A Geometric Framework for Pitch Estimation on Acoustic Musical Signals

TL;DR

This paper introduces a new geometric framework for pitch estimation in acoustic musical signals, aiming to enhance understanding and processing of musical patterns in MIR.

Contribution

It proposes a novel geometric approach to pitch estimation, providing a theoretical basis and experimental results that open new avenues for research in the field.

Findings

Demonstrates the efficacy of the geometric framework

Provides a basis for further research in pitch estimation

Shows potential for integration with machine learning methods

Abstract

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.