Flattone: Difference between revisions
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'''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 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 diminshed fifth (C-G𝄫). | |||
11- and 13-limit extensions are fairly obvious, using the heavily tempered [[chromatic semitone]] for the undecimal quartertone of [[33/32]] and the tridecimal third tone of [[27/26]]. 11/8 is an augmented fourth, and 13/8 is a minor sixth, conflated with [[8/5]]. | |||
See [[Meantone family #Flattone]] for technical data. | |||
== Interval chain == | |||
In the following table, odd harmonics 1–13 are in '''bold'''. | |||
{| class="wikitable center-1 right-2" | |||
! # | |||
! Cents* | |||
! Approximate Ratios | |||
|- | |||
| 0 | |||
| 0.0 | |||
| '''1/1''' | |||
|- | |||
| 1 | |||
| 693.0 | |||
| '''3/2''' | |||
|- | |||
| 2 | |||
| 186.1 | |||
| '''9/8''', 10/9, 11/10 | |||
|- | |||
| 3 | |||
| 879.1 | |||
| 5/3 | |||
|- | |||
| 4 | |||
| 372.1 | |||
| '''5/4''', '''16/13''', 26/21 | |||
|- | |||
| 5 | |||
| 1065.1 | |||
| 11/6, 13/7, 15/8, 24/13 | |||
|- | |||
| 6 | |||
| 558.2 | |||
| '''11/8''', 18/13 | |||
|- | |||
| 7 | |||
| 51.2 | |||
| 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 | |||
|- | |||
| 8 | |||
| 744.2 | |||
| 20/13, 32/21 | |||
|- | |||
| 9 | |||
| 237.3 | |||
| '''8/7''', 15/13 | |||
|- | |||
| 10 | |||
| 930.3 | |||
| 12/7 | |||
|- | |||
| 11 | |||
| 423.3 | |||
| 9/7 | |||
|- | |||
| 12 | |||
| 1116.4 | |||
| 27/14, 40/21 | |||
|- | |||
| 13 | |||
| 609.4 | |||
| 10/7 | |||
|} | |||
<nowiki>*</nowiki> in 13-limit CTE tuning | |||
== Scales == | |||
* [[Flattone12]] – 12-tone chromatic scale in 13-limit POTE tuning | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Meantone family]] | [[Category:Meantone family]] | ||
[[Category:Avicennmic temperaments]] | |||
Revision as of 11:56, 9 May 2024
Flattone is an alternative extension to 5-limit meantone, the temperament that tempers out the syntonic comma (81/80). It is generated by a fifth that is typically flatter than that of 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 diminshed fifth (C-G𝄫).
11- and 13-limit extensions are fairly obvious, using the heavily tempered chromatic semitone for the undecimal quartertone of 33/32 and the tridecimal third tone of 27/26. 11/8 is an augmented fourth, and 13/8 is a minor sixth, conflated with 8/5.
See Meantone family #Flattone for technical data.
Interval chain
In the following table, odd harmonics 1–13 are in bold.
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 693.0 | 3/2 |
| 2 | 186.1 | 9/8, 10/9, 11/10 |
| 3 | 879.1 | 5/3 |
| 4 | 372.1 | 5/4, 16/13, 26/21 |
| 5 | 1065.1 | 11/6, 13/7, 15/8, 24/13 |
| 6 | 558.2 | 11/8, 18/13 |
| 7 | 51.2 | 25/24, 27/26, 33/32, 36/35, 55/54, 64/63 |
| 8 | 744.2 | 20/13, 32/21 |
| 9 | 237.3 | 8/7, 15/13 |
| 10 | 930.3 | 12/7 |
| 11 | 423.3 | 9/7 |
| 12 | 1116.4 | 27/14, 40/21 |
| 13 | 609.4 | 10/7 |
* in 13-limit CTE tuning
Scales
- Flattone12 – 12-tone chromatic scale in 13-limit POTE tuning