90edo

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← 89edo90edo91edo →
Prime factorization 2 × 32 × 5
Step size 13.3333¢
Fifth 53\90 (706.667¢)
Semitones (A1:m2) 11:5 (146.7¢ : 66.67¢)
Dual sharp fifth 53\90 (706.667¢)
Dual flat fifth 52\90 (693.333¢) (→26\45)
Dual major 2nd 15\90 (200¢) (→1\6)
Consistency limit 7
Distinct consistency limit 7

90 equal divisions of the octave (abbreviated 90edo), or 90-tone equal temperament (90tet), 90 equal temperament (90et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 90 equal parts of about 13.3 ¢ each. Each step of 90edo represents a frequency ratio of 21/90, or the 90th root of 2. It tempers out 2048/2025 in the 5-limit, 3125/3087 and 245/243 in the 7-limit, 121/120 and 176/175 in the 11-limit, and 275/273 and 169/168 in the 13-limit. It provides the optimal patent val for the 31&90 temperament in the 7-, 11- and 13-limits. Notably, it is the second lowest in a series of four consecutive EDOs to temper out 117440512/117406179.

Approximation of odd harmonics in 90edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +4.71 +0.35 +4.51 -3.91 -4.65 -0.53 +5.06 +1.71 -4.18 -4.11 -1.61
relative (%) +35 +3 +34 -29 -35 -4 +38 +13 -31 -31 -12
Steps
(reduced)
143
(53)
209
(29)
253
(73)
285
(15)
311
(41)
333
(63)
352
(82)
368
(8)
382
(22)
395
(35)
407
(47)

Interval table

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