2/9-comma meantone

2/9-comma meantone is a meantone tuning which flattens the perfect fifth by 4.779 cents (2/9 of a syntonic comma). This results in a fifth of 697.176 cents.

2/9-comma meantone was described by Lemme Rossi in Sistema musico ouero Musica speculativa (1666), and again by Moritz Wilhelm Drobisch in Über musikalische Tonbestimmung und Temperatur (1852). It tunes 75/64 pure, and 5/4 and 15/8 are off by 1/9 comma each. Of all the known historical temperaments, it is the closest to the optimal 5-, 7-, 11- and 13-limit CTE tunings for meantone. It is approximated by 74edo sharply and is even closer to 105edo, which is slightly flatter than it.

Tuning profile

Projection map:

[⟨	1	8/9	-4/9	-37/9	]
⟨	0	1/9	4/9	10/9	]
⟨	0	2/9	8/7	20/9	]
⟨	0	0	0	0	]]

Tuning map: ⟨1200 1897.1758 2788.7033 3371.7583]

Mistuning map: ⟨0 -4.7792 +2.3896 +2.9323]

Music

Jonatan Sersam - L'architettura dell'alveare (2024)