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METHODS OF COMPUTER-ASSISTED MUSIC ANALYSIS:
HISTORY, CLASSIFICATION, AND EVALUATION

By

Nico Stephan Schuler

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
School of Music

2000

ABSTRACT
METHODS OF COMPUTER-ASSISTED MUSIC ANALYSIS:
HISTORY, CLASSIFICATION, AND EVALUATION
By

Nico Stephan Schuler

Computer-assisted music analysis, which emerged almost 50 years ago, pro-
vides analytical tools that help solve problems, some of which may be unsolvable
without the assistance of the computer. Unfortunately, most research in the area
of computer-assisted music analysis has been carried out, again and again,
without any explicit review of preceding attempts and accomplishments. Even the
most recent research bears traces of two fundamental flaws' that have plagued
most research carried out to date: there is no Classification of analytical methods
within a comprehensive historical framework, and there is no critical evaluation of
those methods.

This dissertation is an attempt to solve the problems related to these two
flaws. Chapters 1 and 2 lays out a historical framework for computer-assisted
music analysis, showing how it has been related to the development of computer
technique and information theory, and how it has been applied to aesthetics. The
source materials for these chapters consist of about 1,700 published and
unpublished writings, including dissertations and internal research papers from

many countries, that were collected and analyzed over the past several years.

Chapter 3 presents, within this historical framework, a general system Of
Classification for computer-assisted music analysis. It gives specific characteris-
tics Of each Classified category of analysis, showing the components and
strategies of the methods, as well as developmental trends within the category.

All three of these chapters (1, 2, 3) that present the history and classifica-
tion of computer-assisted music analysis draw not only on music theory and mu-
sic history, but also consider related developments in linguistics, computer sci-
ence, aesthetics, psychology, and artificial intelligence.

Chapter 4 presents a computer program MUSANA that has been devel-
oped by the author and the German physicist Dirk Uhrlandt for the analysis of
music, as well as for the simulation and evaluation of music-analytical methods.
The chapter presents the results created by using the program to evaluate the
premises of a few Of the analytical methods described in Chapters 2 and 3, and
shows how the program revealed limitations of some of the analytical methods. It
also shows, in one case, how to formulate a new, more successful method. Still,
overall, the Chapter shows that the most important contribution of the program is
the way it enables reflection on the methods used and the awareness it engen-
ders of how those methods effect the outcome and the goal of the analysis.

Finally, the dissertation (chapter 5) suggests new kinds of evaluation and
new methodologies that could be fruitfully employed in the area of computer-
assisted music analysis in the future. An extensive bibliography is provided,
comprising the 1,700 published and unpublished writings on computer-assisted

music analysis, collected as source material for the dissertation.

Copyright by
Nico Stephan Schuler
2000

For My Loving Parents, Karin & Dr. Jflrgen Schuler

ACKNOWLEDGMENTS

I gratefully acknowledge with deep appreciation the criticism and guidance of my
dissertation advisor, Professor Mark Sullivan. He not only taught me many
aspects of music and of English language, but also of reality and life.

I am indebted to the members of my committee for their helpful comments:
Professor Bruce Campbell, Professor Charles Ruggiero, Professor Bruce
Taggart, Professor Michael Largey.

Special recognition is given to my former teachers (in Germany) who
always, and fully, supported my research interests and ideas: Prof. Dr. Manfred
Vetter (1'), Prof. Dr. Gerd Rienacker, Prof. Dr. Reiner Kluge, Dr. Lutz Winkler, and
UMD Ekkehard Ochs.

I am extending a very special word of gratitude to my wife, Sunnie, for her

love, moral support, and extreme patience.

May 5, 2000 V Nico Schiller

vi

PREFACE

This dissertation makes use of author-date citations, i.e. the author's last name
and the year Of publication are given in running text. For direct quotations, the
page number is added after the year, separated by a comma. "Author" means
here the name under which the work is alphabetized in the list of references and
may, thus, refer tO author(s), editor(s), compiler(s), etc. (See The Chicago
Manual of Style, 14th edition, Chicago: The University of Chicago Press, 1993. p.
641 .)

German research plays an important role in computer-assisted music
analysis. If not specified otherwise, all German quotations in this dissertation are
translated by the author.

The most frequently used terminology of measurements derived from
statistics and information theory is defined in Appendix A. Appendix 8 gives a
general overview of the history of computers and computing and provides a
thorough background for readers unfamiliar with these developments. Finally,

Appendix C reproduces the score of the Mozart pieces analyzed in chapter 4.

vii

TABLE OF CONTENTS

LIST OF TABLES ...........................................................................

LIST OF FIGURES ..........................................................................

INTRODUCTION ............................................................................

CHAPTER 1
PHILOSOPHICAL AND REPRESENTATIONAL ASPECTS OF

COMPUTER-ASSISTED MUSIC ANALYSIS ........................................
1.1. The Philosophical Rationale Of Computer-Assisted Music

Analysis: lnforrnation Theory and Aesthetics .......................
1.2. On Developments of Music Encoding ....................................

CHAPTER 2

HISTORICAL ASPECTS OF COMPUTER-ASSISTED MUSIC ANALYSIS ..

2.1. Predecessors and 'Relatives' Of Computer-Assisted Music

Analysis ......................................................................

2.2. Computer-Assisted Music Analysis in the 19505 .....................

2.3. Computer-Assisted Music Analysis in the 19605 .....................

2.4. Computer-Assisted Music Analysis in the 19705 .....................

2.5. Computer-Assisted Music Analysis in the 19805 .....................
2.6. Computer-Assisted Music Analysis in the 19905 .....................
2.7. Synopsis ........................................................................

CHAPTER 3
CLASSIFICATION OF METHODS OF COMPUTER-ASSISTED MUSIC

ANALYSIS .......................................................................... ‘ .............
3.1. Design of a System of Classification ....................................

viii

Page

xi

xii

10

10
15

21

21
33
36
57
74
94
109

114
114

3.2. Approaches to Computer-Assisted Music Analysis and their
General Characteristics .................................................. 1 18
3.2.1. Approaches Drawing on Statistics and Information

Theory ............................................................... 1 18
3.2.2. Analyses Drawing on Set Theory ............................. 119
3.2.3. Other Mathematical Approaches .............................. 119
3.2.4. Hierarchical Approaches ......................................... 120
3.2.5. Spectral Analyses ................................................. 121
3.2.6. Cognitive and Artificial Intelligence Approaches ........... 121
3.2.7. Synopsis: Combined Methods .................................. 122
CHAPTER 4
THE ANALYSIS PROGRAM MUSANA AS AN EVALUATION TOOL FOR
STATISTICAL AND INF ORMATION-THEORETICAL APPROACHES ........ 123
4.1. MUSANA: Possibilities, Use, and Structure ............................ 123
4.1.1. MUSANA'S Music-Analytical Possibilities and Use ....... 124
4.1.2. Encoding and Organization of Memory ..................... 126
4.1.3. Partial Flowcharts of MUSANA and its Procedure
"Analyzing" ......................................................... 129

4.2. Computer-Assisted Comparative Analyses of Haydn and Mozart
Trios via Selected Statistical and Information-Theoretical

Methods ..................................................................... 133
4.2.1. MUSANA Study No. 1 ........................................... 134
4.2.2. MUSANA Study No. 2 ........................................... 140
4.2.3. MUSANA Study No. 3 ........................................... 144
4.2.4. MUSANA Study No. 4 ........................................... 146
4.3. Summary ........................................................................ 153
CHAPTER 5
FINAL REMARKS: DIRECTIONS FOR FURTHER EVALUATION AND
FOR NEW METHODOLOGIES ......................................................... 154

APPENDICES
Appendix A: Overview of Measurements Derived from Statistics
and Information Theory .................................................. 161
Appendix B: The Technical Basis of Computer-Assisted Music
Analysis: Remarks on the History of Computers and

Computing .................................................................. 168

Appendix C: Selections of W. A. Mozart's Ft’infundzwanzig Stdcke
(fanf Divertimenti) ft’ir drei Bassetthdmer (KV 439”) ............. 177
BIBLIOGRAPHY ............................................................................. 192

Table 1:
Table 2:
Table 3:
Table 4:
Table 5:
Table 6:
Table 7:
Table 8:
Table 9:
Table 10:

Table 11:

Table 12:

Table 13:

Table 14:

Table 15:

Table 16:

LIST OF TABLES

Page
Pitch code in MUSANA ........................................................ 127
Tone Durations in their Mathematical Relationship .................... 128
Tone Duration Indices ......................................................... 128
Allegro from Divertimento l, upper voice ................................. 136
Allegro from Divertimento I, middle voice ................................. 136
Allegro from Divertimento l, lower voice .................................. 137
Allegro from Divertimento II, upper voice ................................. 137
Allegro from Divertimento II, middle voice ............................... 138
Allegro from Divertimento ll, lower voice ................................. 138
Allegro l and II. Pitch Averages and Entropies .......................... 142
No. 2 and No. 4 from Divertimento l. Pitch Averages and
Entropies ......................................................................... 143
Allegro I and Il. Average Interval Sizes ................................... 145
No. 2 and No. 4 from Divertimento I. Average Interval Sizes ....... 146
Allegro Ill, upper voice. Entropies (Pitch) and Growths of
Entropy ........................................................................... 149
Allegro Ill, upper voice. Entropies (Pitch and Duration) and
Growths of Entropy ............................................................ 150
Allegro Ill, upper voice. Entropies (Duration) and Growths Of
Entropy ........................................................................... 151

xi

LIST OF FIGURES

Figure 1: Modified Paisley Model for Selecting a Controlled Database

in Studies Of Style ............................................................. 69
Figure 2: System of Classification of Computer-Assisted Music Analysis 117
Figure 3: Word-element in MUSANA ................................................. 129
Figure 4: Partial Flowchart of MUSANA .............................................. 131
Figure 5: Flowchart of the Procedure "Analyzing" ................................. 132

xii

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a.
“

INTRODUCTION

Music analysis, including computer-assisted music analysis, is often practiced
and taught without any reference to, or reflection on, the premises of the
methods employed. One of the few writings acknowledging methodological
concerns in the area of music analysis (Wolfgang Horn 1996) points out that
analysis is not possible without language and concepts, which means that there
is nothing like 'pure cognition.' If 'pure cognition' of composition does not exist,
then practicing analysis and teaching analytical methods must include some
reflection on its purposes. Music analysis is not an independent discipline—and it
depends on very Specific theoretical system5—, nor is it an activity to be defined
once and for all. Rather, music analysis is a method, which means it is a way to
reach specific goals, it is a means to an end.

One way to handle these methodological problems of music analysis is to
examine the premises of different methods; methods of music analysis need to
be classified and described. While this task is partially completed for 'traditional'
methods of music analysis (e.g., by Hermann Beck 1974, Diether de la Motte
1987, and Jonathan Dunsby & Arnold Whittall 1988), classifications and
descriptions are still lacking for new (especially computer-assisted) methods of
music analysis. (An exception are, certainly, the classifications and descritions in
Ian Bent's monograph Analysis from 1987.) A critical evaluation is also urgently
needed, but the question why a methodological approach to music analysis is
necessary? must be answered after introducing other theoretical considerations.

For Wolfgang Horn (1996, 12), analysis is, first of all, neither a doctrine

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nor a theory. It is not a formal-logical activity, but it has to do with the application
Of concepts to Objects of experiences. This is the reason why analytical activity is
so hard to understand and formalize. The activity 'analyzing' is characterized by
examining musical objects that are supposed to be resolved "into simpler
constituent elements" (Bent 1987, 1), and by the manner of resolving them.

But what is 'music analysis' supposed to resolve? Ian Bent's definition
continues: "Music analysis is the resolution of a musical structure into relatively
simpler constituent elements, and the investigation of the functions of those
elements within that structure." (Bent 1987, 1) But the "resolution of a musical
structure" into "constituent elements" is not the resolution of an unknown object,
but of an intemalized experience: Acoustical events, or their notation, function as
a result of experiences and concepts. (Horn 1996, 12)1

Analytical resolutions are usually communicated via language. Here,
language rules need to be applied. The product, the analytical text, can be
verified with the help of logic. Also important, the choice of the concepts on which
the analysis is based needs to conform to the goals of the analysis. The (logical)
terminological frame as well as the conceptional frame are most crucial and must
be explained in the analytical text.

Wolfgang Horn distinguishes between two main approaches: The first

 

1 Horn writes there: "Die 'Auflbsung einer Struktur' in 'konstitutive' Elemente
bedeutet nicht das Zerlegen eines uns fremd gegeni‘rberstehenden Objektes,
sondern einer bereits 'verinnerlichten' Erfahrung. Akustische Ereignisse bzw. ihr
schriftlicher Niederschlag fungieren gleichsam nur als Substrat fi‘rr Erfahrungen
und Begriffe."

answers the question "How is this done?"; the second answers the question
"What is this?". "The results have, in both cases, only illustrative character,
because the theory 'knows' concepts," and you apply concepts, but do so within
a framework relating to a specific Object. These kinds of analyses are important
in historical research for getting an overview, but they are better used to
catalogue compositions and relate them to types. Generally, analyses are
dependent on their methodological basis: "Only if the basis of an analysis is
discovered, can you ask about the relevance of the analysis, and even if the
question is only about the relevance to my subjective, current interest."2 (lbid.,
13-14)

A In summation, analyzing music should not only be done "right" and
"logically," but the framework of the analysis needs to be justified. 'We Should not
only talk about analysis, but also, and especially, about its terms and
conditions!” (lbid., 16) Reflections on the framework of music analysis, its
purposes, and its goals are most important, because they determine which

methods can, and Should, be applied.

Music analysis can be classified with regard to the kind of music analyzed, the

methods used, the general approach taken, etc. Any classification needs to be

 

2 "Erst dann, wenn man den Rahmen einer Analyse erkannt hat, kann man nach
ihrer Relevanz fragen, und sei es auch nur nach derjenigen Relevanz, die eine
Analyse fi.'Ir mein subjektives gegenwartiges lnteresse hat."

3 "Nicht nur fiber Analysen, sondern auch und gerade iner ihre Voraussetzungen

Iohnt es sich zu reden."

in

based on a logical framework; that means that a level of Classification (level of
abstraction) has to group characteristics on the same epistemological level.4
Dieter de la Motte (1987), for example, distinguishes the following

analytical categories:

a) Large-Scale Form -) Detailed Structure
b) Measure-by-Measure Analysis

c) Analysis of a Vocal Music

d) Category Analysis

e) Comparative Analysis

f) Special Analysis

9) Tendency Analysis

h) Statistical Analysis

i) Analytical Details

j) Analysis with no Prerequisites

Here, different epistemological levels are mixed, such as classifying with regard
to musical categories (e.g., form, structure), with regard to the kind of music (e.g.,

vocal music), with regard to certain methods (statistics), etc.

 

‘ Epistemology is the study of the methods and grounds of knowledge, especially
with regard to its limits and validity. "Epistemological level" refers, here, to a level
(in a system of classification) in which all 'members' have one main common

characteristic, eg. all 'members' of that level refer to either a method of analysis,

or to musical categories, or to kinds of music, etc.

“v

Ian Bent and his analytical categories offer a more consistent example.
Bent’s categories of analysis are within the same epistemological level, Since he
only aims at specific theories. To support that notion, he mentions the author of

each theory in parentheses:

a) Fundamental Structure (Schenker)

b) Thematic Process (Réti) and Functional Analysis (Keller)
C) Formal Analysis

d) Phrase-Structure Analysis (Riemann)

e) Category and Feature Analysis (Lomax; LaRue)

f) Musical Semiotics (Ruwet and Nattiez)

9) Information Theory

h) Set Theory

However, if Bent wishes to consider all existing, specific theories, his list is far too
short and eclectic. Other theories would have to be added: different theories of
harmony, melody, rhythm, and so on.

For this reason, another means of classifying music analysis, one
characterized by its categories of musical elements and the relation of the

approach to its goals shall be suggested here:

a) Form Analysis
b) Melodic Analysis
- Thematic Analysis
- Motivic Analysis
- Phrase Structure Analysis
C) Harmonic Analysis
d) Contrapuntal Analysis
e) Rhythmic Analysis
f) Analysis of the Relations Between Text and Music

9) Analysis of Instrumentation

Each of these categories can be sub-divided. Musical categories such as range,
type of motion, type of patterns, timbre, texture, sound, etc. are included.
To complete the classification by relating the approach to the goal of the

analysis—the following categories could be distinguished:

a) Schenkerian Analysis

b) Transformational Grammar Analysis
C) Comparative Analysis

d) Measure-by-Measure Analysis

e) Statistical Analysis

f) lnforrnation Theoretical Analysis

9) Semiotic Analysis

 

'v

 

h) Category and Feature Analysis
i) Cognitive and AI Analysis

j) Process Analysis

This list is certainly not complete. Some of these categories refer to specific
theories; other categories are very broad and refer to established categories of
music analysis. A sub-category could be created which would distinguish the
basis of the analysis: whether it is notational-based or performance-based (i.e. is
the object to be analyzed notated music or performed music).

Another kind classification is conceivable within an epistemological level
that would refer to the "kind of presentation" and to the logical order of the
analytical text. (Here, de la Motte's 'Special Analysis' would fit in, which does not
seek to prove something postulated in the beginning but to discover something
unknown by following a specified procedure.) However, there are SO many
different kinds of presentation possible that a Classification in this respect does
not seem productive. A more interesting question is whether there is a productive
Classification that refers to the goals of analyses, since this is the ultimate aim of
any analytical work. However, a Classification of analytical goals has yet to be
done as does the integration of classificational levels mentioned above in one
system of classification.

Another methodological point needs to be made, relating to theuse of
technology: All analytical methods can be supported by the use of computers in

music analysis. Computer-assisted music analysis provides analytical tools to

fl
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d

 

R.
-\I
"a.

3::

I
'v

 

help solve problems which cannot be solved with traditional methods of music
analysis. For instance, it may clarify stylistic characterizations and questions of
unclear authorship, it helps investigate (historical) musical developments, it is
useful for developing new theoretical systems, for research on acoustics and
performance, as well as for cognitive and artificial intelligence research.
Introductory reading material about the history of computer-assisted music
analysis, such as the overview articles by BO Alphonce (1980, 1989) are highly
selective; dozens of dissertations and numerous American and European articles
are excluded, and most of these articles fail to reflect on the subject critically.
More Specifically, they do not Show the limits of the applications discussed. They
do not show, for example, how some of the first experiments with computer-
assisted music analysis are not complex enough and do not use enough musical

material to support their findings.

Coming back to the twin problems of creating a history of computer-assisted
approaches to music and of creating a system of classification for them leads to
the main epistemological problem of this dissertation. Even though computer-
asslsted music analysis has been conducted for only four and a half decades, it
has been conducted under various premises, using a variety of methodologies.
For that reason, it is almost impossible to talk about a real "history" of computer-
assisted music analysis. For now, the best approach is to place computer-
assisted music analysis within a classificational system based on methods, while

developing the a system of classification through a thorough study of all existing

Add

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u
and

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approaches.

The dissertation covers both: Chapters 1 and 2 lays out a historical
framework for computer-assisted music analysis, including its relationship with
developments in aesthetics that draw on information theory and computer
representations of music. Chapter 3, then, elaborates a system of classification
and shows analytical trends that pertain to each category. Although chapters 1,
2, and 3 include some evaluative statements, chapter 4 evaluates, using the
analysis program MUSANA, selected statistical and information-theoretical
methods that have been widely used for computer-assisted approaches to music
analysis. Chapter 4 also proposes a new, successful method. Finally, chapter 5
suggests directions for further evaluation of methods of computer-assisted music
analysis as well as directions for new methodologies. An extensive bibliography
is provided, comprising the 1,700 published and unpublished writings on
computer-assisted music analysis, collected as source material for the
dissertation.

ln music analysis, most important is the reflection on the methods used
and the awareness of how they affect the outcome and the goal Of the analysis.
Every method of music analysis has its advantages for certain goals of the
analysis. But every analytical method has also its limits. It is most crucial to know
both, advantages and limits; this would include knowledge of when to apply
which method. For methods of computer-assisted music analysis, the integration

of traditional and computer-aided methods seems to be most crucial.

«n

An

II.

VI

 

Chapter 1

PHILOSOPHICAL AND REPRESENTATIONAL ASPECTS OF COMPUTER-
ASSISTED MUSIC ANALYSIS

“Information Theory may well prove generally useful for studying
the creative process of the human mind. I don't think we have to
worry that such analysis will make our art more stilted and
mechanical. Rather, as we begin to understand more about the
property of creativeness, our enjoyment of the arts should increase
a thousandfold.” (Richard C. Pinkerton 1956, 86)

1.1. The Philosophical Rationale of Computer-Assisted Music Analysis:

Information Theory and Aesthetics

The results predicted by Richard C. Pinkerton have hardly been realized. But
especially with regard to certain developments in the area of Artificial Intelligence
during the 19905, research has produced results that came much Closer to
Pinkerton's vision of the usefulness of information theory for studying creative
processes. (See 2.6.)

Pinkerton was one of the first to explore the application of information
theory to music, specifically to music analysis. The philosophical rationale,
however, was ultimately provided by several people: George D. Birkhoff (1931,

1950), Abraham Moles (1956a, 1956b, 1958, 1962, 1966), and by Max Bense

10

“I

 

(1954, 1966, 1969) and his disciples Helmar Frank (1964, 1968), Rul
Guntzenhauser (1962), Siegfried Maser (1971), and Frieder Nake (1974). Using
information theory, all of those people sought either to explain some aspects of
aesthetic reflection and artistic cognition, or both, or to analyze or synthesize
'artistic artifacts'.

Information theory itself was based on a model, partly mathematical and
partly physical, relating to the transmission and reception of messages
(‘inforrnation'). In this context, information was related to the potential variety of
messages in contexts and the probabilities of messages. For instance, if a
melodic phrase in a piece of music occurs for the first time, it is an unexpected
event, i.e. it has a probability of zero; hence, it has a high degree of originality
and it "modifies the behavior of the receptor" (Moles 1967, 22). If a melodic
phrase occurs many times, its probability increases, and the originality, the
degree of 'infonnation', decreases. In 1949, Claude E. Shannon defined a
measure of information, called 'entropy', as a logarithmic function of the statistical
probabilities of different messages. (See Shannon and Weaver 1949, 49 ff.)
Thus, information was considered measurable to the extent that it could --
determine how predictability and unpredictability relate to the variety of a system.

Taking a different tact, Bense's aesthetics had its origin in the theory of
signs. His attempts to create a mathematical notion of aesthetics, a quantitative,
descriptive notion he called 'information aesthetics' ['Informationsasthetik'], came
out of his interest in cybernetics, and was based on the analytical procedures

described by the US-mathematician and physicist George David Birkhoff. In the

11

(ID

ll)

) .

 

 

 

19205, Birkhoff had tried to develop a formula for dealing with aesthetics,
defining aesthetic measure (M) as a quotient Of the order (O) of an 'aesthetic
Object' and its complexity (C): M=O/C. (See Birkhoff 1950, 288-306, and 320-
333.) Moles, on the other hand, in his 'aesthetic perception theory', based his
theory on the evaluation of experimental data and statements, evaluation in
which the relation of innovation and redundancy was very important. (See Moles
1958.) Moles distinguished between semantic information and aesthetic
information, a distinction based on the insight that Shannon's information theory
was hardly applicable to the analysis of art works in terms of their artistic value
('aesthetic information'), but instead was related to what he called the 'inner
structure' of these art works ('semantic information').5

Responding to the aesthetic theories of Bense and Moles, Helmar Frank
proposed an 'exact information theory' (Frank 1964, 1968). He combined
automata theory, system theory, and sign theory, with informatiOn theory and
theories drawn from experimental psychology. To define his ’subject model'
mathematically, using theories of automata (i.e., the subject is viewed as the
addressee of the message, which is the work Of art), he needed such categories
as 'surprise value' ['Uberraschungswert'] and 'conspicuousness value'
['Auffalligkeitswert']. F rank's integration of empirical research and experimental
psychology in his theory is even more important than his theory per se. In this

sense, his theory can be seen as an early case of cognitive research like that

 

5 An overview of "Aesthetics of Music and Information-Theory", mainly based on

Moles' theory, was also given by Jan L. Broeckx (1979, 105-125).

12

done in the 19805 and 19905.

A follower of Bense, Siegfried Maser (1971), proposed the creation of a
'numerical aesthetics', derived from Baumgarten's definition of aesthetics as the
science Of the critical assessment Of beauty. Maser interpreted Baumgarten's
model of aesthetics as an Objective, scientific aesthetics, based on three
sciences: the 'science of the real' ['Realwissenschaft'], the 'science of the formal'
['Fonnalwissenschaft'], and the 'science Of the intellect' ['Geisteswissenschaft'].
He proposed distinctions between 'macro aesthetics’6 ['Makroasthetik'] and 'micro
aesthetics'7 ['Mikroasthetik'] in the process of formulating a 'Complete aesthetic
analysis'8 ['vollstandige asthetische Analyse'] (Maser 1971, 91). Maser's method
Of an 'aesthetics by measurement ['Malsasthetik'] is based on the precise
quantitative description of objects, which he sees as the 'rational basis' for an
'aesthetics of value' [Wertasthetik']. He thinks that the more rigorously the rational
basis for the formulation of values is defined, the more convincing will be the

speculations and conceptions derived from this basis.9

 

6 The formula for calculating the 'Macro Aesthetics' is: Macro Aesthetic Measure
(MAE) = Order 1 Complexity.

7 The formula for calculating the 'Micro Aesthetics' is: Micro Aesthetic Measure
(M...) = Entropy / Redundancy.

8 The formula for calculating the 'Complete Aesthetic Measure' is: Macro
Aesthetic Measure (AE) = [(MAE + M...) I 2] birk.

9 "Je praziser aber diese rationale Basis formuliert wird, desto iiberzeugender
wirken die darauf begrilndeten Spekulationen und Wertkonzeptionen." (Maser
1971, 125).

