Andrew Heathwaite's MOS Investigations: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~Andrew_Heathwaite~~|~~Andrew_Heathwaite~~]] and made on <tt>~~2011~~-12-~~23 03~~:47:15 UTC</tt>.

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2012-12-10 14:33:53 UTC</tt>.

: The original revision id was <tt>~~288263754~~</tt>.

: The original revision id was <tt>390971520</tt>.

: The revision comment was: <tt></tt>

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* MB writes about Porcupine's [[MODMOS Scales|MODMOS]] scales (which I will deal with more below), summarizing, "In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism."

* MB: "In porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3."

* ~~Igliashon Jones~~ argues that Porcupine doesn't do that great in the 5-limit after all, saying, "Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make." (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)

* Someone argues that Porcupine doesn't do that great in the 5-limit after all, saying, "Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make." (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)

* In response to the above, Keenan Pepper says, "You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!" (This is relevant to my work, which assumes composers want 11-limit approximations.)

* I (Andrew Heathwaite) added, "...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy."

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I'm going to zoom in on <a class="wiki_link" href="/Porcupine">Porcupine Temperament</a>, which has been mentioned on the Facebook Xenharmonic Alliance page recently as a xenharmonic alternative to Meantone. Here's a little list of some of the things that were mentioned, so they can be collected in one place and not lost forever in the impenetrable Facebook Caverns:

<ul><li>Keenan Pepper writes about how Porcupine tempers 27/20, 15/11 and 25/18 all to the 11/8 approximation, which, he claims, is a stronger consonance than any of the intervals mentioned.</li><li>Mike Battaglia writes about how 81/80 is &quot;tempered in&quot; to 25/24, making it melodically useful instead of an &quot;irritating mystery interval&quot; which &quot;introduces pitch drift&quot;.</li><li>MB writes about Porcupine's <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales (which I will deal with more below), summarizing, &quot;In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism.&quot;</li><li>MB: &quot;In porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3.&quot;</li><li>~~Igliashon Jones~~ argues that Porcupine doesn't do that great in the 5-limit after all, saying, &quot;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&quot; (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)</li><li>In response to the above, Keenan Pepper says, &quot;You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!&quot; (This is relevant to my work, which assumes composers want 11-limit approximations.)</li><li>I (Andrew Heathwaite) added, &quot;...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy.&quot;</li></ul>

<ul><li>Keenan Pepper writes about how Porcupine tempers 27/20, 15/11 and 25/18 all to the 11/8 approximation, which, he claims, is a stronger consonance than any of the intervals mentioned.</li><li>Mike Battaglia writes about how 81/80 is &quot;tempered in&quot; to 25/24, making it melodically useful instead of an &quot;irritating mystery interval&quot; which &quot;introduces pitch drift&quot;.</li><li>MB writes about Porcupine's <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a> scales (which I will deal with more below), summarizing, &quot;In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism.&quot;</li><li>MB: &quot;In porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3.&quot;</li><li>Someone argues that Porcupine doesn't do that great in the 5-limit after all, saying, &quot;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&quot; (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)</li><li>In response to the above, Keenan Pepper says, &quot;You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!&quot; (This is relevant to my work, which assumes composers want 11-limit approximations.)</li><li>I (Andrew Heathwaite) added, &quot;...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy.&quot;</li></ul>

