|
07 May 08 - 03:33 PM (#2335111) Subject: Godel, Escher, Chopin,and Folkies From: Amos "Familiar relationships between sets of musical notes, such as transposition between chords, directly translate into geometrical structures such as this Möbius strip — where each dot represents a whole class of equivalent two-note chords — or into more complex structures with many dimensions. Composers have an understanding of these geometries without realizing it, says music theorist Dmitri Tymoczko of Princeton University. "Musicians like Chopin had a very direct, intuitive understanding of these spaces at a time when mathematicians still didn't know much about high-dimensional geometry," he says." Full story here in Science News I think the intuitive geometric sense of those who work with music accounts for the argument, "I am in shape!! Round is a shape...". A |
|
07 May 08 - 08:42 PM (#2335336) Subject: RE: Godel, Escher, Chopin,and Folkies From: Jack Campin An intro to this stuff, for mathematicians: http://math.ucr.edu/home/baez/week234.html Mazzola's work referenced there is particularly interesting. I suspect it might eventually have a substantial impact on the way we think about music theory. He's trying to take on the whole analytical tradition from Rameau to Schenker to Schoenberg to Berklee and beat it at its own game. |