Diaschismic: Difference between revisions
From Xenharmonic Reference
mNo edit summary |
mNo edit summary |
||
| Line 5: | Line 5: | ||
[[12edo]] and [[22edo]] are notable Diaschismic tunings. Some tunings of Diaschismic that are more accurate in the 5-limit are [[34edo]] and [[46edo]]. | [[12edo]] and [[22edo]] are notable Diaschismic tunings. Some tunings of Diaschismic that are more accurate in the 5-limit are [[34edo]] and [[46edo]]. | ||
Diaschismic has an [[endoparticular]] extension that adds prime 17, equating the 16/15 generator to 17/16. Adding other primes accurately is harder; [[Pajara]] provides a simple albeit lower-accuracy extension to prime 7. | Diaschismic has an [[endoparticular]] extension that adds prime 17, equating the 16/15 generator to 17/16. Adding other primes accurately is harder; [[Pajara]] provides a simple albeit lower-accuracy extension to prime 7 by tempering out 64/63. | ||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|temperaments}} | {{Cat|temperaments}} | ||
Revision as of 04:39, 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.
12edo and 22edo are notable Diaschismic tunings. Some tunings of Diaschismic that are more accurate in the 5-limit are 34edo and 46edo.
Diaschismic has an endoparticular extension that adds prime 17, equating the 16/15 generator to 17/16. Adding other primes accurately is harder; Pajara provides a simple albeit lower-accuracy extension to prime 7 by tempering out 64/63.
