Implementing Methods for Analysing Music Based on Lerdahl and Jackendoff's Generative Theory of Tonal Music

We describe and discuss our computer implementations of Lerdahl and Jackendoff’s (1983) Generative Theory of Tonal Music (GTTM). We consider this theory to be one of the most relevant music theories with regard to formalization because it captures aspects of musical phenomena based on the Gestalts perceived in music and presents these aspects with relatively rigid rules. However, the theory has several problems in terms of computer implementation. To overcome these problems, we have proposed four different kinds of analyser: an automatic timespan tree analyser (ATTA); a fully automatic time-span tree analyser (FATTA); the σGTTM analyser, which detects local grouping boundaries by combining GTTM with statistical learning using a decision tree; and the σGTTM-II analyser, with which we introduce full parameterization and statistical learning.