1/6-comma meantone

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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.

Tuning profile

Projection map:

[⟨ 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]

Mistuning map: 0 -3.5844 +7.1688 +14.8803]

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