1/5-comma meantone

1/5-comma meantone is the tuning of meantone temperament in which each perfect fifth is tempered by a fifth of a syntonic comma from its just value of 3/2. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.

The major third (5/4) and the fifth are equally off from JI by 1/5 syntonic comma (c. 4.3 cents), with the major third sharp and the fifth flat. The augmented sixth is exactly 225/128, and for septimal meantone, this means the 7/4 is sharp by a septimal kleisma (225/224).

1/5-comma meantone is practically identical to the closed system of 43edo (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)

Tuning profile

Projection map:

[⟨	1	4/5	-4/5	-5	]
⟨	0	1/5	4/5	2	]
⟨	0	1/5	4/5	2	]
⟨	0	0	0	0	]]

Tuning map: ⟨1200 1897.6537 2790.6150 3376.5374]

Error map: ⟨0 -4.3013 +4.3013 +7.7115]