Why a course in the Mathematics of Music?
To mathematicians, mathematics is an intrinsically beautiful subject. Its objects are pure and precise and seem worthy of study unto themselves. However, to many people, these objects may seem dry, remote, and irrelevant. Still, it is demonstrably clear that mathematics is extraordinarily relevant and essential to nearly every human endeavor; science and engineering, medicine, politics, business, etc.. Indeed, mathematics provides a common language to express so many important aspects of human knowledge that in order to attain a better understand of progress in those areas, one must be capable of grasping basic mathematical concepts.
In order to share the richness and beauty of mathematics with as many people as possible, we try to point out the significance of mathematical thinking by pointing out mathematical links to things that excite people. This is where music can play a crucial role. The great mathematician Gottfried Leibniz who is credited with being one of the inventors of calculus, once said that
“Music is the pleasure the human mind experiences from counting without being aware that it is counting.”
Implicit in this statement is the notion that all of us who appreciate music must, on at least a subconscious level, be appreciating its mathematical structure. It seems plausible therefore that one ought to be able use musical appreciation to motivate attaining better understanding of related mathematics. The purpose of a course in the Mathematics of Music is to expose students who appreciate music to mathematical ideas.
The aim of the pages linked to here, is to, by way of introduction, present to the reader some examples of connections between music and mathematics, and hence a sense for the flavor of the Mathematics of Music course, which will be offered for the first time at Johns Hopkins University in July, 2016.
Students taking the course will be exposed to Mathematica, a software platform that provides tools for working with mathematical objects as well as basic tools for learning how to manipulate sounds on the computer. This will provide a fun and informative framework for mathematical and musical discovery. All of the topics described below lead to many possible investigations that students will explore in the Mathematica playground. Most of the materials in these pages have been developed in Mathematica and the course will provide demonstrations as to how this is done.