April 8, 2014
Music in numbers
While the inextricable connection between music and maths has been discussed extensively by musicians, mathematicians, neurobiologists, psychologists and others, computation has seldom been included in the discussion. Thanks to Professor Paul Hudak, Tilde Cafe attendees saw the confluence of the triad come to life beautifully on April 5, at the Willoughby Wallace Memorial Library (video posted at https://www.youtube.com/user/tildecafe).
Professor Hudak’s research includes the areas of functional programming and computer music; in fact he is one of the principal designers of the language Haskell. Functional programming differs from other programming in that it is based (primarily) on algebraic principles and algebraic structures. Using Haskell, his lab has developed Euterpea to compose music with complex rhythms and electronically generated sounds, as well as develop musical representations of conventional instruments. With an open ended PVC tube in hand, Paul demonstrated how all these developments also take into account fundamental principles of physics, such as the sinusoidal pattern of sound waves and the multiples in which they travel and the resulting overtones that one can hear from some instruments (see video around 12:30). In several subsequent examples we heard what could have been clearly mistaken as a flute, but which was in fact the output of an iterative series in Euterpea to fashion the sound of a flute – breaths and all included!
We had an opportunity to hear examples of the different compositional strategies that Paul’s work considers when developing programs (see video around 25:29). One of the many compositional techniques used in generating computer music is a process of training the program to learn the grammar particular to a genre of music. Paul showed us some results from his graduate student Donya Quick’s doctoral dissertation, where she has developed a system called Kulitta that automatically composes music based on a number of criteria including grammar. We heard four different short pieces of music and tried to identify which two were by Bach, and which two were generated by Kulitta – as it turns out, many in the room were fooled (see video around 46:55)! And, as Paul told us, professional musicians have also been fooled!
The afternoon resulted in some really interesting discussions on music and computation, that few had probably considered before this. Thank you, Paul, for sharing with us your absolutely fascinating research. How perfectly well-timed this talk was with April being Mathematics Awareness Month – punctus contra punctum?
With April also being National Poetry Month, it’s hard not to end with this quote attributed to Einstein: “Pure mathematics is, in its way, the poetry of logical ideas” – and dare I say, music!