11367_Toward a Scientific Taxonomy of Musical Styles

Master of Information Technology (Research)

Thesis

“Toward a Scientific Taxonomy of Musical Styles”

Name: Héctor Bellmann

School: Software Engineering and Data Communications
Course: IT60

Date: 21st July, 2006

Principal Supervisor: Associate Professor Joaquin Sitte

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Abstract

The original aim of the research was to investigate the conceptual dimensions of
style in tonal music in order to provide grounds for an objective, measurable catego-
rization of the phenomenon that could be construed as the basis of a scientific taxon-
omy of musical styles. However, this is a formidable task that surpasses the practical
possibilities of the project, which would hence concentrate on creating the tools that
would be needed for the following stage.
A review of previous attempts to deal with style in music provided a number of
guidelines for the process of dealing with the material. The project intends to avoid
the subjectivity of musical analysis concentrating on music observable features. A
database of 250 keyboard scores in MusicXML format was built to the purpose of
covering the whole span of styles in tonal music, from which it should be possible to
extract features to be used in style categorization. Early on, it became apparent that
most meaningful pitch-related features are linked to scale degrees, thus essentially
depending on functional labeling, requiring the knowledge of the key of the music as
a point function.
Different proposed alternatives to determine the key were considered and a method
decided upon. Software was written and its effectiveness tested. The method proved
successful in determining the instant key with as much precision as feasible. On this
basis, it became possible to functionally label scale degrees and chords. This soft-
ware constitutes the basic tool for the extraction of pitch-related features. As its first
use, the software was applied to the score database in order to quantify the usage of
scale degrees and chords. The results indisputably showed that tonal music can be
characterized by specific proportions in the use of the different scale degrees,
whereas the use of chords shows a constant increase in chromaticism.
Part of the material of this work appeared in the Springer-Verlag’s 2006 volume of
Lecture Notes in Computer Science.

Keywords: style, stylometry, MusicXML, key-determination, algorithm, dot prod-
uct, scale degree, chord, functional labeling.

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Table of Contents
Abstract _____________________________________________________iii
Table of Contents _____________________________________________ iv
Index of Figures and Tables _____________________________________v
Statement of Authorship ______________________________________ vii
Statement of Authorship ______________________________________ vii
Acknowledgement____________________________________________ viii
1. Introduction _______________________________________________ 1
1.1 Origin of the Project _______________________________________________________ 1
1.2 Feasibility _______________________________________________________________ 4
1.3 The nature of the solution ___________________________________________________ 4
1.4 Literary stylometry ________________________________________________________ 5
1.4.1 Points of contact with the Music style problem ___________________________ 5
1.4.2 Differences between music and literature _______________________________ 7
1.5 Musical Style_____________________________________________________________ 9
1.6 Musical Analysis _________________________________________________________ 10
1.7 A suggestive analogy______________________________________________________ 11
1.8 Conclusions _____________________________________________________________ 13
2. Previous attempts to deal with musical style_____________________ 17
3. Overview of the Project _____________________________________ 25
3.1 Guiding ideas from previous research _________________________________________ 25
3.2 Rationale _______________________________________________________________ 25
3.3 How to deal with the music _________________________________________________ 27
3.4 Source of the study _______________________________________________________ 32
3.5 Music Database __________________________________________________________ 34
3.6 Data Format_____________________________________________________________ 37
3.6.1 Digital music standard _______________________________________________ 37
3.6.2 The problem of key determination_____________________________________ 38
3.6.3 The algorithm ______________________________________________________ 46
4. Details of the work carried out _______________________________ 53
4.1 MusicXML _____________________________________________________________ 53
4.2 Key determination ________________________________________________________ 56
4.3 The width of the sliding window_____________________________________________ 73
4.4 Measure of tonalness ______________________________________________________ 75
4.5 The labelling of chords ____________________________________________________ 82
4.6 The key profile revisited ___________________________________________________ 88
5. Results___________________________________________________ 91
5.1 Data about scale degrees ___________________________________________________ 93
5.2 Data about chords________________________________________________________ 99
6. Discussion_______________________________________________ 103
6.1 Comparison with Budge’s results ___________________________________________ 103
6.2 Limitations of the programs________________________________________________ 106
6.2.1 The collection procedure____________________________________________ 106
6.2.2 The test for tonalness ______________________________________________ 110
6.3 Conclusions ____________________________________________________________ 112
References_________________________________________________ 113
Appendix I – Listing of the database ____________________________ 116

