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 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). 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 {{w|Lemme Rossi}} in ''Sistema musico ouero Musica speculativa'' (1666), and again by {{w|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.

~~{{todo|expand|comment~~=~~add tuning~~ profile}}

== Tuning profile ==

[[Projection map]]:

[[Category:Meantone]][[Category:Historical ~~temperaments~~]]

{| class="right-all"

|-

| [⟨ || 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]]: {{val| 1200 1897.1758 2788.7033 3371.7583 }}

[[Error map]]: {{val| 0 -4.7792 +2.3896 +2.9323 }}

== Music ==

; [[Jonatan Sersam]]

* [https://www.youtube.com/watch?v=T8kPFzkUAAs ''L'architettura dell'alveare''] (2024)

[[Category:Meantone]]

[[Category:Historical]]

@@ Line 1: / Line 1: @@
 '''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]].
-/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). Of all the known [[historical temperaments]], it is the closest to the optimal 5-, 7-, 11- and 13-limit [[CTE]] tunings for meantone.
+/9-comma meantone was described by {{w|Lemme Rossi}} in ''Sistema musico ouero Musica speculativa'' (1666), and again by {{w|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.
-{{todo|expand|comment=add tuning profile}}
+== Tuning profile ==
+[[Projection map]]:
-[[Category:Meantone]][[Category:Historical temperaments]]
+{| class="right-all"
+|-
+| [⟨ || 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]]: {{val| 1200 1897.1758 2788.7033 3371.7583 }}
+[[Error map]]: {{val| 0 -4.7792 +2.3896 +2.9323 }}
+== Music ==
+; [[Jonatan Sersam]]
+* [https://www.youtube.com/watch?v=T8kPFzkUAAs ''L'architettura dell'alveare''] (2024)
+[[Category:Meantone]]
+[[Category:Historical]]