Formal Syntax and Semantics of Music

Halley Young, NYU


Over 2500 years ago, Pythagoras declared that music is “sounding number,” or math itself. At the same time, at least since the Renaissance, music theorists have viewed even instrumental music as being somehow akin to language, with meaning and grammatical structure. Today, we have determined that math and formal methods are not orthogonal to the study of language, but rather enhance it. Slowly, researchers are realizing that the methods we have developed to talk about language can also be used to bridge the gap between mathematicl and linguistic views of music, and to get at the heart of what musical meaning is. In this talk, I will introduce and discuss several formalisms that could provide a way of talking about the syntax and semantics of music from Western as well as non-Western cultures. These formalisms will include probabilistic methods, generative grammars in the style of Chomsky, the syntax and semantics of musical state space, musical type theory and lambda calculus, and more.