282edo: Difference between revisions

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 [[EDO|equal division of the octave]] into 282 parts of 4.2553 [[cent]]s each.

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|94EDO]] (282 = 3 × 94), as well as [[11/10]] and [[20/17]] (supporting the [[Stearnsmic clan #Garistearn|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|optimal patent val]] for [[Porwell_family|jupiter temperament]]; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for [[Porwell temperaments #Septisuperfourth|septisuperfourth]] temperament. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079.