13

All Of the attempts mentioned above, which tried to describe aesthetic artifacts
with mathematical methods, specifically with methods derived from information
theory, were relatively unsuccessful in formulating meaningful philosophical
generalizations about works of art. The failure to distinguish different levels of
aesthetic information contained in art works was one of the main reasons for the
lack Of success (see, for instance, Kasem-Bek 1978). Although the mathematical
description of complex aesthetic processes and attempts to calculate aesthetic
values produced few significant results, the application of information theory to
the analysis of structural norms of art works, specifically of motives and phrases,
did produce some significant results.10 Since repetition of musical structures is
responsible for creating musical form, the analysis of musical structures based
on the measurement of redundancy was fruitful, particularly when it was

embedded in observations of musical form.11

 

1° Regarding aesthetic perception, Coons and Kraehenbuehl (1958, 128) call this
the level of concept formation. It goes beyond the level of simple perception. In
the same article, they also suggest defining information as a quotient of
'nonconfirming tests of predictions' and 'predictions tested' (ibid., 139). See also
Kraehenbuehl and Coons 1959.

‘1 This notion was already supported in the theoretical articles (i.e. with no
practical analyses of music) by Leonard B. Meyer (1957) Joel E. Cohen (1962),
Fritz \Mnckel (1964), and later by Alfred Huber (1974) and others.

14

1.2. On Developments of Music Encoding12

While aesthetics deals with how to structure productive and meaningful analysis,
encoding of music deals with the means to carry that analysis out. Both areas are
fundamental for discussing methods of computer-assisted music analysis.
Computers can be employed as a tool in composition, in bibliographic
research, to create thematic indices, and to scan, transcribe, print, and analyze
music, and so forth. Historically, the first computer applications in music spanned
two areas, composition and analysis (see 2.2.), but in all the applications that
subsequently developed one thing was required: a representation of the music in
a digital form. Since the first use of computers in the field of music, different
digital codes for representing musical relationships have been developed, and
recurrent problems relating to encoding have emerged. F. P. Brooks et al.
(1957), for instance, used a simple numeric representation of pitch and tone

duration. On the other hand, MUSIC V”, which developed in several different

 

‘2 Christoph Schnell (1985) and Eleanor Selfridge-Field (1997) presented a
detailed description of the problem. — For general information on the history of
computing, see Appendix B.

‘3 Generating sound samples was part of a research project carried out in the
mid-19505 at Bell Telephone Laboratories. (The goal of this research project was
the transmission of telephone conversations in a digitized form.) The Bell
engineer Max Mathews explored the calculation and generation of sound, coming
up with the two experimental programs MUSIC l (1957) and MUSIC II (1958),
which were able to synthesize simple sounds via a limited number of triangle-
wave functions. For this, Mathews used an IBM 704 computer. The first

15

"dialects," used several kinds of representations, many of which are still in use
today. These include the file format of SCORE, which substituted spatial
placement parameters for time—ordered parameters. MUSIC V's differentiation of
global parameters and its event list also prefigured the Standard MIDI file format.
The several hundred codes, developed over the last four decades,
correspond to a wide range of demands: from simple statistical applications to
complex cognitive ones. However, most of them suffer from one or more kinds of
problems: technical problems of their implementation, problems in the flow of
information, problems inherent in a certain type of notation, or the problems in
the limitations of the relation between the system and the user. (Schnell 1985,
289 f.) Fortunately, the means of entering the digital representation into the
computer are independent of the purpose of the code and has posed few
problems. Christoph Schnell (1985, 44) distinguished the following fundamental,
most frequent input possibilities:
0:0 input from a special keyboard,
0:0 input with the help of a mechanized music editor,

0:0 input from a conventional computer keyboard,

 

comprehensive synthesis program, MUSIC III, was completed on an IBM 7094 in
1960. Soon after, James Tenney became involved in the project, followed by
Hubert Howe, Godfrey VIfinham, and Jim Randall. In the mid-19605, MUSIC IV
was re-written in the high-level language FORTRAN, and re-organized and
extended as MUSIC V in 1969 at Bell Laboratories, featuring more global sound-
Control, the possibility of representing individual notes and note-patterns, and

supporting the simulation of performance nuances (like ritardando, crescendo,

etc.).

16

oz. input from a piano keyboard,

0:0 input from a direct recording of analog acoustical information, and

0:0 input from direct scanning of optic-musical information.

These alternatives relate to two basic goals: first, encoding acoustical information
as completely as possible, and, second, to encoding abstract musical
information. The latter usually involves converting the graphical information
(symbols of acoustical events, the notation) into a digital representation. In most
cases, musical information outside the score is not converted, but
sometimes—depending on the application—even notated parameters, such as
dynamics or phrasing, are omitted.

Another factor that has often been a problem, particularly in any
complicated analysis, is related to the amount of computer memory needed for
carrying out any complex analysis. If, for instance, the analysis involved several
parameters of musical events (i.e., not only pitch and tone duration), a relatively
large amount of memory was necessary. In the past, the amount needed was
often more than common computers had available.14 Until smaller computers
with large amount of memory and higher computation capacities were available
(i.e., until about the mid-19805), most applications were developed on mainframe
computers or workstations. Using these computers for musical purposes required
a high degree of technical understanding, which meant that the musicologists or
music theorists could not use their native methodology, but instead , had to use

methods native to the computer and only adapted to musical purposes.

 

1‘ See Appendix B for some examples of memory capacities of early computers.

17

(1'

 

Finally, understanding several key and related problems and solutions
require a brief discussion of some of the most widely used codes for digital
representation Of music.

The Plaine and Easy Code was initially developed by Murray Gould
(sometime before 1964), and then expanded and improved by Gould and Berry
S. Brook. It was intended to enable the transfer of musical bibliographic data to
electronic data-processing equipment (see Brook and Gould 1964, 142). The
Plaine and Easy Code enabled the replacement of conventional, purely
monolinear notation with ordinary typewriter Characters. Thereby, not only tempo,
key signature, meter, pitches, and durations could be encoded, but also some
phrasing marks and embellishments.

Starting in 1962, Jerome Wenker developed the comprehensive music
description code MUSTRAN (see Byrd 1984, and Wenker 1972c, 1974, 1978). It
included all common symbols of traditiOnal music notation, and assigned them an
alphanumeric code which was translated by the computer into an internal
machine—oriented notation. MUSTRAN was mainly used for the analysis of
(single-voice) folk songs, and went through various developments on a number
of platforms.

In the middle of the 19605, Murray Gold also co-authored the ALMA code
(Alphanumeric Language for Music Analysis) together with George W. Logemann
(see Gould and Logemann 1970). ALMA evolved from the Plaine and Easie
Code and was based on characters available on the IBM 029 Keypunch. It

enabled the encoding of data relating to the following categories: composer, title,

18

instruments, movement, tempo, clef, key signature, time signature, dynamics,
expressions (e.g., morendo), pitches, durations, texture markings, and
instrumental techniques. ALMA influenced the development of other early
musical codes and, later, was absorbed into the object-oriented program
MScore.

The Digital Alternative Representation of Musical Scores (DARMS) begun
being developed in 1963 by Stefan Bauer-Mengelberg under the name "Ford-
Columbia Input Language" (see Bauer-Mengelberg 1970) and was developed
further by Raymond Erickson and others. DARMS is strongly print-oriented, and
it includes all information of traditional music notation written for any number of
voices. DARMS "is the earliest encoding language still in use. . . . DARMS offers
a paradigm that is rarely present in the other codes discussed here: namely, that
all files stored in DARMS code may be converted to an unambiguous 'canonical'
version." (Selfridge-Field 1997, 163) It is entirely based on relative spatial
placement and not on sounding pitches. Today, DARMS exists in several
different dialects (see Selfridge-Field 1997a).

In the 19605, Michael Kassler developed IML (Intermediary Musical
Language), together with the programming language MIR (Musical Information
Retrieval). IML represented common music notation and accompanying text on
punched cards, and was designed to represent and solve problems of music
theory.

Finally, MIDI (Musical Instrument Digital Interface) was developed in the

mid-19805 as the result of collaborations between several synthesizer

19

companies. MIDI filled the need for a universal digital representation of
performed music. It originally was intended to be a real-time protocol enabling
communication between different digital hardware devices. Its format is
described in detail in Selfridge-Field 1997a. Since MIDI was exclusively designed
for the creation of performances of sound, MIDI is limited when used for music
theoretical applications. To overcome certain insufficiencies (e.g., MIDI's failure
to represent rests), MIDI extensions have been developed which provide both

performance information and score information. (See ibid.)

Musical representations were usually developed with regard to specific tasks.
Even though musical encoding is one of the bases for computer-assisted music
analysis, there are close relationships between the development of digital
encoding of music and the development Of methods of computer-assisted music
analysis (as one of the many computer applications in music). In the next
chapter, the focus will be on methodological developments of computer-assisted
analysis. However, the problems of encoding, and the codes used, will be
discussed only when when they are important to methodological developments

and when the information was available in the literature.

20

Chapter 2

HISTORICAL ASPECTS OF COMPUTER-ASSISTED MUSIC ANALYSIS

"I should like to suggest that computer analysis will become one of
the most important directions in musicology for the next generation.
One hears frequently the comment that computers will make
musicology mechanistic. Bear in mind, however, that the computer
does what it is told: even its most sophisticated procedures depend
on the imagination of the researcher for instructions; and the final
results always require further interpretation. In these two functions -
- instruction and interpretation - the researcher controls the
fundamental musicality of the investigation. If the results are
mechanistic, he cannot blame the computer." (Jan LaRue 19703,
197.)

2.1. Predecessors and ‘Relatives’ of Computer-Assisted Music Analysis

This chapter focuses on applications of statistical and information-theoretical
measurements to music analysis and on other computational approaches to

music analysis which did not include the use of electronic computers.15 In most

 

‘5 Joseph Schillinger (1948) provided detailed descriptions of mathematical
relationships in music, but he was not primarily trying to provide a methodology
for music analysis or for composition. For that reason, Schillinger's work will not

be discussed here.

21

 

cases, those approaches were direct models for computer-assisted applications,
and an understanding of the development of computer-assisted analysis is not
possible without the knowledge of these early approaches that used no
computer.

Otto Ortmann was an important pioneer of statistical analysis of music. His
article from 1937, still virtually unnoticed, involved an analysis—certainly
conducted without an electronic calculator—that was restricted to interval
frequencies of song melodies by R. Schumann (48 songs), J. Brahms (38
songs), and R. Strauss (40 songs). No distinction was made between ascending
and descending intervals; intervals of equal distance but different nomenclature
(e.g. augmented second and minor third) were grouped together. Ortmann
calculated the interval distributions of each song and an interval average for all
the songs by each composer, the percentage of songs by each composer in
which every specific interval was present, and the range of positions which every
interval holds—with regard to its frequency—in most Of the songs. No matter

what the specific results16 may be worth, and no matter how the question of what

 

‘6 Some parts of each distribution, based on songs by different composers, were
similar to each other. Others were different, and thus interpreted as
"characterizing" for the composer's style. For Schumann, the predominance of
unisons, the relative absence of wide intervals and of chromatic inflection, and
the consistency with which the frequency order unison - major second - minor
second is found (in 65 % Of the songs) was characteristic (Ortmann 1937, 7).
Characteristics of Brahm's songs were the relative absence of unisons, the
preference for thirds (especially minor thirds), the frequency order major second -

22

('1

f‘

 

 

 

validity these results hold generally for songs written by these composers,
Ortmann must be given credit for initiating a new form of analysis and for being
self-critical enough to point out the disadvantages of disregarding other musical
(and non-musical) parameters.

In 1949, Bertrand Bronson described a procedure for using an electro-
mechanical calculator—not a 'Computer'—to carry out a comparative study of
British-American folk-tunes. He used punched cards for encoding general
information (publication, collector, singer, etc.), regional information, and musical
characteristics, such as range, mode, time signature, number Of phrases, phrasal
scheme, final tone, initial interval between the upbeat and the first strong accent,
etc. Then, the sorting machine was able to automatically pick out cards with
desired characteristics. Thereby, certain musical Characteristics could be
matched with certain geographical origins, etc. Results Of this theoretical
procedure were published ten years later (Bronson 1959).

A similar, but much more sophisticated, system called cantometn'cs was

developed by Alan Lomax. It is a system for rating song performances by

 

minor second - unison (in 45 % Of the melodies), and—"not very
pronounced"—the preference for chromatic inflection (ibid., 6 ft.) Finally,
characteristics in Strauss' melodies based on interval frequency (except a slightly
predominant use of sixths) were not found (or, in other words: a uniformity is
typical); in different ways, the distributions were similar to the songs by both of
the other composers, Schumann and Brahms (lbid., 8 f.). This certainly shows
the limitations of this approach, which Ortmann himself was aware of. — In
general, Ortmann concluded a "chronological tendency towards an increase in
pitch-motion" (ibid., 9).

23

qualitative judgements.17 Rhythmic, melodic, instrumental, tempi, and other
performance characteristics, as well as text characteristics, were initially encoded
with a 37 digit rating scale, i.e. the number of slots on an IBM punch card. The
system became, later, the model for further computer-assisted studies (as, for
instance, described in Grauer 1965).

Even though Pinkerton (1956, 84) claimed that Allen I. McHose (1950)
was one of the first to use "modern techniques" for analyzing music, McHose did
not mention any use of computers in his analyses. However, his statistical
analyses of the chord structure of Bach chorales are of importance for later
computer applications in harmonic analysis. In his study from 1950, McHose
calculated the frequency of chord types, harmonic functions, inversions, etC., as
well as the frequency of non-hannonic tones. He also compared root movements
and types Of Chords in works by Bach, Handel, and Graun. But while computer
technique, at the time, was not advanced enough to handle McHose's
calculations, this kind of study became the direct predecessor of the kind of

computer-assisted harmonic analysis which evolved in the 19605.

 

‘7 Lomax' system is based on the hypothesis that "music somehow expresses
emotion; therefore, when a distinctive and consistent musical style lives in a
culture or runs through several cultures, one can posit the existence of a
distinctive set of emotional needs or drives that are somehow satisfied or evoked
by this music." (Lomax 1962, 425) See also Lomax 1976. However, Lomax's
theory is not undisputed; see, for instance, Kongas-Maranda 1970, Henry 1976,
Kolata 1978, Berrett 1979, Locke 1981, and Oehrle 1992.

24

H. Quastler reported in 195618 that Fred and Carolyn Attneave had
analyzed cowboy songs and obtained the transition probabilities for every note
preceding a particular note. Based on the analytical results, they tried to
synthesize "a few dozen" new songs in the same style, but only two of them were
"perfectly convincing" (ibid., 169).

Until the mid-19505 only simple statistical calculations were applied to
music analysis, but Linton C. Freeman and Alan P. Merriam in 1956 used a more
complex statistical method for the differentiation of two bodies of music: the
discriminant function. The discriminant function uses multiple measurements to
discriminate between two groups of music. In this case, the two groups of music
were songs of Trinidad Rada and of Brazilian Ketu. Three characteristics were
examined: the mean values of frequencies of (1) major seconds and (2) minor
thirds in proportion to the lengths of the song, as well as (3) the total interval use.
While each separate Characteristic showed insufficient discrimination of the two
groups Of songs,19 the use of the discriminant function reduced the probability of
misclassifying a single song. However, only 3 measures each of interval use from

a very small sample of only 20 songs diminished the statistical value of the

 

‘8 Quastler's report is part of the discussion, following the article of Fucks 1955,
pp. 168-169. For F. and C. Attneave themselves, the results were probably not
satisfactory enough for publication.

‘9 The mean differences for major seconds and minor thirds were each significant
beyond the one percent level of confidence, but not in the total interval use.
However, the overlaps between the two groups of songs in each separate

characteristic were too large.

25

results. Nevertheless, using a complex statistical method was innovative in that it
provided a method useful for a more sophisticated, computer-assisted analysis of
music that took place in the following decade.

In 1956, Richard C. Pinkerton published a study on "Information Theory
and Melody." In this article, he discussed entropy analysis (i.e., the analysis of
the statistical degree on 'information' in music) and redundancy analysis20 and
how each related to the analysis of 39 nursery songs. Even though all
calculations were done manually, his approach was already designed to make
use of computer assistance (see ibid., 86). Based on the analytical results of
pitch and rhythm probabilities, Pinkerton designed a network of tone relations
which enabled him to define a compositional procedure to create similar tunes.
(However, his 'composed' melodies were "highly monotonous" [Ibid., 84].)
Pinkerton's network and transition patterns could be seen as early
implementations that relate to concepts that have emerged recently in neural
network research: "Thinking of our network scheme, it is fun to speculate that a
composer's individual style may reflect networks of nerve pathways in his brain."
(lbid., 86)

Joseph E. Youngblood's applications of information theory to music
analysis (Youngblood 1958, 1960) were probably the most extensive studies of

all those that could be called the direct 'predecessors' of computer-assisted

 

2° Pinkerton calculated specifically entropy and redundancy of single tones as
well as transition probabilities. See Appendix A for a more detailed explanation of

these concepts drawing on information theory.

26

music analysis. His ambitious calculations showed the need for computer-
assistance. Youngblood's attempts to identify and define musical styles was
based on the assumption that musical style can be characterized by a stochastic
process, specifically a process that can be Characterized using a "Markov

chain“1

(Youngblood 1960, 14-15). Youngblood selected song melodies by
Schubert, Schumann, and Mendelssohn, and calculated frequencies and
probabilities of each scale degree, tone entropies and redundancies, as well as
first-order-transition-probabilities for each melody. Some of the results showed,
for example, that Mendelssohn used chromatic tones less frequently than
Schubert or Schumann, and that Mendelssohn's music was more redundant.
Youngblood also compared those results to analyses of samples of Gregorian
Chant. Almost all of Youngblood's results did not show statistical differences
Clearly enough. Due to the number of songs sampled and due to the false
assumption that redundancies of melodies alone could characterize a musical
style, Youngblood's results were not very significant.22

The analyses of musical rhythm by John G. Brawley (1959) were intended
to provide a means to characterize style. Assuming music to be a discrete
system of communication and assuming that music is an ergodic stochastic

process that has the structure of a stationary Markov chain, Brawley calculated

entropy and redundancy of selected pieces from different time periods. However,

 

2‘ See " Markov Chains" in Appendix A.

22 In comparison with Youngblood, Joel E. Cohen (1962, 152) applied the same
analytical methods to the analysis of two Rock and Roll songs. However, the
critique given here for Youngblood's research is especially true for Cohen's.

27

Brawley stated himself—with regard to an analysis of a Bach invention—"that this
analysis employing information theory is not very valuable. At best, it may tell us
a little about this particular invention, but hardly more than we could arrive at by a
less exhaustive and less painstaking analysis." The number of samples used was
too small to warrant drawing general conclusions. However, Brawley's
conceptual approach became the basis for more successful rhythm research that
followed years later.

Just as philosophical generalizations derived from information theory were
applied in a highly limited way (see 1.1.), mathematical (statistical) approaches
were applied to the analysis of Simple 'aesthetic objects' in a similar limited
manner:

Wilhelm Fucks' "mathematical analyses of the formal structure of music"23
became-an important precedent for the devenlopment of computer applications
(although F ucks' calculations were still made without the computer)“, as well as
for the elaboration of the application of information theory to aesthetics (see, e.g.,
Bense 1969). Fucks' music analytical attempts were connected with his attempts
to analyze language (e.g., Fucks 1956, 1964). His analyses of musical

compositions were usually limited to the analysis of pitch and tone duration in

selected voices. Even though his list of publications is long, most of Fuck's

 

23 See, for instance, Fucks 1975, 1958, 1962, 1963, 1964 and 1968, as well as
Fucks and Lauter 1965.

2‘ Even though Lejaren Hiller (1964, 10) mentioned that Fucks used already a
computer for his study in 1958, there is no indication for the use of computers in 1

any of F ucks' writings themselves.

28

writings are based on the same, or similar, data. Fucks usually calculated
probabilities, transition probabilities, averages, standard deviations, kurtosis and
skewness of distribution curves, as ‘well as entropies. In F ucks' analysis from
1958, for instance, his musical materials were limited to the first violin parts of
some concertos, symphonies and symphonic poems, and to the soprano parts of
some masses (Fucks 1958, 9 f.). While results of his earlier research showed a
correlation between composer, time of composition, and frequencies of pitch and
tone duration, later publications, especially F ucks' analyses of 1963,
demonstrated that standard deviation and entropy of pitches (independent of
each other) increases monotonously with the time of composition. Transition
matrixes of pitches and transition matrixes of intervals provided information on
the probabilities of pitches and intervals following each other. Based on the
transition matrixes, Fucks calculated correlation ellipses. Finally, W. Fucks and J.
Lauter (1965) calculated auto-correlations of pitches and intervals.

At the time, Fucks' methodological approach was already quite complex in
its mathematical form, especially with regard to the comparison of different
frequency distributions (pitches, tone durations, intervals, and tone pairs) and its
comparison to stochasticalIy-generated music. As such, Fuck's approach
revealed the significant potential of mathematical analysis of style. However,
Fucks' conclusions were very restricted to specific selections of compositions,
and his generalizations Of epoch Characteristics were far-fetched. An important
factor for the restricted analytical outcome was themissing distinction between

genre characteristics and personal style in music.

29

5-:

’I

”o-

nu.-

.-
.H.

“\V a\v
.5» I."
z

F ucks' methods and analytical results were harshly criticized and shown to
be erroneous by GiJnther Wagner (1976). Wagner noticed "that relative interval-
frequencies of consecutive tones cannot be seriously considered either for the
question of authenticity or for the proof of a historical development" (ibid., 67)”.
He pointed out "that the standard deviation in compositions of the same genre
and the same composer might vary as much as between compositions of
different genres by composers, which belong to different epochs" (ibid.)26. And
finally, he showed "that the relative pitch distribution is completely ruled out as a
method for answering questions about authenticity or chronology" (ibid., 69)27

A more reliable music theoretical foundation was provided by Walter
Reckziegel (1967a, 1967b, 1967c), a disciple of Fucks, in an extension of Fucks'
notion of 'exact scientific’ ['exaktwissenschaftlichen'] methods. In his analyses,
Reckziegel included the calculation of metrical units and of musical intensity. For
this purpose, Reckziegel defined formulas for calculating the entropy of the
metrical unit and the 'total entropy', which is the product of the entropy value (H)

of u different pitches and v different tone durations [H(u,v)] and of the different

 

25 ". . . dais relative lntervallhaufigkeiten konsekutiver TOne weder fi'Ir
Echtheitsfragen noch fiJr den Nachweis einer historischen Entvvicklung ernsthaft
in Frage kommen kOnnen."

26 ". . . daB die Sigmawerte [Standardabweichung, N.S.] in Werken ein und
derselben Gattung des gleichen Komponisten ahnlich schwanken kbnnen, wie
zwischen Werken unterschiedlicher Gattungen von Komponisten, die
unterschiedlichen EpOChen angehOren."

27 ". . . daB die relative Tonhbhenverteilung als Mittel zur Ldsung von Fragen der

Echtheit Oder Chronologie ganzlich ausscheidet."

30

pitches u: u-H(u,v).28 Furthermore, he calculated the 'Bewegtheit' [kind of motion]
out of the impulse frequency per metrical unit, 'intensity' and 'density' (arithmetic
mean Of metrical units). Sound structures and 'complexities' were analyzed
(deliberately) without considering harmonic progressions. Reckziegel's attempts
Show the desire to formulate methods that can deal with a musical complexity
greater than that attempted by Fucks' analyses. However, Reckziegel's analyses
were still limited with regard to the number and kind of mathematical calculations.
About ten years later, Christian Kaden (1978) discovered an interesting
connection between statistical (not computer-assisted) and traditional music
analysis, including psychological and sociological aspects. Analyzing the second
movement (Allegretto scherzando) of Beethoven's symphony No. 8 op. 93,
Kaden tried to verify his intuitive analytical judgment by statistically calculating
dependencies of elementary structures (Gestalt units), mathematically
describable as tone probabilities of higher orders.29 Kaden's approach was very
successful, and his methodology could have been easily adopted for computer-

assisted analyses.

Generally, researchers interested in non-computer-assisted approaches to music
analysis drawing on mathematics, statistics, and information theory developed an

important repertoire of analytical methods that could easily be formalized in

 

2" The exact formulas can be found in Reckziegel 1967a, 16-17.
29 The basis for this approach, the structural segmentation of music, was already
described and explained in detail by Kaden in 1976.

31

computer programs. From today's point of view, most of these approaches have
to be evaluated very critically, but without them computer-assisted music analysis

could not have emerged.

32

2.2. Computer-Assisted Music Analysis in the 19505

Even in the beginning of the 'computer age' of music analysis, communication
between scholars was very slow. At one of first early conferences on computer
applications in music (1965), Edmund Bowles phrased this problem as follows:
"There exists no clearinghouse, no center of information, no means of
intercommunication between scholars in the humanities using the tools of data
processing. Currently existing journals and learned societies are reluctant to
assume this additional burden, especially outside their own discipline. We need
more scholarly convocations such as this one. We need to avoid needless
duplication of effort." (Bowles 1970a, 38.) Since then, some journals have come
into being, and more and more conferences on the topic have been organized.
However, after looking at the publications in the area of computer-assisted music
analysis, it seems that not much has Changed since the 'beginning': scholars
know little about the history of their area, previous successes and failures are
hardly known. Thus, mistakes are duplicated, and prejudices florish. Ultimately, a
detailed history of computer-assisted music analysis is needed. This study will fill
in gaps, but applications are already too numerous and varied to describe them
comprehensively here. For now, only selected approaches can be discussed
which are representative in their use of methods. 3°

In the previous chapter, some applications which claimed to be the first

application of computers to music analysis were mentioned. However, the first

 

3° However, the bibliography is as complete as possible.

