768edo

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768edo

769edo →

Prime factorization	28 × 3
Step size	1.5625 ¢
Fifth	449\768 (701.563 ¢)
Semitones (A1:m2)	71:59 (110.9 ¢ : 92.19 ¢)
Consistency limit	7
Distinct consistency limit	7

The 768 equal divisions of the octave (768edo), or 768(-tone) equal temperament (768tet, 768et) when viewed from a regular temperament perspective, divides the octave into 768 equal parts of 1.5625 cents each. Its adjacent step is known as Hexamu (sixth MIDI-resolution unit, 6mu, 2⁶ = 64 equal divisions of the 12edo semitone).

Approximation of prime harmonics in 768edo

Harmonic		3	5	7	11	13	17	19	23	29	31	37
Error	Absolute (¢)	-0.393	-0.376	-0.076	+0.245	+0.097	-0.268	-0.638	-0.149	+0.110	+0.277	+0.218
	Relative (%)	-25.1	-24.1	-4.9	+15.7	+6.2	-17.1	-40.8	-9.6	+7.1	+17.7	+14.0
Steps (reduced)		1217 (449)	1783 (247)	2156 (620)	2657 (353)	2842 (538)	3139 (67)	3262 (190)	3474 (402)	3731 (659)	3805 (733)	4001 (161)

768edo is consistent in the 7-limit, tempering out the mutt comma [-44 -3 21⟩ and the 5-limit commatic comma [-37 38 -10⟩ in the 5-limit, and 65625/65536, 250047/250000, 5250987/5242880, [-12 -5 11 -2⟩, [7 18 -2 -11⟩, and [-36 8 4 5⟩ in the 7-limit.

See also

• Equal multiplications of MIDI-resolution units
  • 24edo (1mu tuning)
  • 48edo (2mu tuning)
  • 96edo (3mu tuning)
  • 192edo (4mu tuning)
  • 384edo (5mu 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)