Geometry of Music

In my talk I am going to build on my earlier work into the non-Euclidean geometry of Western harmony (work which led to two papers published in Science, the book "A Geometry of Music," published by Oxford University Press, and an interactive sculpture in the National Museum of Mathematics in Manhattan).  I will show how the mathematical notion of a "vector" corresponds to what musicians refer to as a "voice leading."  Once we understand this correspondence, we can use mathematical and computational tools to study the vectors found in musical structure -- leading to new insights about musical style and also particular pieces.  I will show how these vectors are crucial to understanding the geometrical structure of musical harmonies, and how that geometrical structure in turn helps us expand our conception of a musical vector.  And we will develop new insights into the Renaissance composer Luca Marenzio's musical representations of the afterlife.