33

extensive, systematic use of an electronic computer for analytical purposes was
described by the mathematician Frederick P. Brooks et al. in 1957. Brooks
conducted an analysis-synthesis—project at the Computation Laboratory at
Harvard University“. For this project, high-order probabilities of 37 hymn tunes
were calculated. Those probabilities were then used for the synthesis Of new
melodies, using Markov chains of orders one through eight. Even though this
experiment was limited to (melodic) samples that were not structurally complex,
this procedure "permitted the production of a significant number of acceptable
tunes within a reasonable time." (lbid., 180)32

While Brooks' experiment is rarely mentioned in the literature, the work of
Lejaren A. Hiller and Leonard lsaacson has been extensively noted, specifically
their work on the Illiac Suite (String Quartet NO. 4) is mentioned in almost every
textbook on electronic music.33 The Illiac Suite was composed with the ILLIAC
computer in 1956 at the University Of Illinois. Even though the computer was not
primarily used for analysis but for the generation and selection Of random values
)34

in a type of stochastic modeling (known as the "Monte Carlo Method" , Hiller's

and lsaacson's importance for computer applications in music goes beyond

 

3‘ Youngblood 1960 also mentioned an unpublished term paper from 1955 by F.
P. Brooks, which lets assume that Brook's project was already realized in 1955.
The computer used was the Harvard MARK IV. See Youngblood 1960, 23,
footnote 42. In addition, see Neumann and Schappert 1959.

32 For sample melodies see ibid.

33 Brooks' paper was not widely available, whereas Hiller's and lsaacson's book
(1959) became available in almost every library.

3‘ See Appendix A.

34

composition. In their book (Hiller and lsaacson 1959), they suggest several
computer applications to music analysis:
0:0 statistical and information theoretical applications,
0:0 analysis of musical similarity,
0:0 pattern search,
0:0 analysis of sounds and their physical constitution,
0:0 Optical music recognition,
and based on analytical results:
0:0 realization Of continua and figured bass and to complete part writing,
0:0 missing parts could be reproduced based on statistical style analysis,
0:0 systematic generation Of musical materials for teaching purposes.
(See ibid., 165-170.) All of these suggestions were realized later on.35
With the applications described in this Chapter, not many attempts were
made during the 19505 to use new computer technique in music analysis.
Computers were, at the time, rarely available for music research. However, the
few attempts of the 19505 gave directions for more sophisticated computer-

assisted analysis of the 19605.

 

35 See Hiller 1964, discussed in chapter 2.3.

35

2.3. Computer-Assisted Music Analysis in the 19605

Available hardware severely restricted the computer applications of the 19605.
However, early applications of statistics and of information theory to music
analysis (see 2.1 .)—especially in the US—as well as music-philosophical
reflections (see 1.1.)—especially in Europe—, spurred the boom Of computer-
assisted methods of music analysis. To show specific tendencies Of those
methods, some trendsetting applications will be discussed.

In his studio for experimental music at the University of Illinois, Lejaren A.
Hiller collaborated in several analytical research projects. Three of these projects
are described in Hiller 1964.36 The first project (Bean 1961; see also Hiller and
Bean 1966) involved a comparison of four sonata expositions (by Mozart,
Beethoven, Hindemith, and Berg), mainly based on first-order entropies of
pitches and intervals as well as on the "speed of information" (i.e., of entropy),
which was calculated via note density and tempo. But while Bean's project was
not computer-assisted, Baker's research (Baker 1963)—the second project
mentioned in Hiller 1964—was partly carried out with the assistance of ILLIAC,

the first electronic computer at the University of Illinois.37 (Thus, this study is the

 

3‘6 There, Hiller gives the impression that those projects were mainly his own
research projects. However, he rather collaborated in the dissertation research Of
his students Calvert Bean (1961), Robert A. Baker (1963), and Ramon C. Fuller
(1965).

37 However, exactly how the computer was used was not described in Baker's

dissertation.

36

av

ar-

.A

first dissertation project in the area of computer-assisted music analysis.)
Modulation-free passages of 16 string quartets by Mozart, Haydn, and
Beethoven were analyzed with regard tO transition probabilities of harmonies and
of pitches as well as their relationships.38 Finally, the third project discussed in
Hiller 1964 (Fuller 1965; see also Hiller and Fuller 1967) involved the analysis of
the first movement of Anton Webern's Symphony op. 21. Here, entropy and
redundancy calculations (of higher orders) of pitches and intervals revealed,
among others, the formal structure of the piece.

WIlliam J. Paisley Chose a quite different approach to computer-assisted
music analysis. Based on communication theory, Paisley (1964) made a
fundamental contribution to identifying authorship (and with it, stylistic
characteristics) by exploring "minor encoding habits", i.e. details in works of art
(which would be, for instance, too insignificant for imitators to copy).39 To take an
example from a different field, master paintings can be distinguished from
imitations by examining details like the shapes of fingernails. Similarly, Paisley
showed that there are indeed significant minor encoding habits in music. He
analyzed note-to-note pitch transitions in the first six notes of each of the 320
themes by Bach, Haydn, Mozart, Beethoven and Brahms. He chose the
parameter 'pitch', because pitches can be easily coded for computer processing

and because some research on tonal transitions had already been reported.

 

3" However, the harmonic analysis itself was done traditionally, not computer-

assisted.
” For a general discussion on this topic, especially with regard to text analysis,

see also Paisley 1969.

37

In his first analysis“, Paisley calculated interval frequencies of up to six
semitones within the first 6 notes of two 160-theme—5amples. Furthermore, he
calculated the Chi Square Test for Goodness of Fit of those interval distributions
for the two samples. While these results could not significantly distinguish Haydn,
Mozart, and Beethoven, Paisley Claimed a successful distinction between these
composers with his second analysis, in which he calculated frequencies and chi
squares of two-note transitions between the classes tonic, third, fifth, all other
diatonic tones and all chromatic tones. In both analyses, the results of the chi
square test were then compared with results from "unknown samples" (Mozart,
Beethoven, Handel, and Mendelssohn). The results from analyzing themes by
Mozart and Beethoven could (in the second analysis) be successfully matched
with the "known" Mozart- and Beethoven-samples, while Handel and
Mendelssohn were significantly different. But even though only a modest amount
Of data was involved in this investigation, and even though a reduction of the
number Of possible intervals to seven (based on inversions as well as on
neglecting the direction) seems to be questionable, Paisley's study was well
documented and its results were, considering the time of the study, very
impressive. Several other authors referred later to Paisley's approach.

In 1969, Stefan M. Kostka wrote a set of FORTRAN-programs“1 for

analyzing string quartets by Paul Hindemith“, following IMlliam J. Paisley's

 

‘° Paisley performed the analyses on the Stanford University 7090 computer.

‘1 These programs were implemented on a CDC 3600 computer.

‘2 The music was coded in ANON, an alphanumeric coding system developed in
the course of a seminar at the University of Wisconsin, conducted by Roland

38

definition of "minor encoding habits". His task was "to test the hypothesis that
Hindemith's style shows a consistency in his use Of certain 'hidden
communicators' Of which Hindemith himself may or may not have been aware.
On the other hand,since Hindemith's style did not remain unchanged throughout
his life, it was considered worthwhile to see if his employment of some of these
communicators showed a noticeable and consistent change from the early
quartets to those written in the 19405." (Kostka 1969, 173) Kostka analyzed roots
and classes of chords“, treating each vertical event equally (regardless of their
duration or regardless of whether they contained non-harmonic tones etc.). In his
explanations, Kostka referred to Gabura (1965), who found—analyzing music by
Brahms and BartOk—only small differences in the result of weighting chords by
frequency as opposed to weighting chords by duration. Kostka tried to verify this
for Hindemith's music on the example Of the first movement of his Fifth String
Quartet44 by letting the computer calculate frequencies and percentages Of
chords. Other algorithms counted frequencies of all Chords (both by treating
inversions as independent chords and by dealing with "normal forms") and their

harmonic contexts. Finally, in horizontal analyses, various kinds of melodic

 

Jackson. Since the code originally remained unnamed and untested, Kostka
named it for his study. (See Kostka 1969, 112 ff.)

‘3 Here, the definition of "roots" and "Chords" goes back to Hindemith's theoretical
system itself, described in Hindemith 1945, 94 ff. Another system of chord
Classification, which Kostka applied, was based on the distinction between
lntervallic, Tertian, Quartal and Whole-Tone chords.

4‘ The number of pieces for such a verification remained certainly questionable.

39

intervals were calculated“, and the program searched for melodic patterns which
had been defined by the analyst, including permutations. Even though Kostka
found stringent regularities in the interval frequencies and frequencies of chord
classes in all quartets, one can hardly interpret these distributions as
"Hindemith's melodic style" (Kostka 1969, 263); analyses of other genres used by
Hindemith or other quartets by other composers would be necessary for a
verification. The inconsistencies Kostka found in other analyses (e.g. root
movements, tonality, etc.) led to the conclusion that either those characteristics
are not important for Hindemith's style or the analytical method would need to be
changed.

Kostka's study (1969) also showed a limitation of his computer-aided
approach to music analysis: the enormous volume of data (the huge number of
punched cards) made it impossible to extract, examine and compare the data "for
every theoretical question that came to mind" (ibid., 250). But Kostka's
dissertation is very important in so far as it is based on the study of former
approaches as well as on ('traditional') music-theoretical and musicological
writings pertaining to the style in the music by Paul Hindemith. Some 'traditional'

explorations of Hindemith's style could be verified by Kostka's computer-aided

 

‘5 These included: A) every Single interval; B) minor with major intervals
combined; C) minor with major and their inversions combined (e.g. descending
second and ascending seventh); D) all inversions combined: all seconds with all
sevenths etc.; E) intervals with their mirror inversions combined (minor seconds
up and down, major seconds up and down, etc.); F) all major and minor seconds,

all major and minor thirds, etc., combined.

40

study.

The possibility of quickly processing a large amount Of data with new
computer techniques was recognized in the 1960's, especially by US-scholars in
musicology and music theory. In 1966, Gerald Lefkoff (1967a) and Allen Forte
(1967a) addressed this topic at the "West Virginia University Conference on
Computer Applications in Music". Forte gave 'good' reasons for applying the
computer to music analysis: "The computer can be programmed to deal with
complex structures—such as musical composition—very rapidly. . . . A second
reason for using the computer derives from the requirements of completeness
and precision that form the basis of every computer program. . . . The design of
an algorithm, the formulation of a decision-structure to solve a problem, the
careful Checking out of a malfunctioning program—all these activities provide
clarifications and insights which would be difficult, perhaps impossible, to obtain
othenrvise." (lbid., 33-34.) Without going into details, Forte also described a
computer project46 for the (set theoretical) determination of similarities and
differences of sets, for the interpretation of those with respect to Characteristics Of
the environments in which they occur, and for the design of a structural model in
terms of set-complex theory (ibid., 39).47 Gerald Lefkoff (1967b), on the other

hand, described a system "for the study of computer-residing, score-derived

 

‘6 His set of computer programs was written in MAD.
‘7 A similar program, written in the computer language SNOBOL 3, was
described in Forte 1966.

41

(I)

musical models" (ibid., 45). Written in FORTRAN, Lefkoffs 'model' saved musical
information in time-indexed arrays: pitch, rhythmic values, vocal text, figured
bass symbols, dynamics, articulations, and editorial comments. Lefkoff then
extracted, along with data relating to other relationships, "a complete list of
melodic fragments from a group of compositions, with frequency distribution data
for the fragments within each composition and . . . [then] comparejd] the relative
frequency of occurrence of each fragment in selected groups of compositions."
(lbid., 55.) The value of Lefl<offs model can be seen in its ability to generalize
such analytical procedures and thereby discover stylistic trends. However,
Lefitoff did not describe any concrete analyses; and thus, it is questionable if his
theoretical model was indeed functioning and reaching the envisioned goals.

Milton Babbitt (1955, 1960, 1961), with his analytical approaches to
dodecaphonic and set structures, was of outstanding importance for music
theoretical developments in the US. His research provided the basis for the
manifold (US-) discussions on the use of logic-mathematical procedures in music
analysis (and likewise in composition). Since the mathematical part in set
theoretical analyses is very suitable for implementations in computer programs,
many computer applications in music theory and musicology after the mid 19605
(Babbitt 1965) are related to set theory.

Donald M. Pederson (1968), for instance, described a computer-assisted,
analytical project that used set theoretical and statisticalapproaches. After the

transformation of the musical data (contained in the scores) into a suitable code

42

for music analysis“, a program computed subset and superset relations of a
given set within the score. All set types found were also examined with regard to
interval vector and number of occurrences. Finally, another program computed
frequencies of pitch classes and generated graphic displays that showed pitch
patterns within specific voices and showed the interaction between them; it also
found instances Of fixed registration, found other pitch patterns, and displayed
the registral use of each pitch-class. Pederson analyzed Anton Webern's string
quartet op. 28 in two ways: at first, 'traditionally' "to provide a description of the
structure and the use Of the twelve-tone set and to establish the formal sectioning
Of the composition" (ibid., 73), and then, after this contextual analysis, non-
traditionally, using a computer-aided analysis of the harmonic content applying
the methods described above. Pederson concluded, that "even though the two
approaches examine different aspects of the music, the relationship found
between sections in the contextual analysis are born out by the result of the
computer processing" (ibid., 75). Even though the weaknesses of Pederson's

‘ approach were the—more or less unexplained—segmentation of the score by the
program (to find subsets or supersets of the one set which was identified by
himself) and the use of only very basic statistical measurements, Pederson did

not only combine traditional and computer-aided analysis in general, but also set

 

‘8 Pederson used the "Ford-Columbia Digital Alternate Representation of Musical
Scores" (DARMS), which was developed by Stefan Bauer-Mengelberg. Since
this code was not specifically developed for music analytical investigations,
Pederson modified it slightly. (See Pederson 1968, especially pp. 5-16.)

43

theoretical and statistical approaches.

In 1970, Allen Forte (Forte 1970a, 1970b) described two computer
programs: one calculated set complex relations (with regard to Forte 1964 and
1966), and the second program calculated set class memberships for arbitrary
sets of pitch Classes.

A pilot study that began as an attempt to automate the collection of
bibliographic data from five percent of the 17th century chanson repertory (about
300 pieces) by Lawrence F. Bernstein and Joseph P. Olive (1969) ended up as a
computer-assisted project in stylistic analysis.49 Eleven types of stylistic data
were calculated, each falling into one of the three categories: routine analysis,
statistical analysis, and numeric representation. While routine analysis included
standard harmonic analysis (determination of the roots of all triads)5°,
measurement of the rate of harmonic rhythm, and determination of the range of
the vocal parts, the statistical calculations—also designed to aid in harmonic

analysis—were directed at the number of relatively strong or weak root

 

‘9 For the music representation of this project, the Chicago Linear Music
Language was developed, which especially takes notational necessities of the
16th century chanson into account. The program was written in FAP for an IBM
7094 computer.

5° "In the performance of harmonic analysis, the chords had to be examined each
time a note changed in any of the voices. A chord was rejected for either of the
following reasons: (1) if it contained less than three notes; or (2) if it included
intervals other than thirds and fifths. If neither of these conditions prevailed, the
root of the chord was determined by examining the intervals, concentrating on
the interval of the fifth, and designating its lower member the root." (lbid, 159)

44

movements, the degree to which inversions were used, the ratio of complete and
incomplete Chords, and the frequency of recurrent harmonic adjacencies
(Bernstein and Olive 1969, 158). Numeric and graphic representation involved
ascertaining textural complexity by analyzing the interaction of several (weighted)
parameters Of style (number of voices, the amount of coordinated rhythmic
activity among the voices, the number of separate rhythmic attacks across the
polyphony, duration of the notes; ibid., 159). The authors also expressed the
need for improving the computer program for further research: The program
Should determine more than just the roots of complete triads and it should also
distinguish between structural and ornamental harmonic motion.

Astonishing for such a project in the 19605 was the (positive) reservation
towards the possibilities of using computers for analyzing music: The authors
were never "deluded into believing that the computer was in any way capable of
analyzing a piece Of music. Rather, we used the information made available by
the computer as a means of substantiating or explaining the insights into a given
composition that we gained by means of a direct confrontation with the music."
(lbid, 160)51 Thus, the analyses were indeed 'only' computer-assisted! The
information, which was electronically derived, was only 'helpful' for setting up
stylistic profiles of the composers. Even though all analytical operations could

have been done without the assistance of a computer, the compilation of the

 

5‘ It continues: "In this way, the data supplied by the computer proved to be very
useful in explaining why a particular portion of a chanson generates a sense of
tension, while another section of the same piece creates a feeling of rest." (Ibid.)

45

statistical data would have taken too much time to be considered feasible. (See
ibid.)

Michael Kassler (1966) developed a special-purpose programming
language named MIR—an acronym for "musical information retrieval". Since MIR
is both a programming language and a language for musical information retrieval,
music theoretical functions are directly expressible within the program; at the
same time, the program functions as an evaluation tool. MIR was usually used in
connection with the IML (Intermediate Music Language) music code. As such a
connection between music code and information retrieval language, the acronym
IML-MIR was used.52

Arthur Mendel (1969) applied, together with Lewis Lockwood”, the IML-
MIR system to the analysis of the style of Josquin des Prez. This included
primarily calculations of frequencies of all simultaneities}54 Using the ratio
between the percentages of all the four-part simultaneities that constitute
complete triads and the percentages of complete triads, Mendel tried to show
that one mass subsection was not composed by Josquin des Prez, as scholars

originally assumed. However, the main problem with Mendel's project was the‘

 

52 For a relatively detailed introduction see Robison 1967.

53 Lockwood already presented a progress report on this project at a »Musicology
and the Computer l« conference in 1965 (see Brook 1970a), which was
published five years later (Lockwood 1970).

5“ Future plans included calculations of interval frequencies and of correlations
between the primary accent of a Latin word and the duration of the note set to
the syllable that is immediately following. (See Mendel 1969, 51.)

46

machine-dependent implementation: Because the author had to switch
computers, the project could not be continued as planned.

Maurita P. Brender and Ronald F. Brender (1967) developed a program
for the transcription and analysis of the Bamberg Codex, notated in F ranconian
notation. The digital representation of the music included pitch and tone duration.
The output of the transcription program, punched cards, was used as input for
the analytical programs.55 The analyses focussed on occurrences of part or voice
crossing55, on melodic intervals in each part, on the "average rate of

t"57, and on vertical intervals occurring in the three positions: strong,

movemen
weak, and off beats. The output Of the program also included a graphic
description of the chord usage in every piece. With regard to existing theories of
musical practice of the Middle Ages (and specifically, during the time of the

Bamberg Codex), Brender and Brender tried to verify traditional assertions,

concerning the usage of consonances and dissonances.58 In addition to the

 

55 But here, only five motets with Portare tenors from the Bamberg Codex were
analyzed.

56 Thus, parts Of the analyses were aimed at the determination "to what extent
the motets, tenor, and triplum could be associated with a fixed position in the
Chord structure" (lbid., 206).

57 "Each melodic interval is divided by the duration of the first note of each pair
and the average taken over the whole melodic line." (lbid., 206) A surprising
result was that decreasing intervals were used more commonly than increasing
intervals, i.e. "that descending lines tend to Change or move faster and over
larger intervals than ascending lines. The motetus was normally the most
negative, followed by the triplum, then the tenor." (lbid.)

58 Even though, the assertions could be verified, "the most general fact . . . is that

47

analytical attempts, a formal (context free and only right branching) grammar of
Franconian notation was formulated. Successful translations (transcriptions)
verified the grammar.

Benjamin Suchoff selected transcriptions of Bartok's SerbO-Croatian Folk
Songs (a small collection of 75 women's songs) as a pilot project for
lexicographical orderings by computer. After dividing and numbering the
melodies in accordance with BartOk's determination of the content structure in
every melody section, and after coding”, the computer extracted string interval
sequences60 coded as sequences of positive and negative integers, and sorted
and compared the derived sequences.61 This made further statistical analyses
possible. However, in several short articles (Suchoff 1967a, 1968a, 1968b, 1969,
1970a), the analytical part was mentioned only briefly and only the indexing
approach was described in detail. The purpose of using the computer for the

analysis remained unclear, at least with regard to the identification of melodic

 

the number of exceptions is considerable. In particular, the assertion that a
consonance should begin every perfection is, at best, true only in a simple
majority Of cases." (lbid., 207) ’

59 The calculations were executed by an IBM 1130 computer (Suchoff 1967a),
later by an IBM 360 computer (Suchoff 1968). Most programs of this project were
written in FORTRAN, some in PLI1, and the music was encoded in the Ford-
Columbia code. The indexing system was devised by Harry B. Lincoln (see
Lincoln 1967a, 1967b, 1968a, 1968b, 19693, 1969b).

6° Repeated notes, interval quality, and rhythmic character were omitted from
consideration.

6‘ Thus, a melodic section of a Serbo-Croatian folk song could be presented, for
instance, as "-2 +2 -2 +2 -2 -2".

48

variants, since they were probably realized 'traditionally'. Only in Suchoffs 1968a
article,- the "machine analysis of a string content for frequency occurrences"
(lbid., 6) get mentioned, but without further details. Later, Suchoff (1969)
suggested the use of 'skeleton models' in the search for variants and orders. In
the explanation of a melodic Skeleton, Suchoff referred to BartOk; but it remains
unclear in Suchoffs writings if the skeleton models were actually derived with the
computer or by hand. In Suchoff 1970a, some analytical results were included,
e.g., prevalent types of identical interval sequences, interval frequencies, and
frequencies of phrases with a certain interval structure. Suchoffs research
certainly provided an important impulse for folksong research on the American
confinent

Richard E. Joiner (1969) conducted comparative analyses of eleven
Gregorian chants from the early period (approximately 600-1000 AD.) and
twelve from the late period (approximately 1000-1300 A.D.). His analyses were
based on frequency counts and relative frequencies Of the notes, intervals, and
phrases, and on the average length of phrases per chant. The computer program
also examined each chant for repeated patterns with the length of two to eight
notes. Even though the results—in general formulated by the author
himself—'sounded' characteristic of the music,62 the standard deviations of all

results were too large for a computational model of authentication based on the

 

62 "On the basis of this limited study, Early Chant as opposed to Late chant can
be said to be shorter, have more phrases, shorter phrases, be more limited in
range (of notes), use smaller intervals, and have less shorter repeated patterns
but more longer patterns." (Joiner 1969, 213)

49

statistical calculations mentioned above. Furthermore, no validity check was
described in Joiner's paper.

In Europe, Roland Mix (1967) extended VIfilhelm Fuck's methods of
entropy analysis. Having chosen the first movement of Haydn's string quartet, op.
76 No. 3, and the first movement of Schoenberg's third string quartet, op. 30, Mix
analyzed entropy dependencies of higher orders Of pitches, harmonies, dynamics
and rhythm. Among others, Mix discovered that the values of entropies of chords
and pitches are much higher in Schoenberg's composition than in Haydn's.
However, the relative 'contribution' of the rhythm to the total entropy is larger in
Haydn's piece than in Schoenberg's. The dependencies among the parts are
larger in Haydn's string quartet than in Schoenberg's. In a different experiment,
Mix calculated entropies of pitches (up to order six) Of the first violins of three
Haydn quartets and compared them. But even though Mix's approaches
represent great enhancements of information-theoretical analyses in their
complex application to several musical parameters, his results were limited by
the computer hardware. Methodically, Mix's approaches showed the limits of
using only one measurement for comparative analyses. But while Fucks and
Reckziegel (see 2.1.) focussed on only one voice of multi-voice compositions,
Mix had already attempted a 'vertical' analysis.

The East-German Reiner Kluge (1974)63 analyzed similarities among

 

63 Even though his dissertation was published in 1974, the (dissertation) research
was conducted between 1965 and 1968, and defended in 1968.

50

Altmark‘54 folk songs. More than 130 syntactic Characteristics were discovered
and then used to determine similarities of pairs of melodies (out Of random
samples with each about 40 melodies“). Kluge's research was outstanding,
because he developed a similarity measurement, based on the formula r = -COS
AIN, "whereby A is the number of the coincidences of two elements j, k within N
characteristics, relating to the totality of elements"66 (Kluge 1974, 31). Using
factor analysis, Kluge identified pseudo-individuals, out of which 12 different
types and mixed types were derived. The results of Kluge's analyses were limited

in several ways:

the hardware available for his research was too limited in speed and memory,

the number Of musical characteristics was not large enough,

the definition of his measurement of similarity was insufficient,

the criteria to describe melodic types were insufficient, and

the number of random samples was too small.

However, Kluge's work became very valuable for further research in this area,
because he found several characteristics and groups of characteristics as

suitable for comparative analyses of folk songs.67 Furthermore, Kluge's study

 

6‘ Altmark is an area in Southeastern Germany.

65 The restrictions to limited samples were necessary because Of on the low
efficiency of the computer used (ZRA1).

66 ". . . wobei A die Anzahl der Koinzidenzen zweier lndividuen j, k in N
betrachteten Merkmalen in bezug auf die betrachtete lndividuengesamtheit ist."
67 Those valuable musical characteristics include, for instance, 'inner melody
shape', 'melodic incipits', 'pitch repertory contains the leading tone', 'the lowest
pitch occurs after the highest', 'number Of changes of melodic direction in the first

51

showed that a successful comparative analysis is only possible if many musical

characteristics are analyzed in relation to each other.

Besides numerous articles, partly reviewed above, sources of computer-assisted
music analysis of the 19605 include also three major publications on the use of
computers in music research—Heckmann 19673, Lincoln 1970a, and Brook
1970a—, each containing several analytical articles.

Harald Heckmann's book on "Elektronische Datenverarbeitung in der
Musikwissenschaft" contained five articles on (computer-assisted) music
analysis. George W. Logemann (1967), for instance, described a system for
finding the positions in which the second voices of Bach canons from the Musical
Offering begin; he tried all possible entry points and matched arising interval
structures. Eric Regener (1967) introduced a transcription system as the basis for
analytical research“; however, this system was not fully in Operation at the time.
Tobias D. Robison's (1967) article introduced IML-MIR, but did not include any
practical application of MIR. Walter Reckziegel (1967) wrote on the use of
measurements for inner tempo and individual tempoeg, and Nanna Schoidt and

Bjarner Svejgaard (1967). reported an analysis of Byzantine Sticherarion

 

melodic line', 'unusual melodic intervals', 'unusual transition of tone durations',
and 'time signature'. See Kluge 1974, 155-157.

68 His system was called SAM, "System for Analysis of Music", and was
specifically written for the IBM 7090 computer. The transcription code used was

LMT (Linear Music Transcription).

