Abstract
Scales constructed from pure harmonic ratios often contain enharmonic note pairs that do not sound in tune
when played together. We examine the mathematics behind equal tempered scales that avoid this problem
by insisting that the harmonic ratios between any pair of successive notes be identical. The mathematical
problem is to construct equal tempered scales that do a good job of approximating the notes of scales built
from pure harmonic ratios. Particular old and new solutions to these problems are discussed herein.
