63edo: Difference between revisions

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The <b>63 equal division</b> or <b>63-EDO</b> 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 [[support]]s magic temperament. In the 11-limit it tempers out [[100/99]], supporting 11-limit magic, plus [[896/891]], [[385/384]] and [[540/539]]. In the 13-limit it tempers out 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.

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 736/729. 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.

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 The <b>63 equal division</b> or <b>63-EDO</b> 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 [[support]]s magic temperament. In the 11-limit it tempers out [[100/99]], supporting 11-limit magic, plus [[896/891]], [[385/384]] and [[540/539]]. In the 13-limit it tempers out 275/273, 169/168, 640/637, [[352/351]], [[364/363]] and [[676/675]]. It provides the optimal patent val for the 29&amp;63 temperament in the 7-, 11- and 13-limit. It is divisible by 3, 7, 9 and 21.
-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.
+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 736/729. 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.
 {{Primes in edo|63|columns=10}}