class="commentBody">Kite Giedraitis's approach </span></h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Kite Giedraitis's approach"></a><!-- ws:end:WikiTextHeadingRule:4 --><span class="commentBody">Kite Giedraitis's approach </span></h1> | ||
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<span class="commentBody"> Porcupine divides the perfect 4th into 3 equal steps, thus its <a class="wiki_link" href="/pergen">pergen</a> is (P8, P4/3). </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Ups and downs </a><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">notation</a><span class="commentBody"> can be used. The generator is vM2, and the enharmonic is v</span><span style="vertical-align: super;">3</span><span class="commentBody">A1 (C^</span><span style="vertical-align: super;">3</span><span class="commentBody"> = C#). The genchain is </span><br /> | <span class="commentBody"> Porcupine divides the perfect 4th into 3 equal steps, thus its <a class="wiki_link" href="/pergen">pergen</a> is (P8, P4/3). </span><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Ups and downs </a><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">notation</a><span class="commentBody"> can be used. The generator is vM2, and the enharmonic is v</span><span style="vertical-align: super;">3</span><span class="commentBody">A1 (C^</span><span style="vertical-align: super;">3</span><span class="commentBody"> <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="C#). The alternate generator is G - E"></a><!-- ws:end:WikiTextHeadingRule:6 --> C#). The alternate generator is G - E </h1> | ||
^^m2. The genchain is </span><br /> | |||
<span class="commentBody">...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - <u><strong>P1</strong></u> - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...</span><br /> | <span class="commentBody">...^1 - M2 - vM3 - ^4 - P5 - vM6 - ^m7 - <u><strong>P1</strong></u> - vM2 - ^m3 - P4 - v5 - ^m6 - m7 - v8...</span><br /> | ||
<span class="commentBody">In C, this would be </span><br /> | <span class="commentBody">In C, this would be </span><br /> | ||
<span class="commentBody">...C^ - D - Ev - F^ - G - Av - Bb^ - <u><strong>C</strong></u> - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...</span><br /> | <span class="commentBody">...C^ - D - Ev - F^ - G - Av - Bb^ - <u><strong>C</strong></u> - Dv - Eb^ - F - Gv - Ab^ - Bb - Cv...</span><br /> | ||
<span class="commentBody">Unlike the other proposals here, the notes without ups and downs still form the familiar chain of 5ths ...Eb Bb F C G D A E B F# C#..., and interval arithmetic remains unchanged. Staff notation is as usual, with the addition of up and down accidentals before certain notes.</span><br /> | |||
<br /> | |||
<span class="commentBody">Porcupine[8] in A is A Bv C</span>^ D Ev F^ G Av A. Porcupine[7] would omit Av.<br /> | |||
<br /> | <br /> | ||
<span class="commentBody">Example comma pump, with brackets indicating an enharmonic equivalence:</span><br /> | <span class="commentBody">Example comma pump, with brackets indicating an enharmonic equivalence:</span><br /> | ||