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"Mediant" also refers to a relationship of musical keys. For example, relative to the key of C major, the key of E major is the mediant. Modulation (changes of key) to the mediant are relatively rare, compared with, say, modulation into the dominant.
In mathematics, the mediant of two fractionss a/x and b/y is (a+b)/(x+y); that is to say, the numerator and denominator of the mediant are the sum of the numerators and denominators of the given fractions respectively.