# Pythagorean means

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**Pythagorean means** comprise:

In microtonal terms, the arithmetic mean is the intermediate harmonic, the inverse-arithmetic mean is the intermediate __sub__harmonic, and the geometric mean is the equidistant pitch by cents. Thus the three means of 1/1 and 3/2 are 5/4, 6/5, and sqrt (3/2), respectively.

In math, the three means are known as arithmetic mean (AM), harmonic mean (HM), and geometric mean (GM) respectively. However, *harmonic mean* is said with respect to a length of string to be divided, and collides with the more common usage of *harmonic*, which is said with respect to frequency. For fear of confusion, those terms are avoided and *inverse-arithmetic mean* is preferred instead.