Creativity in Music
Guerino B. Mazzola, Joomi Park · 2011
The functorial approach (functors are structure-preserving maps between mathematical categories) to mathematical music theory and of musical gestures and its implementation in the Rubato software. We discuss musical analyses based upon gestural theory. Then the mathematical approach to musical creativity is introduced. Using Yoneda’s lemma these ideas are applied to understand Beethoven’s six variations of the third movement of sonata op. 109. The paper concludes with the semiotic generalization of this mathematical model and its application to a theory of contemporary counterpoint.