Pentacircle comma
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author jdfreivald and made on 2012-10-07 12:28:09 UTC.
- The original revision id was 370886248.
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Original Wikitext content:
The Pentacircle Comma, 896/891, is similar to the Didymus or syntonic comma, 81/80, in that 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 Pentacircle comma, the major third is 14/11. Pentacircle can be factored into two superparticular commas, 364/363 and 352/351. 364/363 is the difference between (14/11 * 13/11) and 3/2. Tempering out this comma ensures that a major third and a minor third together add up to a perfect fifth; this isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2. [[Cantonpenta]] is an example of a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma. Finally, see the article on [[Pentacircle Chords]].
Original HTML content:
<html><head><title>pentacircle comma</title></head><body>The Pentacircle Comma, 896/891, is similar to the Didymus or syntonic comma, 81/80, in that 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 Pentacircle comma, the major third is 14/11.<br /> <br /> Pentacircle can be factored into two superparticular commas, 364/363 and 352/351. 364/363 is the difference between (14/11 * 13/11) and 3/2. Tempering out this comma ensures that a major third and a minor third together add up to a perfect fifth; this isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2.<br /> <br /> <a class="wiki_link" href="/Cantonpenta">Cantonpenta</a> is an example of a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the pentacircle comma. Finally, see the article on <a class="wiki_link" href="/Pentacircle%20Chords">Pentacircle Chords</a>.</body></html>