69edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author kai.lugheidh and made on 2018-05-15 17:21:24 UTC.
- The original revision id was 629810669.
- 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:
The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes. In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as 126/125 maps to one step. It also supports the 12&69 temperament tempering out 3125/3087 along with 81/80. In the 11-limit it tempers out 99/98, and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.
Original HTML content:
<html><head><title>69edo</title></head><body>The 69 equal division, which divides the octave into 69 equal parts of 17.391 cents each, has been called "the love-child of <a class="wiki_link" href="/23edo">23edo</a> and <a class="wiki_link" href="/quarter-comma%20meantone">quarter-comma meantone</a>". As a meantone system, it is on the flat side, with a fifth of 695.652 cents. It is closer to 2/7-comma meantone than 1/4-comma, and is nearly identical to "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.<br /> <br /> In the 7-limit it is a mohajira system, tempering out 6144/6125, but not a septimal meantone system, as 126/125 maps to one step. It also supports the 12&69 temperament tempering out 3125/3087 along with 81/80. In the 11-limit it tempers out 99/98, and supports the 31&69 variant of mohajira, identical to the standard 11-limit mohajira in 31 but not in 69.</body></html>