Abstract
While analysing large corpora of music, many of the questions that arise involve the proportion of some musical entity relative to one or more similar entities, for example, the relative proportions of tonic, dominant, and subdominant chords. Traditional statistical techniques, however, are fraught with problems when answering such questions. Compositional data analysis is a more suitable approach, based on sounder mathematical (and musicological) ground. This paper introduces some basic techniques of compositional data analysis and uses them to identify and illustrate changes in harmonic usage in American popular music as it evolved from the 1950s through the 1990s, based on the McGill Billboard data set of chord transcriptions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
de Clercq, T., Temperley, D.: A corpus analysis of rock harmony. Popular Music 30(1), 47–70 (2011)
Burgoyne, J.A., Wild, J., Fujinaga, I.: An expert ground-truth set for audio chord recognition and music analysis. In: Leider, C., Klapuri, A.P. (eds.) Proceedings of the 12th International Conference on Music Information Retrieval, Miami, FL, pp. 633–638 (2011)
Pearson, K.: Mathematical contributions to the theory of evolution: On a form of spurious correlation which arise when indices are used in the measurement of organs. Proceedings of the Royal Society of London 60, 489–498 (1897)
Egozcue, J.J., Pawlowsky-Glahn, V.: Basic concepts and procedures. In: [21], ch. 2, pp. 12–28
Aitchison, J.: The statistical analysis of compositional data. Journal of the Royal Statistical Society, Series B 44(2), 139–177 (1982)
Burgoyne, J.A.: Stochastic Processes and Database-Driven Musicology. PhD thesis, McGill University, Montréal, QC (2012)
Snyder, J.L.: Entropy as a measure of musical style: The influence of a priori assumptions. Music Theory Spectrum 12(1), 121–160 (1990)
Aitchison, J.: The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, London (1986)
Fry, T.R.L.: Applications in economics. In: [21], pp. 318–326
McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Monographs on Statistics and Applied Probability, vol. 37. Chapman & Hall/CRC, Boca Raton, FL (1989)
Egozcue, J.J., Pawlowsky-Glahn, V.: Groups of parts and their balances in compositional data analysis. Mathematical Geology 37(7), 795–828 (2005)
Aitchison, J.: On criteria for measures of compositional difference. Mathematical Geology 24(4), 365–379 (1992)
Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figuera, G., Barceló-Vidal, C.: Isometric logratio transformations for compositional data analysis. Mathematical Geology 35(3), 279–300 (2003)
Mateu-Figuera, G., Pawlowsky-Glahn, V., Egozcue, J.J.: The principle of working on coordinates. In: [21], pp. 29–42
Martín-Fernández, J.A., Palarea-Albaladejo, J., Olea, R.A.: Dealing with zeros. In: [21], pp. 43–58.
Benjamini, Y., Yekutieli, D.: False discovery rate—Adjusted multiple confidence intervals for selected parameters. Journal of the American Statistical Association 100(469), 71–81 (2005)
Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B 1(57), 289–300 (1995)
Aitchison, J., Greenacre, M.: Biplots of compositional data. Journal of the Royal Statistical Society, Series C 51(4), 375–392 (2002)
Moore, A.: The so-called ‘Flattened Seventh’ in rock. Popular Music 14(2), 185–201 (1995)
Temperley, D.: The cadential IV in rock. Music Theory Online 17(1) (2011)
Pawlowsky-Glahn, V., Buccianti, A. (eds.): Compositional Data Analysis: Theory and Applications. Wiley, Chichester (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burgoyne, J.A., Wild, J., Fujinaga, I. (2013). Compositional Data Analysis of Harmonic Structures in Popular Music. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-39357-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39356-3
Online ISBN: 978-3-642-39357-0
eBook Packages: Computer ScienceComputer Science (R0)