![]() ![]() This entry was posted in Research and tagged MASS program, music on Septemby John Roe.Applies CQT models to musical analysis. “Geometrical Music Theory.” Science 320, no. “Generalized Voice-Leading Spaces.” Science 320, no. ArXiv e-print, July 4, 2013.Ĭallender, Clifton, Ian Quinn, and Dmitri Tymoczko. ![]() ArXiv e-print, September 3, 2013.īudney, Ryan, and William Sethares. ![]() Modes in Modern Music from a Topological Viewpoint. Referencesīergomi, Mattia G., and Alessandro Portaluri. I’m not really competent to judge the music theory here (as a guitarist, I’m usually sticking with two or three of the innumerable possible scales that the authors identify), but it is a fascinating point (this is also what I got out of Rachel Hall’s paper) that music is full of natural examples of configuration spaces, including knots and Möbius bands and other topological exotica. Spaces of chords are natural examples of configuration spaces (selections of \(n\) distinct points from the space of notes, with order irrelevant) so this allows the representation of a mode as a subspace of a product of two configuration spaces. For instance, Ionian mode is a major seventh (CEGB) plus a minor triad (DFA) Aeolian mode is a minor seventh (ACEG) plus a diminished triad (BDF). The authors analyze a mode into two chords: the seventh chord made by notes I, III, V, and VII of the scale, and the triad made by notes II, IV and VI. Aeolian mode, A,B,C,D,E,F,G) or by using a different starting scale, or both. The familiar major scale of Western music (C,D,E,F,G,A,B) is a mode (Ionian mode), but one can obtain different modes by starting from a different note (e.g. (Dr Hall is a professor at Saint Joseph’s University in Philadelphia and before that was a student in the Geometric Functional Analysis group at Penn State.)Ī mode is a seven-note scale. There have been several papers of this sort recently: the earliest that I’m aware of is Rachel Hall’s article in Science five years ago. This contains some simple ideas about fundamental groups and so on and I was thinking it might make a project for a musically-oriented student in my MASS course. Topology and musicĪ new paper appeared on the arXiv this week applying some simple topological ideas to the analysis of musical modes. This entry was posted in Teaching and tagged books, MASS program, winding number on Septemby John Roe. And, to quote the final sentence of the book, “I wish you much happy winding around in the future.” At present this list is empty, but I doubt if that happy state of affairs will last for long! ( edit: it didn’t) Please contact me with any information about corrections. I will attempt to maintain a list of typos and other corrections here. If you are interested in the book, please visit the AMS bookstore page. Having (I hope) made the case that the winding number concept is the “golden cord which guides the student through the labyrinth of classical mathematics”, I conclude by following a beautiful paper of Michael Atiyah to explain how, by asking one natural question about the winding number, we can be led to the Bott periodicity theorem, a central result in the flowering of topology in the 1960s. This is a book based on by MASS 2013 course of the same title, which looks at the winding number – the central notion in plane topology – from a variety of perspectives, topological, geometrical, analytic and combinatorial. I was excited to receive a package from the American Mathematical Society today! My author’s copies of “Winding Around” have arrived! ![]()
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