EDF: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11~~-30 13~~:28:52 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-01 11:39:06 UTC</tt>.

: The original revision id was <tt>~~601034664~~</tt>.

: The original revision id was <tt>601128146</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] ( http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.

Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an ~~example of it:~~ http://www.youtube.com/watch?v=x_HSMND6RnA

Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an [[http://www.youtube.com/watch?v=x_HSMND6RnA|example]] of it.

[[toc|flat]]

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Division of the 3:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> is still in its infancy. The utility of 3:2 as a base though, is apparent by being one of the strongest consonances after the octave. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Perhaps the first to divide the perfect fifth was <a class="wiki_link" href="/Wendy%20Carlos">Wendy Carlos</a> ( <a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow">http://www.wendycarlos.com/resources/pitch.html</a>). <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> has also made much use of the alpha, beta and gamma scales.

Perhaps the first to divide the perfect fifth was <a class="wiki_link" href="/Wendy%20Carlos">Wendy Carlos</a> ( <a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow">http://www.wendycarlos.com/resources/pitch.html</a>). <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> has also made much use of the alpha, beta and gamma scales.

Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. &quot;Microdiatonic&quot; might be a good term for it if it hasn't been named yet, but in any case here is an ~~example of it: ~~<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=x_HSMND6RnA" rel="nofollow">~~http://www.youtube.com/watch?v=x_HSMND6RnA~~</a>~~~~

Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. &quot;Microdiatonic&quot; might be a good term for it if it hasn't been named yet, but in any case here is an <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=x_HSMND6RnA" rel="nofollow">example</a> of it.

<a href="#Individual pages for EDFs">Individual pages for EDFs</a> | <a href="#EDO-EDF correspondence">EDO-EDF correspondence</a>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-30 13:28:52 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-01 11:39:06 UTC</tt>.<br>
-: The original revision id was <tt>601034664</tt>.<br>
+: The original revision id was <tt>601128146</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 12: / Line 12: @@
 Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] ( http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.
-Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an example of it: http://www.youtube.com/watch?v=x_HSMND6RnA
+Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an [[http://www.youtube.com/watch?v=x_HSMND6RnA|example]] of it.
 [[toc|flat]]
@@ Line 104: / Line 104: @@
 Division of the 3:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of &lt;a class="wiki_link" href="/equivalence"&gt;equivalence&lt;/a&gt; is still in its infancy. The utility of 3:2 as a base though, is apparent by being one of the strongest consonances after the octave. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.&lt;br /&gt;
 &lt;br /&gt;
-Perhaps the first to divide the perfect fifth was &lt;a class="wiki_link" href="/Wendy%20Carlos"&gt;Wendy Carlos&lt;/a&gt; ( &lt;!-- ws:start:WikiTextUrlRule:637:http://www.wendycarlos.com/resources/pitch.html --&gt;&lt;a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow"&gt;http://www.wendycarlos.com/resources/pitch.html&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:637 --&gt;). &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; has also made much use of the alpha, beta and gamma scales.&lt;br /&gt;
+Perhaps the first to divide the perfect fifth was &lt;a class="wiki_link" href="/Wendy%20Carlos"&gt;Wendy Carlos&lt;/a&gt; ( &lt;!-- ws:start:WikiTextUrlRule:638:http://www.wendycarlos.com/resources/pitch.html --&gt;&lt;a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow"&gt;http://www.wendycarlos.com/resources/pitch.html&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:638 --&gt;). &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; has also made much use of the alpha, beta and gamma scales.&lt;br /&gt;
 &lt;br /&gt;
-Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. &amp;quot;Microdiatonic&amp;quot; might be a good term for it if it hasn't been named yet, but in any case here is an example of it: &lt;!-- ws:start:WikiTextUrlRule:638:http://www.youtube.com/watch?v=x_HSMND6RnA --&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=x_HSMND6RnA" rel="nofollow"&gt;http://www.youtube.com/watch?v=x_HSMND6RnA&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:638 --&gt;&lt;br /&gt;
+Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. &amp;quot;Microdiatonic&amp;quot; might be a good term for it if it hasn't been named yet, but in any case here is an &lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=x_HSMND6RnA" rel="nofollow"&gt;example&lt;/a&gt; of it.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextTocRule:4:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#Individual pages for EDFs"&gt;Individual pages for EDFs&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#EDO-EDF correspondence"&gt;EDO-EDF correspondence&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;