2/9-comma meantone: Difference between revisions
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'''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''' 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. | 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 == | == Tuning profile == | ||
Revision as of 09:48, 24 August 2024
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
| [⟨ | 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]