Dominant (temperament): Difference between revisions
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{{Infobox | {{Infobox regtemp | ||
| Title = Dominant | | Title = Dominant | ||
| Subgroups = 2.3.5.7 | | Subgroups = 2.3.5.7 | ||
| Comma basis = [[36/35]], [[64/63]] | | Comma basis = [[36/35]], [[64/63]] | ||
| Edo join 1 = 12 | Edo join 2 = 17c | | Edo join 1 = 12 | Edo join 2 = 17c | ||
| | | Generators = 3/2 | Generators tuning = 701.1 | Optimization method = CWE | ||
| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]] | | MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]] | ||
| Mapping = 1; 1 4 -2 | | Mapping = 1; 1 4 -2 | ||
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== Chords and harmony == | == Chords and harmony == | ||
Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords|didymic]] and [[archytas chords|archytas]]. | Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords|didymic]] and [[archytas chords|archytas]]. The dominant seventh chord represents the harmonic seventh chord, whereas the [[German sixth chord|(German) augmented sixth chord]] is more or less equivalent to meantone's dominant seventh chord, as a tuning of [[28:35:42:50|1–5/4–3/2–25/14]]. | ||
== Tunings == | == Tunings == | ||
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=== Tuning spectrum === | === Tuning spectrum === | ||
{{todo|complete table|comment=add the missing 11- and 13-limit eigenmonzo tunings}} | |||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
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| [[1/5-comma meantone|1/5 syntonic comma]] | | [[1/5-comma meantone|1/5 syntonic comma]] | ||
|- | |- | ||
| [[12edo|7\12]] | | '''[[12edo|7\12]]''' | ||
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| 700.000 | | '''700.000''' | ||
| Lower bound of 7- and 9-odd-limit diamond monotone | | '''Lower bound of 7- and 9-odd-limit diamond monotone''' | ||
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| 1/2 septimal comma | | 1/2 septimal comma | ||
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| [[5edo|3\5]] | | '''[[5edo|3\5]]''' | ||
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| 720.000 | | '''720.000''' | ||
| Upper bound of 7- and 9-odd-limit diamond monotone | | '''Upper bound of 7- and 9-odd-limit diamond monotone''' | ||
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