52

melodies. The latter project is of special importance and will be discussed here in
more detail. It is of special importance, because it was, together with the
research by Brender and Brender (1967; see above), one of the first projects of
computer-assisted music analysis aimed at Medieval music. The task was to find
musical formulas in Gregorian chant, whereby neumes were encoded with a
special alphanumerical code. The computer program found all commonly used
formulas, whereby the authors verified the results via conventional analytical
methods. However, one of the most important results of this study relates to the
proportion of expenditure to benefit. In most computer applications to music
analysis—to this day—the coding and input process takes much too long, i.e. the
proportion Of expenditure to benefit is unsatisfactory. On the contrary, the
analysis of Byzantine neumes seems to be much faster with the help of a
computer: "After half an hour you have learned the code so well that you can
type the code symbols a little faster than you can write the neumes out by hand.
If you want to study the hymns 'by hand' they have to be written out in different
ways in any case. Sometimes you may have to write them out in a new way for
each new detail you want to study. Working with the computer you only need to
write the hymns out once. Aftenrvards you put the punched paper tape in the
machine and you can ask whatever question concerning the encoded material
that might enter your mind. . . ." (lbid., 194.)

Harry B. Lincoln's edition (19703) of many papers on computer-assisted

 

‘59 Thus, Reckziegel's research included further developments Of his

measurements introduced already in Chapter 2.1.

53

music analysis70 include several statistical and combinatorial approaches to the
analysis Of atonal music. Mary E. Flore (1970), Ramon Fuller (1970), and
Roland Jackson (1970) made use of frequency counts of pitches, intervals, types
of dissonances, and chord types (with a certain interval structure). Gerald Lefl<off
(1970) analyzed twelve tone rows and computed the 48 permutations as well as
similar segments within these permutations. A computer program by Ian Morton
and John Lofstedt (1970) calculated frequencies of Chordal roots (in tonal music)
and their relation to certain beats of a measure. Joseph Youngblood (1970) tried
to determine whether a composer's style is characterized by the distribution of
root progressions; mathematical measurements applied were frequency,
probability, redundancy, and chi-square probability. However, the most important
paper in Lincoln's volume with regard to computer-assisted music analysis was
probably the paper on analyzing Javanese music by Fredric Lieberman (1970)".
This research is a Classic example of dissatisfaction with results that are only
partially acceptable. While the synthesis of Javanese-style melodies on the basis
Of analytical results retained by a 'nearest-neighbor Markov process' was not
completely satisfactory, a complex system of interacting variables was
developed, which could characterize Javanese music much better than just
Markov chains by themselves. This complex System of variables included,

among others, frequencies of pitches, transition frequencies of higher orders, and

 

7° They all used either FORTRAN or SNOBOL as programming languages.
7‘ See also Hood 1967.

54

various (melodic) cadence forms.72

Barry S. Brook's book (1970a) is of importance in so far as it is a collection
of papers presented at three Greater New York Chapter meetings73 of the
American Musicological Society, two of which were on the topic "Musicology and
the Computer". There, Allen Forte, Lewis Lockwood, Barry S. Brook, Murray J.
Gould, and many others presented research on new developments in computer-
assisted music analysis.74 These two conferences as well as the "West Virginia
University Conference on Computer Applications in Music" in 1966 (Lefl<off
1967a) were the only conferences in the 19605 specifically on the topic of
computer applications in music.

A passage in Jan LaRue's article in the volume "Musicology 1960-2000"
(Brook 1970a) represents a common way of thinking during the 19605 in the area
Of computer-assisted music analysis: "May | recommend the computer to you as
an instrument without human prejudices. It has its own prejudices, numerical and
procedural. But these often act as stimulants and correctives, as healthy
balances and supplements to human attitudes. With this new aid, the coming
generation of musicologists should develop a style analysis that is

comprehensive rather than selective, broad rather than personal, and rich in

 

72 Other articles in this volume (Lincoln 1970) referring to computer-assisted
music analysis (in one way or the other) are by Frederick Crane and Judith
Fiehler (1970), James Gaburo (1970), Barton Hudson (1970), W. Earle Hultberg
(1970), Theodore Karp (1970), and Michael Kassler (1970b).

73 Two meetings took place in 1965, and the third one in 1966.

7‘ This research has been discussed already earlier in this Chapter.

55

musical insight." (LaRue 1970a, 197.) LaRue was certainly right in his implication
that, at least up to the end of the 19605, computer-assisted analysis of style was
anything but comprehensive and rich in musical insight. Moreover, the goal of a
comprehensive and inter-personal, computer-assisted analysis could not even be

reached in the following decade.

56

2.4. Computer-Assisted Music Analysis in the 19705

From its beginning, computer-assisted music analysis was frequently used in folk
song research. The statistical methods used to analyze art music did not differ
from those which were most commonly applied to the analysis of folk songs.
However, folk music is smaller in scope and less complex, often involving only a
single voice. These are the main reasons computer-assisted analysis continued
to be centered on folk songs up to the end of the 19705, even though computers
became more and more powerful, easily capable of handling the greater
complexity of multi-part art music.

Many approaches of computer-assisted analysis, applied to folk songs,
followed BartOk's methods of analysis and Classification. BartOk's cataloging of
East-European melodies not only was based on melody and text incipits, but also
on different inner-musical characteristics. BartOk's methods of classification were
then further developed by Alice Elschekova (1966, 1975) and Ludwig Bielawski
(1973). Hereby, 'Classification' means "the division of a great variety [of songs]
into sub-groups on the basis of similarity with regard to certain characteristics

and the arrangement of the sub-groups"75 (Jesser 1991, 39).76 The main focus of

 

75 ". . .das Einteilen einer VIeIfalt in Unterabteilungen aufgrund von Ahnlichkeit in
bestimmten Eigenschaften und das Ordnen der so gewonnenen Gruppen".

76 The problem of similarity of musical structures cannot be discussed here,
because it goes far beyond the question Of using the computer as an analytical
tool. Instead, it must be referred to such extensive and specialized publications
like Kluge 1974, Steinbeck 1982, and Jesser 1991. See also the literature Cited in

57

computer-assisted analysis of folk music was the search for rules that put
melodies into a specific category and the search for procedures that determined
melodic variants. This, in turn, led to the development of analytical methods that
investigated single or combined Characteristics of music.

Dalia Cohen and Ruth Katz (1973, 1977), for instance, analyzed Arabic
and Israeli folk songs, attempting to construct a stylistic comparison. Calculations
included pitch frequencies and their relation to specific modes (major, Dorian,
Mixolydian, and hedjaz), transition frequencies, frequencies of certain tone
groupings, and pitch distributions in certain contexts of the songs (opening notes,
final notes, phrase endings). Furthermore, the characteristics related to style
included tone durations and rhythmic groupings. Finally, the occurrences of
certain musical characteristics were matched with each other to find specific
correlations. Findings of this research were discriminations Of songs in different
modes, eg. with regard to the existence of non-immediate repetition, the location
Of the finalis, the appearance of upbeats, the existence of exceptional meters, the
appearance of specific metric patterns, the maximum number of time values, the
maximum proportion between the longest and the shortest note, etc. Cohen's
and Katz' approach was successful, or at least has not been falsified up to this
point, because of the combination of many musical Characteristics and the

calculation of correlations between them.

 

these monographs. In Jesser 1991, see also detailed comments and references
regarding classification of melodies in general and regarding rules to bring the
melodies in a specific order.

58

Deborah and Philip Scherrer (1971) developed a measurement of melodic
variation by correlating melodic contour with rhythmic movement. The degree of
'alikeness' between two graphs of melodic motion was calculated, whereby a 'lag'
could shift the graphs horizontally to avoid calculation errors in case of
differences in tone durations between the two melodies. Thus, the computer
program" was able to calculate correlation coefficients of the contour of two
melodies, even if the rhythmic structures of the two melodies were very
divergent.

With regard to the computer-assisted analysis of. art music, one important
project of the 19705 was Dorothy Susan Gross' dissertation research and her
subsequent investigations. Her dissertation (Gross 1975a) was more or less
'only' a description of a new "set of computer programs to aid in music

analysis“, which had the goal "to duplicate the more routine aspects of analysis"

 

77 The computer program was written in FORTRAN IV. The computer used was
the CDC 6600 computer at the Space Science Laboratory of the University of
California.

78 The CAL SNOBOL programs were written for a CDC 6600 computer. The
music was encoded with MUSTRAN; besides tone duration and pitch, this
alphanumerical code also included all the dynamic and articulation markings as
well as descriptive words. The software included programs for translating the
input data (i.e., music, encoded in MUSTRAN) into an internal numerical code
(on which the calculations were based) and for Checking the data for errors. The
'dialog' between user and computer was realized mostly via punched cards. A
later version was developed in SPITBOL for an IBM 370/168 computer; see
Gross 1975b and 1981 (which are still only descriptions of the programs without
presenting fundamental analytical, and musicologically useful, results, based on

59

(lbid., 165). Since Gross' research was not primarily directed at analyzing a great

number of compositions, the value Of her research should be seen in her

methodological ideas and in the potentials as well as the structure of the

programs. The latter will be described here in more detail, as they were unique at

the time for their complexity and interactivity. The following lists of procedures

and "switches"79 also show the great variety of Characteristics analyzed. The

software included the following programs:

.0 Linear Grouping Program (looking for linear patterns formed by up to 12
consecutive events in the same voice),

0:0 Vertical Grouping Program (listing and counting the vertical structures in a
piece of music without identifying them),

0:0 Program for Thematic Analysis (searching for themes submitted by the user),

0:0 Program for Harmonic and Set Analysis (labeling the chords [roots and
quality]80 and/or sets in a piece, using the list of groups from the Vertical
Grouping Program as reference), and

0:. Program for cumulative counting (accumulating data from two or more
pieces).

Each program used switches for specifying and 'individualizing' the analytical

 

an acceptable amount of compositions).

79 Those "switches" would select one of two sets Of instructions.

8° Incomplete chords, which could not be identified, were labeled "ambiguous".
(Gross 1975a, 109.)

60

process.81 Switches of the "Linear Grouping Program" comprised

interval calculations (included; not included; diatonic; measured upwards in
semitones),

rhythmic and metric calculations (disregard rhythmic positions; calculate
rhythmic positions; calculate metric positions),

minimum number of occurrences in order for a pattern to be printed,
parameter to be grouped (pitch; rhythm; articulation; dynamics; chords; sets),
inversion and retrograde (no consideration of both; scan for inversions; scan
for inversions, retrogrades, and retrograde inversions),

setting the minimum number of occurrences lower, for patterns found in the
top voice in order to be printed out (or count equally),

treatment of rests and repeated notes (no elision over rests or repeated
notes; ignoring rests and repetitions of a note; ignoring deviations of a certain
number of semitones from the previous note),

largest number Of notes in a group,

punching cards for the cumulative counting program (no cards; punching

captions and information; punching information). (lbid., 77)

Switches of the "Vertical Grouping Program" comprised

O

’0 margins (in beats and/or fractions of beats),

O

 

8‘ These user-controlled switches represent a feature, developed mainly in the

19705 for a rather controlled dialog between analyst and computer program.

Unfortunately, most descriptions of music analysis programs did not include such

details, so that a reconstruction of the history of this methodological feature is not

possible.

61

minimum number Of occurrences in order for a pattern to be printed,
ordering of groups (unordered groups; ordered groups of struck notes;
ordered groups of sounding notes),

parameters to be printed (pitch; rhythms; articulation; dynamics),

storing results for use in the "Harmonic and Set Analysis Program" (yes; no),
octave reduction of pitches (yes; no),

interval calculation (yes; no),

punching cards for the "Cumulative Counting Program" (no cards; punch

captions and information; punch information). (lbid., 88)

The "Thematic Analysis Program" had switches for

interval calculations (included; not included; diatonic; measured upward in
semitones),

rhythmic and metric calculation (disregard rhythmic positions; calculate
rhythmic positions; calculate metric positions),

parameter to be scanned (pitch),

treatment of rests and repeated notes (no elision over rests or repeated
notes; ignoring rests and repetitions; ignoring deviations of a certain number

of semitones from the previous note). (lbid., 101)

Switches of the "Harmonic and Set Analysis Program" were .

O
0..

style of analysis (chords including ninth, eleventh, and thirteenth chords;
chords excluding ninth, eleventh, and thirteenth chords; sets in optimal

normal order),

treatment Of dissonances (no skipping of non-chords; disregard non-chords if

62

there is a chord nearby; disregard non-chords). (lbid., 110)

The accuracy of the set of computer programs was demonstrated by
analyzing one piece each by J. S. Bach, J. Haydn, F. Chopin, and L.
Dallapiccola. However, Gross' project was important because of the combination
of melodic, harmonic, as well as set theoretical analyses within a comprehensive
set of programs.

Already in the early 19705, Ian A. Morton (1974) modeled a FORTRAN-
program82 for the analysis of tonal music on the level of perception, whereby the
program was based on a musical-psychological, 'auditory harmony model'.83
Program data included key signature, letter names of the notes, as well as their
time value and octave. The program supplied every note in a composition with at
least one numeric that relates to the key signature, to the tones that sound with it,
and to those that precede and follow it. These numerics were "obtained solely on
the basis Of relational context within a stringently defined architecture of musical
structures and keys" (Morton 1974, 265). From the numerics, the following
information could be extracted: the melodic relationships between consecutive
notes in each voice, the harmonic relationships between consecutive events,

summaries of compound events, summaries of ambiguous events, durations of

harmonies, and a graphic representation of the harmonic flow of the composition

 

82 The program was executed on a CDC 6600 computer. — See also Morton
1967 and Morton and Lofstedt 1970.

83 This model was proposed by J. C. R. Licklider and was applied to several
features of tonal music by P. C. Boomsliter and W. Creel; see Morton 1974, 262.

63

(ibid.). Using this program, Morton analyzed Bach chorales as well as the first
two harmonized measures of Tristan. In the Bach chorales, an unexpected
number Of (harmonic) ratios of greater complexity, such as 81/80, 128/105 or
160/147 (besides the classic diatonic ratios 3/2, 5/4, 5/3 etc.), were found, and
even such unusual relationships as 1323/1280 and 1701/1600 (ibid.). The
analysis of the first two measures of Tristan also reflected the complexity of
human perception. With this research, Morton developed an early cognitive
approach to computer-assisted music analysis, and was, thus, one of the heralds
of the cognitive boom in the 19805 and 19905.

In 1974, Bo Alphonce presented a computer-assisted foundation of set
theoretical analyses and provided, with it, a basis for later approaches in this
field. He developed a new algorithm for computing prime forms of sets from
cardinality 0 to 12 over a binary exponential series and their transformations,
based on all (4095) transpositions and lnversions of every prime form.84 Another
(SNOBOL3-) computer program produced a complete list Of subsets for all prime
forms of the twelve-tone-system. Furthermore, Alphonce developed an analytical
approach for invariance relations of sets or subsets: the results can be
mathematically represented (and visualized) in invariance matrices and used as
analytical tOOls. Different possibilities of interpreting similarity relations were

described as a power Of his analytical model. Alphonce' two analytical

 

8‘ Alphonce was interpreting the pc integers as exponents to the base 2 and
summing up the corresponding powers of 2. — The program was written in
FORTRAN.

64

programs”, using this methodological framework, were for either monophonic or
polyphonic/homophonic input (in the latter case, for pieces in which the set
cannot be assumed to be mostly linearly). These programs which, as Alphonce
points out, require interaction between the analyst and the program, could be
used for either calculating characteristics of sets or twelve-tone rows or for
analyzing—even tonal—pieces of music with regard to their inner structure of
subsets.

Later on, the invariance matrices calculated by Alphonce were used as
databases for several other analytical programs drawing on set theory. But
Alphonce also reached the limits of his computer applications, especially
cOncerning computer-aided segmentation: "In some early runs I came
dangerously Close to the proverbial truckload of output. Measure 1 of
Schoenberg's op. 23 no. 4 generated a pile of output about an inch thick when
scanned for all equivalent pitch-Class collections. . . . Clearly, some output
segments would quickly strike me as analytically convincing, but the price was
too high, wading through large numbers of irrelevant and coincidental finds. . . .
In general, however, I had to turn to human pre-segmentation."86

David Stech (1976, 1981) went a different methodological direction in that

he developed a FORTRAN-program for the analysis of small musical models. His

goal was to detect different types of rhythmic, melodic or intervalic patterns and

 

85 These programs were written in FORTRAN for an IBM 370 computer. About
the history Of those programs see Alphonce 1974, 171.
86 BO Alphonce in a personal communication with Peter Castine, cited after

Castine 1994, 17.

65

their inversion, retrograde and retrograde-inversion in strictly linear music, i.e. in
music in which a fixed number of voices is defined. The objects of Stech's
analyses were John Dunstable's isorhythmic motet "Veni Sancte Spiritus", Paul
Hindemith's "Fuga none in B-flat" (from Ludis Tana/is) and Edgar Varése's
"Density 21.5". Stech demonstrated, that the computer can process such
analyses very fast and accurately, but he did not take perceivable variations of
such patterns into account, i.e. he did not pay attention to the problem of
variation and similarity.

Norbert BOker—Heil (1974) developed forms of graphical representation for
interpretative analysis. He used different graphs showing the progress
0:0 of sound-density (how many voices participate, in average, in sound events in

every measure),

0:0 of the dissonant behavior”,
0:0 of the melodic activity (tone progressions or sizes of intervals), and
0:0 of tone durations.
BOker—Heil also introduced three-dimensional diagrams, in which different
conditions were connected with each other. Based on this, it was possible to

determine "style-specific forming constants" ["stilspezifische

 

87 "Here, every vertical 'chord' is considered to be 'dissonant', which does not
belong to the group of perfect consonances (two-voices) of the major or minor
triads or of corresponding sixth chords." ["Als dissonant gilt hierjede
Tonschichtung, die nicht zur Gruppe der vollkommenen Konsonanzen
(zweistimmig), der Dur- bzw. Moll-Dreiklange Oder der entsprechenden
Sextakkorde gehdrt."] (lbid., 109).

66

Formungskonstanten"] (lbid., 111) of polyphonic music, which could practically
not be found in any other way.

In the Soviet Union, music theorists also developed unique approaches to
mathematical and computer-assisted music analysis. M. I. Rojterstejn (1973), for
instance, calculated graphs and matrices Of pitch-transition probabilities of
compositions by Bach and Shostakovich. Using statistical analysis, Moisej G.
Boroda explicated "metric-rhythmic melody units" (Boroda 1977) as well as
(purely) rhythmic units (Boroda 1978), which can be found in a variety of musical
styles. Boroda (1977) showed that the segmentation of every melody is
dependent on the metric-rhythmical structure, speCifically their interrelations.
Boroda also showed that the average length of a "metric-rhythmic melody unit"
can be compared to the length of words in language. Citing compositions from
different style periods, Boroda gave examples for the arrangement of melodic
fragments as "metric-rhythmic melody units". M. A. Iglickij (1973) developed an
algorithm for stepwise modulation between any major and minor key; he
suggested using this system for analyzing strategies of modulations and their
frequencies. B. M. Gasparov (1974) developed a structuralist approach-to music
analysis; as a specific application of his approach, Gasparov analyzed harmonic
distributions in early compositions by Beethoven. Finally, T. P. Karlina and V. K.
Detlovs (1968) analyzed sequences, and melodic shiftings, in melodies and
harmonies; these sequences and shifting were then classified, depending on
interval and pitch repertoire. Karlina and Detlovs analyzed works by Bach,

Haydn, and Tchaikovsky, and showed that the application of statistical

67

measurements (e.g., mean, standard deviation) made it possible to identify
personal characteristics as well as evolutionary tendencies in the use of certain
melodic or harmonic sequences.

Fred T. Hofstetter (1979) developed a different approach to the analysis of
tonal music: Referring to earlier investigations by William Paisley, especially
referring to procedures for extracting a database in studies of style, Hofstetter
modified Paisley's model for analyzing natural language as shown in Figure 1.
This model shows how different norms, i.e. sources of variation, influence a

message:

68

UNIVERSAL ALL-MUSIC NORM

 

NOTATIONAL NORM

 

 

V

 

I l L__

REGIONAL NORM ' ‘

 

CHANNEL NORM SITUATIONAL NORM

 

 

 

SCHOOL NORM

V ' V
STRUCTURAL NORM —i 1 PROGRAM NORM
O£M

INDIVIDUAL N

 

 

 

I

TIME NORM
MESSAGE

Figure 1: Modified Paisley Model for Selecting a Controlled Database
in Studies Of Style (Hofstetter 1979, 111)

Hofstetter's methodical procedure was characterized by isolating national

influences on 130 'melodies' from 16 string quartets by Czech, French, German

and Russian composers of the 19th century. Isolating national influences was

accomplished by specifically choosing two string quartets each by Dvorak,

Smetana, D'lndy, Saint-Saens, Mendelssohn, Schumann, Borodin and

Tschaikowski. Thus, time norm (19'h century), notational norm (traditional

Western notation), "channel norm" (only string quartets were analyzed),

69

situational norm (all quartets chosen for the study were mature works), and
program norm (no extra musical associations) were each controlled. Through
quantitative analyses of the interval repertory (using the chi-square-test of
independence), it was possible to verify 'qualitative' analyses”. Hofstetter could
Show that, first, national differences between Czech, French, German and
Russian Chamber music exist, second, French chamber music was influenced by
German music, and third, Russian chamber music shows the greatest national
influence. With this method, Hofstetter demonstrated, furthermore, similarities
between Czech and Russian chamber music. These similarities were probably
due to geographical dependencies.

While Hofstetter's study can be criticized with regard to insufficient
verification Of his method and insufficient musical material analyzed, his study is
a great advance compared to most of the studies carried out during the 19605
and early 19705: different normative levels (see figure 1) are acknowledged. This
seems especially important for the categorization of different genres, but also of
different voices; not only different genres have different structural characteristics,
but also different voices within a composition are characterized by such structural
features.

In the 19705, the search for a musical grammar was probably the most
important development in computer-assisted music analysis. The basis for this
search was provided by the insight that specific compositions could be

represented in terms of a list of grammatical production rules. One Of these forms

 

‘38 Here, Hofstetter referred to Cobbett 1929.

70

of representation is the parse tree which graphically represents the syntactic
structure of a composition. One of the first attempts of applying Schenker's
theory of tonality to computer-assisted analysis of music was made by Michael
Kassler (1975a, 1975b, 1977; see also Kassler 1964). He explicated the
middleground of Schenker’s theory and programmed89 the decisions procedures
for formalized languages that constitute this explication (see Kassler 1975b, 7). A
LISP-based system for the study of Schenkerian analysis was developed by
Robert E. Frankel, Stanley J. Rosenschein, and Stephen W. Smoliar (1976,
1978). Since the programmed procedures were essentially a description of
Schenker's hearing of the musical works, this approach was one of the first to
model musical perception on a digital computer. Schenker's tonal and
transformational hierarchies were represented within the context of a symbol-
manipulation system in terms of tree transformations. A data structure was
implemented that modeled the process by which the hierarchy was (supposedly)
created. To demonstrate their computerized modeling, Frankel, Rosenschein,
and Smoliar analyzed parts of Beethoven's "Ode to Joy". They summarized their
work as follows: "Although we have not yet reached the axiomatisation stage, our
LISP-based system may prove of immediate value to the musicologist and the
composer. Computer-aided musicological and compositional projects have a long
history. We feel our formalism of Schenker's notions of musical structure could

significantly effect future developments of both fields. In almost all documented

 

89 Kassler wrote his programs in the APL programming language and used IBM
360/50 and CDC Cyber 72 computers.

71

attempts to use the computer as a tool for stylistic analysis, the data structures
employed represented musical information in the form of strings of characters. . .
. The representations fail to capture any hierarchical structure internal to a
composition. . . . We have, in fact, the capabilities for modeling such a growth
process in our LISP system as shown above by our analysis. By contrast, those
data and control structures which are based entirely on string manipulation are
inadequate in this respect. In fact, with a LISP-based model the musicologist may
more readily ask questions about 'deep structure' and its transformations which
he may use to establish criteria for stylistic analysis." (Frankel, Rosenschein, and
Smoliar 1976, 29-30)

Already in the early 19705, Otto Laske's search for a grammar of music
was an exploration of a "generative theory of music" (Laske 1972, 1973, 1974,
1975). But Laske's grammar concept was based not on notated music, but on a
formal model of empirically acquired musical activity. Thus, Laske's studies were
early studies in musical cognition. He was interested in formal properties of
cognitive tasks that process musical input. "Instead of producing a taxonomic
analysis of musical structures, Laske has turned to what is essentially a project in
cognitive psychology." (Roads 1979, 52) Laske's understanding of 'sonology'
expressed "the relationship between the syntactic structure of a music and its
physical representation in so far as this relationship is determined by
grammatical rules" (Laske 1975, 31). Laske tried to explicate musical grammars
as computer programs in so far as they, more or less, relate to musical activity,

such as composing or listening. This provided the basis for a unique analytical

72

approach developed in the early 19805 (Laske 1984; see 2.5.).

The 19705 were a rich decade for computer-assisted music analysis. Existing
(statistical and information-theOretical) methods were refined, separate
measurements were converted into complex, multi-factor analyses, and, most
importantly, the core of computer-assisted, analytical methods was extended by
psychological and set theoretical approaches as well as approaches drawing on

Schenkerian analysis and generative grammars.

73

2.5. Computer-Assisted Music Analysis in the 19805

Many research projects conducted during the 19805 aimed at the development Of
new methods Of computer-assisted music analysis. Some projects discovered
new possibilities related to using computers to simulate human cognition and
perception, drawing on cognitive musicology and artificial intelligence, areas that
were themselves spurred on by new technical developments and by
developments in computer program design. Approaches that had already
established historical precedents, those drawing on statistics and information
theory, also developed further.

