Dissertation/Thesis Abstract

Some Statistical Properties of Tonality, 1650-1900
by White, Christopher Wm., Ph.D., Yale University, 2013, 332; 3578472
Abstract (Summary)

This dissertation investigates the statistical properties present within corpora of common practice music, involving a data set of more than 8,000 works spanning from 1650 to 1900, and focusing specifically on the properties of the chord progressions contained therein.

In the first chapter, methodologies concerning corpus analysis are presented and contrasted with text-based methodologies. It is argued that corpus analyses not only can show large-scale trends within data, but can empirically test and formalize traditional or inherited music theories, while also modeling corpora as a collection of discursive and communicative materials. Concerning the idea of corpus analysis as an analysis of discourse, literature concerning musical communication and learning is reviewed, and connections between corpus analysis and statistical learning are explored. After making this connection, we explore several problems with models of musical communication (e.g., music's composers and listeners likely use different cognitive models for their respective production and interpretation) and several implications of connecting corpora to cognitive models (e.g., a model's dependency on a particular historical situation).

Chapter 2 provides an overview of literature concerning computational musical analysis. The divide between top-down systems and bottom-up systems is discussed, and examples of each are reviewed. The chapter ends with an examination of more recent applications of information theory in music analysis.

Chapter 3 considers various ways corpora can be grouped as well as the implications those grouping techniques have on notions of musical style. It is hypothesized that the evolution of musical style can be modeled through the interaction of corpus statistics, chronological eras, and geographic contexts. This idea is tested by quantifying the probabilities of various composers' chord progressions, and cluster analyses are performed on these data. Various ways to divide and group corpora are considered, modeled, and tested.

In the fourth chapter, this dissertation investigates notions of harmonic vocabulary and syntax, hypothesizing that music involves syntactic regularity in much the same way as occurs in spoken languages. This investigation first probes this hypothesis through a corpus analysis of the Bach chorales, identifying potential syntactic/functional categories using a Hidden Markov Model. The analysis produces a three-function model as well as models with higher numbers of functions. In the end, the data suggest that music does indeed involve regularities, while also arguing for a definition of chord function that adds subtlety to models used by traditional music theory. A number of implications are considered, including the interaction of chord frequency and chord function, and the preeminence of triads in the resulting syntactic models.

Chapter 5 considers a particularly difficult problem of corpus analysis as it relates to musical vocabulary and syntax: the variegated and complex musical surface. One potential algorithm for vocabulary reduction is presented. This algorithm attempts to change each chord within an n-grams to its subset or superset that maximizes the probability of that trigram occurring. When a corpus of common-practice music is processed using this algorithm, a standard tertian chord vocabulary results, along with a bigram chord syntax that adheres to our intuitions concerning standard chord function.

In the sixth chapter, this study probes the notion of musical key as it concerns communication, suggesting that if musical practice is constrained by its point in history and progressions of chords exhibit syntactic regularities, then one should be able to build a key-finding model that learns to identify key by observing some historically situated corpus. Such a model is presented, and is trained on the music of a variety of different historical periods. The model then analyzes two famous moments of musical ambiguity: the openings of Beethoven's Eroica and Wagner's prelude to Tristan und Isolde. The results confirm that different corpus-trained models produce subtly different behavior.

The dissertation ends by considering several general and summarizing issues, for instance the notion that there are many historically-situated tonal models within Western music history, and that the difference between listening and compositional models likely accounts for the gap between the complex statistics of the tonal tradition and traditional concepts in music theory.

Indexing (document details)
Advisor: Quinn, Ian
School: Yale University
School Location: United States -- Connecticut
Source: DAI-A 75/05(E), Dissertation Abstracts International
Subjects: Linguistics, Music
Keywords: Computation, Data mining, Modeling, Music theory, Musicology
Publication Number: 3578472
ISBN: 978-1-303-71563-1
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