63edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author iamcamtaylor and made on 2016-07-08 01:06:56 UTC.
- The original revision id was 586694489.
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Original Wikitext content:
The 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21. 63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7. Audio: https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams https://archive.org/details/17_63EDOEarlyDreamsTwo https://soundcloud.com/cam-taylor-2-1/12tone63edo1
Original HTML content:
<html><head><title>63edo</title></head><body>The 63 equal division divides the octave into 63 equal parts of 19.048 cents each. It tempers out 3125/3072 in the 5-limit and 875/864, 225/224 and 245/243 in the 7-limit, so that it supports magic temperament. In the 11-limit it tempers out 100/99, supporting 11-limit magic, plus 896/891, 385/384 and 640/539. In the 13-limit it tempers put 275/273, 169/168, 640/637, 352/351, 364/363 and 676/675. It provides the optimal patent val for the 29&63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.<br /> <br /> 63 is also a fascinating division to look at in the 23-limit, as its regular augmented fourth (+6 fifths) is less than 0.3c sharp of 23/16, therefore tempering out 729/726. Although it doesn't deal as well with primes 5, 17, and 19, it excels in the 2.3.7.11.13.23 group, and is a great candidate for a rank-1 or rank-2 gentle tuning. As a fifths-system, the diesis after 12 fifths can represent 32:33, 27:28, 88:91, and more, making chains of fifths 12 or longer very useful in covering harmonic and melodic ground while providing a lot of different colour in different keys. A 17-tone fifths chain looks on the surface a little similar to 17edo, but as -17 fifths gets us to 64/63, observing the comma becomes an essential part in progressions favouring prime 7.<br /> <br /> <br /> Audio:<br /> <br /> <!-- ws:start:WikiTextUrlRule:10:https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts --><a class="wiki_link_ext" href="https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts" rel="nofollow">https://soundcloud.com/camtaylor-1/63edobosanquetaxis-8thjuly2016-237111323-seconds-and-otonal-shifts</a><!-- ws:end:WikiTextUrlRule:10 --><br /> <!-- ws:start:WikiTextUrlRule:11:https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams --><a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams" rel="nofollow">https://soundcloud.com/cam-taylor-2-1/17-out-of-63edo-wurly-those-early-dreams</a><!-- ws:end:WikiTextUrlRule:11 --><br /> <!-- ws:start:WikiTextUrlRule:12:https://archive.org/details/17_63EDOEarlyDreamsTwo --><a class="wiki_link_ext" href="https://archive.org/details/17_63EDOEarlyDreamsTwo" rel="nofollow">https://archive.org/details/17_63EDOEarlyDreamsTwo</a><!-- ws:end:WikiTextUrlRule:12 --><br /> <!-- ws:start:WikiTextUrlRule:13:https://soundcloud.com/cam-taylor-2-1/12tone63edo1 --><a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/12tone63edo1" rel="nofollow">https://soundcloud.com/cam-taylor-2-1/12tone63edo1</a><!-- ws:end:WikiTextUrlRule:13 --></body></html>