Stephon Alexander (Brown University)

Title: Jazz of the Spheres

Abstract: In this talk, Alexander explores the profound connections between mathematics, cosmology, and music with a focus on Jazz music.

Noam Elkies (Harvard University)

Title: G-sharp, A-flat, and the Euclidean algorithm

Or, why we divide the octave into 12 = 7+5 notes

Abstract: The familiar repeating pattern of white and black piano keys, and of the notes it represents (with multiplicities such as the identification of G-sharp with A-flat), lies at a fascinating crossroads of physics, music, and mathematics.  We use the piano and audience voices, as well as more traditional lecture materials, to outline this background for the division of the octave into 12 semitones, the repeating 7+5 pattern of white and black keys, and the resulting compromises such as the "commas" separating G-sharp from A-flat and the piano's major chords from pure harmonic triads.

Katherine M. Kinnaird (U.S. Air Force Academy and Smith College)

Title: Songs are Matrices are Songs: From mathematics, statistics, and computer science to music and back again!

Abstract: Music is deeply entrenched in our daily lives, from our playlists to the background songs in our favorite television shows. The multidisciplinary field of Music Information Retrieval (MIR) is motivated by the comparisons that we, as humans, make about music and the various contexts of these comparisons. By defining tasks such as building better song recommendation systems, finding structural information in a given recording, or generating new music with artificial intelligence, MIR seeks to algorithmically make these musical comparisons in the same manner that a human being would, but on a much larger scale. In this talk, we will introduce the field of MIR, including popular tasks and cutting-edge techniques. Then we will present aligned hierarchies, a structure-based representation that can be used for comparing songs, and new extensions of aligned hierarchies that leverage ideas from topological data analysis.

Dmitri Tymoczko (Princeton University)

Title: The Concept of Musical Space

Abstract: Musicians deal with many different kinds of spaces, from the physical space of a piano keyboard to the conceptual space of four-beat rhythmic patterns. Very often these spaces come equipped with some notion of symmetry that models our sense that different points are closely related: for instance, that two four-beat rhythms can be instances of the same general pattern. For this reason, music is a situation where we have direct perceptual experience of complicated mathematical phenomena such as "orbit spaces," and where we have a practical need to answer abstract questions like "what properties do all spaces share?" In my talk I will describe a comprehensive theory of musical spaces, and illustrate some of its interesting musical consequences. This theory sheds light on nonmusical issues such as the relation between physical maps and the Google maps app.