2/7-comma meantone: Difference between revisions

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In '''2/7-comma meantone''', the JI fifth of [[3/2]] is flattened by 2/7 of a syntonic comma ([[81/80]]).

'''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]]) – that is, to about 695.81 [[cents]]. 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]] sharply and [[69edo]] flatly, and near perfectly by [[119edo]] using the b val flat 5th.

~~It is one of the meantone tunings proposed early on, by Gioseffo Zarlino, Francisco Salinas and Vincenzo Galilei.~~

== Tuning profile ==

[[Projection map]]:

~~It may be described as the regular tuning which tempers out 81~~/~~80 and tunes~~ 2/~~1 and [[25~~/24]] ~~purely.~~

{| 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 || ]]

|}

~~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)~~.

[[Tuning map]]: {{val| 1200 1895.8103 2783.2414 3358.1035 }}

~~It is approximated roughly by~~ [[~~50edo~~]] ~~and~~ [[~~69edo~~]] ~~sharply and flatly, respectively, and near perfectly~~ by ~~[[119edo]~~] ~~using the b val flat 5th.~~

[[Error map]]: {{val| 0 -6.1447 -3.0723 -10.7224 }}

== Music ==

; [[Juhani Nuorvala]]

* [https://www.youtube.com/watch?v=kus7w1O6pCw ''Ten Chords from a Piece by Feldman''] (2025)

== See also ==

* [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft ~~article on~~ 2/7 comma meantone]

* [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft Encyclopedia | ''2/7-comma meantone'']

[[Category:Meantone]]

[[Category:Historical]]

@@ Line 1: / Line 1: @@
-In '''2/7-comma meantone''', the JI fifth of [[3/2]] is flattened by 2/7 of a syntonic comma ([[81/80]]).
+'''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]]) – that is, to about 695.81 [[cents]]. 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]] sharply and [[69edo]] flatly, and near perfectly by [[119edo]] using the b val flat 5th.
-It is one of the meantone tunings proposed early on, by Gioseffo Zarlino, Francisco Salinas and Vincenzo Galilei.
+== Tuning profile ==
+[[Projection map]]:
-It may be described as the regular tuning which tempers out 81/80 and tunes 2/1 and [[25/24]] purely.
+{| 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 || ]]
+|}
-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).
+[[Tuning map]]: {{val| 1200 1895.8103 2783.2414 3358.1035 }}
-It is approximated roughly by [[50edo]] and [[69edo]] sharply and flatly, respectively, and near perfectly by [[119edo]] using the b val flat 5th.
+[[Error map]]: {{val| 0 -6.1447 -3.0723 -10.7224 }}
+== Music ==
+; [[Juhani Nuorvala]]
+* [https://www.youtube.com/watch?v=kus7w1O6pCw ''Ten Chords from a Piece by Feldman''] (2025)
 == See also ==
-* [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft article on 2/7 comma meantone]
+* [http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft Encyclopedia | ''2/7-comma meantone'']
 [[Category:Meantone]]
 [[Category:Historical]]