Defining the Height of Time-Span Trees in GTTM in terms of Prolongational Tree Generation

Music Information Processing has gained popularity in computer science, with the Generative Theory of Tonal Music (GTTM) used in various applications, such as music analysis and melody generation. However, the ambiguity of GTTM and the inconsistency of its rules make its computerized implementation difficult. This paper addresses a specific ambiguity related to the height of the time-span tree, a key component of GTTM. We propose three methods for defining this height and evaluate their effectiveness in generating prolongational trees, another output of GTTM. Our experiments demonstrate that one of the proposed methods is somewhat useful. We conclude that overall stability rather than local stability conditions is crucial for generating a prolongational tree. The proposed method advances the automatic application of GTTM, especially in generating prolongational trees, and ultimately contributes to the further development of research based on GTTM.