Morphisms in Musical Analysis
University of Michigan-Dearborn
April 17, 2013
Bailey Hall 207
Refreshments will be served in Bailey Hall 204
Music theorists draw upon mathematics to analyze works of music, to reconstruct musical notions, and to compose music. In this talk I will discuss just one of these three aspects: the analysis of music. We will study Schoenberg's String Quartet in D minor from a transformational point of view.
A transformational analysis, in the sense of Lewin, asks: which transformations are idiomatic for a work of music? In other words, how do musical materials such as pitch, melody, chord, and rhythm change in a piece over time, which changes do they undergo, and how do these changes "make the piece work"? These changes are transformations, i.e. functions in the sense of mathematics. Over the centuries, mathematicians have learned a great deal about functions. For instance, functions can have different roles. On the one hand, a function can be applied to an input, e.g. if $f(x)=x^2$ then $f(3)=9$. On the other hand, functions can be composed to form a structure themselves, e.g. the symmetries of a triangle form a group. Yet, there is a third role: functions can map one structure to another, e.g. the exponential map $e^x$ takes addition to multiplication. This third role of a function is called a morphism . In Schoenberg's String Quartet in D minor, we will meet a musical morphism: a function which maps one musical structure into another.
This is joint work with Thomas Noll and Ramon Satyendra.
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