Diaschismic: Difference between revisions
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'''Diaschismic''', 2.3.5[10 & 12], is a 5-limit temperament equating 45/32 to the half-octave, thereby | '''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. | 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. | 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. | Notable tunings of Diaschismic that are more accurate in the 5-limit are [[34edo]] and [[46edo]]. [[22edo]] is another notable Diaschismic tuning. | ||
Revision as of 04:31, 28 March 2026
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.
