Ph.D. Thesis, Yale University, 2013.
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Paper abstract bibtex
Paper abstract bibtex 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.
@PhDThesis{ white2013-some,
author = {White, Christopher William},
year = {2013},
title = {Some Statistical Properties of Tonality, 1650-1900},
abstract = {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.},
isbn = {9781303715631},
keywords = {0290:Linguistics,0413:Music,Communication and the
arts,Computation,Data
mining,Language,Linguistics,Modeling,Music,Music
theory,Musicology,literature and linguistics,music and
mathematics},
mendeley-tags= {music and mathematics},
number = {December},
pages = {332},
pmid = {1495950055},
school = {Yale University},
type = {Ph.D. Dissertation},
url = {https://search.proquest.com/docview/1495950055?accountid=26641%5Cnhttp://link.periodicos.capes.gov.br/sfxlcl41?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&genre=dissertations+%26+theses&sid=ProQ:ProQuest+Dissertations+%26+Theses+Glob}
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