Uncovering Group Structures in Western Musical Harmony by Theodore Cohen ’23, Mathematics Colloquium, Wednesday, April 5, 1 – 1:50 pm, North Science Building 113, Wachenheim.
Abstract: The vast majority of Western music is built on the triad, a certain three note chord built on a root note. Triads can be built on any of the notes in the 12-tone scale and come in two main forms: major and minor. Taking the set of all 24 major and minor triads and following the work of 19th century music theorist Hugo Riemann, we define two groups that act on this set and, in turn, reveal a beautiful group structure underlying chordal relationships. We subsequently show that these two group actions are dual on this set.