1/6-comma meantone
1/6-comma meantone is the tuning of meantone temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 cents. This means the fifth is flattened by 1/6 of the syntonic comma (81/80) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone 45/32 is tuned justly, and it can be characterized fully as the regular tuning tempering out 81/80 and tuning 2 and 45/32 justly. 55edo and 67edo approximate it flatly and sharply, respectively, while 122edo using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.[1]
Tuning profile
| [⟨ | 1 | 2/3 | -4/3 | -19/3 | ] |
| ⟨ | 0 | 1/3 | 4/3 | 10/3 | ] |
| ⟨ | 0 | 1/6 | 2/3 | 5/3 | ] |
| ⟨ | 0 | 0 | 0 | 0 | ]] |
Tuning map: ⟨1200 1898.3706 2793.4825 3383.7062]
Error map: ⟨0 -3.5844 +7.1688 +14.8803]
Links
- Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone by Ross W. Duffin (WebCite)
- Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone by Joseph Monzo (Internet Archive WebCite)
References
- ↑ Chesnut, John (1977) Mozart's Teaching of Intonation, Journal of the American Musicological Society Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) doi.org/10.2307/831219, https://www.jstor.org/stable/831219