Name

Formula

Solution

Mean of octave (2/1)

Arithmetic

a − b = b − c

b = (a + c)/2

B = 3/2 (perfect fifth)

Geometric

a/b = b/c

b = $\sqrt{\text{ac}}$

b = $\sqrt{2}$ (tritone)

Harmonic

(a − b)/a = (b − c)/c

b = 2ac/(a + c)

b = 4/3 (perfect fourth)