Mediant (operation): Difference between revisions

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In the context of [[JI]] ratios, the '''mediant''' M of two ratios a/c and b/d in lowest terms is M=(a+b)/(c+d). It will always be between the two ratios (a/c < M < b/d, assuming a/c < b/d).

In the context of [[just intonation]] ratios, the '''mediant''' M of two ratios a/c and b/d in lowest terms is M=(a+b)/(c+d). It will always be between the two ratios (a/c < M < b/d, assuming a/c < b/d).

== Examples ==

The following table shows the mediant ''m'' of some fraction pairs ''f1'', ''f2''.

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== Generalization ==

The mediant operation can also be used to find generators and scales in [[edo]]s representing temperaments. For example, the perfect fifth ([[3/2]]) in 12edo which [[support]]s [[meantone]] is 7 steps out of 12, and the fifth in [[19edo]], another meantone tuning, is 11 steps out of 19. Hence the perfect fifth in 31edo (which is a meantone tuning because 31 = 12 + 19; more precisely, the 5-limit [[val]] of 31edo is the sum of the 5-limit vals of 12edo and 19edo) is (7+11)\(12+19) = 18\31, which is in between the sizes of the 12edo fifth and the 19edo one.

== See also ==

* [[Merciful intonation]]

* [http://en.wikipedia.org/wiki/Mediant_(mathematics) Wikipedia article on the mediant]

[[Category:Theory]]

[[Category:Terms]]

[[Category:Interval ~~ratio~~]]

[[Category:Interval]]

[[Category:Elementary math]]

[[Category:Method]]

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-In the context of [[JI]] ratios, the '''mediant''' M of two ratios a/c and b/d in lowest terms is M=(a+b)/(c+d). It will always be between the two ratios (a/c &lt; M &lt; b/d, assuming a/c &lt; b/d).
+{{Wikipedia|Mediant (mathematics)}}
+In the context of [[just intonation]] ratios, the '''mediant''' M of two ratios a/c and b/d in lowest terms is M=(a+b)/(c+d). It will always be between the two ratios (a/c &lt; M &lt; b/d, assuming a/c &lt; b/d).
 == Examples ==
 The following table shows the mediant ''m'' of some fraction pairs ''f1'', ''f2''.
@@ Line 31: / Line 31: @@
 == Generalization ==
 The mediant operation can also be used to find generators and scales in [[edo]]s representing temperaments. For example, the perfect fifth ([[3/2]]) in 12edo which [[support]]s [[meantone]] is 7 steps out of 12, and the fifth in [[19edo]], another meantone tuning, is 11 steps out of 19. Hence the perfect fifth in 31edo (which is a meantone tuning because 31 = 12 + 19; more precisely, the 5-limit [[val]] of 31edo is the sum of the 5-limit vals of 12edo and 19edo) is (7+11)\(12+19) = 18\31, which is in between the sizes of the 12edo fifth and the 19edo one.
 == See also ==
 * [[Merciful intonation]]
-* [http://en.wikipedia.org/wiki/Mediant_(mathematics) Wikipedia article on the mediant]
 [[Category:Theory]]
 [[Category:Terms]]
-[[Category:Interval ratio]]
+[[Category:Interval]]
 [[Category:Elementary math]]
 [[Category:Method]]