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Appendix II – Tables _________________________________________ 128
Appendix III – Musical notation basics __________________________ 147
Appendix IV – Format example ________________________________ 160
Appendix V – Application example _____________________________ 176
Appendix VI – Scores_________________________________________ 183
Index of Figures and Tables
Figure 1 – Life span of the composers in the database____________________________________ 36
Table 1 – Krumhansl-Kessler key profile ______________________________________________ 42
Table 2 – Budge’s Overall Chord Frequencies__________________________________________ 43
Table 3 – Frequencies of scale degrees_______________________________________________ 45
Figure 2 – Major (left) and minor (right) key profiles ____________________________________ 48
Figure 3 -Theme from Fugue No.1___________________________________________________ 49
Table 4 – Accumulated durations for Fugue 1 __________________________________________ 49
Figure 4 -Accumulated durations wheel ______________________________________________ 49
Figure 5 – Second measure from a Scarlatti’s Sonata ____________________________________ 62
Table 5 – Numerical Code for Note Names ____________________________________________ 66
Figure 6 – Effect of changing the window width ________________________________________ 69
Figure 7- Main keys for Handel’s Sarabande __________________________________________ 71
Figure 8 – Main keys for Shostakovich Prelude _________________________________________ 72
Figure 9- Sonata in G, narrow window _______________________________________________ 73
Figure 11- Sonata in G, wide window ________________________________________________ 74
Figure 12 – Range of dot product values ______________________________________________ 76
Figure 13 – Scarlatti Frequency Histogram____________________________________________ 78
Figure 14 – Krenek Frequency Histogram_____________________________________________ 78
Table 6 – Data from Krenek’s pieces _________________________________________________ 81
Table 7 – Key profile for the Baroque ________________________________________________ 89
Table 8 – Key Profile Improvement __________________________________________________ 90
Table 9 – Duration Statistics _______________________________________________________ 94
Table 10 – Duration and pages______________________________________________________ 94
Table 11 – Further improvement in Key Profile_________________________________________ 95
Figure 15 – Scale degrees with highest frequencies______________________________________ 95
Figure 16 – Scale degrees with lowest frequencies ______________________________________ 97
Table 12 – Overall Frequency of Triads _____________________________________________ 100
Table 13 – Overall Frequency of Seventh Chords ______________________________________ 100
Table 14- Number of diatonic chords________________________________________________ 101
Figure 47 – Percentage of use of the main diatonic chords _______________________________ 102
Table 15 – Comparison with Budge’s results __________________________________________ 104
Figure 58 – Beginning of Mozart’s Sonata K.545_______________________________________ 107
Table 16 – Effect of tonalness test on Liszt’s works _____________________________________ 111
Table 17 – Average Percentage of Use of Scale Degrees in Major_________________________ 128
Table 18 – Average Percentage of Use of Scale Degrees in Minor _________________________ 129
Figure 69 – Confidence Intervals for Tonic Major______________________________________ 130
Figure 20 – Confidence Intervals for Mediant Major____________________________________ 130
Figure 71 – Confidence Intervals for Dominant Major __________________________________ 130
Figure 82 – Confidence Intervals for Tonic minor ______________________________________ 131
Figure 93 – Confidence Intervals for Mediant minor____________________________________ 131
Figure 104 – Confidence Intervals for Dominant minor _________________________________ 131
Figure 25 – Confidence Intervals for Raised Tonic Major________________________________ 132
Figure 116 – Confidence Intervals for Raised Supertonic Major___________________________ 132
Figure 127 – Confidence Intervals for Raised Subdominant Major_________________________ 132
Figure 138 – Confidence Intervals for Raised Tonic minor _______________________________ 133
Figure 29 – Confidence Intervals for Raised mediant minor ______________________________ 133
Figure 30- Confidence Intervals for Raised Subdominant minor___________________________ 133
Table 19 – Chords in Major mode, part 1 ____________________________________________ 134
Table 20 – Chords in Major mode, part 2 ____________________________________________ 135

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Table 21 – Chords in Major mode, part 3 _____________________________________________ 136
Table 22 – Chords in Minor mode, part 1 _____________________________________________ 137
Table 23 – Chord in Minor mode, part 2______________________________________________ 138
Table 24 – Chords in Minor mode, part 3 _____________________________________________ 139
Table 25 – Chords in Major mode in percentage, part 1__________________________________ 140
Table 26 – Chords in Major mode in percentage, part 2__________________________________ 141
Table 27 – Chords in Major mode in percentage, part 3__________________________________ 142
Table 28 – Chords in Minor mode in percentage, part 1__________________________________ 143
Table 29 – Chords in Minor mode in percentage, part 2__________________________________ 144
Table 30 – Chords in Minor mode in percentage, part 3__________________________________ 145
Table 31 – Percentages for grouped diatonic chords ____________________________________ 146

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Statement of Authorship

The work contained in this thesis has not been previously submitted to meet
requirements of an award at this or any other education institution. To the best
of my knowledge, the thesis contains no material previously published or writ-
ten by another person except where due reference is made.

