A geometric framework for pitch estimation on acoustic musical signals

Tom Goodman, Karoline Van Gemst, Peter Tino

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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, while 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 theoretical and experimental perspectives, we present a novel framework, a basis for further work in the area, and results that (while 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.
Original languageEnglish
JournalThe Journal of Mathematics and Music
Early online date6 Oct 2021
Publication statusE-pub ahead of print - 6 Oct 2021

Bibliographical note

Publisher Copyright:
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.


  • Pitch estimation
  • geometry
  • music information retrieval
  • signal processing
  • visualization

ASJC Scopus subject areas

  • Modelling and Simulation
  • Music
  • Computational Mathematics
  • Applied Mathematics


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