Flattone: Difference between revisions
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{{Infobox regtemp | {{Infobox regtemp | ||
| Comma basis=[[81/80]], [[ | | Title = Flattone | ||
| Edo join 1=19 | | Subgroups = 2.3.5.7 | ||
| Edo join 2=26 | | Comma basis = [[81/80]], [[525/512]] | ||
| Generator=3/2 | | Edo join 1 = 19 | Edo join 2 = 26 | ||
| Generator tuning=693. | | Mapping = 1; 1 4 -9 | ||
| | | Generator = 3/2 | ||
| MOS scales=[[5L 2s]], [[7L 5s]], [[7L 12s]] | | Generator tuning = 693.1 | ||
| Optimization method = CWE | |||
| Pergen=(P8, P5) | | MOS scales = [[5L 2s]], [[7L 5s]], [[7L 12s]] | ||
| Pergen = (P8, P5) | |||
}} | }} | ||
'''Flattone''' is an alternative [[extension]] to [[5-limit]] [[meantone]], the [[temperament]] that [[tempering out|tempers out]] the [[81/80|syntonic comma (81/80)]]. It is generated by a fifth that is typically flatter than that of [[septimal meantone]], and nine of those reach the [[pitch class]] of [[8/7]], so that [[7/4]] is a diminished seventh (C–B𝄫), [[7/6]] is a diminished third (C–E𝄫), and [[7/5]] is a doubly diminished fifth (C–G𝄫). Although 7/4 is simpler than in septimal meantone, the full [[9-odd-limit]] [[tonality diamond]] is more complex as the 5 and 7 are reached by going in opposite directions, while also being less accurate. | '''Flattone''' is an alternative [[extension]] to [[5-limit]] [[meantone]], the [[temperament]] that [[tempering out|tempers out]] the [[81/80|syntonic comma (81/80)]]. It is generated by a fifth that is typically flatter than that of [[septimal meantone]], and nine of those reach the [[pitch class]] of [[8/7]], so that [[7/4]] is a diminished seventh (C–B𝄫), [[7/6]] is a diminished third (C–E𝄫), and [[7/5]] is a doubly diminished fifth (C–G𝄫). Although 7/4 is simpler than in septimal meantone, the full [[9-odd-limit]] [[tonality diamond]] is more complex as the 5 and 7 are reached by going in opposite directions, while also being less accurate. | ||
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|- | |- | ||
| 1 | | 1 | ||
| 693. | | 693.1 | ||
| '''3/2''' | | '''3/2''' | ||
|- | |- | ||
| Line 43: | Line 41: | ||
|- | |- | ||
| 3 | | 3 | ||
| 879. | | 879.2 | ||
| 5/3 | | 5/3 | ||
|- | |- | ||
| 4 | | 4 | ||
| 372. | | 372.2 | ||
| '''5/4''', '''16/13''', 26/21 | | '''5/4''', '''16/13''', 26/21 | ||
|- | |- | ||
| 5 | | 5 | ||
| 1065. | | 1065.3 | ||
| 11/6, 13/7, 15/8, 24/13 | | 11/6, 13/7, 15/8, 24/13 | ||
|- | |- | ||
| 6 | | 6 | ||
| 558. | | 558.3 | ||
| '''11/8''', 18/13 | | '''11/8''', 18/13 | ||
|- | |- | ||
| 7 | | 7 | ||
| 51. | | 51.4 | ||
| 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | | 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | ||
|- | |- | ||
| 8 | | 8 | ||
| 744. | | 744.4 | ||
| 20/13, 32/21 | | 20/13, 32/21 | ||
|- | |- | ||
| 9 | | 9 | ||
| 237. | | 237.5 | ||
| '''8/7''', 15/13 | | '''8/7''', 15/13 | ||
|- | |- | ||
| 10 | | 10 | ||
| 930. | | 930.5 | ||
| 12/7, 22/13 | | 12/7, 22/13 | ||
|- | |- | ||
| 11 | | 11 | ||
| 423. | | 423.6 | ||
| 9/7 | | 9/7 | ||
|- | |- | ||
| 12 | | 12 | ||
| 1116. | | 1116.6 | ||
| 27/14, 40/21 | | 27/14, 40/21 | ||
|- | |- | ||
| 13 | | 13 | ||
| 609. | | 609.7 | ||
| 10/7 | | 10/7 | ||
|} | |} | ||
<nowiki/>* In 13-limit | <nowiki/>* In 13-limit CWE tuning, octave reduced | ||
=== As a detemperament of 7et === | === As a detemperament of 7et === | ||