Diaschismic

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.

Extensions

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.

List of patent vals

The following patent vals support 2.3.5 Diaschismic, not including vals contorted in 2.3.5.

Edo	Generator (3/2)
2	600.000
14	685.714
12	700.000
70	702.857
58	703.448
46	704.348
126	704.762
80	705.000
114	705.263
148	705.405
34	705.882
124	706.452
90	706.667
56	707.143
78	707.692
22	709.091
54	711.111
32	712.500
10	720.000