This article is intended as a minimal introduction to some basic musical ideas which fall within the intersection of mathematics and music. We discuss the science underlying the construction of Pythagorean and other tunings, giving mathematically clear definitions of the necessary musical terms. Careful distinction is made between the frequential and perceptual measures of pitch. The admissible changes of scale for each of these measures are derived. It is shown that commutative diagrams can provide a useful tool for the construction and analysis of scales. All needed musical notions are explained.
