2/7-comma meantone: Difference between revisions

(11 intermediate revisions by 7 users not shown)

Line 1:

In 2/7-comma meantone, the JI 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 ~~also~~ be described as the regular tuning which tempers out 81/80 and tunes 2 and 25/24 purely.

'''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.

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

== 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 }}

[[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 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.) It is one of the meantone tunings proposed early on, by Gioseffo Zarlino, Francisco Salinas and Vincenzo Galilei. It may also be described as the regular tuning which tempers out 81/80 and tunes 2 and 25/24 purely.
+'''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.
-[http://www.tonalsoft.com/enc/number/2-7cmt.aspx Tonalsoft article on 2/7 comma meantone]
+== 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 }}
+[[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 Encyclopedia | ''2/7-comma meantone'']
+[[Category:Meantone]]
+[[Category:Historical]]