Signature

Date:

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Acknowledgement

I wish to thank my Principal Supervisor Dr. Joaquin Sitte for his patience and
his open-mindedness; Ray Duplock, for his continued support and help with
statistical matters; and very specially, to Raj Singh, who opened BlackBox for
me, and devoted a lot of time to solving the problems of input-output in this
language, which made programming in it possible for me.

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1. Introduction
1.1 Origin of the Project
The long-term motivation for this work is the total inexistence of tools for
measuring musical style in an objective, scientific manner. For the outsider it
would seem hard to believe that the 20th century had ended without any pro-
gress in music attributional studies beyond the mere opinion of the experts.
Apart from the dating of manuscripts or of contemporary copies, the possible
recognition of the musical calligraphy and similar devices of history scholars,
attribution in music is left to the opinion of musicians, often composers, whose
lack of objectivity and scientific attitude is notorious. Often an ancient work of
dubious or unknown composer turns up, and the specialists are quick to attrib-
ute it to their favorite old master, even if they can only count with the aid of
the flimsiest evidence. The process is riddled with emotion and wishful think-
ing, and understandably has led to a long list of famous misattributions among
which probably the most well known are:
U.W. van Wassenaer’s “Concerti Armonici” formerly attributed to
Handel and later to Pergolesi;
Bernhard Flies’ Wiegenlied, for long time attributed to Mozart;
Leopold Mozart’s “Toy Symphony” first attributed to Haydn;
Friedrich Witt’s “Jena Symphony” first thought to be early Beethoven.
In the 1960s, a supposed Fifth Orchestral Suite by J.S. Bach made its way to
recordings but has since vanished without a trace.
A more recent example is the inclusion in the Searle official catalog of the
works of Liszt, under the number S.715, of a piece for piano and orchestra that
for almost a century, had been attributed to its most likely composer, the pian-
ist and composer Sophie Menter. This was done entirely on the basis of the
presence of superficial Liszt-like piano mannerisms in the piece – not surpris-
ing in a piece by a Liszt’s disciple whom he had described as “my only legiti-

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mate piano daughter” –, plus pure speculation to “explain” why Menter had
asked Tchaikovsky to orchestrate it and conduct it at the premiere without ever
revealing that the piece was Liszt’s. More importantly, such attribution disre-
garded the fact that the style of Liszt at the time the work was written, had
practically nothing in common with the early Lisztian style the piece suppos-
edly resembles. However, when the work made its first appearance on records
in 1982, Maurice Hinson, editor of the American Liszt Society wrote for the
liner notes:
This Concerto in the Hungarian Style contains plenty of Lisztian charac-
teristics and any pianist that had played Liszt will find no difficulty in
detecting them and assigning the composition to Liszt […] Furthermore,
listening to the work provides the definitive proof. I played this re-
cording for a professional pianist who was unaware of the story. He ex-
claimed: “Liszt!” before reaching the opening cadenza. Listening to the
complete work confirmed the initial verdict.
This paragraph serves as a perfect example to demonstrate the status of at-
tributional studies in music, in which biased “expert” opinions are averred
even if the supporting evidence is lacking. Needless to say, the latest edition of
the New Grove (2000) does not list the piece as Liszt’s but Menter’s.
Understandably, given the lack of authenticity checking, in the history of mu-
sic there had been a considerable number of deliberate forgeries, in which a
composer presented a work of his own, pretending to have found the manu-
script of a hitherto unknown work by a master of the past. This was the case
with Marius Casadesus’ “Adelaide” violin concerto, attributed to Mozart, or
the various pieces by Fritz Kreisler that he attributed to Vivaldi, Couperin,
Pugnani, Dittersdorf, Francoeur, Stamitz and others.
As a last example, an interesting and rather extreme case of doubtful author-
ship is the most famous of organ pieces, J.S.Bach’s Toccata and Fugue in D
minor BWV 565, which music lovers refer to as The Toccata and Fugue. Al-
though the public view it as quintessential Bach, there is no manuscript and

