612edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author keenanpepper and made on 2012-03-29 18:13:24 UTC.
- The original revision id was 315983130.
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Original Wikitext content:
The //612 equal division// divides the octave into 612 equal parts of 1.961 cents each. It is a very strong [[5-limit]] system, a fact noted by Bosanquet and Barbour. It tempers out the sasktel comma, |485 -306>, in the 3-limit and in the 5-limit |-52 -17 34>, the septendecima, |1 -27 18>, the ennealimma, |-53 10 16>, the kwazy comma, |54 -37 2>, the monzisma, |-107 47 14>, the fortune comma, and |161 -84 -12>, the atom. In the 7-limit it tempers out 2401/2400 and 4375/4374, so that it supports [[Ragismic microtemperaments#Ennealimmal|ennealimmal temperament]], and in fact provides the [[optimal patent val]] for ennealimmal. The 7-limit val for 612 can be characterized as the ennealimmal commas plus the kwasy comma. In the 11-limit, it tempers out 3025/3024 and 9801/9800, so that 612 supports [[Ragismic microtemperaments#Ennealimmal|hemiennealimmal temperament]]. The 612 division has been proposed as a logarithmic [[interval size measure]]; since one step is nearly the same size as the schisma, (32805/32768) it's been called the skisma, notated sk. Since 612 is divisible by 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 and 306, it can readily express the step sizes of the 12, 17, 34, 68 and 72 divisions. [[Table of 612edo intervals|Here]] can be found a table of intervals approximated by 612.
Original HTML content:
<html><head><title>612edo</title></head><body>The <em>612 equal division</em> divides the octave into 612 equal parts of 1.961 cents each. It is a very strong <a class="wiki_link" href="/5-limit">5-limit</a> system, a fact noted by Bosanquet and Barbour. It tempers out the sasktel comma, |485 -306>, in the 3-limit and in the 5-limit |-52 -17 34>, the septendecima, |1 -27 18>, the ennealimma, |-53 10 16>, the kwazy comma, |54 -37 2>, the monzisma, |-107 47 14>, the fortune comma, and |161 -84 -12>, the atom. In the 7-limit it tempers out 2401/2400 and 4375/4374, so that it supports <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">ennealimmal temperament</a>, and in fact provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for ennealimmal. The 7-limit val for 612 can be characterized as the ennealimmal commas plus the kwasy comma. In the 11-limit, it tempers out 3025/3024 and 9801/9800, so that 612 supports <a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">hemiennealimmal temperament</a>.<br /> <br /> The 612 division has been proposed as a logarithmic <a class="wiki_link" href="/interval%20size%20measure">interval size measure</a>; since one step is nearly the same size as the schisma, (32805/32768) it's been called the skisma, notated sk. Since 612 is divisible by 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 and 306, it can readily express the step sizes of the 12, 17, 34, 68 and 72 divisions. <a class="wiki_link" href="/Table%20of%20612edo%20intervals">Here</a> can be found a table of intervals approximated by 612.</body></html>