Diminished (temperament): Difference between revisions
+ Infobox Regtemp; fix error (strongly consistent circle means tempered comma is less than 25% of a step, which is not the case) |
→Tuning spectrum: Added vals accordingly for tuning spectrum Tags: Mobile edit Mobile web edit Advanced mobile edit |
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| de = Verminderte Temperaturen | | de = Verminderte Temperaturen | ||
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{{Infobox | {{Infobox regtemp | ||
| Title = Diminished | | Title = Diminished | ||
| Subgroups = 2.3.5, 2.3.5.7 | | Subgroups = 2.3.5, 2.3.5.7 | ||
| Comma basis = [[648/625]] (2.3.5) | | Comma basis = [[648/625]] (2.3.5); <br>[[36/35]], [[50/49]] (2.3.5.7) | ||
| Edo join 1 = 4 | Edo join 2 = 12 | | Edo join 1 = 4 | Edo join 2 = 12 | ||
| Mapping = 4; 1 1 1 | | Mapping = 4; 1 1 1 | ||
| | | Generators = 3/2 | ||
| | | Generators tuning = 696.0 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| MOS scales = [[4L 4s]], [[4L 8s]], [[12L 4s]] | | MOS scales = [[4L 4s]], [[4L 8s]], [[12L 4s]] | ||
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| Color name = Quadguti | | Color name = Quadguti | ||
| Odd limit 1 = 5 | Mistuning 1 = 15.6 | Complexity 1 = 8 | | Odd limit 1 = 5 | Mistuning 1 = 15.6 | Complexity 1 = 8 | ||
| Odd limit 2 = | | Odd limit 2 = 7-limit 21 | Mistuning 2 = 33.1 | Complexity 2 = 12 | ||
}} | }} | ||
'''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned. | '''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the [[5-limit]], and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned. | ||
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! Comments | ! Comments | ||
|- | |- | ||
| 2\4 | | [[4edo|2\4]] | ||
| | | | ||
| 600.000 | | 600.000 | ||
| Line 132: | Line 132: | ||
|- | |- | ||
| | | | ||
| 49/48 | | [[49/48]] | ||
| 635.697 | | 635.697 | ||
| | | | ||
|- | |- | ||
| | | | ||
| 7/4 | | [[7/4]] | ||
| 668.826 | | 668.826 | ||
| | | | ||
|- | |- | ||
| | | | ||
| 25/24 | | [[25/24]] | ||
| 670.672 | | 670.672 | ||
| 1/2-comma | | 1/2-comma | ||
|- | |- | ||
| 9\16 | | [[16edo|9\16]] | ||
| | | | ||
| 675.000 | | 675.000 | ||
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|- | |- | ||
| | | | ||
| 21/20 | | [[21/20]] | ||
| 684.467 | | 684.467 | ||
| | | | ||
|- | |- | ||
| | | | ||
| 21/16 | | [[21/16]] | ||
| 685.390 | | 685.390 | ||
| | | | ||
|- | |- | ||
|16\28 | | [[28edo|16\28]] | ||
| | | | ||
| 685.714 | | 685.714 | ||
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|- | |- | ||
| | | | ||
| 5/4 | | [[5/4]] | ||
| 686.314 | | 686.314 | ||
| 1/4-comma | | 1/4-comma | ||
|- | |||
| [[40edo|23\40]] | |||
| | |||
| 690.000 | |||
| 40d val | |||
|- | |||
| [[52edo|30\52]] | |||
| | |||
| 692.308 | |||
| 52dd val | |||
|- | |||
| [[64edo|37\64]] | |||
| | |||
| 693.750 | |||
| 64dd val | |||
|- | |- | ||
| | | | ||
| 15/8 | | [[15/8]] | ||
| 694.134 | | 694.134 | ||
| 1/8-comma | | 1/8-comma | ||
|- | |- | ||
| 7\12 | | [[12edo|7\12]] | ||
| | | | ||
| 700.000 | | 700.000 | ||
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|- | |- | ||
| | | | ||
| 3/2 | | [[3/2]] | ||
| 701.955 | | 701.955 | ||
| Untempered | | Untempered | ||
|- | |||
| [[32edo|19\32]] | |||
| | |||
| 712.500 | |||
| 32cd val | |||
|- | |- | ||
| | | | ||
| 9/5 | | [[9/5]] | ||
| 717.596 | | 717.596 | ||
| -1/4-comma | | -1/4-comma | ||
|- | |- | ||
| | | | ||
| 15/14 | | [[15/14]] | ||
| 719.443 | | 719.443 | ||
| | | | ||
|- | |||
| [[20edo|12\20]] | |||
| | |||
| 720.000 | |||
| 20cd val | |||
|- | |- | ||
| | | | ||
| 9/7 | | [[9/7]] | ||
| 735.084 | | 735.084 | ||
| | | | ||
|- | |- | ||
| 5\8 | | [[8edo|5\8]] | ||
| | | | ||
| 750.000 | | 750.000 | ||