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the oldest extant copies date from Mozart’s time. Peter Williams, in his notes
for Peter Hurford’s recording for Argo stated:
…questions now beset it: […] Was it the work of Bach at all? […] Famil-
iar though the work is, it does contain many touches very untypical of
Bach and his period. Indeed, some of the most distinctive features are
problematic. For example, where else in the music of Bach is there a mi-
nor plagal cadence at the close? Is it not odd to have a solo pedal entry in
a fugue? What other organ piece begins in octaves? And are such simple
effects as the dramatic diminished sevenths really characteristic of its
supposed composer?
All these objections are stylistic in nature, and major ones at that. More re-
cently, a strong case has been made for this composition to be originally a solo
violin piece, and Bach’s authorship has become even more doubtful.
In general, when scholars analyze the style of a composer they refer to one as-
pect at the time, e.g. their repeated use of particular devices, such as certain
sequences, harmonic progressions, falling melodies, rhythmic combinations or
formal preferences. Such considerations often offer important insights into the
composer style, but it is apparent that observations of this sort are not quantita-
tive in nature.
In “Numerical Methods of Comparing Musical Styles”, F.Crane and J. Fiehler
state: “A musical style is so complex an organism that common- sense meth-
ods can hardly deal with it, except one element at the time” (Crane & Fiehler,
1970). This is true about practically all of the stylistic observations of scholars.
Moreover, there is no standardized systematic approach that would allow for
comparative studies, such as trying to determine the differences between two
composers of similar style like Mozart and Haydn. In this computer age, there
is a clear need of a rational tool for dealing with attributional studies and
chronological problems in music.
To put it briefly, in musicology there are no objective tools to measure style
and their absence creates serious problems for authorship studies.

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1.2 Feasibility
There is an a-priori question: Is it possible to characterize musical style in a
quantitative way?
In order to answer, the starting point should be the awareness that, when
someone is conversant enough with the music of the common practice period,
the audition of just a short fragment of an unknown piece – ‘short’ meaning
often less than one minute long – provides grounds to establish with good ac-
curacy the approximate date of composition of the piece, and – with favorable
circumstances –, additional details about it such as the nationality of the com-
poser. Undoubtedly, the stylistic elements allowing for such process must be
present in the music, even if they have not been explicitly disentangled. At this
level, attribution could be viewed as a series of successive approximations.
There are large-scale elements that tell the specialist in a matter of seconds
which of the major periods of music history the piece being heard belongs to.
The following steps are in search for finer details that would narrow down the
possibilities.
1.3 The nature of the solution
Assuming it is possible to create a rational tool to measure styles, what would
this rational tool be? In the article “Computers and Music” for the first edition
of The New Grove, Michael Kassler and Hubert S. Howe (jr.) wrote:
To appreciate the importance of explicating musical and musicological
processes as algorithms, consider that having an algorithm that verified
or falsified the statement ‘x is in the style of Beethoven’ for any given
composition ‘x’, would be equivalent to understanding the style of Bee-
thoven so well that one could direct a machine to recognize compositions
written in this style. Hence, if one’s understanding of this style is insuffi-
cient to achieve algorithmic explication, one’s knowledge of the style is
less certain than it might be. (Kassler & Howe, 1980).

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The authors clearly recognized the desirability of the existence of such algo-
rithm, although their position is a bit extreme. In light of the success of literary
stylometry, which certainly does not claim to understand the style of the au-
thors whose writing it recognizes, their claim of equivalence between “under-
standing” and “recognizing” an author’s style is unsubstantiated. It is apparent
that style understanding is a sufficient but not necessary condition for style
recognition. It would be possible to come to a more restricted view of what
this algorithm needs to be. It is convenient to start by referring to literary
stylometry in order to clarify similarities and differences.
1.4 Literary stylometry
1.4.1 Points of contact with the Music style problem
In contrast with the sad state of affairs in music, literary stylometry has existed
and bloomed for some forty years. Popular science magazines and TV pro-
grams have reported the most spectacular cases in which a computer program
has reliably ratified or rejected an attribution, such as the case of the poem
“Shall I die” attributed to Shakespeare, or the solution of the two-century old
controversy about the author of The Federalist Papers. Text style analysis is no
longer a matter of subjective opinion. Computers have made possible to estab-
lish numerical criteria to assign probabilities to particular authors.
David Holmes in “The Evolution of Stylometry in Humanities Scholarship”
(1998) has given a concise coverage of forty years of studies in the area. He
began stating that at the heart of stylometry “lies an assumption that authors
have an unconscious aspect to their style, an aspect which cannot consciously
be manipulated but which possesses features which are quantifiable and which
may be distinctive.”
“The historical development of stylometry”, Holmes wrote, “is reflected in the
choice of quantifiable features used as authorial discriminators”. Those tried
have been, successively, word length, sentence length, ‘Yule’s characteristic
K’ (a measure of word frequencies based on Zipf’s law), all found to be not re-
liable, until the breakthrough in 1964 by Mosteller and Wallace, who used fre-

