Vengeance: Difference between revisions
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{{Infobox regtemp | |||
| Title = Vengeance | |||
| Subgroups = 2.5.17, 2.5.7.17 | |||
| Comma basis = [[78608/78125]] (2.5.17) <br>[[2023/2000]], [[4165/4096]] (2.5.7.17) | |||
| Edo join 1 = 16 | Edo join 2 = 25 | |||
| Mapping = 1; 3 -5 7 | |||
| Generators = 34/25 | Generators tuning = 527.718 | Optimization method = CWE | |||
| MOS scales = [[2L 5s]], [[7L 2s]] | |||
| Pergen = (P8, M10<sup>5</sup>/3) | |||
| Odd limit 1 = 2.5.7.17 17 | Mistuning 1 = 8.88 | Complexity 1 = 16 | |||
| Odd limit 2 = 2.5.7.17 25 | Mistuning 2 = 8.88 | Complexity 2 = 16 | |||
}} | |||
'''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s|antidiatonic scale]] and [[7L 2s|superdiatonic scale]] 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]]. The name "vengeance' 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]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone. | '''Vengeance''' (CompactStar's name) or '''pentagoth''' (groundfault's and Userminusone's name) is a 2.5.17 [[subgroup temperament]]. It is notable for having a structure similar to [[mavila]] with an [[2L 5s|antidiatonic scale]] and [[7L 2s|superdiatonic scale]] 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]]. The name "vengeance' 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]]. The minor triad is 17:20:25, which makes it far simpler than the major triad of 68:85:100, in contrast to [[5-limit]] major and minor triads as used in mavila and meantone. | ||
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| C | | C | ||
|- | |- | ||
|3 | | 3 | ||
| 383.784 | | 383.784 | ||
| '''5/4''' | | '''5/4''' | ||
| Line 56: | Line 68: | ||
| 767.568 | | 767.568 | ||
| 25/16 | | 25/16 | ||
| | | augmented 5th | ||
| | | A# | ||
|- | |- | ||
| 7 | | 7 | ||