Towards a General Computational Theory of Musical Structure

The General Computational Theory of Musical Structure (GCTMS) is a theory that may be employed to obtain a structural description (or set of descriptions) of a musical surface. This theory is based on general cognitive and logical principles, is independent of any specific musical style or idiom, and can be applied to any musical surface. The musical work is presented to GCTMS as a sequence of discrete symbolically represented events (e.g. notes) without higher-level structural elements (e.g. articulation marks, time-signature etc.)-although such information may be used to guide the analytic process. The aim of the application of the theory is to reach a structural description of the musical work that may be considered as 'plausible' or 'permissible' by a human music analyst. As style-dependent knowledge is not embodied in the general theory, highly sophisticated analyses (similar to those an expert analyst may provide) are not expected. The theory gives, however, higher rating to descriptions that may be considered more reasonable or acceptable by human analysts and lower to descriptions that are less plausible. The analytic descriptions given by GCTMS may be said to relate to and may be compared with the intuitive 'understanding' a listener has when repeatedly exposed to a specific musical work. Although the theory does not make any claim of simulating cognitive processes as these are realised in the mind, it does give insights into the intrinsic requirements of musical analytic tasks and its results may be examined with respect to cognitive validity. The proposed theory comprises two distinct but closely related stages of development: a) the development of a number of individual components that focus on specialised musical analytic tasks, and b) the development of an elaborate account of how these components relate to and interact with each other so that plausible structural descriptions of a given musical surface may be arrived at. A prototype computer system based on the GCTMS has been implemented. As a test case, the theory and prototype system have been applied on various melodic surfaces from the 12-tone equal-temperament system. iii Acknowledgements I would like to express my gratitude to: My supervisors, Mr Peter Nelson and Dr Alan Smaill, for their guidance and support throughout this research study, and for all their invaluable comments and advice that helped me crystallise the views presented in this thesis. My colleagues from the Faculty of Music and the Department of Artificial Intelligence at the …