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quencies of function words – such as conjunctions, prepositions, and articles –
an approach that is still valid. Burrows, between 1987 and 1992 established
the method that “has now become the standard port-of-call for attributional
problems in stylometry” by applying multivariate statistics to the same fea-
tures, “indicating that the way in which authors use large sets of common
function words such as ‘by’, ‘the’, ‘from’, ‘to’, etc, appears to be distinctive.
He had tapped into that subconscious usage of words for which, at the lexical
level, stylometrists had been searching for effective quantifiable descriptive
measures.
Holmes stated that the use of multivariate methods was well established in
stylometry, mentioning studies in the 1990s that use cluster analysis, principal
components, discriminant analysis and correspondence analysis. Simultane-
ously, since stylometry can be construed as a problem of pattern recognition,
there has been an influx of methods from artificial intelligence, beginning with
neural networks in two papers from 1993 and 1994 and genetic algorithms in
1995. He concluded that “the role of artificial intelligence techniques in
stylometry seems one of vast potential. They appear to be excellent classifiers
and require fewer input variables than standard statistical techniques”. As for
the future, he said, “we can expect expansion in the use of automated pattern
recognition techniques such as neural networks, to act as tools in the resolu-
tion of outstanding authorship disputes”. He also mentioned the then recent in-
troduction of content analysis as a stylometric tool and the exciting prospect of
the “transition from lexically based stylometric techniques to syntactically
based ones”. In this respect is worth mentioning the contribution of Cynthia
Whissell, a proponent of “emotional stylometry” touted as “a new stylometric
technique – one which adds some degree of meaning to word-counting analy-
ses” (Whissell, 1997). She argues that
a combination of stylometric measures with emotional measures pro-
vides an improved method of text description which comes closer to rep-
resenting the complexity of critical commentaries that describe authors’
styles than do techniques which do not quantify emotion.

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The technique, pioneered by Osgood (1969), considers two dimensions that
explain about 80% of the variance in semantic differential ratios.
It must be apparent that music stylometry faces similar problems and, a priori,
a great number of ideas from literary stylometry could be directly applicable to
music, beginning with the application of multivariate techniques. The initial
assumption by Holmes quoted above, “that authors have an unconscious as-
pect to their style, an aspect which cannot consciously be manipulated but
which possesses features which are quantifiable and which may be distinctive”
is at least equally reasonable if not more in music than in language since for a
certain musical composer, given the range of available choices, these are
freely determined according to personal preferences rather than constrained by
semantics.
1.4.2 Differences between music and literature
But the translation of stylometric methods to music is not straightforward.
Language and music occur along time, and both seem to consist of phrases and
paragraphs. But, in spite of this superficial similarity, music and language are
radically diverse. In his insightful article on musical style for the New Grove,
Robert Pascall states that language is essentially oriented towards meaning
whereas “music is oriented toward relationships rather than meaning” (Pascall,
2001). A language is a system of symbols, words, that stand for objects, ac-
tions and qualities referred to as articulated by grammar, whereas musicolo-
gists repeatedly have warned that “music is not a language, there is no gram-
mar of music” (Roger Lustig, 1990). “Music cannot be treated as a symbol
system. It is unreasonable to inquire about the meaning of music” […] “The
analogy to language is entirely false. Musical syntax does not at all function in
the same way as linguistic syntax. Music has no semantics.” (Eliot Handel-
man, 1990).
In language, the meaning is something lying behind the words, but music is it-
self the message. If it conveys a meaning, that is none other than the mutual
relationships of the sounds. “The pitches and durations that define the style of

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a composition also constitute its content” (Gustafson, 1986). R. Pascall, in the
aforementioned article, states:
There is no consistent natural meaning in music in relation to natural
events, and there is no specific arbitrary meaning as in language. The
meaning in music comes from arbitrary order evolved into inherited
logic and developed dynamically.
Were a composer asked about the meaning of his music, he could only reply:
“I only mean what I am expressing, i.e. music”.
This should have been always clear but it has been muddled by some compos-
ers who were so immersed in their subjectivity that really believed their craft
somehow managed to transmogrify the landscape surrounding them – or even
mundane events in their everyday life during the composition of a work –
turning them into music. There are many composers that have indicated a par-
ticular spot in some score that ‘represents’ a certain event that took place
while at work on the piece. They even believed, against all evidence, that their
music can convey to the listeners the ideas that occupied their mind during the
composition process. Granted, there are some pieces that are ‘descriptive’ in
the sense that the music literally imitates sounds of nature, – cuckoo calls, the
roll of thunder, the noise of the wind or air raid sirens –, but those resem-
blances are extra-musical and to take them as the ‘contents’ of music would
amount to mistake mimic for meaning.
Another main difference between music and language is that language is al-
ways, necessarily linear – i.e. it consists of a string of successive words,
whereas (unless the analysis is limited to music consisting of a single melody
such as a flute solo or plainchant) western music, at least after the 9th century,
has not less than two dimensions, a horizontal one (melodic) and a vertical one
(textural). In literary stylometry, the central issue has always been what words
to use as discriminators, or perhaps in what order they are placed, but there
have been no doubts that “no potential parameter of style below or above that

