192edo

← 191edo

192edo

193edo →

Prime factorization	26 × 3
Step size	6.25 ¢
Fifth	112\192 (700 ¢) (→ 7\12)
Semitones (A1:m2)	16:16 (100 ¢ : 100 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

192edo is closely related to 96edo, but the patent vals differ on the mapping for 7. Using the patent val, it tempers out the pythagorean comma, 531441/524288 in the 3-limit; the Würschmidt comma, 393216/390625 and the unicorn comma, 1594323/1562500 in the 5-limit; 2401/2400, 3136/3125, and 1594323/1568000 in the 7-limit; 243/242, 441/440, 5632/5625, and 131769/131072 in the 11-limit; 676/675, 1287/1280, 1573/1568, and 2704/2695 in the 13-limit. Using the alternative 192f val, 351/350, 1001/1000, 1575/1573, 3584/3575, and 5445/5408 are tempered out in the 13-limit.

Significance in digital audio

Its adjacent step is known as Tetramu (fourth MIDI-resolution unit, 4mu, 2⁴ = 16 equal divisions of the 12edo semitone).

Odd harmonics

Approximation of odd harmonics in 192edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.96	+1.19	-0.08	+2.34	-1.32	-3.03	-0.77	+1.29	+2.49	-2.03	+2.98
	Relative (%)	-31.3	+19.0	-1.2	+37.4	-21.1	-48.4	-12.3	+20.7	+39.8	-32.5	+47.6
Steps (reduced)		304 (112)	446 (62)	539 (155)	609 (33)	664 (88)	710 (134)	750 (174)	785 (17)	816 (48)	843 (75)	869 (101)

See also

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