As a concert pianist and harpsichordist, I am devoted to extracting expression and meaning out of the silent abstractions of a musical score. Behind the preparation for any performance is my stark wonder at how such innovative, suggestive sonic domains are realized by composers, literally out of thin air. We’ll explore some basic mathematic principles that underlie all musical discourse, with a focus, given time constraints, on Western classical music. With recorded and live examples from the keyboard, we’ll look at Harmony: from the acoustical demonstrations of Pythagoras, through the contentious battles over tunings and temperaments during the Baroque, to the microtonal experiments of modern times in the work of Harry Partch and Iannis Xenakis. And Rhythm: another vast realm of experimentation and invention, how did we get from 2/4 to the polymeters and irrational meters of Conlon Nancarrow and Thomas Adès?

Looking at music through a mathematical lens is one effort out of many to understand—though never explain—how this remarkable acoustic phenomenon can move us to tears.