Manfred Leppig (1987a), for instance, analyzed selected folk songs, using
new, and in many ways more productive, analytical criteria, such as 'affinities of
tone sequences' ['Tonfolgeaffinitaten'], 'tone identities' ['Tonidentitaten'], 'parallel
affinities' ['Parallelaffinitaten'] and 'affinities of tone environment' ['Ton-
Umgebungsaffinitaten']. Leppig also examined melodic similarities; for example,
he deleted one note in a melody and calculated statistical differences between
the original and its variation. Furthermore, with his 'phrase-analysis', he looked
for phrases or partial phrases and their retrograde, inversion or retrograde
inversion within the melodies. In other writings (Leppig 1987b, 1987c), he
described procedures that could be used to search for certain patterns and forms
like 'cascades', 'plateau-cascades', 'linearitles', 'roofs', 'stairs', 'terraces', 'chains',
'rows', etc. However, Leppig did not perform complex analyses of extensive song

material or any other existing music.

74

More complex research—with regards to the analytical objects and with
regards to the methods used—was carried out by Wolfram Steinbeck (1982),
who attempted a "classification of 500 melodic segments" of German folk songs.
This sample of 500 melody segments was randomly selected from a stock of
4500 melodies. Steinbeck described 35 characteristics. The catalog of
Characteristics comprised statistical frequencies relating to pitch (tones; repeated
tones; foreign tones to the scale; tones above, on and under the tonic; change of
direction), statistical frequencies relating to duration and proportions (change in
duration, duration sequences short-long, long-short and equal as well as clotted
and half-long transitions), pitch attributes (ambitus, minimal and maximal pitch;
mean pitch and standard deviation; key tone position within ambitus; maximal
and mean size of intervals and standard deviation; mean ascent), and duration
qualities (mean duration and standard deviation; mean duration interval; duration
share and mean duration as well as propOrtion of duration mean values of
measure emphasis or of unaccented tones). (lbid., 132 ft.) The classifications
were finally made by hierarchic cluster analysis using the correlation coefficient
rjk=Sjk/(Sj8k) as a measure for similarity, whereby Sjk is the covariance of the
Characteristic values or pitch values of the melodiesj and k, and s,- as well as 5.,
are standard deviations of each melody (ibid., 253 f.). However, Steinbeck (as
Reiner Kluge; see 2.3.) could not solve the problem of determining the similarity
between melodies in a manner that is relevant to the actual perception and
cognition of the melodies. (For such a determination of melodic similarity that is

relevant to cognition and perception, computer-assisted analyses would need to

75

be combined with empirical, psychological studies.) Instead, the characteristics of
different classes Of melodies were illustrated by the trend of melodic direction
(contour): ascending or descending melody, roof form, V-form etc.

Norbert BOker-Heil (1981) wrote a program that searched for melodic
idioms, i.e., melodic phrases that are widely used and characteristic of a group of
melodies. His goal was to determine by analysis of these characteristics the
specific region of Southern Tyrolean folk songs in which a song originated. He
used the analytical criteria of range, melodic contour, tone duration, rhythmic
groups, and phrase design. The main result of BOker—Heil's project was that 92
melodies out of 192 Southtirol folk songs (48%) could be assigned to the correct
region of origin.

Reiner Kluge (1987) presented an application of his theory of active
(complex) musical systems to the analysis of (Afro-Cuban and Algerian) ostinato
rhythms. Using the model of a 'complex system', which includes hierarchic
structures, self regulation, accidental effects, etC., the analyses were directed at
the statistical evaluation of the rhythms (specifically by calculating correlations)
and at the psychological and historical-cultural structures that were involved in
the creation of these rhythms.9° The analysis was also directed at the "inner time
organization," i.e. the time that is 'experienced' by the listener. Thus, Kluge's
analytical approach could only becarried out by linking the statistical calculations

(and their procedures) with interpretative activities of the musicologist. Even

 

9° ". . . 'dahinter' sichtbar werdende psychisch und physisch representierte,
geschichtliCh-kulturell bedingte Erzeugungsstrukturen" (ibid., 26).

76

though not actually realized with the aid of a computer, Kluge's approach to
complex data processing was an important step towards further research in the
field of Artificial Intelligence.

Alda de Jesus Oliveira (1986) used a computer program to determine,
which musical traits best characterize folk songs from Bahia (Brazii).91 Her
ultimate goal was to formulate a model that would allow music educators to teach
music using characteristics of Bahian folk music. Oliveira's calculations included
statistical frequencies related to several musical elements found in a sample of
56 folk songs.92 Based on her interpretations of the statistical results, Oliveira
Claimed to have found characteristics specific to Bahian folk song. This claim,
however, does not hold: the standard deviations Of the statistical means
(averages) were too large to characterize any selection of folk songs, and
Oliveira even stated that the "results across genres seemed to indicate more
differences than similarities" (Oliveira 1986, 131). Surprisingly, Oliveira did not
even try to verify her results using other statistical measurements and
procedures for verification. Mere statistical frequencies that are derived without

applying complex statistical measurements (e.g., multi-variate analysis or cluster

 

9‘ These characteristics included various beat contents, anacruses, rhythmic
textures, tempi, melodic ranges, intervals, melodic directions, modes I scales,
last note Of phrases, and formal structures Of melodies.

92 The songs belonged to the genres "play songs", "work songs", "religious
songs", and "dance songs". Oliveira analyzed 14 songs of each genre. The
computer program was written in BASIC and machine language for a home
computer with 64 KB memory. The encoding system used was M-PARC (see
Kostka 1984).

77

analysis), are not sufficient to characterize any group of songs, and Oliveira did
not compare Bahian folk songs with songs from other geographic areas. Without
such a comparison, and without other forms of verification, the statement that
she found "several unique characteristics of folk songs from Bahia-Brazil" (ibid.,
149) cannot be justified. In the pedagogical conclusions, her study accomplished
little more than the general assertion that regional musical characteristics are
important for the development of music educational curricula.

Another group of studies conducted during the 19805 was centered upon
the analysis of works of art music. Ann K. Blombach (1982) analyzed the
relationship between harmonic and contrapuntal elements in Bach chorales. To
determine whether harmonic or contrapuntal elements are more important in
Bach chorales, Blombach organized computer-assisted analyses of fifty
randomly selected chorales.93 This selection was limited to chorales in major ,
keys to provide a consistent set of data which is necessary for comparisons. The
computer-assisted portion of the analyses was intended to measure the (degree
of) equality of the voices and the relative musical interest (which was equated
with 'musical variety') of each voice. After transposing all chorales to C, a variety
of calculations were performed: statistical frequencies of tones (diatonic or
chromatic), duration values, first-order-intervals, pitch patterns, duration patterns,
rhythmic elements, average range of each voice, etc. Blombach used the chi-
square test to determine significant differences between the voices (i.e. at the

.001 level of the chi square test). The results showed that the settings were

 

93 The programs were written in Spitbol for an Amdahl 470 computer.

78

neither purely harmonic nor contrapuntal“. Furthermore, Ann K. Blombach used
the computer— without describing the process in detail—for frequency
calculations of scale changes in each voice, since frequent scale changes,
especially within the bass, have a primarily harmonic function.95 Blombach found
a clear contrapuntal influence in the harmonic structure of Bach chorales,
because two or more voices made frequent use of different scales at the same
time.96 The success of Blombach's study can be explained by her focus upon the
musical significance of the computational results rather than on issues of
programming; thus, she focussed on achieving an insightful combination of
computer assistance and traditional music theoretical research.

Using a concept derived from C. P. E. Bach's concept of the harmonic

circle of fifths and its two primary relationships (that between tonic and dominant

 

9" The voices were not as equal as in strong harmonic settings: the soprano
voices (i.e., the tunes) showed the greatest deviations from all other parts
(because most of them were written by other composers), but the remaining
voices were significantly different from each other, too. On the other hand, the
bass line showed—especially through frequent intervals of fourths and
fifths—strong harmonic evidence. Also, the alto and the tenor seemed to be less
'interesting' and more alike than the other voices.

95 "Usually a change of scale does not make a voice more interesting, but rather
a chromatically altered note is usually part of a harmonic structure with a specific
harmonic purpose -- for example, a secondary dominant." (Blombach 1982, 87)
96 "Bach's chorales are an ingenious combination of harmonic and contrapuntal
elements in a harmonic framework, and both elements are vital to the chorale

settings' musical success. Similarly, a careful consideration of the two elements,

79

and that between the tonic and its relative key), C. G. Marillier (1983) developed
a computer-assisted, statistical method for quantifying "tonal distance" (including
a graphical representation) and for extracting the norms of tonal structure of
classical symphonies. After creating traditional (by-hand) harmonic analyses of
all symphonies by Joseph Haydn, computer programs calculated, for instance,
the mean average duration of key areas, standard deviations and the most
remote keys reached (in means of modulation). The results showed, for example,
an outward expansion of the most remote keys reached by modulation
throughout Haydn's symphonic career (while the outward expansion is more
pronounced and consistent on the flat side), a decreasing mean tonal level, and
an upward trend in the standard deviation from the means of tonal levels. Thus,
Marillier verified his hypotheses that there is "a tendency to balance time spent in
keys sharper than the tonic with a similar time spent in flatter keys, and, that, in
the case of sonata form movements, this flattening is most noticable in
development sections" (Marillier 1983, 192). After further comparative analyses
of symphonies by Haydn, Mozart, Beethoven, C. P. E. Bach and Sammartini,
Marillier suggested "that tonal architecture can be quite idiosyncratic and could
possibly aid in ascription disputes, given large enough numbers of authenticated

works for statistically meaningful comparisons to be made" (Ibid. 199),97 his point

 

and the interactions between them, is vital to the music theorist's success in
analyzing and understanding this music." (lbid.)

97 Marillier continued: "Mozart, for instance, visits flat-side keys in his early
symphonies noticably less often than Haydn does. C. P. E. Bach is different from
all the others in his nervous habit of lengthily delaying key-establishment,

80

being that the tonal architecture may be used for solving questions of unclear
authorship.

Another example of stylistic characterization of art music based on
statistical analysis is the research by Alison Crerar (1985). Crerar analyzed 105
incipits of compositions by Valentini, Corelli, \fivaldi, Bach and Beethoven
(especially with the goal to compare Valentini with Corelli and Vivaldi), following
W. J. Paisley's earlier research (Paisley 1964). After refining and extending
Paisley's procedures by statistical calculations of pitch, intervals, and scale
degrees etc., Crerar showed that it is possible thereby to distinguish between the
works of different composers and to clarify the authorship of specific
compositions.

Dean Keith Simonton's research was also based on Paisley's analytical
attempts. Simonton (1980a) combined computer-assisted analyses of two-note
transitions within the first 6 notes of 5046 classical themes (by ten well-known
composers) with broader, more encompassing, analyses of psychological and
sociocultural factors. His goal was to find musical characteristics that make a
musical theme 'famous.’ 'Thematic fame' was defined, on the one hand, with
regard to the frequency of performances, recordings, and citations (ibid., 210).
On the other hand, "melodic originality was operationalized as the sum of the
rarity scores for each of the theme's 5 transitions" (ibid., 211). Chromaticism and

dissonant intervals played an important role in the statistical calculations. But

 

resulting in a characteristic histogram of percentage incidence of key levels."
(lbid., 199)

81

Simonton neither calculated note transitions of higher orders (beyond two-note
transitions), nor did he calculate transitions related to duration or rhythm. Even
though some of his results98 are still valid, most of them are not, especially those
dealing with the empirical determination of 'thematic fame'99 and with the
correlation of 'creativity' and Simonton's calculations of 'melodic originality'
(interpreted as 'novelty'). Recent research on musical creativity1°° does not

support Simonton's understanding of 'melodic originality'. Nevertheless, within a

 

98 Simonton's main results were: 1. 'thematic fame' is a positive linear function of
melodic originality; 2. melodic originality of themes increases over historical time;
3. melodic originality of a theme increases when composed under stressful
circumstances in a composer’s life; and 4. melodic originality is a curvilinear
inverted backwards-J function of the composer's age. (lbid., 213-215.)

99 The recognition and 'fame' of a composer and/or of some of his/her themes, for
instance, varies within different historical periods. Composers, whose themes
were very famous and recognized as 'creative' at the time, can be forgotten today
(as, for instance, the Austrian song and chanson composer Ralph Benatzky
[1884-1954]; see Schiller 1998b). However, Simonton's empirical sources were
even mostly sources of our time. Today's 'fame' of composers and their music
can also depend on political situations (see, for instance, the German composer
Hanning Schroder [1896-1987]; Schuler 1996c), on the influence of mass-media,
on traditions in music research (see the discussion on the 'music history of
heros'; Schiller 1998a) etc. etc. Even the "stressful circumstances in a
composer's life", which supposedly increase the creativity, cannot be
'compressed' into 5-year age periods as Simonton did.

10° See, for instance, Gardner 1993 as well as Feldmann, Csikszentmihalyi, and
Gardner 1994.

82

history of computer-assisted music analysis, the attempt of combining
psychological and sociocultural factors and statistical analyses was an important
step.

Later on, Simonton (1980b, 1983) refined his approach usimg 15,618
musical themes by 479 classical composers, and he considered further analytical
variables, e.g. "zeitgeist melodic originality", which is "the degree to which the
structure of a given theme departs from contemporaneously composed themes"
(Simonton 1980b, 974). With this approach, he gained more detailed and more
accurate results.101 In 1984, Simonton presented two-note transition tables from
his former studies as well as three-note transitions and more thorough
interpretations of them to support his (earlier) results. Finally, one of the goals of
Simonton's studies was to stimulate further research in music psychology and
aesthetics. However, only a few of further research projects in music psychology

and aesthetics followed Simonton's methodology, and those who did produced

 

“’1 Simonton corrected, for instance, that "thematic fame" was then represented
by an inverted-J function of "repertoire melodic originality" (i.e., unusual melody
in comparison to the entire repertiore of music listening) and that "thematic fame"
was also represented by a J function of "zeitgeist melodic originality" (ibid., 977).
Furthermore, the "thematic fame" was a curvilinear inverted-U function of a
composer's age (lbid., 979). Simonton stated, that "as the thematic richness of a
work increases, the fame of any single theme within the work becomes less
dependent on the intrinsic properties of melodic originality and becomes more
dependent on associations with other themes via the formal structure of the
piece" (ibid, 979); this shows also the problem of the definition of "theme" and the
differentiation between 'theme' and 'motive'.

83

insignificant results.

Norbert Boker-Heil (1989) tested whether compositions belonged to the
literature making up the ars subtilior (a style of late 14th century music), using a
computer-algorithm, which included calculations of several characteristics”? In
conjunction with a 'significance' function based on the relative frequency of these
characteristics, Boker-Heil noticed, for instance, that the motive C-B-C-A that
was often used by Guillaume de Machaut was also used beyond and after
Machaut (ibid., 13), but not in the ars subtilior.

Another direction of computer-assisted music analysis during the 19805
involved the application of set theory. J. Timothy Kolosick (1981) carried out "a
computer-aided, set-theoretical investigation of vertical simultaneities in selected

piano compositions by Charles lves"1°3. The main computer program, written in

APPLESOFT”, was a "Time Slicer" which extracted all simultaneous events

 

102 Those characteristics are: number of all different tone durations; number of all
different pitches; number of all notes, which have a higher duration than a dotted
eighth note (this is an arbitrary threshold); number of different 'attack-moments'
['Einsatz-Zeitpunkte'], at which the sonority changes through the entry of an
'event' within a voice or within several voices simultaneously; number of different
distances, which can be observed between two successive attack-moments;
number of active voices at a specific time; (fictitious) duration of the composition;
total number of all 'events'; etc. Hereby, an 'event' is defined as an 'entry' of a
note within a voice or the beginning of a rest. (lbid., 11.)

‘03 lves' compositions analyzed here were: The Anti-Abolitionist Riots, Some
Southpath Pitching, Study Number 22, Three-Page Sonata, Varied Air and
Variations.

1°" APPLESOFT is a BASIC-dialect. The programs were written for an Apple II

84

‘05. After translating the pitches into pitch classes and

(chords) from the score
eliminating duplicated pitches—the durations of the chords were also stored— a
program derived prime forms (based on Forte's principles). Since the names of
all prime forms were stored in the program, the output also included all set
names as well as the interval vectors. Another program searched for each Kh-
related subcomplexes and printed out their location in the composition. Also, any
two adjacent sets were compared with regard to the interval vector, and a degree

of similarity was calculated (based on Morris 1980‘”). Thus, with "some

refinement" of the theory‘°7, Kolosick wanted to show the "flow of similarity"

 

Plus Microcomputer with one disk drive. (See ibid., 21 .)

1°5 The music was coded in DARMS and stored in DATA statements of the "Time
Slicer" program.

”6 There, Morris suggested, among others, an "absolute similarity index"
("ASIM") based on the sum of the differences between the absolute frequencies
of each interval class. This sum is to be divided by the total number of intervals of
both sets. The result is a value between 0 and 1 (inclusive), whereby 1 indicates
total dissimilarity and 0 identical interval vectors. The fact that divisions by larger
numbers (larger sets) reduce the similarity index (indicating higher similarity) is
explained with the perceptive assessment that larger sets are more similar to
each other than smaller sets. Thus, in contrast to Forte's similarity relation, the
sets to be compared need not be of the same cardinality. However, Bo Alphonce
(1974, 151 ff.) originally had the idea of calculating a difference vector. But
neither Kolosick nor Morris mentioned Alphonce' fundamental work even in their
bibliography.

‘07 Kolosick's critique of Morris' similarity measure—after the analyses of lves'
compositions—was based on principles of music perception: for instance,
register or spacing have a major effect on the aural perception of chord

85

within entire compositions (Kolosick 1981, 36). Finally, a program compared any
two adjacent "time slices", where one pitch was added to an existing set to form
the next set, with regard to the Kh relationship. Then, the probability of the Kh-
relation to such sets was calculated.108 As these few examples could show, the
methodology of computer-assisted analysis based on set theory—in constrast to
all other methodologies developed for computer-assisted music analysis—did not
differ from the methodology of the original set theory at all. Here, the computer
'only' extended the capabilities of the original methodology in speed and
practicality.

Based on set theory, Mary Hope Simoni (1983) developed another

‘09. While the segmentation had to be done by hand by the

computer program
music theorist, the purpose of the program was to reduce the probability of
human error and the amount of time required for finding prime form sets with
cardinalities two to ten, their vectors, set complements, "basic interval
succession" patterns, set complex relations, similarity relations and invariances
for all pairings of sets. The program used two databases: one for all prime forms,
their set names, vectors and set complements (derived from "Appendix One" of
Forte 1973 with the addition of sets with cardinalities two and ten), and one for all

subsets and supersets of each set from the first database (obtained from

"Appendix Nine" of Alphonce 1974). Simoni used the program to analyze Five

 

similarities as well as the manner of changes within the interval vector.

1°“ For this, Kolosick used the "sign test".

“’9 The program was written in the programming language BASIC-PLUS 2 for the
computer "DEC VAX 1 1/7 80".

86

Pieces for Piano by George Crumb; she showed the usefulness and flexibility of
horizontal and vertical set-theoretical analyzes.

Probably the first commercially available set theory program for Macintosh
computers was the "Computer-Assisted Set Analysis Program" (CASAP) by
Charles H. Ruggiero and James P. Colman (1984/1990)”°. It is based on Forte's
atonal set theory as described in "The Structure of Atonal Music" (Forte 1973).111
The program allows the user to enter sets by pitch classes (integer, note names)
or as whole sets (using Forte names). The segmentation needs to be done in
advance. Every entered set receives an internal reference number so that, later
on, those sets are tracked. The calculations comprise prime forms (identified also
by Forte names), number of occurences, as well as (Forte's) similaritiy and set
complex relations (taken from Forte's Appendices). All entered sets can be saved
in an editable file. Hence, CASAP is a useful tool for the purely mathematical part
of Allen Forte's theory.

Craig R. Harris' and Alexander R. Brinkman's "Contemporary Music
Analysis Package" (CMAP; Harris/Brinkman 1987) can be seen as the most
powerful of the set theory programs. The input is pitch class sets which can have

the size of cardinality zero to twelve. All information about set classes and set

class membership is pre-calculated and stored in a database. The set of

 

11° The first version became available in 1984. The latest version is version 1.13

from 1990.
"1 But Forte's lists of possible pitch class sets are extended by sets with

cardinalities 2 and 10.

87

computer programs, developed for UN IX- and DOS-computers"? can calculate:

- prime forms (one may choose between Forte's and John Rahn's prime form
algorithms),

- ordered or unordered interval class vectors,

- invariance,

- adjacent interval vectors,

- transpositions,

- inversions,

- complementations,

- similarity, and

- sub set and set complex relations.

Optional filters could reduce the output to certain set representations (e.g.,

names, vectors, pitch class contents). The access to the set class database

allows users to write their own functions for tasks, which are not directly provided

by CMAP. In the early 1990s, Peter Castine adapted CMAP to Macintosh

computers (see Castine 1994) and implemented MIDI support.

The development of new models of syntactic structures in' linguistics
suggested new ways to describe syntactic structures in musical compositions.
Specifically the application of concepts derived from Noam Chomsky's
generative-transforrnational grammar113 to the analysis of music was of special

importance to several developments in music theory. A generative grammar is

 

"2 The program was written in C.
"3 See Chomsky 1965, 1969, and 1972.

88

based on a theory that could specify a structural description for any
(grammatically correct) syntactic structure and the rules for creating variations of
it (no matter whether the structure occurs in a sentence or a phrase of music),
instead of enumerating which sentences or pieces of music are possible. And
just as Chomsky was concerned, while developing his grammar, with with the
cognitive representation and the perception of language, those who applied
Chomsky's grammar to music theory also wanted to understand musical
cognition. As used in linguistics or music theory, a generative-transformational
grammar involves the application of a number of transformational rules and rules
for constructing phrase structures to a set of elementary relationships. Since the
model was mostly restricted to structures that are hierarchical in nature,
structural trees were often used to visualize structural dependencies, and have
become a useful concept in various aspects of (computer-assisted) music
analysis.

Fred Lerdahl and Ray Jackendoff (1983) developed another model of the
analysis of hierarchical structures; they extended the notion of a generative
grammar into a notion of "a generative theory of tonal music". Lerdahl and
Jackendoff distinguished four structural components of music: 'grouping
structure' (hierarchical segmentation into motives, phrases and sections),
'metrical structure' (hierarchical beat levels), 'time-span reduction' (hierarchy of
'structural importance') and 'prolongational reduction' (hierarchical harmonic and
melodic levels). All structural components are described by rules of the following

three types: 'well-formedness rules', 'preference rules', and 'transformational

89

rules'. Applying this theory to computer-assisted analysis, Leilo Camilleri

described grammatical structures of the melodies of Schubert's Lieder. Camilleri

developed a methodology for analyzing phrases of songs taken from Die schb'ne

Mt'illerin, Wmterreise, and Schwanengesang. This methodology was based on

the following principles:

0:0 "generation of a possible 'initial phrase' of a melody of a Schubert Lied by
means of a syntactically structured grammar with rewriting rules, based on
previous observation, subjective knowledge, etc.;

0:0 verification of the suitability of the grammar through examination of the
corpus;

oz. adjustment of the grammar by means of the formulation of other rules which
permit a correct description and generation of the phrases." (lbid., 229.)

A LISP program was entrusted to verify Camilleri's model, which showed that

specific rules (transition rules, cadence rules, and ornamentation rules) could

indeed be explicated to describe the grammatical structure of music.

Stephen W. Smoliar (1980) applied a different concept of musical
grammars to computer-assisted music analysis. Already at the beginning of the
20th century, Heinrich Schenker worked out a specific concept of musical
grammar, in which hierarchical subdivisions of the 'Vordergrund' ['foreground'],
'Mittelgrund' [middleground] and 'Hintergrund' ['background'] were analyzed. In
Schenker’s theory, the surface structure was obtained through the extension of
smaller structural units (of the background). The aim of the analytical process

was to find an 'Ursatz' [fundamental structure]. Based on this theory, Stephen W.

90

Smoliar discussed the establishment of a system for experiments in computer-
assisted Schenkerian analysis. Structural levels were represented through logical
combinations of elements (tones, chords). Smoliar's system embodied successful
Schenkerian transformations. The program provided analytical tools in the form
of macro definitions of constructs and transformations (within different levels).
Smoliar's goal was to fill a database of analyses, which can be used for analyzing
other compositions.

Other approaches to computer-assisted music analysis in the 19805 were
derived from Artificial Intelligence, an interdisciplinary area which uses computer
models to examine the intellectual capabilities of humans and the nature of their
cognitive activity. Already in the 19703, Otto Laske founded a "cognitive
musicology" that was directed at musical activities. The goal of Laske's cognitive
musicology was an empirically supported theory of musical intelligence (Laske
1977). The computer is the most important tool in formulating theories of musical
actions which are empirically verifiable. As Laske pointed out, musical artifacts
should not only be analyzed as pure syntactic structures, but also with regard to
the underlying human competence involved in the performance of music. Inthis
case, competence is defined as knowledge concerning the structure of the
medium in which a communicative act takes place; performance, on the other
hand, is understood as knowledge concerning the ways in which this
competence is utilized in the act of communication (Laske 1975, 1). In making
such a distinction, music is conceived as a series of tasks; its cognitive structure

and processes need to be analyzed. To develop this methodology, Laske drew

91

on linguistics, psychology, computer science, and artificial intelligence, and
adopted the premise that the understanding of music requires an understanding
both of structures of musical tasks and of musical processes.114 Thus, for
instance, the reading of a score by a conductor, by a musicologist, or by a music
analyst are different tasks (performance), although they require a common
music-analytical competence.115

In 1984, Otto Laske described the set of computer programs he
developed, called "KEITH," as a rule-based system generating musical
discoveries. A number of distinctions evolved from his work with this system. He
began to distinguish between three kinds of musical representations: ’what is
heard' ('sonological representation'), 'what is understood' ('music-analytical
representation'), and what is said ('linguistic or music-analytical representation'),
and saw each as a component of the analytical project. Given that Laske sought
to model both the analytical concepts of his test subjects and the problem solving
behavior involved in their music-analytical behavior, it is not surprising that in the

realm of computer-assisted analysis he would be specifically interested in what a

 

"4 An introduction to (Laske's) cognitive musicology was provided by Nico
Schiller (1995a). There, a complete bibliography of Laske's writings can also be
found. See also Balaban, Ebcioglu and Laske 1992, Schiller 1995, 1997, 19980,
1999, and Tabor 1999a, 1999b. For further developments in cognitive
musicology see Laaksamo and Louhivuori 1993 and Seifert 1993a.

