Vengeance
Vengeance is a 2.5.17 subgroup temperament, which is notable for having an antidiatonic scale similar to mavila, but being comparatively very low in error and badness, because the flat fifth generator is represented by 25/17 rather than 3/2 (or equivalently, 34/25 rather than 4/3). It is defined by tempering out the comma 78608/78125. Its name was coined by CompactStar and derives from 25/17's name as the "vengeance subfifth". Like with mavila, 3 generators reach the major third represented by 5/4, but the minor third is represented by 20/17. In contrast to 5-limit major and minor triads as used in mavila and meantone, the minor triad is 17:20:25 which makes it far simpler than the major triad of 68:85:100.
The harmonic [7 can be added in a similar way to how mavila is extended to armodue, by having 7/4 reached as -5 generators of 34/25 (or the "minor seventh" in antidiatonic terms).
For technical data, see no-threes subgroup temperaments#Vengeance.
Interval chain
| # | Cents* | Approximate ratios | Melodic antidiatonic notation |
|---|---|---|---|
| 0 | 0.00 | 1/1 | D |
| 1 | 527.928 | 34/25 | G |
* in 2.5.7.17 subgroup CTE tuning WIP