1/3-comma meantone: Difference between revisions

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In '''1/3-comma meantone''' temperament, each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]).

'''1/3-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]). In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[Eigenmonzo|eigenmonzo (unchanged interval)]] of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (''c''. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter).

~~In other words, 1/3-comma meantone is the specific tuning of~~ [[~~meantone~~]] ~~temperament with an [[eigenmonzo]] (unchanged-interval) of 6/5.~~

== Tuning profile ==

[[Projection map]]:

~~The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by~~ 1/3 ~~syntonic comma (''c''. 7.2 cents) than that in the JI.~~

{| class="right-all"

|-

| [⟨ || 1 || 4/3 || 4/3 || 1/3 || ]

|-

| ⟨ || 0 || -1/3 || -4/3 || -10/3 || ]

|-

| ⟨ || 0 || 1/3 || 4/3 || 10/3 || ]

|-

| ⟨ || 0 || 0 || 0 || 0 || ]]

|}

~~1/3-comma meantone is practically identical to the closed system of~~ [[~~19edo~~]] ~~(although technically there is a slight difference)~~.

[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }}

[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }}

== External links ==

* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Lehrklaenge.de | ''Die mitteltönige Stimmung mit reinen kleinen Terzen''] (explanation of 1/3 comma meantone, German)

* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Die mitteltönige Stimmung mit reinen kleinen Terzen] (explanation of 1/3 comma meantone, German)

* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on [[Tonalsoft Encyclopedia]]

[[Category:Meantone]]

[[Category:Historical]]

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-In '''1/3-comma meantone''' temperament, each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]).
+'''1/3-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]). In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[Eigenmonzo|eigenmonzo (unchanged interval)]] of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (''c''. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter).
-In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[eigenmonzo]] (unchanged-interval) of 6/5.
+== Tuning profile ==
+[[Projection map]]:
-The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (''c''. 7.2 cents) than that in the JI.
+{| class="right-all"
+|-
+| [⟨ || 1 || 4/3 || 4/3 || 1/3 || ]
+|-
+| ⟨ || 0 || -1/3 || -4/3 || -10/3 || ]
+|-
+| ⟨ || 0 || 1/3 || 4/3 || 10/3 || ]
+|-
+| ⟨ || 0 || 0 || 0 || 0 || ]]
+|}
-/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference).
+[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }}
+[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }}
 == External links ==
+* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Lehrklaenge.de | ''Die mitteltönige Stimmung mit reinen kleinen Terzen''] (explanation of 1/3 comma meantone, German)
-* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Die mitteltönige Stimmung mit reinen kleinen Terzen] (explanation of 1/3 comma meantone, German)
+* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on [[Tonalsoft Encyclopedia]]
 [[Category:Meantone]]
 [[Category:Historical]]