384edo

← 383edo

384edo

385edo →

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

• Equal multiplications of MIDI-resolution units
  • 24edo (1mu tuning)
  • 48edo (2mu tuning)
  • 96edo (3mu tuning)
  • 192edo (4mu tuning)
  • 768edo (6mu tuning)
  • 1536edo (7mu tuning)
  • 3072edo (8mu tuning)
  • 6144edo (9mu tuning)
  • 12288edo (10mu tuning)
  • 24576edo (11mu tuning)
  • 49152edo (12mu tuning)
  • 98304edo (13mu tuning)
  • 196608edo (14mu tuning)