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

Theory

384edo is consistent in the 7-odd-limit. The equal temperament tempers 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.

As a tuning standard

A step of 384edo is known as a pentamu (fifth MIDI-resolution unit, 5mu, 2⁵ = 32 equal divisions of the 12edo semitone). The internal data structure of the 5mu requires one byte, with the first two bits reserved as flags, one to indicate the byte's status as data, and one to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and one other bit which is not used.

Prime harmonics

Approximation of prime harmonics in 384edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.17	+1.19	-0.08	-1.32	+0.10	+1.29	-0.64	-0.15	-1.45	-1.29
	Relative (%)	+0.0	+37.4	+38.0	-2.4	-42.2	+3.1	+41.4	-20.4	-4.8	-46.5	-41.1
Steps (reduced)		384 (0)	609 (225)	892 (124)	1078 (310)	1328 (176)	1421 (269)	1570 (34)	1631 (95)	1737 (201)	1865 (329)	1902 (366)

Subsets and supersets

Since 384 factors into 2⁷ × 3, 384edo has subset edos 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, and 192.

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)

External links

• 5mu / pentamu on Tonalsoft Encyclopedia