Abstract:

The purpose of this established liberal arts course, A survey of mathematics, is to change student attitudes towards mathematics through an innovative introduction to musical acoustics. This approach is particularly effective for those students who may not like mathematics or may have some phobia towards it. The topics and structure of the course are built around the quadrivium of mathematics attributed to Pythagoras. This includes four disciplines: arithmetic (today's number theory); music; geometry; and astronomy. Added to these topics are: numeration systems; algebra; finance; and probability and statistics. Sequences of musical scale ratios associated with lengths of vibrating strings and the frequencies of related sounds in the ``major'' scale were invented by Pythagoras, Claudius Ptolemy, and musical theorists of the sixteenth-century Renaissance. The study of the development of these three scales and their comparison, together with Mersenne's law of vibrating strings and some work with graphing sine functions, provide students with their first look at the mathematics of music. Music and acoustics provide the vehicle for students to gain a better understanding of the often troublesome areas of ratios, proportions, formulas, and graphs. This paper includes the course outline and structure, examples of topics and assignments, and student response.