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 |
