Geometric Approaches to the Pitch Estimation of Acoustic Musical Signals

Goodman, Thomas Antony ORCID: 0000-0001-9283-5010 (2022). Geometric Approaches to the Pitch Estimation of Acoustic Musical Signals. University of Birmingham. Ph.D.

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Abstract

Multi Pitch Estimation (MPE) is a challenging problem in the field of Music Information Retrieval (MIR). In recent literature in particular, it has been approached with Machine Learning (ML) methods, which are largely opaque, hard to interpret, and often difficult to reproduce from just the information provided in the literature. This Thesis presents a model for pitch detection that reduces the problem of MPE to that of distinguishing between false fundamentals (⊗) and their real counterparts. Initially the model is explored from a discrete viewpoint—one that is generally understudied in the field—before incorporating the notion of intensity and assigning Real values to tones. It further provides an in depth characterisation of precisely the ways in which these so-called edge cases can occur, looking in particular at the notion of ‘basic’ edge cases—ones in which the constituent parts are satisfied precisely once. From there, their occurrence is reduced to eight basic edge types (and a ninth type, which is proved to be the only irreducible non-basic type). The results of analysing simulated data on the model are then presented, highlighting the prevalence of the various types with respect to the number of simultaneous fundamentals. In addition, some insight into the use of the model on real data is given, alongside evaluation of a number of simple algorithms utilising the acquired knowledge of edge cases. Finally, this Thesis presents a range of logical future additions and directions for research, including the possibility of adopting a similar approach for other data—not necessarily musical audio.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):