20ed5
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Kosmorsky and made on 2011-09-02 00:48:38 UTC.
- The original revision id was 250237560.
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Original Wikitext content:
20th root of 5 "Hieronymus' Tuning" An [[harmonic entropy]] minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are <span class="commentBody">13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of high-limit harmony it also approximates the harmonics and their pentave reductions:</span> <span class="commentBody">8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.</span> <span class="commentBody">One component of its essence, or one way of looking at it, is constructing it by four tempered 3/2 each of which is divided</span> in 5 tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 the pentave. So calling it some kind of quintuple non-octave meantone makes a certain sense but it goes beyond that, as a temperament making use of the 2nd, 3rd, 5th, 7th, 11th, 13th harmonic factors and probably many more.
Original HTML content:
<html><head><title>20ed5</title></head><body>20th root of 5 "Hieronymus' Tuning"<br /> <br /> An <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> minimum, that has better approximations of a variety of just intervals than Bohlen Pierce (of course, not the same intervals) among which are <span class="commentBody">13/12, 7/6, 14/11, 11/8, 3/2, 13/8, 7/4, 21/11, 33/32, ~9/4, 39/32, 21/16, 10/7, 20/13, 10/3 ... etc. In terms of high-limit harmony it also approximates the harmonics and their pentave reductions:</span><br /> <span class="commentBody">8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.</span><br /> <br /> <span class="commentBody">One component of its essence, or one way of looking at it, is constructing it by four tempered 3/2 each of which is divided</span> in 5 tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 the pentave. So calling it some kind of quintuple non-octave meantone makes a certain sense but it goes beyond that, as a temperament making use of the 2nd, 3rd, 5th, 7th, 11th, 13th harmonic factors and probably many more.</body></html>