Diaschismic

From Xenharmonic Reference
Revision as of 04:31, 28 March 2026 by Inthar (talk | contribs)

Diaschismic, 2.3.5[10 & 12], is a 5-limit temperament equating 45/32 to the half-octave, thereby equating a stack of two 5/4's and two 9/8's to the octave; equivalently, it equates a stack of one 5/4 and two 16/15's to the half-octave. The generator of Diaschismic can be taken to be ~16/15 or ~3/2.

Notable tunings of Diaschismic that are more accurate in the 5-limit are 34edo and 46edo. 22edo is another notable Diaschismic tuning.

Diaschismic has an endoparticular extension that adds prime 17, equating the 16/15 generator to 17/16. Adding prime 7 accurately is harder; Pajara provides a simple albeit lower-accuracy extension to prime 7.