Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Pitch Estimation With Mean Averaging Smoothed Product Spectrum And Musical Consonance Evaluation Using MASP

Murat Yasar Baskin

TL;DR

The paper proposes MASP, a Mean Averaging Smoothed Product Spectrum, to robustly estimate pitch even when spectra are deceptive or inharmonic, by smoothing each subharmonic component before forming a multiplicative product. It also extends MASP to musical consonance evaluation through a harmonicity measure H, linking periodicity in the MASP spectrum to perceived consonance and showing consistency with traditional theories. MASP includes normalization and a logarithmic reformulation to align with perceptual scales and uses a Constant-Q/Mel-like representation to capture frequency uncertainty across the spectrum. Demonstrations on artificially generated tones and real instruments show improved pitch detection, while MASP-based consonance analysis yields interpretable peaks at common intervals, suggesting a shared spectral basis for pitch and consonance with potential for robust audio analysis and music-theory applications.

Abstract

This study introduces Mean Averaging Smoothed Product (MASP) Spectrum, which is a modified version of the Harmonic Product Spectrum, designed to enhance pitch estimation for many algorithm-wise deceptive frequency spectra that still lead clear pitches, for both harmonic and inharmonic cases. By introducing a global mean based smoothing for spectrum, the MASP algorithm diminishes the unwanted sensitivity of HPS for spectra with missing partials. The method exhibited robust pitch estimations consistent with perceptual expectations. Motivated upon the strong correlation between consonance and periodicity, the same algorithm is extended and, with the proposition of a harmonicity measure (H), used to evaluate musical consonance for two and three tones; yielding consonance hierarchies that align with perception and practice of music theory. These findings suggest that perception of pitch and consonance may share a similar underlying mechanism that depend on spectrum.

Pitch Estimation With Mean Averaging Smoothed Product Spectrum And Musical Consonance Evaluation Using MASP

TL;DR

The paper proposes MASP, a Mean Averaging Smoothed Product Spectrum, to robustly estimate pitch even when spectra are deceptive or inharmonic, by smoothing each subharmonic component before forming a multiplicative product. It also extends MASP to musical consonance evaluation through a harmonicity measure H, linking periodicity in the MASP spectrum to perceived consonance and showing consistency with traditional theories. MASP includes normalization and a logarithmic reformulation to align with perceptual scales and uses a Constant-Q/Mel-like representation to capture frequency uncertainty across the spectrum. Demonstrations on artificially generated tones and real instruments show improved pitch detection, while MASP-based consonance analysis yields interpretable peaks at common intervals, suggesting a shared spectral basis for pitch and consonance with potential for robust audio analysis and music-theory applications.

Abstract

This study introduces Mean Averaging Smoothed Product (MASP) Spectrum, which is a modified version of the Harmonic Product Spectrum, designed to enhance pitch estimation for many algorithm-wise deceptive frequency spectra that still lead clear pitches, for both harmonic and inharmonic cases. By introducing a global mean based smoothing for spectrum, the MASP algorithm diminishes the unwanted sensitivity of HPS for spectra with missing partials. The method exhibited robust pitch estimations consistent with perceptual expectations. Motivated upon the strong correlation between consonance and periodicity, the same algorithm is extended and, with the proposition of a harmonicity measure (H), used to evaluate musical consonance for two and three tones; yielding consonance hierarchies that align with perception and practice of music theory. These findings suggest that perception of pitch and consonance may share a similar underlying mechanism that depend on spectrum.

Paper Structure

This paper contains 32 sections, 16 equations, 16 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Definition of the Problem, Problem of Definition
  4. Intuitive definition vs scientific definition
  5. Frequency vs pitch
  6. Ambiguities in pitch perception
  7. Common Pitch perception Algorithms and Common Errors
  8. Lowest partial model
  9. Partials spacing model
  10. Greatest common divisor model
  11. Spectral Models and MASP
  12. Subharmonic Histogram
  13. Too many peaks
  14. Discrete definition of frequency
  15. Flaw of Subharmonic Histogram
  16. ...and 17 more sections

Figures (16)

  • Figure 1: A simple pattern-matching model described by Cheveigne [1].
  • Figure 2: The effect of mean-averaging smoothing on a spectrum, original spectrum on top. As $k$ increases, the spectrum approaches to become uniform.
  • Figure 3: Frequency (above) and MASP (below) spectra of a modified sawtooth wave with first and second partials removed
  • Figure 4: Frequency (above) and MASP (below) spectra of a modified square wave with first partial removed
  • Figure 5: Frequency (above) and MASP (below) spectra of a slightly inharmonic complex with partials 930, 1770, 2730... Hz
  • ...and 11 more figures