Lane Hughston, Professor of Mathematics in the School of Computing at Goldsmiths University of London to give talk in the Bush House Lecture Theatre 3 BH(NE)0.01 as part of the Engineering seminar series. There will be refreshments after the talk, courtesy of the NMES Research Culture Fund.

If you are unable to attend in person, you may use the following MS Teams link to attend the event virtually: Engineering Seminar — Professor Lane Hughston

Abstract:

We show that the Eulerian tonnetz, which associates three minor chords to each major chord and three major chords to each minor chord, can be represented by a bipartite graph with twelve white vertices signifying major chords and twelve black vertices signifying minor chords. This so-called Levi graph uniquely determines the combinatorial geometry of a certain remarkable configuration of twelve points and twelve lines on the real projective plane with the property that three points lie on each line and three lines pass through each point. Interesting features of the tonnetz, such as the existence of Cohn’s four hexatonic cycles, crucial for the understanding of nineteenth-century voice leading and extended harmony, can be read off rather directly as properties of the configuration. We show that analogous tone networks can be constructed for pentatonic music and twelve-tonal music. Based on collaborative research with Jeffrey Boland, Syndikat LLC, Los Angeles.

Speaker's Info:

Lane Hughston is Professor of Mathematics in the School of Computing at Goldsmiths University of London. His DPhil is from the University of Oxford where he was a student of Roger Penrose. Lane works across a number of different areas of mathematics and physics, including quantum theory, relativity theory, financial mathematics, and the mathematical theory of music.