384edo: Difference between revisions

{{ED intro}}

384edo is [[consistent]] in the [[7-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[misty comma]] {{monzo| 26 -12 -3 }} and provides the [[optimal patent val]] for the 5-limit misty temperament. It also supports the 324 & 384 temperament which is an extension of misty that divides the octave into 12, reaches [[11/7]] and [[13/8]] within two steps, and is representable with a 36-note scale. It also tempers out the 5-limit tritriple comma {{monzo| 31 20 -27 }} in the 5-limit, and [[3136/3125]], [[5120/5103]], [[Landscape comma|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.  

{{Harmonics in equal|384|intervals=prime}}

 

=== Subsets and supersets ===

Since 384 factors into {{factorization|384}}, 384edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, and 192 }}.