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of the word is equally effective” (Tallentire, cited by Holmes, 1998). On the
contrary, in music there is nothing equivalent to the word.
1.5 Musical Style
Let us take a closer look at what is musical style. Pascall points out that the
term ‘style’ “may be used to denote music characteristic of an individual com-
poser, of a period, of a geographical area or centre, or of a society or social
function”. These characteristics, of course, are the result of the composers’
choices. These choices are more alike among those of the same epoch, of the
same geographical area, and of those composing for the same social function –
such as liturgical or dance music, which is the reason why there is, for exam-
ple, a style of the classical or baroque period, a style of church music, or a
style of Czech music in the Romantic period. Pascall states that the composer
inherits an usable past and acts by intuitive vision. The product of his vi-
sion builds on a stylistic heritage, has a style and import of its own and
bequeaths an altered heritage. The stylistic heritage may be seen as gen-
eral procedures which condition the composer’s intuitive choice and in-
vention (Pascall, op.cit)
Epoch is the strongest of these elements, so that for the historian, who groups
examples of music according to similarities between them, “a style is a distin-
guishing and ordering concept, both consistent of and denoting generalities”,
so much so that “Adler described music history as the history of style” (Pas-
call).
Interestingly, however, Pascall remarks that personal style is not an important
feature in many non-Western musical cultures, in plainchant or in Western
folk music. “The relative importance of personal style is a significant and to
some extent distinguishing feature of the Western tradition, and it may be seen
with notation as part of the process of comparatively fast development in the
West” (Pascall, op.cit). Consequently, music stylometry will have to be proba-
bly limited to the period of common practice in the West up to the present day.

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1.6 Musical Analysis
There is a well-developed tradition of musical analysis in the West dating
from the earliest times within the period of common practice, but its area of
concern is centered on particular works, which it intends to explain structur-
ally as one would disassemble clockwork to figure out the way it is put to-
gether. The question that analysis tries to answer is ‘How does it work’. By
means of comparison, its central activity, analysis determines the structural
elements and discovers their function (Bent & Pople, 2001) Hence, analysis
does not deal with style except by implication, such as the identification of
similar structural elements between different works of the same composer or
epoch.
Nicholas Cook, in his Guide to Musical Analysis, explains:
There are a large number of analytical methods, and at first sight they
seem very different; but most of them, in fact, ask the same sort of ques-
tions. They ask whether it is possible to chop up a piece of music into a
series of more-or-less related independent sections. They ask how com-
ponents of the music relate to each other, and which relationships are
more important than others. More specifically, they ask how far these
components derive their effect from the context they are in. (Cook,
1987).
In the first five chapters of his book Cook gives an insightful coverage of the
most important current analytical methods – traditional methods, Schenkerian,
Psychological approaches (Meyer, Reti), Formal approaches (Set-theoretical,
Semiotic), and Comparative techniques –, and in the sixth concludes that “the
principal types of musical analysis current today do not have any real scien-
tific validity, and we therefore need to rethink what it is that they can tell us
about music”. Thus, given that the main preoccupation of analysis is not
closely related to our quest, and any of its trends “do not have a sufficiently
sound theoretical basis to become a scientific discipline in its own right”

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(Cook, op.cit.), we do not need to concern ourselves with musical analysis any
more.
1.7 A suggestive analogy
On a more philosophical level, this search could be seen as more concerned
with the structure of style as a phenomenon than the markers of style. The idea
is: Are there conceptual dimensions to the “style” construct that can be objec-
tively identified? And if so, what are they?
This is the kind of result that has been obtained in an unrelated field that could
prove a source of ideas and guidelines for this research, the area of Psychology
known as Personality Theory. From olden times, it had been observed that
people differ in their predominant desires, characteristic feelings and the way
to express them, and they do so in consistent ways across time and situations.
The Ancient Greek were the first to notice that personality traits do not occur
at random but following patterns, and produced the first taxonomy of person-
ality, the Four Temperaments of Hippocrates, which contemporary research
has validated through the Eysenck Personality Inventory. Other researchers in
the area have looked for different approaches to the problem. One of particular
interest is Raymond Cattell’s. Starting from an unabridged dictionary from
which a list of 18,000 trait terms was extracted, he reduced it eliminating
synonyms and difficult or uncommon words, until he was left with an irre-
ducible set of 171 terms. A group of judges was then asked to rate subjects us-
ing this set of words. Their ratings were factor analyzed and clustered, yield-
ing a set of 16 main personality dimensions. Two of his second-order factors
coincide with Eysenck’s. Cattell wrote that “source traits promise to be the
real structural influences underlying personality”. “Measuring behaviours in
factors [is] the first step in an analytical procedure aiming to discover the
structure and function of personality”. (Cattell, 1965).
In the 1990s a certain consensus was reached about a five factor model such as
Costa and McRae’s, the so-called “Big Five” personality variables. This set of
five variables (Conscientiousness, Agreeableness, Openness or Intellect, Ex-