"5 In this sense, musicology itself becomes a task; the understanding of its
structure and process is one goal of cognitive musicology. See Schiller 1994, 3-
4.

92

computer program had to 'know' to pursue an analysis of a specific composition.
Perhaps the most unique aspect of Laske's approach to music analysis was that
he developed a theory of analytical processes: He pointed out that a theory of
product, the kind of theory formulated by most music theorists, can be, and
should be, complemented by a theory of process. Laske conceived of music
analysis "as a discovery process that generates new concepts and conceptual
linkages between them, in a search based on systematically derived examples."
(O. Laske in Schiller 1999, 148.) His theories have much to offer for new efforts
in the realm of computer-assisted music analysis.

An approach to musical analysis that draws on Artificial Intelligence first
began to develop in the late 1980s. It is characterized by the use of a
programming concept called neural networks. Neural networks are programs with
units connected in networks, analogous to the network of neurons in the nervous
system. Specifically, neural networks are a class of dynamic computer programs
that are used by theorists (including music theorists) to analyze some activity by

"6 It involves the study of how

simulating the behavior of the nervous system.
massive numbers of various kinds of elementary units, governed by relatively
simple rules, can generate complexity and change within a large, dynamic

system. Although the approach was promising, it was not until the 19903 that

important contributions to music analysis started to be made.

 

"6 Mark Leman (1991) gave, for instance, an introduction to artificial neural
networks and their applications in musicology.

93

2.6. Computer-Assisted Music Analysis in the 19905

The 19903 ushered in revolutionary methods of music analysis, especially those
drawing on artificial intelligence research. Some of these approaches started to
focus on musical sound, rather than scores. They allowed music analysis to
focus on how music is actually perceived. In some approaches, the analysis of
music and of music cognition merged. But statistical and the other mathematical
approaches also continued to develop in substantial and sometimes astonishing
ways.

Barbara Jesser (1991) investigated an 'interactive' approach to the
analysis of folk songs, i.e., the program user was able to influence the analysical
process while the program was running. She concentrated on characteristics that
could be used to classify folk songs, e.g. the set of pitches used, the mode or
tonality, the repertory of intervals, durations, range, rhythmic incipits, accented
tones, and finally, cadence tones. In addition to her own computer program,
Jesser used a commercial database system (STAIRS)"7. She tested her
theoretical conjectures on several collections of German folk songs: a large one

containing the same 4000 19th century folk songs Steinbeck had already used

 

"7 The manner of representation of folk songs in database systems used in
Jesser's approach goes back to Helmuth Schaffrath's investigations on the use of
databases for ethnomusicological tasks (Schaffrath 1984, 1985a, 1986, and
1987). Jesser's research was conducted as part of Helmuth Schaffrath's

research project on the analysis of German and Chinese folk music at the
Universitat-Gesamthochschule [University of] Essen.

94

(see 2.5.) and some smaller ones based on German ballads. Her goal was to
define and describe different folk song types. The results of the research were
disappointing in two ways: no satisfactory measure of the degree of similarity
between songs was computed, and the songs themselves were not sufficiently
differentiated. Nevertheless, Jesser's approach was successful in developing an
interactive computer program, which allowed a further refinement in the
formulation of the complex problem of song classification.

Dirk Uhrlandt and Nico Schiller wrote the (T URBO-PASCAL-) program
MUSANA113 to analyze statistical and information related aspects of traditionally
notated music, especially Western art music.119 The statistical measurements
and measurements of information used in this program include several standard,
and a few unique, measures: mean, standard deviation, frequency, correlation,

, auto-correlation, entropy (including those of higher orders), as well as complex
measurements, like entropy profiles and entropy progressions (see chapter 4).
The program enables comparative analyses of personal style, genre, or period

styles. MUSANA takes an interactive approach and includes 'traditional' methods

 

"8 The program is available as freeware and documentated by Schiller and
Uhrlandt 1994/1996. The version 1.1 was exhibited at the International Computer
Exhibition "CeBIT '96" in Hannover / Germany in March 1996. — MUSANA
makes use of a unique music code, but a program procedure allows the
conversion of MIDI files into the MUSANA code.

"9 See Schiller 1992. There, statistical and information-theoretical calculations
could verify discoveries, that had been made 'traditionally', and could partly
represent them more plausibly and clearly, oftentimes confirm the mere
guesswork. —-See also Uhrlandt and Schiller 1992.

95

of music analysis in addition to more computationally oriented methods.

David Leon Butts (1992) also used methods of statistical analysis in a
study of the solo guitar compositions of Fernando Sor. The statistical procedures
included frequency counts, percentages, and variances, and were directed at the
keys, time signatures, forms, tempo indications, measure lengths, ornaments,
harmonics, tuning, etc. Applying the method of multi-variate analysis, several
parameters were weighted, and cross-classification tables were compiled,
correlations, and multivariate comparisons of means were utilized. Butt's results
establish Sor's compositional preferences: he liked the key of C major, the tempo
andante, but his preferences also included such complex manifestations related
to the density of activity, concentrated in certain parts of the measure. These
results were then used to draw didactic conclusions for the pedagogical use of
Sor's compositions in a logical fashion.

The Swiss mathematician Guerino Mazzola (1985, 1990) is one of the
advocates of a mathematical theory of music. The most important distinctions he
made are those involving mathematical descriptions of local musical structures
and those involving mathematical descriptions of global structures in music. He
developed a theory of musical modules which are in specific mathematical
relationships with each other. While Mazzola used mathematical formulas for
detailed descriptions of the manifold modular relationships, his computer system
RUBATO is able to manipulate single musical components within each complex
structure of music. (See also Stange-Elbe 2000.) He, thus, has access to audible

results of slight mathematical changes in his analytical descriptions of music.

96

Continuing a trend that had already started in the 1980s, computer-
assisted analytical methods shifted from statistical methods to methods drawn
from artificial intelligence and cognitice sciences. This shift can be exemplified by
several important research projects. John Schaffer (1992, 1994), for instance,
proposed and developed a PROLOG-based computer program120 that enabled
the user to define and change analytical criteria while the program was running,
i.e. without having to rewrite the program itself. Thus, "the user interacts with the
program by repeatedly asserting sets of criteria that the program tests, refines,
and feeds back as relevant information to the user - or, if deemed significant, to
itself, for further examination. . . . The power of the system comes not from what
it does, but from how it does it. In the best sense, it emulates the human
processes of heuristic exploration, but it does it much more quickly, more
consistently, and, more importantly, in an interpretative manner. The computer is
no longer relegated solely to the role of user-interpreted data generation and
manipulation, instead it is empowered with the ability to assess and adjust
continuously to new information while continuously interacting with the human
analyst." (Schaffer 1992, 147.) Using the concept of nodes and spines, Schaffer
formalized a flexible PROLOG data structure for expert systems. Nodes
represent all discrete dynamic objects such as notes and rests. All discrete

nodes are linked by spines, creating sequentially ordered lists. The advantage of

 

12° PROLOG is a programming language for rule-based or logic programming,
oriented to action when declared conditions are met. It is based on the first-order
predicate calculus of mathematical logic.

97

this system is that all analytical structures need to be created only once; editing
the event lists is made very easy. The program, then, is able to "use various
programmer-defined concepts to begin inferring relationships and refining search
strategies without significant user input. . . . In this sort of exploration, the
program begins by examining all combinations of event groupings employing a
forward-referencing depth-first search heuristic intrinsic to the Proiog
environment." (lbid., 153.) Schaffer used this system to analyze selected atonal
music, in a manner related to analysis based on set theory. He used fuzzy logic
to include certain degrees of uncertainty. Schaffer found‘this procedure
especially useful with respect to searching for the manifold hierarchies and
interrelationships in music. Through inclusion of fuzzy logic, the program "could
gain the ability to evaluate and assess musical materials in a manner enhanced
by continuous reassessment and adjustment based on the ever-changing
vagueness weights of previously observed" phenomena (ibid., 155-156). To
exemplify the value of his new analytical procedures, Schaffer analyzed Anton
Webern's Six Bagatelles, op. 9.

Marc Leman (1995a) designed a psycho-acoustical model for "tone center
recognition and interpretation" drawing on research in musicology, psychology,
computer science, neurophysiology, and philosophy. Leman used his model to
analyze perceivable tone centers in music, using musical sound as the program
input, thereby avoiding symbol-based paradigms in which music is conceived as
a set of symbols (like in a score). Instead, he developed a "subsymbolic"

representation of music, that is a representation of the sound. Leman's computer

98

program is strongly grounded in psychoacoustic research and includes, for
instance, self-organization and the ability to learn. The main approach is based
on "schemas" in that the perception of specific incoming (perceived) images
might be actively controlled. His approach allows for the notion of context
sensitivity. "The role of an active schema is particularly relevant in cases where
previous semantic images are reconsidered in the light of new evidence.
Consider a sequence containing the chords IV-V-l. After hearing the first chord,
the tone center will point to the tonic that corresponds with degree IV. It is only
after hearing the rest of the sequence that the first chord can be interpreted in
terms of its subdominant function. The schema should thus control the matching
process and adapt the semantic images in view of new evidence." (Leman
1995a, 126) The output of the computer analyses was compared with 'traditional'
analyses by a musicologist. Using what he calls "tone center recognition
analysis" and "tone center interpretation analysis", Leman discussed differences
between analyzing mere melodic pieces and analyzing predominantly harmonic
pieces. While Leman's approach to tone center recognition was less successful
in analyzing melodic pieces, his results also suggested that tone center
recognition and rhythmic grouping are interrelated.

Similar to Leman's connectionist model, i.e. a model that makes use of

121

brain-style computation , Don L. Scarborough, Ben O. Miller, and Jacqueline A.

 

121 Connectionist systems make use of 'brain-style' computation, i.e. making use
of a large number of interconnected processors operating in a strong parallel
distributed fashion. Connectionist approaches embody learning, constraint

99

Jones (1991) suggested a connectionist model for tonal analysis. Unlike other,
similar, approaches to tonal analysis that fail to deal with aspects of human
perception of music and that fail to explain musical similarity, the approach of
Scarborough et al. included the design of a network for "tonal induction," which
simulates the perception of tonal relations and similarity. In their network, the
"key node" that is most active controls the mapping of the notes, i.e. the various
relationships between the keys. "Singling out one key node and disabling the
others can be accomplished by letting the output of key nodes be a non-linear
sigmoidal function of the input, and by adding inhibitory connections between key
nodes." (lbid., 58) Unfortunately, the model described has neither been tested on
a Iargeamount of musical data nor has it been compared to a psychological
experiment that could demonstrate how well the networks simulate human
perception.

llya Shmulevich (1997), while carrying out dissertation research on
properties and applications of monotone boolean functions and stack filters,
designed a computer system to recognize and classify musical patterns. His goal
was to create a system which could minimize pitch and rhythm recognition errors
produced when trying to match a scanned pattern with a corresponding target
pattern. To recognize perceptual errors, Shmulevich applied (a modified version

of) Carol L. Krumhansl‘s key-finding algorithm, which provides a most likely tonal

 

satisfaction, feature abstraction, and intelligent generalization properties. (See
especially Todd and Loy 1991 .)

100

context for given musical patterns.122 Based on this algorithm, the computer
calculated a sequence of maximum correlations. The results were then weighted
for perceptual and absolute pitch errors. Other parts of the program computed
the complexity of rhythm patterns with the goal of weighting possible pitch errors.
Shmulevich concluded that a future application of this system could be the
computerized search for compositions containing the closest match with a
memorized melody (target pattern).

David Cope (1991, 1996) developed the LISP-computer system
"Experiments in Musical Intelligence" (EMI), which combines analysis and
composition processes. His goal was to write music in a specific musical style.
Cope's analyses are based on hierarchical analysis, drawing on Schenkerian
analysis and on Chomsky's generative grammar of natural languages. Cope's
EMl as well as his "Simple Analytic Recombinancy Algorithm" (SARA) can
analyze each component of a composition for its hierarchical musical function,
match patterns for "signals" of a certain composer's style, and reassemble the
parts sensitively, using techniques drawing on natural language processing
(Cope 1996, 28). Part of the analysis process involves a pattern searching
algorithm that, in contrast to pattern-searching algorithms by other authors, seek
patterns without any preconceived notion of their content. That means, the

analyst does not need to know which patterns are supposed to be matched. "EMI

 

‘22 See Krumhansl 1990 and Takeuchi 1994. This key-finding algorithm is based
on the observation that tones that are sounded most frequently are, in a specific
tonal context, the ones with a high probe of tone ratings. See also Shmulevich
1997, 65.

101

employs a limited set of variables called controllers, which affix musical
parameters to vague outlines within which patterns are accepted as viably
recognizable." (lbid., 36.) Many compositions generated on the basis of analytical
results are proof of Cope's success.

Mira Balaban (1992) described computational procedures that focus on
hierarchical relationships in musical activities and on the aspect of time in such
activities. The formalisms used in this approach support the following
descriptions of music:

- partial descriptions (musical structures and patterns of a composition),

- complete descriptions (fully specified pieces),

- implicit descriptions (some processing is needed to find out the denoted
structured piece), and

- explicit descriptions (explicitly specifies the sound properties).

Balaban's representation allows grouping of musical structures (hierarchies) over

time, without implying conclusions about the "grouped object". Balaban's

formalism was intended to explore musical activities in a standardized form.

Analysis is only one of these activities that the system can support. Others are

composition and tutoring. However, the analytical extension of this system has

not completely been realized yet.

H. John Maxwell (1984, 1992) developed a rule-based expert system that
performed harmonic analysis of tonal music. One of the main problems of this
project was the distinction between vertical sonorities that are "chords", i.e.

sonorities that have a harmonic function, and other sonorities that don't: "IF a

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sonority consists of only one note, OR it consists of two notes that form a
consonant interval other than a perfect fourth, OR it contains of three or more
notes forming only consonant intervals, THEN it is a consonant vertical,
OTHERWISE it is a dissonant vertical" (Maxwell 1992, 337.) Maxwell
distinguished between several dissonance levels, several strengths of beats for
various meters, and several strengths of harmonic functions. All rules were
implemented in a LISP-program. But while some rules could be transformed into
a relatively simple LISP-syntax, others required extensive programming, for
instance, a rule on finding pivot chords for modulations. "The rules are
interpreted by a forward-chaining inference engine that uses a prioritized agenda
to control conflict resolution. The rule base is partitioned into various phases of
analysis such as non-harmonic tone identification, chord recognition,
determination of cadence and modulation, and functional analysis of chords. This
partitioning, along with priorities that are assigned to individual rules, helps to
focus the activity of the system. In addition, the mechanism that matches rules
against the musical network uses a list of currently active nodes called a 'focus of
attention' to restrict the size of the conflict set. Several control-oriented rules were
added which manipulate the agenda and the focus of attention." (lbid., 345.)
Maxwell analyzed three movements of J. S. Bach's Six French Suites. While
most parts of the analyses were correct, a few failures helped clarify some
problems inherent in building a knowledge base for musical analysis.

For her dissertation research, Judy Farhart (1991) developed a GCLISP-

computer program that could identify keys. It was a knowledge-based (expert)

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system with rules of musical syntax and syntactic procedures, and was written to
simulate intelligent behavior, specifically learning processes as well as interactive
and interpretative procedures. The input data (MIDI) were interpreted to identify
note names by reiterating possible paths in a tree structure, applying the
knowledge rules of recognizing the tonality in a specific key. Farhart's artificial
intelligence procedures of key identification had its potential to identify proper
note names, matching them with all other notes within a specific key.

At the University of Nijmegen in the Netherlands, Peter Desain and
Henkjan Honing launched one of the most extensive research projects that
involves research on music cognition and that applies means of artificial
intelligence.123 Some of the projects and procedures, developed as part of this
broad research project, named "Music, Mind, Machine," are related to computer-
assisted music analysis.124 All of their analytical procedures are part of the LISP-
based POCO software package (see, for instance, Honing 1990). Most of the
projects within "Music, Mind, Machine" use digital sound as the source of the
analyses, aiming at performance practice and related issues, including structures

of performed music.

 

‘23 This research is based on preceding studies by Peter Desain and Henkjan
Honing, published partly in Desain and Honing 1992. The large-scale project was
Iounched in 1996/97 with several post-doctoral and other positions, which initially
were filled by Peter Desain, Henkjan Honing, Rinus Aarts, Hank Heijink, llya
Shmulevich, Renee Timmers, and Luke V\findsor. In 1998, Huub van Thienen
and Paul Trilsbeek joined the team; llya Shmulevich and Luke VWndsor left.

'2‘ A detailed description of the research projects, many of the published articles,
and the software package are available on-line at http://www.nici.kun.nl/mmm/.

104

As part of the "Music, Mind, Machine" studies, a current project deals with
matching performences (in the form of digital sound) with their printed score (see
Desain 1998a). Hereby, the timing is of special interest, since expressions in
timing (of performed music) can vary by up to multiples of the original (notated)
value of notes. The program developed was able to extract patterns of
expressive timing and calculate local tempi. The matching editor made use of
structural information, taken from the score, and produced better results than
already existing 'structure-matcher.’125 However, more detailed knowledge of the
wide variety of musical structures is necessary to make the program more robust
and more successful.

Another project of the "Music, Mind, Machine" studies is related to vibrato.
The project's goal is to investigate empirically the relationship between vibrato,
musical instruments, and global tempo. The digital audio of several commercial
recordings of "Le Cygne" by Saint-Saens as well as performances of the same
piece with different instruments have been analyzed specifically regarding
expressions in vibrato. The knowledge obtained from these analyses was
condensed into a formal computational model that can predict the nature of '

vibrato performed on different instruments in different structural relationships.

 

‘25 Those existing 'structure—matchers' are developed and used in different
contexts and for different tasks. Some focus on real-time matching (Dannenberg
1984; Vercoe 1984; Vantomme 1995), others on off-line analyses, for which the
analysis is more important than the efficiency of the program. Most of the
'structure-matchers' match primarily pitch, sometimes in combination with time
information. The "Music, Mind, Machine" matcher matches pitch and time.

105

Furthermore, it can be applied to make synthesizers more 'intelligent' in their
implementation of vibrato to signals. (See Desain 1998a; Desain, Honing, Aarts,
and Timmers 1998.)

Another project within "Music, Mind, Machine" is directed at the perception
and performance of grace notes. Results of analyses suggested that not only
tempo but also the structural function of a grace note might influence its duration.
From the musicological literature, the research team drew several hypotheses
about the structural classification of grace notes and the effect of this
classification on their durations. They found that, although grace notes in certain
structural categories are consistently played longer than grace notes in other
categories, the major influence on grace note timing seems to be stylistic. They
also found that some grace notes get longer as the tempo decreases, while
others retain approximately the same duration. The authors considered this as
strong evidence against the notion of relational invariance across different tempi.
(Desain 1998a, 8; see also V\findsor, Desain, Honing, Aarts, Heijink, and
Timmers 1998.)

The quantization of temporal patterns'za, i.e. their subdivision into small
finite increments that are measurable, is another project within the "Music, Mind,
Machine" studies. Objects of this project are the actual tone durations in

performed music, which deviate considerably from the notated durations. The

 

'26 Quantization of temporal patterns is the subdivision of these temporal patterns
into small finite increments. These increments are also called "grids." In this
project, quantization is used to objectively measure deviations of performed note

values from the notated tone durations.

106

research shows that those deviations are related to the musical structure.
Several elementary models for tempo deviation and for grid-based quantization
have been developed. The research is ongoing, like many other projects within
"Music, Mind, Machine." (See Desain 1998a; Trilsbeek and Thienen 1999;
Cemgil, Desain, and Kappen 1999.)

Another computer program that was used in several research projects is
David Huron’s Humdrum toolkit (Huron 1993c, 1995, 1999a). It makes use of the
kem (alphanumerical) music representation. The capabilities of Humdrum's
toolkits, a collection of more than 70 interrelated software tools, are broad and
range from statistical analysis regarding pitches, tone durations, and intervals to
classifications of musical events, melodic search procedures, and harmonic
analysis. Several researchers have used Humdrum for specific music analytical
tasks. Denis Collins and David Huron, for instance, collaborated in a project on
voice-leading in cantus firmus-based canonic compositions. They specifically
analyzed the canonic compositional rules of Zarlino, Berardi, and Nanino. The
study showed how well described musical practice is in theoretical treatises
(Collins and Huron 2000).

Unjung Nam (1998) analyzed pitch distributions in Korean court music.
Using Humdrum, Nam found evidence (similar scale intervals, similar phrase-
ending tones, and similar tone-duration distributions) that a genre-related tonal
hierarchy may exist in traditional Korean court music.

Analyzing 75 fugues by J. S. Bach with the Humdrum toolkit, David Huron

and Deborah Fantini (1989) provided music theoretical evidence for the

107

experimentally observed phenomenon that, in polyphonic music, entries of inner
voices are more difficult to perceive than entries of outer voices. The study
showed that Bach was allegedly much more reluctant to use inner-voice entries
in five-voice textures than in three- or four-voice textures. Huron and Fantini
hypothesized that Bach tried to minimize perceptual confusion in compositions
with a higher textural density.

A different approach to computer-assisted music analysis is taken at the
University of Karlsruhe in Germany in a research project on information
structures in music. Scholars there are currently trying to model musical
structures with rule-based systems. Stylistic characteristics are of special
interest. As part of this research, Dominik Hornel (2000) described a neural
network system for analyzing chorales, in which 'harrnonic expectations' are
central measurements. The analyses are based on probability calculations.
Homel showed how this neural network system could be used to falsify the

authorship of a chorale attributed to Johann Sebastian Bach.

108

2.7. Synopsis

Computer-assisted music analysis developed rapidly since first attempts during
the 1950s and 1960s. While analytical methods drawn from statistics and
information theory dominated up to the end of the 19703, other approaches
became more important around 1980 and thereafter: set theoretical analyses,
transformational and Schenkerian analyses as well as cognitive and artificial
intelligence approaches. During the 19903, computer-assisted music analysis
became more oriented towards performance-based analyses in connection with
cognitive and artificial intelligence.

However, communication among the researchers appears to have been
minimal. At least before the 19903, many attempts of computer-assisted music
analysis were not recognized by researchers in the same field. Thus, music
theorists were unable to learn from one another's mistakes. One reason could be
the lack of a journal related to the problems of computer-assisted music analysis.
Journals like Computers in the Humanities and the Computer Music Journal were
much broader in their orientation. In 1973, Jerome Wenker tried to establish the
Computational Musicology Newsletter; he wrote in the Editorial Foreword of the
first issue: "During the past few years the number of individuals active in the
applications of computers to musicology has greatly increased. A3 a result of
this, it seems that an attempt to distribute information on activities in this field
would, even on a relatively informal basis, be of general assistance. . . . The

major emphasis is on increasing communications in order to minimize wasted

109

time and resources caused by duplication of efforts. This will make it possible for
individuals beginning projects to obtain assistance from - while also providing
fresh insights to - more experienced researchers and for individuals of all levels
of experience to exchange ideas and approaches in the forum of a continuous
conversation." (Wenker 1973b, 1) However, the Computational Musicology
Newsletter was short-lived. More successful in publishing new methods of
computer-assisted music analysis and establishing a basis for communication
were, later, the series Computing in Musicology (successor of the Directories of
Computer Assisted Research in Musicology, founded in 1985 by the Center for
Computer Assisted Research in the Humanities), the journal Computers in Music
Research, founded in 1989, and the Journal of New Music Research which grew
out of Interface in 1994.

Another problem of the recognition of research has been the acceptance
of dissertation research as a valuable source for the methodological discourse
within the field of computer-assisted music analysis. In general, American
dissertation research has often been influenced and stimulated by the research
of faculty members, by existing software, or by theoretical systems. But even
though some dissertations have been indispensable for spurring further
developments in this area, many of them had little academic value. On the
contrary, European dissertations, though infrequent, have had usually much
more impact on academic research. But the more recent research in cognition
and artificial intelligence has intensified interest in computer-assisted music

analysis. The main reasons for American dissertations not yet having been

110

widely disseminated is that, unlike European dissertations, they are not routinely
published. Thus, they are excluded from historical overviews and other research
papers.

From today's point of view, the first approaches to computer-assisted
music analysis seem relatively simplistic, as they strongly emphasized the
computer and less the research (i.e. the music theoretical problems). They
usually dealt with only a few compositions, or single voice melodies, or even with
short phrases of single voices. This limitation obviously effected the outcome of
the research and its academic value. However, the simplistic nature of the
research was mainly determined by the capacities of the computers in these
early years. Negative evaluations of computer-assisted music analysis during the
19603 and 19703 were responsible for reservations against computer
applications in music research. Our field still has to recover from this negative
image.

A few conclusions can be drawn from studying the history of computer-

assisted music analysis:

- Though many publications are of little value, some of them make important
contributions and deserved to be more widely disseminated. However, even
with newest cognitive research and research in the area of artificial
intelligence, the proportion of expenditure to benefit is in most cases

unsatisfactory.

111

The productive use of different methods in computer-assisted music analysis
seems to be independent of the musical genre. Most methods have been

applied to many different musical genres.

More complex analyses in the sense of interactive methods—comprising
traditional, sociological, psychological, and historic-cultural aspects—show
that neither a pure 'traditional' nor a pure computer-assisted analysis produce
valuable results. Instead, computer-assisted music analysis needs to use

both computational and traditional analytical methods.

Several studies showed that the application of methods drawn on statistics
and information theory is only successful when the greatest possible number

of numerical characteristics are used as discriminators.

Using methods derived from linguistics, from theories of structural levels, and
from set theory, computer-assisted music analysis is based on 'traditional'
music theory—in the sense of studying musical structures. Some successful
research showed that the computer makes it possible to verify the analytical
results and algorithms by using the reverse process, generating

compositions.

