384edo

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← 383edo384edo385edo →
Prime factorization 27 × 3
Step size 3.125¢
Fifth 225\384 (703.125¢) (→75\128)
Semitones (A1:m2) 39:27 (121.9¢ : 84.38¢)
Dual sharp fifth 225\384 (703.125¢) (→75\128)
Dual flat fifth 224\384 (700¢) (→7\12)
Dual major 2nd 65\384 (203.125¢)
Consistency limit 7
Distinct consistency limit 7

384 equal divisions of the octave (384edo), or 384-tone equal temperament (384tet), 384 equal temperament (384et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 384 equal parts of about 3.13 ¢ each.

Theory

384edo is consistent in the 7-limit, tempering out the misty comma [26 -12 -3⟩, and the 5-limit tritriple comma [31 20 -27⟩ in the 5-limit, and 3136/3125, 5120/5103, 250047/250000, and the mistisma 458752/455625 in the 7-limit.

Relation to powers of two

Its adjacent step is known as Pentamu (fifth MIDI-resolution unit, 5mu, 25 = 32 equal divisions of the 12edo semitone).

In addition, in light of 384 being a multiple of 32, 384bc val supports windrose temperament in the 7-limit.

Prime harmonics

Approximation of prime harmonics in 384edo
Harmonic 3 5 7 11 13 17 19 23 29 31 37
Error absolute (¢) +1.170 +1.186 -0.076 -1.318 +0.097 +1.295 -0.638 -0.149 -1.452 -1.286 -1.344
relative (%) +37 +38 -2 -42 +3 +41 -20 -5 -46 -41 -43
Steps
(reduced)
609
(225)
892
(124)
1078
(310)
1328
(176)
1421
(269)
1570
(34)
1631
(95)
1737
(201)
1865
(329)
1902
(366)
2000
(80)

See also