1/6-comma meantone: Difference between revisions
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== Links == | == Links == | ||
* [http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink] | * [http://music.case.edu/~rwd/baroquetemp/XMT.intro.html Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone] by Ross W. Duffin [http://www.webcitation.org/5zW8FuybZ permalink] | ||
* [http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[ | * [http://sonic-arts.org/monzo/55edo/55edo.htm Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone] by [[Joseph Monzo]] [http://www.webcitation.org/5zW910Jax permalink] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Historical]] | [[Category:Historical]] | ||
Revision as of 08:38, 9 August 2023
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 ratio) 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.
Fractional projection matrix
The fractional projection matrix defining 7-limit 1/6 comma meantone is
| [1 | 0 | 0 | 0> |
| [2/3 | 1/3 | 1/6 | 0> |
| [-4/3 | 4/3 | 2/3 | 0> |
| [-19/3 | 10/3 | 5/3 | 0> |