255edo

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← 254edo255edo256edo →
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

255 equal divisions of the octave (abbreviated 255edo), or 255-tone equal temperament (255tet), 255 equal temperament (255et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 255 equal parts of about 4.71 ¢ each. Each step of 255edo represents a frequency ratio of 21/255, or the 255th root of 2.

Theory

255et 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 -17 -9 +12 -16 +39 -30 -22 +49 +21 -32
Steps
(reduced)
255
(0)
404
(149)
592
(82)
716
(206)
882
(117)
944
(179)
1042
(22)
1083
(63)
1154
(134)
1239
(219)
1263
(243)

Regular temperament properties

Subgroup Comma List Mapping Optimal 8ve
Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
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

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
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)