Mediant (operation)

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).

The mediant operation can also be used to find generators and scales in edos representing temperaments. For example, the perfect fifth (3/2) in 12edo is 7 steps out of 12, and the fifth in 19edo is 11 steps out of 19. Hence the perfect fifth in 31edo (= 12 + 19) is (7+11)\(12+19) = 18\31.

Wikipedia article on the mediant

also see:

The Noble Mediant: Complex ratios and metastable musical intervals, by Margo Schulter and David Keenan