282edo

The 282 equal divisions of the octave (282EDO), or the 282(-tone) equal temperament (282TET, 282ET) when viewed from a regular temperament perspective, is the equal division of the octave into 282 parts of 4.2553 cents each.

Theory

282EDO is the smallest equal temperament uniquely consistent through to the 23 odd-limit, and also the smallest consistent to the 29 odd-limit. It shares the same 3rd, 7th, and 13th harmonics with 94EDO (282 = 3 × 94), as well as 11/10 and 20/17 (supporting the garistearn temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out 16875/16807, 19683/19600 and 65625/65536 in the 7-limit, and 540/539 and 5632/5625 in the 11-limit, so that it provides the optimal patent val for jupiter temperament; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for septisuperfourth temperament. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079.