Algebraic varieties of musical performances

Rok, strany: 2001, 59 - 69

In this article first, we give an overview, without any pretension of being exhaustive, of some theoretical tool of the modern theory of musical performance. Then, we present a mathematical model of performance which is based on the principles of mathematical music theory. We prove a structure theorem describing the algebraic variety of performance system parameters which induce a determined performance. This algebro-geometric model has inspired a statistical model that concretely answers a typical question about the way a player performs. Accordingly, a claim like “Horowitz has a more local way than Cortot to play Schumann's ‘Träumerei’ ” has a strong statistical evidence.

ISO 690:

Ferretti, R., Mazzola, G. 2001. Algebraic varieties of musical performances. In Tatra Mountains Mathematical Publications, vol. 23, no.3, pp. 59-69. 1210-3195.

APA:

Ferretti, R., Mazzola, G. (2001). Algebraic varieties of musical performances. Tatra Mountains Mathematical Publications, 23(3), 59-69. 1210-3195.