Porcupine notation: Difference between revisions
Wikispaces>k9assassin **Imported revision 561698735 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602867018 - 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: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 06:00:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602867018</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="messageBody">William Lynch's Approach </span>== | ==<span class="messageBody">William Lynch's Approach </span>== | ||
William Lynch generally likes to reinvent the wheel. He proposed a system of notation for 15 EDO based on porcupine[8] as the fundamental scale. | William Lynch generally likes to reinvent the wheel. He proposed a system of notation for 15 EDO based on porcupine[8] as the fundamental scale. | ||
//I think it's worthwhile to explore these scales from scratch with no previous associations. I chose this old-english based alphabet as the nominals of porcupine[8]. They work for porcupine[7] as well if you leave out "ð" from the scale.// | //I think it's worthwhile to explore these scales from scratch with no previous associations. I chose this old-english based alphabet as the nominals of porcupine[8]. They work for porcupine[7] as well if you leave out "ð" from the scale.// | ||
//Porcupine 8 alphabet: b c d ð// //e f þ æ// | //Porcupine 8 alphabet: b c d ð// //e f þ æ// | ||
//Porcupine 7 alphabet:// //b c d e f þ æ// | //Porcupine 7 alphabet:// //b c d e f þ æ// | ||
//------------// | //------------// | ||
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//<span class="text_exposed_show"> That's my proposal for expanding the Porcupine notation [[https://www.facebook.com/MikeBattagliaMusic|Mike Battaglia]] has described into the 13-limit. Does this make sense to people?</span>// | //<span class="text_exposed_show"> That's my proposal for expanding the Porcupine notation [[https://www.facebook.com/MikeBattagliaMusic|Mike Battaglia]] has described into the 13-limit. Does this make sense to people?</span>// | ||
//<span class="commentBody">BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.</span>//</pre></div> | //<span class="commentBody">BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.</span>// | ||
=<span class="commentBody">Kite Giedraitis's approach </span>= | |||
[[xenharmonic/Ups and Downs Notation|Ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]]<span class="commentBody"> can be used even though we don't know which edo we are in. We know that porcupine divides the perfect 4th into 3 equal steps. Also the aug 4th is 3 major 2nds. And from P4 to A4 is A1. So any edo which divides the aug1 into 3 equal steps will temper out porcupine. These are the edos marked on the scale tree as sharp-3, sharp-6, etc. For sharp-3 edos (15, 22, 29, etc.), the generator is </span> | |||
<span class="commentBody"> generator = P4 / 3 = (A4 - A1) / 3 = A4 / 3 - A1 / 3 = M2 - ^</span><span style="font-size: 90%; vertical-align: super;">3</span><span class="commentBody">1 / 3 = M2 - ^1 = vM2. For sharp-6 edos (30, 37, ... 72), we have P4 / 3 = vvM2. Sharp-9 edos are rarely used, but it would be vvvM2.</span> | |||
<span class="commentBody">For sharp-3 edos, the genchain is </span> | |||
<span class="commentBody">P1 -- vM2 -- ^m3 -- P4 -- v5 -- ^m6 -- m7 -- v8</span> | |||
<span class="commentBody"> </span> | |||
<span class="commentBody"> | |||
</span></pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Porcupine Notation</title></head><body><a class="wiki_link" href="/Mike%20Battaglia">Mike Battaglia</a> posted the following description of a <a class="wiki_link" href="/Porcupine">Porcupine</a> notation to the Xenharmonic Alliance Facebook Group:<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Porcupine Notation</title></head><body><a class="wiki_link" href="/Mike%20Battaglia">Mike Battaglia</a> posted the following description of a <a class="wiki_link" href="/Porcupine">Porcupine</a> notation to the Xenharmonic Alliance Facebook Group:<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-William Lynch's Approach"></a><!-- ws:end:WikiTextHeadingRule:2 --><span class="messageBody">William Lynch's Approach </span></h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-William Lynch's Approach"></a><!-- ws:end:WikiTextHeadingRule:2 --><span class="messageBody">William Lynch's Approach </span></h2> | ||
William Lynch generally likes to reinvent the wheel. He proposed a system of notation for 15 EDO based on porcupine[8] as the fundamental scale. <br /> | William Lynch generally likes to reinvent the wheel. He proposed a system of notation for 15 EDO based on porcupine[8] as the fundamental scale.<br /> | ||
<br /> | <br /> | ||
<em>I think it's worthwhile to explore these scales from scratch with no previous associations. I chose this old-english based alphabet as the nominals of porcupine[8]. They work for porcupine[7] as well if you leave out &quot;ð&quot; from the scale.</em> <br /> | <em>I think it's worthwhile to explore these scales from scratch with no previous associations. I chose this old-english based alphabet as the nominals of porcupine[8]. They work for porcupine[7] as well if you leave out &quot;ð&quot; from the scale.</em><br /> | ||
<br /> | <br /> | ||
<em>Porcupine 8 alphabet: b c d ð</em> <em>e f þ æ</em> <br /> | <em>Porcupine 8 alphabet: b c d ð</em> <em>e f þ æ</em><br /> | ||
<em>Porcupine 7 alphabet:</em> <em>b c d e f þ æ</em> <br /> | <em>Porcupine 7 alphabet:</em> <em>b c d e f þ æ</em><br /> | ||
<br /> | <br /> | ||
<em>------------</em><br /> | <em>------------</em><br /> | ||
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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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:7:&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:7 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:8:&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:8 --><br /> | ||
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<span class="messageBody"><!-- ws:start:WikiTextLocalImageRule: | <span class="messageBody"><!-- ws:start:WikiTextLocalImageRule:9:&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:9 --></span><br /> | ||
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<em><span class="text_exposed_show"> That's my proposal for expanding the Porcupine notation <a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow">Mike Battaglia</a> has described into the 13-limit. Does this make sense to people?</span></em><br /> | <em><span class="text_exposed_show"> That's my proposal for expanding the Porcupine notation <a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow">Mike Battaglia</a> has described into the 13-limit. Does this make sense to people?</span></em><br /> | ||
<em><span class="commentBody">BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &quot;staff switches&quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.</span></em></body></html></pre></div> | <em><span class="commentBody">BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &quot;staff switches&quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.</span></em><br /> | ||
<br /> | |||
<!-- 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> | |||
<br /> | |||
<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 even though we don't know which edo we are in. We know that porcupine divides the perfect 4th into 3 equal steps. Also the aug 4th is 3 major 2nds. And from P4 to A4 is A1. So any edo which divides the aug1 into 3 equal steps will temper out porcupine. These are the edos marked on the scale tree as sharp-3, sharp-6, etc. For sharp-3 edos (15, 22, 29, etc.), the generator is </span><br /> | |||
<span class="commentBody"> generator = P4 / 3 = (A4 - A1) / 3 = A4 / 3 - A1 / 3 = M2 - ^</span><span style="font-size: 90%; vertical-align: super;">3</span><span class="commentBody">1 / 3 = M2 - ^1 = vM2. For sharp-6 edos (30, 37, ... 72), we have P4 / 3 = vvM2. Sharp-9 edos are rarely used, but it would be vvvM2.</span><br /> | |||
<br /> | |||
<span class="commentBody">For sharp-3 edos, the genchain is </span><br /> | |||
<span class="commentBody">P1 -- vM2 -- ^m3 -- P4 -- v5 -- ^m6 -- m7 -- v8</span><br /> | |||
<br /> | |||
<span class="commentBody"> </span><br /> | |||
<span class="commentBody"><br /> | |||
</span></body></html></pre></div> | |||