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Analysis and Visualization of Musical Structure using Networks

Alberto Alcalá-Alvarez, Pablo Padilla-Longoria

TL;DR

The paper addresses the problem of revealing musical structure through network representations of symbolic scores. It introduces a pipeline that parses scores with Music21, builds graphs such as the pitch-chord-rhythm (p-c-r) graph, and computes centrality, entropy, and modularity, using sliding time windows to produce time-series for form and texture analysis; dynamic time warping aids cross-score comparison. Key contributions include the formulation of the p-c-r graph and related variants, demonstration of communities corresponding to harmonic regions, and the use of multiple entropy measures to track texture changes, with connections to Schenkerian and generative theories. The approach offers a computational visualization and quantitative framework that can generalize across styles and repertoires, potentially enabling automated form segmentation and comparative musicology across both Western and non-Western traditions.

Abstract

In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations among them, and are built from quantitative or categorical data contained in digital music scores. They are helpful in visualizing musical features at once, thus leading to a computational tool for understanding the general structural elements of a music fragment. Data obtained from a digital score undergoes different analytical procedures from graph and network theory, such as computing their centrality measures and entropy, and detecting their communities. We analyze pieces of music coming from different styles, and compare some of our results with conclusions from traditional music analysis techniques.

Analysis and Visualization of Musical Structure using Networks

TL;DR

The paper addresses the problem of revealing musical structure through network representations of symbolic scores. It introduces a pipeline that parses scores with Music21, builds graphs such as the pitch-chord-rhythm (p-c-r) graph, and computes centrality, entropy, and modularity, using sliding time windows to produce time-series for form and texture analysis; dynamic time warping aids cross-score comparison. Key contributions include the formulation of the p-c-r graph and related variants, demonstration of communities corresponding to harmonic regions, and the use of multiple entropy measures to track texture changes, with connections to Schenkerian and generative theories. The approach offers a computational visualization and quantitative framework that can generalize across styles and repertoires, potentially enabling automated form segmentation and comparative musicology across both Western and non-Western traditions.

Abstract

In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations among them, and are built from quantitative or categorical data contained in digital music scores. They are helpful in visualizing musical features at once, thus leading to a computational tool for understanding the general structural elements of a music fragment. Data obtained from a digital score undergoes different analytical procedures from graph and network theory, such as computing their centrality measures and entropy, and detecting their communities. We analyze pieces of music coming from different styles, and compare some of our results with conclusions from traditional music analysis techniques.
Paper Structure (20 sections, 13 equations, 15 figures)

This paper contains 20 sections, 13 equations, 15 figures.

Table of Contents

  1. Preliminaries.
  2. Graphs and networks.
  3. Node Centrality.
  4. Entropy.
  5. Entropy in networks.
  6. Communities.
  7. Discrete time series.
  8. Methodology
  9. Some graphs associated with sequences of musical events.
  10. Pitch-chord-rhythm (p-c-r) graph.
  11. Analysis of the p-c-r graph.
  12. Communities of the p-c-r graph.
  13. Entropy of the p-c-r graph.
  14. Pitch and chord graphs associated with sequences of events.
  15. Vertical pitch class graph.
  16. ...and 5 more sections

Figures (15)

  • Figure 3.1: p-c-r graph for measures $1\text{\textendash}8$ of J. S. Bach's Contrapunctus I from The Art of Fugue BWV 1080.
  • Figure 3.2: The five communities in the p-c-r graph for mm. $1\text{\textendash}8$ of J. S. Bach's Contrapunctus I from The Art Of Fugue BWV 1080.
  • Figure 3.3: Vertical pitch class graph for mm. $1\text{\textendash}8$ of J. S. Bach's Contrapunctus I from The Art Of Fugue BWV 1080.
  • Figure 3.4: Horizontal pitch class graph for mm. $1\text{\textendash}8$ of J. S. Bach's Contrapunctus I from The Art Of Fugue BWV 1080.
  • Figure 3.5: Event sequence graph for mm. $1\text{\textendash}8$ of J. S. Bach's Contrapunctus I from The Art Of Fugue BWV 1080.
  • ...and 10 more figures

Theorems & Definitions (5)

  • Definition 1.1
  • Example 3.1
  • Example 3.2
  • Example 3.3
  • Example 4.1