63edo

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 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.

Music:

Seconds and Otonal Shifts by Cam Taylor

those early dreams by Cam Taylor

Early Dreams 2 by Cam Taylor

Improvisation in 12-tone fifths chain in 63EDO by Cam Taylor