1/6-comma meantone: Difference between revisions
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== Fractional projection matrix == | == Fractional projection matrix == | ||
The [[Fractional monzos|fractional projection | The [[Fractional monzos|fractional projection matrix]] defining [[7-limit]] 1/6 comma meantone is | ||
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Revision as of 20:55, 6 November 2021
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. It is closely related to 55edo in terms of its tuning.
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> |