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traversion or Surgency and Neuroticism or Emotional Stability) includes the
same basic two dimensions already mentioned, i.e. extraversion/introversion
and emotionality, which suggests through convergent validity (Anastasi) that
these two dimensions possess an objective reality.
All this suggests two basic ideas for the music stylometry problem. Firstly, the
variety of individual variation in human personalities is at first glance bewil-
dering. However, it takes some methodical application of multivariate statis-
tics to reveal conceptual dimensions underlying the phenomenon and the pat-
terns they create. In a similar way, at first glance, the variety of musical styles
may seem bewildering. But there must be objective dimensions in personal
music style. It should take the same kind of approach to reveal the pattern un-
derneath. The resemblance of both areas is not coincidental: Individual musi-
cal style is largely a reflection of the personality of the creator. Since music
creation is so free, so arbitrary, as composers write just what they want, there
is little doubt that the main influence in their musical style is their personality.
Cattell, as well as other psychologists, thought that there might be a mapping
of the universe of personality to the universe of musical style, and conceived
the possibility of devising a test of Personality based on musical preferences.
But he was also the one that went ahead and created the test, which came out
to the public through the Institute for Personality and Abilities Testing (Cat-
tell, R. and McMichael, R. (1960).) The test included one hundred musical ex-
cerpts, which were played for the subjects, who had to choose for each
whether Like, Dislike or Indifferent. Cattel and Saunders factor-analyzed the
results and reported finding 11 main factors, about which they say:
Our general hypothesis that these independent dimensions of choice will
turn out to be personality and temperament factors rather than patterns of
specific musical content or school seems sufficiently sustained. (Cattell
& Saunders, 1953)
Cattell found similar results for a test of preferences for paintings. While these
findings have to be taken with some caution because of the practical defects of

13

the procedure, it is a first indication of a number of personality factors aligned
with the perception of musical styles.
The ultimate goal of this project is to build a method to classify tonal music
identifying the main dimensions of style so that every tonal work can be
mapped to the region where it belongs according to its parameters. Whatever
the variables used to categorize style turn out to be, it is a mandatory result
that works of indisputably similar style cluster together. Furthermore, a work
very similar to others that are included in the training set will have to cluster
with them, thus providing a clear-cut way to assess the success of the method.
Due to the current lack of consensus about the dimensions of style, the prob-
lem calls for a method of unsupervised learning, since
Unsupervised learning considers the case where there are no output val-
ues and the learning task is to gain some understanding of the process
that generated the data. This type of learning includes density estimation,
learning the support of a distribution, clustering and so on (Cristianini &
Shauwe-Taylor, 2000).
In this way, the application of such methods to the musical database would of-
fer a first glimpse into the dimensions of musical style.

1.8 Conclusions
J. Rudman, addressing the problems of stylometry, suggested:
Study style in its totality. Approximately 1,000 style markers have al-
ready been isolated. We must strive to identify all of the markers that
make up “style” – to map style the way biologists are mapping the gene.
…The autoradiogram with its multiple markers does not claim infallibil-
ity but does claim probabilities approaching certainty…It is important to
look at as many of the myriad style markers as possible – some markers
will overlap with those of the controls and of the other suspects, but a
matching pattern should emerge (Rudman, 1998).

14

This program should be equally applicable to music. The goal is to character-
ize as wide a range of musical styles as possible by means of the widest vari-
ety of variables that could be derived from the observable elements of the ma-
terial. The emphasis should be on a comprehensive view of musical style in
the manner suggested by Rudman. This approach is basically what has been
described as “category analysis” by Bent and Pople, meaning a method that
starts with the breaking down of its material into those facets that are con-
stantly present. This would provide, in LaRue’s words, ‘a set of categories that
are satisfactorily distinct’. Each category would then be given a scale of meas-
urement, and this measurement is what would be the critical operation of the
analysis. As David Stech observes, “the depth of study required for a musical
analysis is determined by the particular goals of the analyst. To draw a few
general conclusions concerning a large number of compositions, detailed
analysis of each work may not be necessary” (Stech, 1981).
For these reasons, it would be desirable to approach the material with the open
mindedness of someone free of cultural bounds. For example, if one of the
variables of interest concerns harmonic progressions, something the composer
of the classical period was acutely aware of, there is no problem applying the
same analysis to pre-baroque or serial works for which harmonic progression
was a non-existing concept. We are interested in the parameters of the mate-
rial, not the features that the composers were conscious about. Hence, it is
immaterial if the concept of harmonic progression is anachronistic to the work
being considered.
This is the long-term goal that has served as the motivation for this project.
The great success achieved by literary stylometry has taken more than forty
years and the combined effort of many individuals. In music, nothing had been
done yet, and very little practical methodology can be adopted from that field.
It should be necessary to consider all the available aspects of music in which
conceivably a composer’s style could be distinguishable. Certain composers,
such as Finzi, are easily recognized by some inflexions of their melodies; oth-

