37edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2010-10-23 12:45:59 UTC.
- The original revision id was 172988221.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
37edo is the scale derived from dividing the octave into 37 microtonal steps of approximately 32.43 cents each. It offers close approximations to [[OverToneSeries|harmonics]] 5, 7, 11, and 13: 12\37 = 389.2 cents 30\37 = 973.0 cents 17\37 = 551.4 cents 26\37 = 843.2 cents However, the just [[perfect fifth]] of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo: 21\37 = 681.1 cents 22\37 = 713.5 cents 37edo thus has the distinction of being the first [[edo]] which occupies two spaces on the syntonic spectrum. 21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6 "minor third" = 10\37 = 324.3 cents "major third" = 11\37 = 356.8 cents 22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1 "minor third" = 8\37 = 259.5 cents "major third" = 14\37 = 454.1 cents 37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.
Original HTML content:
<html><head><title>37edo</title></head><body>37edo is the scale derived from dividing the octave into 37 microtonal steps of approximately 32.43 cents each. It offers close approximations to <a class="wiki_link" href="/OverToneSeries">harmonics</a> 5, 7, 11, and 13:<br /> <br /> 12\37 = 389.2 cents<br /> 30\37 = 973.0 cents<br /> 17\37 = 551.4 cents<br /> 26\37 = 843.2 cents<br /> <br /> However, the just <a class="wiki_link" href="/perfect%20fifth">perfect fifth</a> of frequency ratio 3:2 is not well-approximated, and falls between two intervals in 37edo:<br /> <br /> 21\37 = 681.1 cents<br /> 22\37 = 713.5 cents<br /> <br /> 37edo thus has the distinction of being the first <a class="wiki_link" href="/edo">edo</a> which occupies two spaces on the syntonic spectrum.<br /> <br /> 21\37 generates an anti-diatonic, or mavila, scale: 5 5 6 5 5 5 6<br /> "minor third" = 10\37 = 324.3 cents<br /> "major third" = 11\37 = 356.8 cents<br /> <br /> 22\37 generates an extreme superpythagorean scale: 7 7 1 7 7 7 1<br /> "minor third" = 8\37 = 259.5 cents<br /> "major third" = 14\37 = 454.1 cents<br /> <br /> 37edo has great potential as a xenharmonic system, which high-prime chords such as 8:10:11:13:14 with no perfect fifths available for common terrestrial progressions.</body></html>