Journal Club

It’s time for the second journal club of the 2020! The topic of this talk will topology of musical data. Just in case you have never been to our Journal Club: it’s a great opportunity to come along and listen to a talk about some fun science. There will be free pizza and everyone is more than welcome to join!

Abstract:
The musical realm is a promising area in which to expect to find nontrivial topological structures. This paper describes several kinds of metrics on musical data, and explores the implications of these metrics in two ways: via techniques of classical topology where the metric space of all-possible musical data can be described explicitly, and via modern data-driven ideas of persistent homology which calculates the Betti-number barcodes of individual musical works. Both analyses are able to recover three well-known topological structures in music: the circularity of octave-reduced musical scales, the circle of fifths, and the rhythmic repetition of timelines. Applications to a variety of musical works (for example, folk music in the form of standard MIDI files) are presented, and the barcodes show many interesting features. Examples show that individual pieces may span the complete space (in which case the classical and the data-driven analyses agree), or they may span only part of the space.