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:k9assassin|k9assassin]] and made on <tt>2015-10-07 20:41:32 UTC</tt>.<br>
: 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>561698735</tt>.<br>
: 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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==&lt;span class="messageBody"&gt;William Lynch's Approach &lt;/span&gt;==  
==&lt;span class="messageBody"&gt;William Lynch's Approach &lt;/span&gt;==  
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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//&lt;span class="text_exposed_show"&gt; 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?&lt;/span&gt;//
//&lt;span class="text_exposed_show"&gt; 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?&lt;/span&gt;//
//&lt;span class="commentBody"&gt;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.&lt;/span&gt;//</pre></div>
//&lt;span class="commentBody"&gt;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.&lt;/span&gt;//
 
=&lt;span class="commentBody"&gt;Kite Giedraitis's approach &lt;/span&gt;=
 
[[xenharmonic/Ups and Downs Notation|Ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]]&lt;span class="commentBody"&gt; 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 &lt;/span&gt;
&lt;span class="commentBody"&gt; generator = P4 / 3 = (A4 - A1) / 3 = A4 / 3 - A1 / 3 = M2 - ^&lt;/span&gt;&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span class="commentBody"&gt;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.&lt;/span&gt;
 
&lt;span class="commentBody"&gt;For sharp-3 edos, the genchain is &lt;/span&gt;
&lt;span class="commentBody"&gt;P1 -- vM2 -- ^m3 -- P4 -- v5 -- ^m6 -- m7 -- v8&lt;/span&gt;
 
&lt;span class="commentBody"&gt; &lt;/span&gt;
&lt;span class="commentBody"&gt;
&lt;/span&gt;</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Mike%20Battaglia"&gt;Mike Battaglia&lt;/a&gt; posted the following description of a &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; notation to the Xenharmonic Alliance Facebook Group:&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Mike%20Battaglia"&gt;Mike Battaglia&lt;/a&gt; posted the following description of a &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; notation to the Xenharmonic Alliance Facebook Group:&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-William Lynch's Approach"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span class="messageBody"&gt;William Lynch's Approach &lt;/span&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-William Lynch's Approach"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;span class="messageBody"&gt;William Lynch's Approach &lt;/span&gt;&lt;/h2&gt;
  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. &lt;br /&gt;
  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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;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 &amp;quot;ð&amp;quot; from the scale.&lt;/em&gt; &lt;br /&gt;
&lt;em&gt;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 &amp;quot;ð&amp;quot; from the scale.&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;Porcupine 8 alphabet: b c d ð&lt;/em&gt; &lt;em&gt;e f þ æ&lt;/em&gt; &lt;br /&gt;
&lt;em&gt;Porcupine 8 alphabet: b c d ð&lt;/em&gt; &lt;em&gt;e f þ æ&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;Porcupine 7 alphabet:&lt;/em&gt; &lt;em&gt;b c d e f þ æ&lt;/em&gt; &lt;br /&gt;
&lt;em&gt;Porcupine 7 alphabet:&lt;/em&gt; &lt;em&gt;b c d e f þ æ&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;------------&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;------------&lt;/em&gt;&lt;br /&gt;
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Some diagrams by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; to illustrate:&lt;br /&gt;
Some diagrams by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; to illustrate:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:5:&amp;lt;img src=&amp;quot;/file/view/porcupine%20spectrum%20with%20letter%20names.png/353430856/499x462/porcupine%20spectrum%20with%20letter%20names.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 462px; width: 499px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:5 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:7:&amp;lt;img src=&amp;quot;/file/view/porcupine%20spectrum%20with%20letter%20names.png/353430856/499x462/porcupine%20spectrum%20with%20letter%20names.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 462px; width: 499px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:7 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:6:&amp;lt;img src=&amp;quot;/file/view/porcupine%20circles%2022edo.png/353430910/499x462/porcupine%20circles%2022edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 462px; width: 499px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:6 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:8:&amp;lt;img src=&amp;quot;/file/view/porcupine%20circles%2022edo.png/353430910/499x462/porcupine%20circles%2022edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 462px; width: 499px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:8 --&gt;&lt;br /&gt;
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&lt;span class="messageBody"&gt;&lt;!-- ws:start:WikiTextLocalImageRule:7:&amp;lt;img src=&amp;quot;/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:7 --&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span class="messageBody"&gt;&lt;!-- ws:start:WikiTextLocalImageRule:9:&amp;lt;img src=&amp;quot;/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:9 --&gt;&lt;/span&gt;&lt;br /&gt;
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&lt;em&gt;&lt;span class="text_exposed_show"&gt; That's my proposal for expanding the Porcupine notation &lt;a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow"&gt;Mike Battaglia&lt;/a&gt; has described into the 13-limit. Does this make sense to people?&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;&lt;span class="text_exposed_show"&gt; That's my proposal for expanding the Porcupine notation &lt;a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow"&gt;Mike Battaglia&lt;/a&gt; has described into the 13-limit. Does this make sense to people?&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
&lt;em&gt;&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &amp;quot;staff switches&amp;quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.&lt;/span&gt;&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;em&gt;&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &amp;quot;staff switches&amp;quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Kite Giedraitis's approach"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;span class="commentBody"&gt;Kite Giedraitis's approach &lt;/span&gt;&lt;/h1&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;Ups and downs &lt;/a&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;span class="commentBody"&gt; 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 &lt;/span&gt;&lt;br /&gt;
&lt;span class="commentBody"&gt; generator = P4 / 3 = (A4 - A1) / 3 = A4 / 3 - A1 / 3 = M2 - ^&lt;/span&gt;&lt;span style="font-size: 90%; vertical-align: super;"&gt;3&lt;/span&gt;&lt;span class="commentBody"&gt;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.&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;span class="commentBody"&gt;For sharp-3 edos, the genchain is &lt;/span&gt;&lt;br /&gt;
&lt;span class="commentBody"&gt;P1 -- vM2 -- ^m3 -- P4 -- v5 -- ^m6 -- m7 -- v8&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;span class="commentBody"&gt; &lt;/span&gt;&lt;br /&gt;
&lt;span class="commentBody"&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>