A Geometric Framework for Pitch Estimation on Acoustic Musical Signals
This work offers a new theoretical perspective on pitch estimation, which is a foundational problem for researchers in Music Information Retrieval.
This paper introduces a novel geometric framework for pitch estimation (PE) in acoustic musical signals, addressing the computational and conceptual challenges of both mono-pitch and multi-pitch estimation. The framework demonstrates relative efficacy, though it does not achieve state-of-the-art results.
This paper presents a geometric approach to pitch estimation (PE)-an important problem in Music Information Retrieval (MIR), and a precursor to a variety of other problems in the field. Though there exist a number of highly-accurate methods, both mono-pitch estimation and multi-pitch estimation (particularly with unspecified polyphonic timbre) prove computationally and conceptually challenging. A number of current techniques, whilst incredibly effective, are not targeted towards eliciting the underlying mathematical structures that underpin the complex musical patterns exhibited by acoustic musical signals. Tackling the approach from both a theoretical and experimental perspective, we present a novel framework, a basis for further work in the area, and results that (whilst not state of the art) demonstrate relative efficacy. The framework presented in this paper opens up a completely new way to tackle PE problems, and may have uses both in traditional analytical approaches, as well as in the emerging machine learning (ML) methods that currently dominate the literature.