64/63: 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:jdfreivald|jdfreivald]] and made on <tt>2012-10-08 13:41:35 UTC</tt>.

: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-08 13:53:44 UTC</tt>.

: The original revision id was <tt>~~371174932~~</tt>.

: The original revision id was <tt>371179634</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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The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 >.

It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)

It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine family|Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)

If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.

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The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &gt;.

It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that <a class="wiki_link" href="/Porcupine">Porcupine</a>, which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)

It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that <a class="wiki_link" href="/Porcupine%20family">Porcupine</a>, which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)

If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.

@@ 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:jdfreivald|jdfreivald]] and made on <tt>2012-10-08 13:41:35 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-08 13:53:44 UTC</tt>.<br>
-: The original revision id was <tt>371174932</tt>.<br>
+: The original revision id was <tt>371179634</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 10: / Line 10: @@
 The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &gt;.
-It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)
+It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that [[Porcupine family|Porcupine]], which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)
 If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.
@@ Line 21: / Line 21: @@
 The Archytas comma is a 7-limit comma with monzo | 6 -2 0 -1 &amp;gt;.&lt;br /&gt;
 &lt;br /&gt;
-It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;, which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)&lt;br /&gt;
+It is similar to the Didymus or syntonic comma, 81/80, in that when it is tempered out it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Archytas comma, the major third is 9/7. (Note that &lt;a class="wiki_link" href="/Porcupine%20family"&gt;Porcupine&lt;/a&gt;, which tempers out 64/63, uses a minor tone as a generator and generally is considered to have 5/4 major thirds, so it doesn't depend on this equivalency.)&lt;br /&gt;
 &lt;br /&gt;
 If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both 9/8 and 8/7: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.&lt;br /&gt;