Finally, computer-assisted music analysis in the field of artificial intelligence is

much more interdisciplinary. Especially the strong integration of psychological

112

and cognitive aspects of music allows theorists to focus on basic human
activities: on the creation of knowledge as well as on processes of
composition and perception. This kind of research then focuses more on the

philosophical question: How can I know / discover myself and the world?

113

Chapter 3

CLASSIFICATION OF METHODS OF COMPUTER-ASSISTED MUSIC
ANALYSIS

"Bear in mind, however, that the computer does what it is told: even
its most sophisticated procedures depend on the imagination of the
researcher for instructions. . . ." (Jan LaRue 1970a, 197.)

3.1. Design of a System of Classification

The history of computer-assisted music analysis includes a great number of
approaches. As was mentioned earlier, an important step to handle the
methodological problems of music analysis involves reflecting on different
methods. That includes the necessity of designing a system of classification. Up
to this point, a classification of methods of computer-assisted music analysis was
not possible, because neither a history of computer-assisted music analysis nor a
complete bibliography were available. Both have been provided here.

Like 'traditional' methods of music analysis, methods of computer-assisted
music analysis can be classified with regard to the kind of music analyzed, the
methods used, the general approach taken, and so forth. But any classification
needs to be based on a logical framework, which means that a certain

classificational level (level of abstraction) has to be on an identical

114

epistemological level (see Introduction). For the various approaches to, and
studies of, computer—assisted music analysis, we can distinguish three main
epistemological levels which would be important for a system of classification:
0:. the analytical methods applied,

0:0 the form in which the music is analyzed, and

0:0 the kind of music analyzed.

The kind of music analyzed refers to general 'types' of music, which can
be distinguished from each other by either musical characteristics or the
sociological function of the music. Those general kinds of music are Western art
music, not Western art music excluding popular music (that can be either
Western folk music or non-Western music), and popular music.

The form in which the music is analyzed refers to either notated music or
performed music. Furthermore, notated music can be classified with regard to
different types of notation.

The analytical methods, applied to computer-assisted music analysis, are
statistical methods, information theoretical methods, set theoretical methods,
other mathematical methods, hierarchical ltransformational methods, spectral
analysis, and methods drawn from cognitive sciences and artificial intelligence.
All these general approaches can then, again, be divided into specific methods,
as statistical methods comprise measurements for frequencies, probabilities, the
chi square test, etc.

Since the outcome of any music analysis is strongly dependent on the

methods applied, general methodological approaches need to be—in a system of

115

classification of computer-assisted music analysis—on the highest
epistemological level. Divisions into sub-methods are possible. The methods
applied strongly depend on the representation in which the music is analyzed;
thus, notation-based analysis and performance-based analysis should create the
second highest epistemological level in a system of classification. That would

leave the kind of music analyzed as a basis for the third epistemological level:

116

Computer-Assisted Music Analysis

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117

 

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3.2. Approaches to Computer-Assisted Music Analysis and their General

Characteristics

In the following, each category of the general methodological approaches will be

defined and characterized. Most commonly used sub-methods will be named.

3.2.1. Approaches Drawing on Statistics and Information Theory

Statistical and information-theoretical approaches were (historically) the first
methods applied to computer-assisted music analysis. Even though statistical
methods and information-theoretical methods are distinct from each other, in
computer-assisted music analysis they are usually applied together. Statistical
and information-theoretical approaches comprise frequency, mean (average),
variance, standard deviation, correlation, regression, the chi square test, entropy,
Markov chains, probability, redundancy, and other measurements.

As was stated earlier, the application of methods drawing on statistics and
infOrmation theory to music analysis is only successful when many different
measurements are used. Positive correlations between these measurements
enhance their efficiency as discriminators. While some approaches of the 19803
and 19903 included such a complex view on the use of statistical methods in
music analysis, many did not. This led to false assumptions about the validity and
usefulness of statistical methods in music analysis. Since the application of
statistics and information theory to music analysis is not only the oldest, but also

the historically most extensive, branch in computer-assisted music analysis,

118

further verifications and evaluations of these methods are urgently needed.

Chapter 4 of this text will contribute to this task.

3.2.2. Analyses Drawing on Set Theory

For the analysis of atonal music, a number of computer programs draw on Allen
Forte's set theory and on further developments of Forte's theory. Most of these
programs comprise such standard procedures as calculating prime forms (most
often using Forte names), interval vectors, number of occurrences, as well as
similarity and set complex relations.

Within the limits of set theory, specifically within the limits of each function
of similarity or set relation, computer-assisted music analysis drawing on set
theory is doubtless a useful tool, because it is based on the same mathematical
procedures that 'traditional' set theoretical analyses are based on. Computers
reduce the time needed for calculation, and thus provide more time for the more
important part of the analysis: the interpretation of the results of set theoretical

data.

3.2.3. Other Mathematical Approaches

In some approaches, mathematical procedures, other than those mentioned
already in 3.2.1. and 3.2.2., are applied to music analysis. Structural relationships
can be explicated in many mathematical ways, some of which are fractal-like
descriptions, formulas for symmetrical structures or for the relationships between

groups of motives (describing their characteristics), as well as formulas for

119

calculating the inner tempo of a composition, depending on meter, metrical

relationships, and rhythmical structures, etc.

3.2.4. Hierarchical Approaches

Hierarchical approaches to music analysis try to apply reduction procedures to
music in a sense that different hierarchies of musical structures show certain
dependencies as well as, on a remote and abstract level, large-scale
relationships (especially melodic and harmonic relationships). The basis for
hierarchical approaches to music analysis is twofold: linguistic methods,
especially those from the structuralistic grammar developed by Noam Chomsky,
and Heinrich Schenker's concept of musical grammar. Regarding those two main
approaches, "hierarchical approaches" can be divided into "transformational

analyses" and "Schenkerian analyses":

 

Hierarchical

Analyses

 

 

 

 

Transfonna- Schenkerian
tional Analyses

Analyses

 

 

 

 

120

Both methodological approaches comprise different abstraction levels, which can

be obtained by applying certain abstraction rules (see 2.5.).

3.2.5. Spectral Analysis
In some cases of performance-based music analysis, spectral analysis is
involved. Usually in those approaches, the sound spectrum is broken up to
identify, for instance, the chord structure. While spectral analysis has been used
in pure sound analysis for several decades, it became part of structural analysis
of music in the late 19803 and early 19903.

Spectral analysis is most often combined with other methods of computer-

assisted music analysis.

3.2.6. Cognitive and Artificial Intelligence Approaches

Computer-assisted approaches of music analysis that draw on cognitive research
and artificial intelligence use computer systems to simulate functions that are
usually associated with human intelligence. Those functions include reasoning,
learning, and self-organization (or self-improvement). Approaches of artificial
intelligence to music analysis can exist in forms of neural network systems (see

127

2.6.) or expert systems . The goal of expert systems is to solve problems by

drawing inferences from a knowledge base acquired by expertise; expert

 

‘27 The terms 'expert system' and 'knowledge-based system' are often used

synonymously.

121

systems process information pertaining to a particular application and perform

functions in a manner similar to that of a human who is an expert in that field.
Approaches drawing on artificial intelligence and cognitive research are,

towards the end of the 20‘" century, more and more part of interactive music

systems that combine both analysis and composition.

3.2.7. Synopsis: Combined Methods

In some applications of computer-assisted music analysis, several
methodological approaches are combined in one computer system. Those
systems are oriented towards interactivity, so that the user can choose in real
time, which methods of music analysis to apply. These choices depend strongly

on the goal of the specific research.

122

Chapter 4

THE ANALYSIS PROGRAM MUSANA AS AN EVALUATION TOOL FOR
STATISTICAL AND INFORMATION-TH EORETICAL APPROACHES

"In these two functions -- instruction and interpretation - the
researcher controls the fundamental musicality of the investigation.
It the results are mechanistic, he cannot blame the computer." (Jan
LaRue 1970a, 197.)

4.1. MUSANA: Possibilities, Use, and Structure

After constructing a historical account of the development of computer-assisted

music analysis, and then developing a system for classifying the methods applied
in computer-assisted music analysis, the claims of analytical methods need to be
evaluated. One way of evaluating the claims of analytical methods involves using

a computer program to formalize certain aspects of the methods of music

d128 129

analysis, aspects that then can be falsifie or verified. It was exactly for this

 

‘28 Falsification is the act of showing one instance of something to be false or
erroneous to reflect on the potential of a theory. If such an instance is falsified,
then its falsification also falsifies the theory from which it was logically deduced.
(See Popper 1959, 33.)

‘29 Verification is the act of showing one or more instances of something to be
true or acceptable to reflect on the potential of a theory. Such a verfication is only
temporary, for subsequent falsification(s) may overthrow it.

123

purpose that the computer program MUSANA was developed by the author and
the German physicist Dirk Uhrlandt. MUSANA can be used for the actual
analysis of music, as well as for the simulation and evaluation of analytical
methods that can be applied to music, particularly those methods that draw on
statistics and information theory. And in fact, MUSANA was used to evaluate
premises of a few of the analytical methods described in chapter 2. The
analytical results revealed the limitations of some analytical methods (and/or their
implementation), while also showing the strengths and potentials of others.
Reforrnulating the methods that emerged during the last few decades succeeded
in two ways: it allowed a useful modification towards more successful methods,
and it allowed other methods to merge into a new method.

In the following passages, MUSANA's potentials, its musical
representation (code), its organization of memory, and its program structure will
be briefly described to provide the significance of MUSANA's statistical and
information-theoretical measurements. Then, four analytical studies are
summarized. The statistical and information-theoretical methods embedded in
them are evaluated, and finally another method is proposed, one that draws on

information theory and that extends the methods to new domains.

4.1.1. MUSANA's Music-Analytical Possibilities and Use
The first version of the computer program MUSANA was developed in 1992. It
has been refined since, and various means of obtaining statistical and

information-theoretical measurements have been added. MUSANA is written in

124

the programming language Turbo-Pascal130

, specifically the Borland-Pascal
version. MUSANA makes use of Borland-Pascal's procedure and unit concept.
Furthermore, the program makes extremely efficient use of memory, especially
since it uses dynamic memory when compiled in the 'protected mode'. When the
MUSANA program was created, memory was very limited, so that almost all the
memory available to the program—including the computer memory beyond the
memory supported by the operating system DOSm—was used to store the
encoded representation of music pieces. As more memory became available with
new computers, more complex measurements drawn from information theory
could be added.

MUSANA allows each separate voice to be entered via the standard
computer keyboard and also allows standard MIDI files to be converted into the
musical representation used in MUSANA. Standard notation can be displayed on
the screen and edited, and the composition can be listened to via the internal
loudspeaker of the computer. The methods of analysis help carry out stylistic
analysis and classification of the music. The program creates histograms (of
pitch and tone duration), searches for melodic or rhythmic patterns, calculates

mean values of pitch and duration (as well as their standard deviations),

computes correlations, and finally calculates different kinds of entropy.

 

13° Pascal is a high-level programming language based on ALGOL. It
emphasizes aspects of structured programming. Standard Pascal and Turbo-
Pascal are different dialects of Pascal.

‘31 MUSANA runs on all IBM compatible computers under DOS, in the DOS
window of Windows, or under Virtual PC on a Macintosh computer.

125

MUSANA extends traditional methods of music analysis by computer-
assisted methods, it does not replace them. It is crucial for the outcome of
computer-assisted analysis to integrate both, computer-assisted fl! traditional

methods of music analysis.

4.1.2. Encoding and Organization of Memory
MUSANA encodes only pitch, tone durations, and bar lines. Phrasing marks,
dynamics, and other musical information are not included in MUSANA's code.
For MUSANA, a numeric code was developed which can easily be processed by
procedures drawing on statistics and information theory.

After the input of each note (from a standard computer keyboard or from a
converted standard MIDI file), pitches are assigned to integers in ascending

order, not differentiating between enharmonic equivalents:

126

| Octave

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sub- Con- Great Small One Two Three Four Five

contra tra line line line line line

C 1 13 25 37 49 61 73 85 97

C# 2 14 26 38 50 62 74 86 98

D 3 15 27 39 51 63 75 87 99
D# 4 16 28 40 52 64 76 88 100
E 5 17 29 41 53 65 77 89 101
F 6 18 30 42 54 66 78 90 102
F# 7 19 31 43 55 67 79 91 103
G 8 20 32 44 56 68 80 92 104
G# 9 21 33 45 57 69 81 93 105
A 10 22 34 46 58 70 82 94 106
A# 1 1 23 35 47 59 71 83 95 107
B 12 24 36 48 60 72 84 96 108

 

In the MUSANA-code, the smallest possible tone duration is the 1/64-triplet,

which is assigned two 'time units'. Following the mathematical relationships

Table 1: Pitch Code in MUSANA

between the tone durations, all tone durations have the following values:

127

 

_t._r_c.5_-s_lw_ m ........ L. \Lflm

 

 

 

 

 

 

 

 

 

 

 

Double dotted Dotted Normal Triplet
Whole note -- -- 192 --
Half note 168 144 96 64
Quarter note 84 72 48 32
Eighth note 42 36 24 16
Sixteenth note 21 18 12 8
1/32 note -- 9 6 4
1/64 note --- -- 3 2

 

 

 

 

Table 2: Tone Durations in their Mathematical Relationship

To reduce the amount of memory required to store the encoded data, all values

are encoded a second time via a field (2, 3, 4, 6, 8, 9, 192) with the indices 2,

 

 

 

 

 

 

 

 

 

3, 4, 23:

Double dotted Dotted Normal Triplet
Whole note —- —- 23 --
Half note 22 21 20 19
Quarter note 18 17 16 15
Eighth note 14 13 12 11 '
Sixteenth note 10 9 8 7
1/32 note -- 6 5 4
1/64 note --- -- 2

 

 

 

 

 

Table 3: Tone Duration Indices

It was already mentioned earlier that all musical data are saved dynamically by

using all the memory that is available, that means beyond the 640K limit of the

128

 

 

DOS operating system. Hereby, each note is assigned to a 2-byte-variable
(word). In the "High-byte" of the word element, measure line (if needed) and pitch
(the value for rests is 127) are saved, whereby ties (if needed) and tone duration

index are saved in the "Low-byte" of the word element:

HIGH LOW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X | pitch | tie| tone duration index

measure line

Figure 3: Word-element in MUSANA

4.1.3. Partial Flowcharts of MUSANA and its Procedure "Analyzing"
The flowcharts below show the structure of the main program and the procedure

"analyzing" in MUSANA. Hereby, the following shapes are used:

L/

 

- Data input expected:

129

 

 

- Procedures, which aim at,

 

 

or prepare, output:

 

- Start / End:

130

 

C Start D

 

Initializing (Graphics Driver, Paths, Printer, etc.)

I

/ Main Menu
/Eiad Musi New Music Cont. Music Edit Music ave Music
Listenin Patt.Searc ‘ rint Option Analyzin Quit /

* l A

g l .

Ill ill

 

 

 

\

 

 

 

 

 

 

 

 

Analyzing

 

 

Music
saved?

in

Saving
7 v

C End >

Figure 4: Partial Flowchart of MUSANA

 

H

 

 

 

 

 

 

131

Procedure "Analyzing":

 

l

Gm of the Procedure "AnalyzinD

 

 

Initializing (Maximums, Means, Standard Deviation)

 

 

 

Gd of the ProcedurD

Menu of the Procegure "Analyzing"

 

Duratio/

Analyses

Pitch
Analyses

/ Melody
A

nalyses

Back to Main
Menu

 

Means et

/A

uto-Correlatio

/Entropie

 

l

 

 

Means/Pitch
Graphics

 

 

 

4

 

l

 

Duration
Analyses

 

 

Pitch

 

 

’suration Anls

 

Entropy

Analyses Profile

 

 

 

 

Auto-

 

Correlation

 

 

Figure 5: Flowchart of the Procedure "Analyzing"

 

 

 

Duration
Analyses

 

 

 

 

 

 

 

 

. was /,.
A /

/ Duration / Intervals/Duration Pitcl/
itch/Duration I Compari/

 

 

V

 

l.

 

 

Entropy Developments

 

 

132

4.2. Computer-Assisted Comparative Analyses of Haydn and Mozart Trios via

Selected Statistical and Information-Theoretical Methods

The goal of the following studies was to evaluate some of the methods that have
occupied a prominent position in the history of computer-assisted music analysis.
The main methodological approach taken here (in evaluating certain analytical
procedures) is falsification. Falsification, the act of showing one instance of
something to be false or erroneous to reflect on the potential of a theory, is a
powerful tool for evaluating methods of computer-assisted music analysis for two
reasons: it neither requires analyzing a large number of compositions nor
carrying out extensive verification. In addition, one of the studies will also
introduce a new method (drawing on information theory) and show its
effectiveness and its potential.

All of the following studies are based on analyses of Wolfgang Amadeus
Mozart's 25 Pieces (five Divertimenti) for Bassett Homs KV 439”. Limiting the
pieces to be analyzed to those of a specific composer and in a specific genre is
necessary to eliminate distinguishing musical characteristics that are deduced by
the following stylistic differences:

- the differences between styles from different periods,

- the differences between different personal styles, and

- the differences between different genres.

Focussing on analyzing only one set of compositions (in the same genre) allows

one to reduce the probability of error, which could occur when different

133

characteristics of style or genre influence the outcome of statistical and
information-theoretical analyses. Analyses that focus on differences between
genres, personal styles, or time periods can only be carried out after successfully
applying certain measurements to analyzing music with a reduced number of
distinguishing characteristics. If such an analysis with a reduced number of
distinguishing characteristics did not precede, characteristics of time, style or
genre can hardly be distinguished, i.e. personal style, for instance, can influence
analyses of genre characteristics, and so forth.

Mozart's 25 Pieces (five Divertimenti) for Bassett Homs KV 439b were
composed in 1783; the original instrumentation is not certain.132 Wlth the
selection of divertimenti, a musical form was chosen that was historically a
continuation of the suite; the character of the divertimento belongs to
Gebrauchsmusik. All five divertimenti in this group of compositions have five

movements.

4.2.1. MUSANA Study No. 1
Historically, many attempts to analyze music with a computer have concentrated

only on the beginnings of compositions (incipits), making these the object of their

 

‘32 See Kochel 1964, 471 ff., but especially 474. The Neue Mozart Ausgabe
(Mozart 1975) assigned three bassett horns in F. The Neue Mozart Ausgabe,
Serie Vlll (Kammermusik), Werkgruppe 21 (Duos und Trios filr Streicher und
Blaser) was used for the analyses in this chapter. All pieces analyzed in this
chapter are reprinted in Appendix C.

134

analyses. This was usually justified by the insufficient memory capacity of the
computer. However, the authors usually did not reflect on the possible effects
that the length of the musical excerpts has on the analytical results. MUSANA
Study No. 1 will compare analyses performed with different lengths of the
excerpts (incipits).

Each part of the first movements (Allegro) of both, Divertimenti l and II, of
KV 439b are analyzed in the following lengths:

- only the first 10 notes (and rests)

- only the first 20 notes (and rests)

- only the first 40 notes (and rests)

- only the first 60 notes (and rests)

- the whole piece.
The task is to compare the following statistical values, most often used in the
past to supposedly characterize a certain musical style:

- average pitch (using the internal numerical code [of MUSANA] and

considering the duration of each note) and its standard deviation

- the average interval size (disregarding the direction; half step = 1)

- the average tone duration (statistically, here, as a partial of a whole note)

- first order entropy (considering the duration of each note, not just their

number of appearances)

The MUSANA results of the analyses are as follows:

135

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 notes 20 notes 40 notes 60 notes All (834)
Average Pitch & 57.0 1 2.7 58.2 :I: 3.6 57.8 :I: 3.0 58.4 :I: 3.4 58.2 :I: 3.6
Stand. Deviation (g#') (a') (a') (a') (a')
Average Interval 0.8 1.1 1.8 2.1 2.4
Size
Average Tone 0.2125 1: 0.1776 :l: 0.2279 :I: 0.2255 i 0.2386 :I:
Duration & 0.0976 0.0843 0.2089 0.1836 0.2106
Stand. Deviation
First Order 0.95604 1 .65300 1 .89431 2.01050 2.47483
Entropy

Table 4: Allegro from Divertimento l, upper voice

10 notes 20 notes 40 notes 60 notes All
Average Pitch & 48.5 :I: 3.7 52.1 :I: 5.8 53.4 t 4.1 53.6 :I: 4.2 52.9 :I: 4.2
Stand. Deviation (c#') (d#') (e') (f') (e')
Average Interval 1.3 1.4 1.7 1 .9 2.5
Size
Average Tone 0.2125 :I: 0.1776 i 0.2286 :I: 0.2052 :t 0.1922 :1;
Duration & 0.0976 0.0843 0.1650 0.1418 0.1302
Stand. Deviation
First Order 0.95604 1.75553 2.00176 2.06143 2.47987
Entropy

 

 

 

 

 

 

Table 5: Allegro from Divertimento l, middle voice

136

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 notes 20 notes 40 notes 60 notes All
Average Pitch & 36.9 :I: 5.3 36.7 1: 5.8 41.1 i 6.6 38.7 :I: 7.0 41.6 :I: 6.1
Stand. Deviation (c) (c) (e) (d) (f)
Average Interval 4.0 4.5 3.0 5.2 3.8
Size
Average Tone 0.2125 :t 0.1964 :I: 0.2311 :I: 0.2170 :I: 0.1976 :I:
Duration & 0.0976 0.0911 0.0821 0.1333 ' 0.1258
Stand. Deviation
First Order 1.21820 1.46880 2.35662 2.20022 2.71846
Entropy

Table 6: Allegro from Divertimento I, lower voice .

10 notes 20 notes 40 notes 60 notes All (416)
Average Pitch & 57.1 i 3.7 57.6 :I: 3.5 57.8 :I: 3.3 59.2 i 3.8 58.8 :t 3.8
Stand. Deviation (g#') (a') (a') (a#') (a#')
Average Interval 2.8 2.2 2.1 2.1 2.4
Size
Average Tone 0.2222 :I: 0.1776 :I: 0.1757 :I: 0.178 :I: 0.1812 :I:
Duration & 0.1534 0.1169 0.1179 0.1332 0.1368
Stand. Deviation
First Order 1.95212 2.04701 2.09673 2.35861 2.40463
Entropy

 

 

 

 

 

 

Table 7: Allegro from Divertimento ll, upper voice

137

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 notes 20 notes 40 notes 60 notes All (410)
Average Pitch & 48.1 :I: 2.2 51.0 :I: 4.3 50.0 :I: 4.0 51.8 :I: 4.3 52.3 :I: 4.6
Stand. Deviation (b) (d') (c#') (d#') (d#')
Average Interval 1.9 1.8 2.0 2.0 2.3
Size
Average Tone 0.2344 :I: 0.1806 1 0.1786 :I: 0.1838 :t 0.1826 :I:
Duration & 0.1159 0.0952 0.0958 0.1190 0.1231
Stand. Deviation
First Order 1.68077 2.27938 2.34430 2.3097 2.51913
Entropy

Table 8: Allegro from Divertimento ll, middle voice

10 notes 20 notes 40 notes 60 notes All (486)
Average Pitch & 40.8 :I: 3.6 41.4 :t 3.4 41.2 i: 3.2 40.1 :t 3.6 39.9 :I: 4.9
Stand. Deviation (e) (e) (e) (d#) (d#)
Average Interval 1.3 1.8 1.9 2.3 3.0
Size
Average Tone 0.1250 1: 0.1324 :I: 0.1326 :I: 0.1297 :I: 0.1288 :I:
Duration & 0.0000 0.0294 0.0298 0.0238 0.0240
Stand. Deviation
First Order 0.32508 1.18372 1.13290 1.53338 2.14939
Entropy '

 

 

 

 

 

 

Table 9: Allegro from Divertimento ll, lower voice

138

 

 

Evaluative results of the few calculations presented above provide an astonishing

picture of the value of such calculations, at least taken separately, i.e. not as one

component of more complex statistical measurements as multi-variate analysis,

cluster analysis, or factor analysis. The interpretation of the test results can be

summarized as follows:

0
0..

00

0.

While the mean values of pitch do not vary much, their standard deviations
may vary by more than 100%. In the middle voice of the Allegro from
Divertimento II, for instance, the standard deviation from the pitch average for

the first 10 notes is 2.2, but for the entire piece 4.6.

Similarly, the average interval size varies considerably. The values for shorter
Incipits (10 and 20 notes/rests), in particular, are far from being close to the
average of the entire voice. The upper voice of the Allegro from Divertimento
I, for instance, shows 0.8 as the average interval size for the first 10 notes
and 1.1 for the first 20 notes, but the average interval size of the entire voice

is 2.4, i.e. three times more than the value for the first 10 notes.

Not only can incipits not accurately characterize the entire piece, but even the
values of the same parts (voices) within different pieces are not comparable.
The average tone durations of the lower voices of both Allegros are 0.1976

and 0.1288, respectively—a difference of more than a sixteenth note.

139

0:0 The calculations with regards to the lower voice of the Allegro from
Divertimento II demonstrate the falseness of the assumption that an incipit's
standard deviation from the average tone duration can be used to
characterize a larger part of the piece or the whole piece. While the standard
deviation of the first 10 notes is zero, the standard deviation of the first 20

notes is already 0.0294.

0’0 F irst-order entropies seem not to be significant for a 10-note incipit. The

O

entropies of all larger excerpts show a natural, and consistent, growth when

the incipits become longer.

Using incipits as if they were representative of the whole composition has been
common practice in computer-assisted music analysis since its beginning. Since
evaluations of this practice have not been available, even during the 19903,
calculations based on incipits were put forth as adequate characterizations of
compositions or even of a composer's style. The data provided in this study
clearly show that there is no statistical basis for the assumption that incipits have

a sufficient size for discriminatory tasks or style characterizations.

4.2.2. MUSANA Study No. 2
In the ovenrvhelming majority of statistical analyses of music, researchers used
the number of instances of tones as the statistical basis for calculating values like

average (e.g., of pitch) and its standard deviation, without considering the

140

durations of the tones. However, characterizing the lengths of tones provides
structurally important information. For that reason, Study No. 2 focuses on the
differences between using just the number of tones and the number of tones
along with their durations. The analytical objects of this study were, again, each
of the first movements (Allegros) of Divertimenti I and II of KV 439° by W. A.
Mozart. The task was to compare the following measurements derived from
statistics and information theory:
- average of pitch (using the internal numerical code) and its standard
deviation, considering the duration of each note,
- average of pitch (using the internal numerical code) and its standard
deviation, considering the number of appearances of each note,
- first—order entropy, considering the duration of each note,
- first-order entropy, considering the number appearances of each note.

