Mediant (operation): Difference between revisions

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 Given a target interval x (written logarithmically in octaves), the [[relative error]] of the mediant of two edo approximations a\m and b\n to x is the sum of the respective relative errors of a\m and b\n. Since x is exactly equal to xm\m in m-edo and xn\n in n-edo, the absolute error of the approximation (a+b)\(m+n) is
-[(a+b)\(m+n) &minus; x](m+n) = (a+b)\(m+n) &minus; x(m+n)\(m+n) = [(a-xm)+(b-xn)]\(m+n).
+(a+b)\(m+n) &minus; x = (a+b)\(m+n) &minus; x(m+n)\(m+n) = [(a-xm)+(b-xn)]\(m+n).
 The relative error in edo steps is thus