Diaschismic

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Revision as of 04:30, 28 March 2026 by Inthar (talk | contribs) (Created page with "'''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 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 ...")
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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 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.