A Survey of Western Music for Mathematically Inclined Students

The close relationship between mathematics and music has been well documented in Western cultures since at least the time of the ancient Greeks. While many connections have been made between math and music over the centuries, it seems that many modern researchers have attempted to create interdisciplinary bridges between these disciplines by using mathematical principles to explain several essential aspects of music: harmony, melody, form, and rhythm. Using these established connections, in addition to several of my own, I have created an undergraduate level survey of Western music course for a population of mathematically inclined students. This approach makes music history comprehensible, relevant, and engaging to my target demographic.

The course is organized into three units. The first unit begins with the music of Ancient Greece and Early Christianity and concludes with music of the Renaissance (roughly 1300-1600). The second unit will cover what classical musicians call the “common practice period” (roughly 1600-1900). This span of time covers three musical eras – Baroque, Classical, and Romantic. The final unit will cover the 20th century up to the present. During this course, I introduce the students to Western music using examples, concepts, terminology, and methodology derived from the world of mathematics. These include Pythagorean mathematics, geometry, simple algebra and fractions, the golden mean, the Fibonacci sequence, matrices, set theory, and many more. I have written the chapters as scripts for an online version of the class. The writing style in the chapters is therefore informal and contrasts with the tone of the other parts of the thesis.