Augmented (temperament): Difference between revisions
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{{Infobox | {{Infobox regtemp | ||
| Title = Augmented | | Title = Augmented | ||
| Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.11 | | Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.11 | ||
| Comma basis = [[128/125]] (5-limit);<br>[[64/63]], [[126/125]] (7-limit);<br>[[56/55]], [[64/63]], [[100/99]] (11-limit) | | Comma basis = [[128/125]] (5-limit); <br>[[64/63]], [[126/125]] (7-limit); <br>[[56/55]], [[64/63]], [[100/99]] (11-limit) | ||
| Edo join 1 = 12 | Edo join 2 = 15 | | Edo join 1 = 12 | Edo join 2 = 15 | ||
| Mapping = 3; 1 0 -2 -2 | | Mapping = 3; 1 0 -2 -2 | ||
| | | Generators = 3/2 | ||
| | | Generators tuning = 711.6 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| MOS scales = [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]] | | MOS scales = [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]] | ||
| Pergen = (P8/3, P5) | | Pergen = (P8/3, P5) | ||
| Odd limit 1 = 7 | Mistuning 1 = 13.7 | Complexity 1 = 12 | | Odd limit 1 = 7 | Mistuning 1 = 13.7 | Complexity 1 = 12 | ||
| Odd limit 2 = | | Odd limit 2 = 11 | Mistuning 2 = 22.4 | Complexity 2 = 15 | ||
}} | }} | ||
'''Augmented''' is a [[regular temperament|temperament]] that sets [[5/4]] to one third of an [[2/1|octave]], [[tempering out]] the diesis, [[128/125]], and has a [[generator]] of a [[3/2|perfect fifth]]. The fifth can be tuned to [[12edo]], but a sharper tuning is often perferred for it to blend with the sharp 5/4. This gives rise to the natural [[7-limit]] [[extension]] (known as '''augene''') that tempers out [[64/63]] and [[126/125]], where the whole tone stands in for [[8/7]][[~]][[9/8]]. | '''Augmented''' is a [[regular temperament|temperament]] that sets [[5/4]] to one third of an [[2/1|octave]], [[tempering out]] the diesis, [[128/125]], and has a [[generator]] of a [[3/2|perfect fifth]]. The fifth can be tuned to [[12edo]], but a sharper tuning is often perferred for it to blend with the sharp 5/4. This gives rise to the natural [[7-limit]] [[extension]] (known as '''augene''') that tempers out [[64/63]] and [[126/125]], where the whole tone stands in for [[8/7]][[~]][[9/8]]. | ||
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| 715.789 | | 715.789 | ||
| | | 57bce val | ||
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