2/7-comma meantone: Difference between revisions
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'''2/7-comma meantone''' is the tuning of [[meantone]] temperament in which the just perfect fifth of [[3/2]] is flattened by 2/7 of a syntonic comma ([[81/80]]). It is one of the meantone tunings proposed early on, by Gioseffo Zarlino, Francisco Salinas and Vincenzo Galilei. It may be described as the regular tuning which tempers out 81/80 and tunes 2/1 and [[25/24]] purely. It is also the tuning where the major third ([[5/4]]) and the minor third ([[6/5]]) are equally flat from JI by 1/7 syntonic comma (''c''. 3.1 cents). It is approximated roughly by [[50edo]] and [[69edo]] sharply and flatly, respectively, and near perfectly by [[119edo]] using the b val flat 5th. | |||
== Tuning profile == | |||
[[Projection map]]: | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 8/7 || 4/7 || -11/7 || ] | |||
|- | |||
| ⟨ || 0 || -1/7 || -4/7 || -10/7 || ] | |||
|- | |||
| ⟨ || 0 || 2/7 || 8/7 || 20/7 || ] | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || ]] | |||
|} | |||
[[Tuning map]]: {{val| 1200 1895.8103 2783.2414 3358.1035 }} | |||
[[Mistuning map]]: {{val| 0 -6.1447 -3.0723 -10.7224 }} | |||
== See also == | == See also == | ||
* [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft | * [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft Encyclopedia | ''2/7-comma meantone''] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Historical]] | [[Category:Historical]] | ||
Revision as of 08:25, 1 October 2023
2/7-comma meantone is the tuning of meantone temperament in which the just perfect fifth of 3/2 is flattened by 2/7 of a syntonic comma (81/80). It is one of the meantone tunings proposed early on, by Gioseffo Zarlino, Francisco Salinas and Vincenzo Galilei. It may be described as the regular tuning which tempers out 81/80 and tunes 2/1 and 25/24 purely. It is also the tuning where the major third (5/4) and the minor third (6/5) are equally flat from JI by 1/7 syntonic comma (c. 3.1 cents). It is approximated roughly by 50edo and 69edo sharply and flatly, respectively, and near perfectly by 119edo using the b val flat 5th.
Tuning profile
| [⟨ | 1 | 8/7 | 4/7 | -11/7 | ] |
| ⟨ | 0 | -1/7 | -4/7 | -10/7 | ] |
| ⟨ | 0 | 2/7 | 8/7 | 20/7 | ] |
| ⟨ | 0 | 0 | 0 | 0 | ]] |
Tuning map: ⟨1200 1895.8103 2783.2414 3358.1035]
Mistuning map: ⟨0 -6.1447 -3.0723 -10.7224]