2.  Mathematical and Computer-Aided Music Theory

Our discussion of computer-aided experiments in Mathematical Music Theory is especially motivated by the concept of the RUBATO software for musical analysis and performance.⁵

For both disciplines it is characteristic that the involved researchers spend a lot of time and energy for large portions of scientific work that are not directly motivated by music theoretical interests. However, there is a complex interaction between the direct and indirect research interests, that can hardly be classified into proper research on the one side and service on the other. Another domain makes this evident: the influence of Psychology and Sociology on Systematic Musicology in the last decades goes far beyond mere service, because there is a significant influence of these disciplines on the dynamics of musicological interest.

First we give a very short characterization of Mathematical Music Theory as a subdiscipline of General Music Theory. We especially refer to the Zürich School of Mathematical Music Theory, which has been initiated, developed and programmatically inspired by Guerino Mazzola.

There are two complementary research interests within General Music Theory, namely

1. Analysis, i.e., understanding of concrete ideosyncratic musical structures
2. Theory, i.e., understanding of general principles and rules behind musical structures

The dymanics of interest in General Music Theory is characterized by a permanent change of focus between analytical and theoretical approaches.

Something similar can also be observed within Mathematical Music Theory. On the one hand, there are approaches providing methods intended to represent concrete musical structures in terms of concrete mathematical objects: Denotators. These denotators are then further investigated by suitable mathematical methods in order to obtain insights into the concrete musical structures. On the other hand, there are approaches aiming at solving a specific problem within music theory by explanatory power of a suitable mathematical model. Hence there are four channels of transfer to be considered: