2/9-comma meantone: Difference between revisions
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Created page for 2/9 comma. Since it was described in both 1666 and 1852, and since it is so close to the CTE tuning, I think it deserves a page :) |
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'''2/9-comma meantone''' is a [[meantone]] tuning which flattens the [[perfect fifth]] by 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 | 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. | ||
== Tuning profile == | |||
[[Projection map]]: | |||
[[Category:Meantone]][[Category:Historical | {| 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]] | |||
Latest revision as of 01:27, 8 November 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]
Error map: ⟨0 -4.7792 +2.3896 +2.9323]
Music
- L'architettura dell'alveare (2024)