<h1 id="toc7"><a name="Porcupine Chromaticism"></a>Porcupine Chromaticism</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-23 03:47:15 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2012-12-10 14:33:53 UTC</tt>.<br>
-: The original revision id was <tt>288263754</tt>.<br>
+: The original revision id was <tt>390971520</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>
@@ Line 232: / Line 232: @@
 * MB writes about Porcupine's [[MODMOS Scales|MODMOS]] scales (which I will deal with more below), summarizing, "&lt;span class="commentBody"&gt;In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism.&lt;/span&gt;"
 * MB: "I&lt;span class="commentBody"&gt;n porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3&lt;/span&gt;."
-* Igliashon Jones argues that Porcupine doesn't do that great in the 5-limit after all, saying, "&lt;span class="commentBody"&gt;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&lt;/span&gt;" (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)
+* Someone argues that Porcupine doesn't do that great in the 5-limit after all, saying, "&lt;span class="commentBody"&gt;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&lt;/span&gt;" (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)
 * In response to the above, Keenan Pepper says, "&lt;span class="commentBody"&gt;You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!&lt;/span&gt;" (This is relevant to my work, which assumes composers want 11-limit approximations.)
 * I (Andrew Heathwaite) added, "&lt;span class="commentBody"&gt;...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy.&lt;/span&gt;"
@@ Line 1,574: / Line 1,574: @@
   &lt;br /&gt;
 I'm going to zoom in on &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine Temperament&lt;/a&gt;, which has been mentioned on the Facebook Xenharmonic Alliance page recently as a xenharmonic alternative to Meantone. Here's a little list of some of the things that were mentioned, so they can be collected in one place and not lost forever in the impenetrable Facebook Caverns:&lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;Keenan Pepper writes about how Porcupine tempers 27/20, 15/11 and 25/18 all to the 11/8 approximation, which, he claims, is a stronger consonance than any of the intervals mentioned.&lt;/li&gt;&lt;li&gt;Mike Battaglia writes about how 81/80 is &amp;quot;tempered in&amp;quot; to 25/24, making it melodically useful instead of an &amp;quot;irritating mystery interval&amp;quot; which &amp;quot;introduces pitch drift&amp;quot;.&lt;/li&gt;&lt;li&gt;MB writes about Porcupine's &lt;a class="wiki_link" href="/MODMOS%20Scales"&gt;MODMOS&lt;/a&gt; scales (which I will deal with more below), summarizing, &amp;quot;&lt;span class="commentBody"&gt;In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism.&lt;/span&gt;&amp;quot;&lt;/li&gt;&lt;li&gt;MB: &amp;quot;I&lt;span class="commentBody"&gt;n porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3&lt;/span&gt;.&amp;quot;&lt;/li&gt;&lt;li&gt;Igliashon Jones argues that Porcupine doesn't do that great in the 5-limit after all, saying, &amp;quot;&lt;span class="commentBody"&gt;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&lt;/span&gt;&amp;quot; (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)&lt;/li&gt;&lt;li&gt;In response to the above, Keenan Pepper says, &amp;quot;&lt;span class="commentBody"&gt;You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!&lt;/span&gt;&amp;quot; (This is relevant to my work, which assumes composers want 11-limit approximations.)&lt;/li&gt;&lt;li&gt;I (Andrew Heathwaite) added, &amp;quot;&lt;span class="commentBody"&gt;...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy.&lt;/span&gt;&amp;quot;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Keenan Pepper writes about how Porcupine tempers 27/20, 15/11 and 25/18 all to the 11/8 approximation, which, he claims, is a stronger consonance than any of the intervals mentioned.&lt;/li&gt;&lt;li&gt;Mike Battaglia writes about how 81/80 is &amp;quot;tempered in&amp;quot; to 25/24, making it melodically useful instead of an &amp;quot;irritating mystery interval&amp;quot; which &amp;quot;introduces pitch drift&amp;quot;.&lt;/li&gt;&lt;li&gt;MB writes about Porcupine's &lt;a class="wiki_link" href="/MODMOS%20Scales"&gt;MODMOS&lt;/a&gt; scales (which I will deal with more below), summarizing, &amp;quot;&lt;span class="commentBody"&gt;In short, when you're playing in porcupine, you should never feel like you're limited to just the 7 or 8-note MOS. Just freeform modify notes by L-s as much as you want, deliberately, in a willful attempt to explore porcupine chromaticism. It's even easier than meantone chromaticism.&lt;/span&gt;&amp;quot;&lt;/li&gt;&lt;li&gt;MB: &amp;quot;I&lt;span class="commentBody"&gt;n porcupine, bIII/bIII/bIII = IV/IV. This is the same thing as saying that 6/5 * 6/5 * 6/5 = 4/3 * 4/3&lt;/span&gt;.&amp;quot;&lt;/li&gt;&lt;li&gt;Someone argues that Porcupine doesn't do that great in the 5-limit after all, saying, &amp;quot;&lt;span class="commentBody"&gt;Its only real selling-point over optimal meantone is simpler 7-limit and 11-limit approximations, but that assumes that these are a good in their own right and thus worth sacrificing some 5-limit efficiency; for anyone other than a dyed-in-the-wool xenharmonist, that's a questionable assumption to make.&lt;/span&gt;&amp;quot; (As for me, I want those 7- and 11-limit approximations, and I could care less about a 5-limit temperament to rival meantone. I don't compose in 5-limit temperaments, period.)&lt;/li&gt;&lt;li&gt;In response to the above, Keenan Pepper says, &amp;quot;&lt;span class="commentBody"&gt;You mentioned that almost every interval in the diatonic scale is a 9-limit consonance? Well, every interval in porcupine[7] is an 11-limit consonance! 1/1 10/9 9/8 6/5 5/4 4/3 11/8 16/11 3/2 8/5 5/3 16/9 9/5 2/1. Bam!&lt;/span&gt;&amp;quot; (This is relevant to my work, which assumes composers want 11-limit approximations.)&lt;/li&gt;&lt;li&gt;I (Andrew Heathwaite) added, &amp;quot;&lt;span class="commentBody"&gt;...maybe another description for what Porcupine is good for is a *gateway* from 5 and 7 to 11, for those comfortable with the former and curious about the latter. As a full 11-limit temperament, it is efficient and easy.&lt;/span&gt;&amp;quot;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Porcupine Chromaticism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Porcupine Chromaticism&lt;/h1&gt;
   &lt;br /&gt;