Vengeance: Difference between revisions

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'''Vengeance''' is a 2.5.17 [[subgroup temperament]], which is notable for having an [[2L 5s|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 [[User:CompactStar|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).

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]].

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 '''Vengeance''' is a 2.5.17 [[subgroup temperament]], which is notable for having an [[2L 5s|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 [[User:CompactStar|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).
+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]].