Music Theory and the Math Behind It
By Andrew Woodruff
Ever wonder how music works, from a math and science perspective? There’s actually a lot of math and physics involved in music! Take this course to explore musical intervals, chords, and tuning … and to understand how these work.
Your instructor, Andy Woodruff, will start by teaching some basic music theory … as needed based on the your background. Then he will explain concepts such as the physics of sound transmission and the math behind scales and intervals. Starting with simple ratios, he will show the mathematical contradictions and trade-offs that we face if we try to “perfectly” tune all the notes of the scale. He will introduce some vocabulary involved with tuning, and he will show the mathematical compromises that we need to make in tuning.
Maybe you love math and you would love to see the math behind music theory. This topic is seldom taught … either by music teachers or by school math teachers. We’re lucky to be able to offer it!
Or maybe you hate math … and you don’t see how math affects your life. Take this class, and you will understand your music better. And you will be able to tune better.
Or maybe you just missed some math classes due to school closures … and you would like to re-connect to math.
This class will work for you, if you are a student of at least 5th grade … or if you are an adult … because Andy adjusts the teaching level to your math background. He will start from the math that you already know … and he’ll teach additional math concepts … with homework that involves both music and math. You’ll learn lots of math and may see math in a new light. After studying with Andy, you will probably become “ahead of grade level” in school math classes. One of his former students (2008) is currently a graduate student in physics at MIT.
This class is appropriate for players of all instruments.
About the Online Teaching Method
Andy Woodruff teaches this course with more than the usual amount of technology at his end. His online teaching desk is outfitted with multiple video cameras (not “webcams”, but high quality cameras). One camera is located overhead to view downward so that you can clearly see what he writes on paper. His setup also includes a video switcher, a graphics tablet for online drawing, and multiple large monitors.
About the Instructor
Andy Woodruff is ideally suited to teach this workshop about the mathematics of music, because he has studied both math and music. In fact, he has pursued dual careers as an engineer and as a cellist.
Regarding engineering, Andy has an ScB degree in physics from Brown University, a Masters degree in electrical engineering from Rensselaer Polytechnic Institute (with a perfect 4.0 GPA), and Professional Engineer licenses in three states.
Regarding music, Andy studied cello with Ronald Feldman of the Boston Symphony. He received chamber music coaching from Noël Regney. Andy is currently a section cellist in the Ridgefield Symphony Orchestra and a member of the Half Mile Common Piano Trio. In the past, he has performed with Trio di Camerati (50 performances in this flute/clarinet/cello trio), Café Musette (75 performances in this violin/cello/guitar/accordion quartet), the Fiddlers’ Brawl (200 performances), the Cumberland String Quartet, and the Vladimiroff Piano Quartet.
Andy came from a family that emphasized both science and music. His parents have PhD’s in physics and math, and his mother worked as a math professor … and she also taught the math of music. Andy’s sister studied viola, and his cousin serves as concertmaster of the Springfield (Missouri) Symphony. Andy started learning about the mathematics of music, as a teenager, by tuning his family’s harpsichord with non-standard tunings.
Andy has been teaching the math of music theory to individual private students since 2005. He presented a workshop on this subject to instrumental teachers, for their continuing education credits, at the Fairfield County String Teachers Association in 2012. And he is currently preparing a video about the subject.