Mozart's Formula, Beethoven and Group Theory

There is an intimate, if not absolutely essential, relationship between mathematics and music. At the very least, they share a large number of the most fundamental properties in common, starting with the fact that the chromatic scale is a simple logarithmic equation (see Chapt. Two, Section 2) and that the basic chords are ratios of the smallest integers. Now few musicians are interested in mathematics for mathematics' sake. However, practically everyone is curious and has wondered at one time or other whether mathematics is somehow involved in the creation of music. Is there some deep, underlying principle that governs both math and music? In addition, there is the established fact that every time we succeeded in applying mathematics to a field, we have made tremendous strides in advancing that field. One way to start investigating this relationship is to study the works of the greatest composers from a mathematical point of view. The following analyses contain no inputs from music theory.