255edo

← 254edo

255edo

256edo →

Prime factorization	3 × 5 × 17
Step size	4.70588 ¢
Fifth	149\255 (701.176 ¢)
Semitones (A1:m2)	23:20 (108.2 ¢ : 94.12 ¢)
Consistency limit	11
Distinct consistency limit	11

Theory

The equal temperament tempers out the parakleisma, [8 14 -13⟩, and the septendecima, [-52 -17 34⟩, in the 5-limit. In the 7-limit it tempers out cataharry, 19683/19600, mirkwai, 16875/16807 and horwell, 65625/65536, so that it supports the mirkat temperament, and in fact provides the optimal patent val. It also gives the optimal patent val for mirkat in the 11-limit, tempering out 540/539, 1375/1372, 3025/3024 and 8019/8000. In the 13-limit it tempers out 847/845, 625/624, 1575/1573 and 1716/1715.

Prime harmonics

Approximation of prime harmonics in 255edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.78	-0.43	+0.59	-0.73	+1.83	-1.43	-1.04	+2.31	+1.01	-1.51
	Relative (%)	+0.0	-16.5	-9.2	+12.4	-15.5	+38.8	-30.3	-22.2	+49.2	+21.5	-32.0
Steps (reduced)		255 (0)	404 (149)	592 (82)	716 (206)	882 (117)	944 (179)	1042 (22)	1083 (63)	1154 (134)	1239 (219)	1263 (243)

Subsets and supersets

Since 255 factors into 3 × 5 × 17, 255edo has subset edos 3, 5, 15, 17, 51, and 85.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-404 255⟩ | [⟨255 404]] | +0.246 | 0.246 | 5.22 |- | 2.3.5 | [8 14 -13⟩, [-36 11 8⟩ | [⟨255 404 592]] | +0.226 | 0.203 | 4.30 |- | 2.3.5.7 | 16875/16807, 19683/19600, 65625/65536 | [⟨255 404 592 716]] | +0.117 | 0.257 | 5.46 |- | 2.3.5.7.11 | 540/539, 1375/1372, 8019/8000, 65625/65536 | [⟨255 404 592 716 882]] | +0.136 | 0.233 | 4.95 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 39\255 | 183.53 | 10/9 | Mirkat (255f) |- | 1 | 52\255 | 244.71 | 15/13 | Subsemifourth (255) |- | 1 | 67\255 | 315.29 | 6/5 | Parakleismic (5-limit) |- | 1 | 74\255 | 348.24 | 11/9 | Eris (255) |- | 3 | 82\255
(3\255) | 385.88
(14.12) | 5/4
(126/125) | Mutt (7-limit) |- | 5 | 53\255
(2\255) | 249.41
(9.41) | 81/70
(176/175) | Hemipental / hemipent (255) / hemipentalis (255f) |- | 5 | 106\255
(4\255) | 498.82
(18.82) | 4/3
(81/80) | Pental (5-limit) |- | 17 | 53\255
(7\255) | 249.41
(32.94) | [-25 -9 17⟩
(1990656/1953125) | Chlorine (5-limit) Template:Rank-2 end Template:Orf