15

ers like Stravinsky, by their peculiar rhythms and absence of melody; others
like Delius, by their harmonic language; still others by their dense textures, or
violent dynamic changes. Probably, some of these aspects will prove good
markers, but it will be unavoidable to start testing them all and submit the re-
sults to statistical analyses.
The preceding discussion gives ground to consider that:
 Music contains enough stylistic information to make possible the exis-
tence of music stylometry.
 The radical differences between music and language means that both
stylometries could only share general methods of research.
 The use of computers for multivariate techniques applied to a suitable
set of markers might result in comparable success to literary studies.
 These studies should be based on the observable elements of music,
specifically disregarding musical analysis.
 The long-term goal is to identify the main dimensions of the phenome-
non of musical style.
During the preparatory work for this project it became gradually clearer that
for most of the features of interest that are related to pitch, a prerequisite was
the knowledge of the key at each point in the musical excerpt. Therefore, the
extraction of features hinges on the determination of key. This considerable
additional problem had to be tackled first. In the process, the inadequacy of
the MusicXML format for this purpose also became apparent. MusicXML is
not conducive to harmonic studies either, as the notes of a single chord are
generally spread along several pages of text. It was decided that a new format
was required so that the vertical information was presented together in a
workable way; the new format was devised and a program was written to con-
vert the files in the database to it.
With the converted database it was possible to calculate accurately the key as
a point function. A further problem that could be solved in a pragmatic way

16

was the determination of a criterion to decide that there was no detectable key
in the music. Unfortunately, these previous tasks that had to be carried out in
order to provide the tools necessary for the extraction of features consumed
most of the available time for the project. Consequently, the feature selection
and extraction and the application of multivariate statistics had to be left for a
further stage and complete this one with a first feature-extraction program that
functionally labeled notes and chords, so that its application to the database al-
lowed obtaining basic information about tonal music in general.
Chapter 2 gives a summary coverage of previous attempts to study musical
style which furnished valuable ideas or guidelines for this project. Chapter 3
gives a general explanation of the chosen approach and the reasons for the
treatment of the material, often in view of previous work. Chapter 4 gives a
detailed account of the way the different problems were dealt with. Chapter 5
presents the results of the application of the programs to the database, and
Chapter 6 discusses the limitations of the procedure and suggests some ways
for improvement. Appendix I is a list of the pieces in the database. Appendix
II contains tables with the figures for the frequency of use of scale degrees and
chords. Appendix III provides an introduction to musical notation for people
not familiar with it. Appendix IV gives a format example for MusicXML. Ap-
pendix V is a report on the keys of the fugue themes of the first volume of Das
wohltemperirte Klavier extracted from the program output. Finally, Appendix
VI contains the scores of pieces referred to repeatedly in this project.

17

2. Previous attempts to deal with musical style
Constant Lambert (1948) observed that the composers of the Baroque and the
Classicism had no interest in developing a personal style. They borrowed from
one another, and their craft included a series of standards that allowed the me-
diocre ones to reach “the honorable level that makes them still listenable”. The
interest in the idea of style, and the fact that it is a characteristic feature of in-
dividual creators arose during the Romantic period. Consequently, during the
19th and 20th centuries there had been an interest in characterizing the style of
particular artists, writers and composers. While in music this idea has never
been pursued in a scientific and systematic manner, there have been a number
of attempts that had centered on peculiar details of individual creators’ style,
typically their consistent preference for some particular choices.
Alfred Sentieri tried to systematize this idea in his PhD dissertation “A method
for the specification of style change in music” (1978) where he proposed to
measure change in selected style details. He started with a definition: “The
commonality, the frequency and the relative occurrence of [characteristic] de-
tails make up the information which analysts observe and quantify in order to
define style” (Sentieri, 1978). Moreover, his study assumes that “aspects of
style can be detected in the order and pattern of the music symbols found on
the written page” (p.9). He proposed “a quantitative approach to analysis
based on identifying and measuring various details from the works. Specifi-
cally, he stated: “The development of style can be measured by specifying
rates of growth and decay in the use of various aspects of style”. Following
Paisley, who had defined personal style as ‘an individual’s deviations from
norms”, he views the composer as a chooser of a reduced number of elements
within the potential complete set they belong to: “A musical artist’s preference
for certain details […] can therefore be expressed statistically”.
Sentieri applied this method to the study of the measurement of stylistic
changes in the sacred vocal works of the Venetian Baroque, namely a group of
composers associated with the St. Mark Basilica between 1600 and 1750 –