The MUSANA results of the analyses are as follows:

141

 

 

 

 

 

 

 

 

Average Pitch Average Pitch Entropy Entropy
(duration) (number) (duration) (number)
Allegro I, 58.2 :I: 3.6 58.3 :I: 3.9 2.47483 2.45432
upper voice (a') (3')
Allegro I, 52.9 :I: 4.2 53.1 1: 4.5 2.47987 2.52007
middle voice (e') (e')
Allegro I, 41.6 :t 6.1 42.0 t 5.9 2.71846 2.72288
lower voice (f) (f)
Allegro II, 58.8 1: 3.8 58.3 t 3.6 2.40463 2.33449
upper voice (a#') (a')
Allegro II, 52.3 i: 4.6 52.7 t 4.7 2.51913 2.48277
middle voice (d#') (e')
Allegro II, 39.9 :I: 4.9 40.0 :t 4.9 2.14939 2.26933
lower voice (d#) (d#)

 

 

 

 

 

Table 10: Allegro l and Il. Pitch Averages and Entropies

The results above do not show major differences between the values based on

tone durations and those based on the number of occurrences. On the contrary,

the results not only show a strong correlation between the values based on tone

durations and those based on the number of occurrences, but also a strong

correlation between the same voices of each Allegro (except for the entropy

values of the lower voices). Based on the results shown above, it can be

assumed that the statistical measurements average, standard deviation, and

entropy may be useful for characterizing the harmonic and contrapuntal function

of each voice within the three-voice texture.

While the attempt failed to falsify the statistically equivalent use of

142

 

weighting average, standard deviation, and first-order entropy by either number

or duration, the results above can be compared to results of analyzing other

pieces in order to falsify the assumption. Hence, the second movement and the

fourth movement of the first Divertimento (both are Menuettos with Trios) shall be

analyzed in the following:

 

 

 

 

 

 

 

 

 

 

 

 

Average Pitch Average Pitch Entropy Entropy

(duration) (number) (duration) (number)
Menuetto l (2) 59.1 t 3.4 58.8 i 3.3 2.42058 2.42907
upper voice (a#') (a#')
Menuetto l (2) 52.1 t 3.9 51.6 :I: 4.5 2.43248 2.50914
middle voice (d#') (d#')
Menuetto l (2) 40.2 i 5.8 40.0 i 6.0 2.52766 2.53871
lower voice (d#) (d#)
Menuetto l (4) 57.7 :I: 4.6 57.8 :I: 4.0 2.50437 2.39214
upper voice (a') (a')
Menuetto I (4) 49.1 .t 5.5 48.9 :t 5.1 2.62501 2.56372
middle voice (c') (c')
Menuetto I (4) 39.2 :I: 5.5 40.3 :I: 5.2 2.45548 2.57779
lower voice (d) (d#)

 

Table 11: No. 2 and No. 4 from Divertimento l. Pitch Averages and Entropies

These results also show no large differences between the values based on tone

durations and those based on the number of occurrences. The only exception is

the lower voice of the the second Menuetto (no. 4), which shows a difference of a

little bit more than a half step in the average of pitch. No. 4 also shows, in both

143

 

upper and lower voices, a larger difference in the entropy value. However, no
meaningful generalization could be made about the closeness of the values.
Within the framework of the chosen methodology (of falsification), the
attempt failed to falsify the assumption that weighting average, standard
deviation, and first-order entropy by either number or duration are equivalent.
However, this failure certainly does not mean an automatic verification of the
assumption. Such verification would require a much more extensive analytical

foundation.

4.2.3. MUSANA Study No. 3
Earlier in this paper, a historical account of the development of computer-
assisted music analysis was compiled. One unevaluated assumption could be
found whenever the average size of intervals was used as a discriminatory
characteristic. The authors usually did not consider the effect of the direction of
the interval on the average interval size. Showing the differences between the
general average of the interval size and the averages of ascending and
descending intervals would require the calculation of all three values:

- the average interval size, disregarding the direction (half step = 1)

- the average size of all ascending intervals (half step = 1)

- the average size of all descending intervals (half step = 1).
Those values will be compared as follows, analyzing all voices of both, Allegro l

and Allegro II:

144

 

Average interval

Average of

Average of

 

 

 

 

 

 

 

size descend. intervals ascend. intervals
Allegro l, upper 2.4 2.7 3.2
voice
Allegro I, middle 2.5 2.6 3.1
voice
Allegro I, lower 3.8 4.4 4.4
voice
Allegro ll, upper 2.4 2.7 2.5
voice
Allegro ll, middle 2.3 2.5 2.7
voice
Allegro II, lower 3.0 5.2 5.7

voice

 

 

 

 

Table 12: Allegro I and II. Average Interval Sizes

In some cases, the averages for both, descending and ascending intervals, show

major deviations from the general average of the interval size. The extreme case

is the lower voice of Allegro II, for which the difference between any of the

averages of ascending or descending intervals is larger than a whole step. But

even other voices show differences of up to a half step. The analyses of No. 2

and No. 4 of Divertimento I show similar results:

145

 

 

 

 

 

 

 

 

 

 

 

 

Average interval Average of Average of
size descend. intervals ascend. intervals

Menuetto l (2) 2.4 2.4 2.7
upper voice

Menuetto l (2) 2.5 2.6 3.1
middle voice

Menuetto I (2) 2.8 4.6 3.7
lower voice

Menuetto I (4) 2.8 2.9 3.2
upper voice

Menuetto l (4) 4.0 4.7 3.6
middle voice

Menuetto l (4) 3.6 3.7 3.6
lower voice

 

Table 13: No. 2 and No. 4 from Divertimento I. Average Interval Sizes

It can be concluded that the differences are too large to use the general interval
size, separately from the averages of ascending and descending intervals, as a

discriminatory characteristic.

4.2.4. MUSANA Study No. 4

The last study draws on information theory. In the past, the authors of many
projects in computer-assisted analysis verified the idea that entropy is a useful
tool for giving syntactical information about, and characterizing the structure of,
musical compositions. If the measure of information, the entropy, is an

expression of the syntactical structure of the music, then it must be possible to

146

 

find the length of structurally important units in each piece of music by calculating
the entropy for each order, i.e. for all possible lengths of such structural units.
Then, the mathematical difference between the entropy of order n and the
entropy of order n-1 should be the essential measurement for finding lengths of
structurally important units in music. This difference is the growth of the entropy

value for the next higher order (i.e. with one more tone):

(growth of entropy)" = entropyn - entropy "-1

This growth ("entropy development") can also be explicated by calculating the

percentages of the growth of entropy of order it compared to the growth of

entropy of order n-1, i.e. always taking the growth of entropy of order n-1 as

100%:

(growth f entropy)n-1 = 100%

(growth of entropy)n % = (100% - (growth of entropy)..) / (growth of entropy)n-1

Defined by the entropy of higher orders, the percentage of (growth of entropy)n is

always smaller than (growth of entropy)n-1. But when (growth of entropy)"

suddenly decreases by a large percentage, i.e. whenever only little "syntactical

information" is gained by adding one note to the unit, then this order must mark

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the length of structural units that are used more often throughout the
composition.

Some observations on the basis of analyses of the Mozart trios for basset
horns KV 439b may substantiate our hypothesis, which includes
- that there are, in fact, significant changes in the growth of entropy, and
- that the growth of entropy can indeed be used for identifying the length of

structurally important units.

Derived from an analysis of the upper voice of Allegro Ill (i.e., the first
movement of the third Divertimento), Tables 14 through 16 display the MUSANA
results of calculating. entropies of orders one through sixteen for three
characteristics: entropies of pitches; entropies considering both, pitch and tone
duration; entropies of tone durations. For all entropy values, the growth of
entropy (i.e. the mathematical difference between the entropy of order n and the
entropy of order n-1) as an absolute value as well as in percentage, are

calculated:

148

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Order Entropy (Pitch) Growth of Entropy in %

1 2.5264

2 4.2612 1.7348

3 5.3100 1.0488 60
4 5.6245 0.3145 30
5 5.7596 0.1351 43
6 5.8293 0.0697 52
7 5.8780 0.0487 70
8 5.9125 0.0345 71
9 5.9328 0.0203 59
10 5.9478 0.0150 74
11 5.9602 0.0124 83
12 5.9726 0.0124 100
13 5.9814 0.0088 71
14 5.9902 0.0088 100
15 5.9936 0.0034 37
16 5.9971 0.0035 103
17 6.0006 0.0035 100
18 6.0041 0.0035 100
19 6.0075 0.0034 97
20 6.0110 0.0035 103

 

Table 14: Allegro Ill, upper voice. Entropies (Pitch) and

Growths of Entropy

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Order Entropy (Pitch) Growth of Entropy in %

1 3.3253

2 4.9284 1.6031

3 5.5212 0.5928 37
4 5.6921 0.1709 29
5 5.7927 0.1006 59
6 5.8545 0.0618 61
7 5.8969 0.0424 69
8 5.9251 0.0282 67
9 5.9428 0.0177 63
10 5.9552 0.0124 70
1 1 5.9639 0.0087 70
12 5.9726 0.0087 100
13 5.9814 0.0088 101
14 5.9902 0.0088 100
15 5.9936 0.0034 37
16 5.9971 0.0035 103
17 6.0006 0.0035 100
18 6.0041 0.0035 100
19 6.0075 0.0034 97
20 6.0110 0.0035 103

 

Table 15: Allegro Ill, upper voice. Entropies (Pitch and Duration) and

Growths of Entropy

150

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Order Entropy (Pitch) Growth of Entropy in %
1 0.9454
2 1.5489 0.6035
3 2.0828 0.5339 88
4 2.5704 0.4876 91
5 3.0134 0.4430 91
6 3.361 1 0.3477 78
7 3.6064 0.2453 71
8 3.7915 0.1851 75
9 3.9666 0.1751 93
10 4.1135 0.1469 84
11 4.2424 0.1289 88
12 4.3536 0.1112 86
13 4.4534 0.0998 90
14 4.5424 0.0890 89
15 4.6265 0.0841 94
16 4.7070 0.0805 96
17 4.7771 0.0701 87
18 4.8359 0.0588 84
19 4.8942 0.0583 99
20 4.9520 0.0578 99

 

 

Table 16: Allegro Ill, upper voice. Entropies (Duration) and

Growths of Entropy

Considering only tone duration, the values relating to the growth of entropy do
not reach below 71%; only three values (of orders 6, 7, and 8) are below 80%.

The reason for the insignificance of rhythmic units must be seen in the

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dominance of long eighth-note runs in this piece and the uneventful rhythmic
stucture in general. This is a result of a general characteristic of the genre
chosen here (divertimento): the uneventful motivic—thematic structure as an
inheritance from the suite.

The growths of entropy considering pitch or pitch and tone duration show
values that are significantly low (below 50%) for the orders 4, 5, and 15, or 3, 4,
and 15, respectively, i.e. for units with 4, 5, and 15, or 3, 4, and 15 notes.
MUSANA also calculated the actual appearance of the most frequent units with
3, 4, 5, and 15 notes: These units refer to groups of notes with tone repetitions,
triadic pitch organization, and a chromatic neighboring figure (ascending minor
second - descending minor second). A by—hand-analysis of Allegro Ill supports
the notion that these units are structurally most important for the composition.

Already the few results show the potentials of the proposed procedure of
calculating the growth of entropy ("entropy development"). The procedure will
especially be helpful In collecting and categorizing melodic and rhythmic units for

melody and rhythm databases. (See the proposals in chapter 5.)

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4.3. Summary

The music-analytical program MUSANA has been introduced here as a tool for
music analysis drawing on statistics and information theory. It includes the
statistical and information-theoretical measurements most commonly used for
computer-assisted music analysis. It can be used for the evaluation of methods
of music analysis proposed in the past. Two studies performed with MUSANA
showed that the use of incipits is not statistically useful for characterizing a whole
composition‘(especially not for characterizing a composer's style) and the
general average of interval sizes is not useful without considering the directions
of the intervals within these calculations. A third study failed to falsify the
assumption that weighting average, standard deviation, and first-order entropy by
either number of tones or by tone duration are equivalent. The last study showed
how the growth of entropy could be used to identify structurally important melodic
and/or rhythmic units by increasing the order (i.e. the size of the units); this
procedure seems to be very valuable for further studies in computer-assisted

music analysis.

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Chapter 5

FINAL REMARKS: DIRECTIONS FOR FURTHER EVALUATION

AND FOR NEW METHODOLOGIES

"I should like to suggest that computer analysis will become one
of the most important directions in musicology for the next
generation. . . (Jan LaRue 1970a, 197.)

A methodological approach that uses falsification in the manner demonstrated in

chapter 4 provides a powerful way to evaluate methods of computer-assisted

music analysis. However, many questions remain about verification or

falsification of methods of computer-assisted music analysis:

- To which kind of music are the chosen methods of analysis applicable?

- Using a specific method of analysis, which musical characteristics can
influence the analytical results?

- How does each musical characteristic influence the analytical results?

- How can we separate those musical characteristics that influence the
analytical results?

- Which of these musical characteristics are most influential for the chosen
method of analysis?

- Is it possible to weight the musical characteristics in order to receive more

objective analytical results?

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Which methods of music analysis are less useful and can be eliminated?
How can we design a more interactive process of analysis, so that traditional
methods of music analysis and computer-assisted methods of music analysis

can merge in more useful ways?

Bearing in mind that all analytical results are influenced by the method used,

answering all of these and similar other questions can help improve methods of

computer-assisted music analysis. Some directions will now be suggested, which

may be useful for new methodologies in the area of computer-assisted music

analysis. Those directions can partly be applied to further research with

MUSANA; most directions refer to a general methodology of computer-assisted

music analysis:

The studies with MUSANA showed that even single measurements drawn on
statistics and information theory can be responsible for the success or failure
of computer-assisted music analysis. But most measurements are interrelated
with others. In future research, it will be necessary to describe in detail the
correlations between the measurements applied, and how those correlations

affect the analytical results.

To evaluate different measurements and methodologies, the influence of

period style, personal style, and genre on the analytical results should be

minimized by conducting comparative analyses of music from only one genre,

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one composer, etc. In a second step, the comparative analyses can be

extended to compositions with more differences in style and genre.

Measurements like entropy are useful for describing the syntactical
relationships within the music. But it is necessary to ask how such
measurements and their analytical results relate to actual human perception.

Empirical studies are necessary that correlate with structural analyses.

Some approaches to computer-assisted music analysis were connected with
the reverse process: composition. Composition is a powerful tool to verify
analytical results, if the analytical results are complete enough to explicate
rules for generating music. Not all approaches would allow reversing the
analytical process, but if they do, such a reversal should be part of the

methodology.

Different methods of analysis are directed at different elements of music or at
different kinds of structural descriptions etc. Combining different
methodologies would result in more complete analytical descriptions. While
such "combined analyses" have been rare in the past, they should be strongly

supported in the future.

Conducting structural analyses as described in MUSANA Study No. 4 show

the necessity of databases for the most common melodic and l or rhythmic

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units in a certain style of music. Such databases are especially useful if they
contain information about the style in which the melodic or rhythmic units
most commonly occur, by which composers they were written, etc. The
process of data collection can be automated by applying the method of
analyzing the growth of entropy ("entropy development") and by saving the

results in databases.

The most recent approaches which draw on cognition and artificial
intelligence aim at performance practices by analyzing musical sound rather
than musical scores. Our knowledge of music and of cognitive processes
related to performance would benefit from focussing on the relationships
between notated music and performed music. The influence of musical
structure on melodic or rhythmic expressions in music would be of special
interest. This research may have a very practical goal in that it can make

music technology more 'musical'.

The design of a system of classification of computer-assisted music analysis
was an important step for further research in this area. However, a more
detailed catalog is needed which lists comprehensively all methods of
computer-assisted music analysis that are available, and which lists the
goal(s) of analysis that are supported by these methods. Such a catalog
should include cross-references to the kind of music to which each specific

method can be applied.

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At the conference "Musicology 1966-2000: A Practical Program", on May 26,
1966, Jan LaRue speculated "that computer analysis will become one of the
most important directions in musicology for the next generation." (Jan LaRue
1970a, 197.) Having reached the year 2000, we have to realize that LaRue's
prediction did not come true. The question remaining is twofold: Why did
computer analysis not come one of the most important directions in musicology?
And: Do we really want computer analysis to become one of the most important
directions? The history of computer-assisted music analysis as well as a few
attempts of falsifying long-used methods show that:

- Researchers have not sufficiently been working together to advance in
computer-assisted analysis.

- Many researchers had, and still have, only little knowledge of the
methodological variety and of the vast number of attempts taken in computer-
assisted music analysis.

- Results of computer-assisted music analysis have been accepted too easily,
without sufficient verifications or falsifications.

While a history of computer-assisted music analysis and a system of

classification of its methods have been provided here, researchers still need to

become more critical of the methodologies used. Such a critical view should

include our general goal: Music is the ultimate object of our profession, which

158

certainly includes the discourse around it. The discourse around music is a
specific goal and need of human intelligence. And while artificial intelligence can
be used as a tool to observe and to stimulate the human intelligence, it cannot,

and should not, replace it.

159

APPENDICES

160

APPENDIX A

OVERVIEW OF MEASUREMENTS DERIVED FROM STATISTICS AND

INFORMATION THEORY

As a basis for the understanding of specific methodological discussions in this
dissertation, some measurements derived from statistics and information theory
will be briefly explained here. The measurements most frequently mentioned in
this text are listed in the following in alphabetical order. For more detailed
information or mathematical formulas see such standard works as Glass and

Hopkins 1996, Golden 1952, Shannon and Weaver 1949, or Goldman 1968.

Arithmetic Mean (Average)
The arithmetic mean (sometimes called 'average') is calculated by dividing the
sum of all elements (e.g., pitches, coded as a numerical value) by the number of

elements.

Auto-Correlation
Auto-correlation gives information about the relation of one characteristic (e.g.,

pitch) to itself, shifted in time. — See also Correlation.

Chi Square Test for Goodness of Fit
The Chi Square Test for Goodness of Fit can calculate whether two samples

(e.g., melodies) are equal or not. Thus, it compares observed and expected

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frequencies.

Correlation and Regression

Correlation gives information on the relationship between two (or more)
characteristics, e.g. if two characteristics such as pitch and tone duration are
dependent on one another linearly or not. The correlation coefficient is a
statistical measure for linear dependence of characteristics.

For example, if the melodic contour of a song tends to move in a certain
direction (ascending or descending), then there is a strong linear correlation of
pitch and direction. In this case, the correlation coefficient would be either close
to the positive maximum, one (ascending), or to the negative maximum, minus
one (descending).

If two characteristics are correlated approximately in a linear fashion, it is
often useful to estimate the progress of the characteristics through a progression
line. The increase of this progression line (regression line) is determined by the

regression coefficient.

Discriminant Function
The discriminant function uses multiple measurements to discriminate between
two groups (e.g., to disciminate between two groups of folk songs that originate

in different areas).

162

Entropy133

Entropy is a form of measurement found in the conceptual methodology of
information theory and is not related to semantics but to syntax. It is an index of
the degree of 'information' found by analyzing single elements (e.g., pitches or
tone durations) or groups of elements taken as a unit. In the latter case, the
entropy is of 'higher order'. The entropy is specifically the negative sum of all
logarithms of the probability of each event multiplied by the probability of each
event. (See Shannon and Weaver 1949, 49f.) The average entropy of a melody,
for instance, is the negative sum of all logarithms of the probability of each note
multiplied by the probability of each note. In case of calculating the entropy of the

second order, the specific succession of two notes are seen as one element.

Entropy Profile134

The entropy profile is a measurement for degree of average 'information' found
by analyzing a class of elements (i.e., all occurrences of the pitch 0' taken as a
unit). For example, the entropy profile of pitches would determine the average

degree of 'information' of all c‘ in a piece of music.

 

‘33 Entropy, in information theory, was first defined by Claude E. Shannon in
1949. See Shannon and Weaver 1949, 49 f.

‘3‘ For the mathematical basis of the entropy profile see Bandt and Pompe 1993.
First applications of the entropy profile in music analysis was described in detail
by Uhrlandt and Schiller 1992.

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Factor Analysis

Factor analysis is a mathematical tool, which can be used to examine a wide
range of data sets. The goal is to find factors which can be used to characterize a
group of objects (e.g., songs), i.e. to find a group of objects with common

characteristics.

Frequency

There are two types of frequencies: absolute frequency and relative frequency.
Absolute frequency is the exact number of a specific class of elements (e.g.,
pitch class c), while relative frequency is the absolute frequency of a specific
element related to the total number of elements. The relative frequency is always
smaller or equal to one, because the denominator is always larger than or equal
to the numerator. The quotation in percent results from the multiplication with the

factor 100.

Kurtosis
Kurtosis refers to the flatnes or peakedness of a (distribution) curve, relative to

the size of the standard deviation.

Markov Chains
A Markov Chain is a model for a sequence of events in which the probability of a
given event (or grouping of events, i.e. event of 'higher orders') is dependent only

on the preceding event (or event of 'higher orders'). For instance, the probability

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of a sequence of five pitches, i.e. a group of pitches of order five, would be

dependent only on the preceding group of five pitches.

Monte Carlo Method

The Monte Carlo Method is a method of obtaining an approximate solution to a
numerical problem by the use of random numbers. In music, this method was
first applies to composition. by Hiller and lsaacson (1959). Here, random
sequences of integers were equated to notes, durations, dynamic values and
playing techniques. These random integers were then screened by applying

various rules and rejected or accepted, depending on the rules.

Probability

Probability is a measurement for the likelihood of occurrence of a chance event

(element).

Redundancy

Redundancy is a measurement, taken from information theory, that gives
information about the partial (or complete) repetition of 'message content', i.e.
elements. (See also Entropy.) For instance, if there is an increasing number of a
certain pitch or a certain melodic phrase, the entropy of this pitch or melodic

phrase decreases and the redundancy increases.

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Regression

See Correlation.

Skewness

Skewness refers to a (distribution) curve, which is asymmetrical.

Standard Deviation
The standard deviation is the square root of the variance (see also there). It

refers to the average distance of elements (e.g., pitches) from their mean value.

Transition Frequency
Transition Frequency is the frequency with which certain elements (e.g., pitches)
occur in some places when it is known that certain others occur in previous

places.

Transition Probability
Transition probability is the probability of an element (e.g., a note or a group of

notes) which follows another specific element (note or group of notes).

Variance and Standard Deviation
Variance and standard deviation give information about the distribution of the
elements (e.g. pitches, tone durations, or intervals) around the mean, i.e. the

average distance of all elements from the mean. The variance is calculated by

166

permanently subtracting the mean from each element, squaring all results,
adding them together and dividing them by the total number of all elements

minus one. The standard deviation is the square root of the variance.

167

APPENDIX B

THE TECHNICAL BASIS OF COMPUTER-ASSISTED MUSIC ANALYSIS:

REMARKS ON THE HISTORY OF COMPUTERS AND COMPUTING

The history of computers and computing cannot be seen as merely a history that
starts with electronic calculators in the 19403. The history of calculating
machines and the science of computational strategies goes back hundreds of
years. However, a comprehensive history of computing cannot be part of this
dissertation. Only a short overview of the development of electronic computers
and computing shall be given here, to help understand the history of computer-
assisted music analysis.135 The emphasis on the history of computing between
the 19403 and the 19703 is related to the fact that this knowledge is often absent
in contemporary discussions of computer applications in music.

The first functioning computer was “23,” created in 1941 by the German
Konrad Zuse. It was a program-controlled computer that used punched tape.
However, computers—like the “Z3” —that used the dual system and floating
point numerical representation were almost electro-mechanical machines
because of their relay technique.

More important than Zuse’s computers was the IBM Automatic Sequence

Controlled Calculator, usually known as “Harvard Mark I.” This computer was

 

‘35 This overview is based on Campbell-Kelly & Asprey 1996, Rechenberg 1991,
and Nash 1990.

168

constructed for Harvard University between 1937 and 1944. Its main designer
was the Harvard researcher Howard H. Aiken. Once running, the electro-
mechanic computer could store as many as 72 numbers, and “was capable of
three additions or subtractions a second. Multiplication took six seconds, while
calculating a logarithm or a trigonometrical function took over a minute”
(Campbell-Kelly & Asprey 1996, 72-73). The input source for program codes
were punched paper tapes. However, the machine was incapable of conditional
branching, i.e. causing the program to select an alternative set of instructions, if a
specified condition was satisfied, or otherwise to proceed in the normal
sequence.

John Presper Eckert and John Mouchly’s "ENIAC" (Electronic Numerical
Integrator and Calculator; 1946) was the first fully electronic computer. It made
calculations about one hundred times faster than calculations by a mechanical
differential analyzer. A serious problem of this computer was the time it took to
reprogram the machine, since it could not use punched cards for real time
operations at the speed of 5,000 operations per second. (Punched cards could
only be read at a much lower speed.) Instead, changing the program required re-
wiring the computer: hundreds of patch chords connected different units of the
computer to each other. Re-programming took between several hours and
several days. Other problems were too little storage (only twenty numbers!) and
too many tubes. However, after the famous mathematician John von Neumann
became a consultant to the ENIAC project in 1944, deficiencies were resolved

and a new design was developed. It was one of the most crucial designs for

169

further computer developments: The idea of the “stored-program computer" was

. born, outlined in a plan for the post-ENIAC “EDVAC" (Electronic Discrete
Variable Automatic Computer). Virtually all computers up to the present have
been based on the John-von-Neumann-principle of "stored programs”—using the
same memory for numbers as well as for instructions—enabling a rapid change
from one program to another. After von Neumann's design, computers have had
five functional divisions: input, memory unit, control unit, arithmetic unit, and
output. Other new features were the use of binary numbers (ENIAC still used
decimal numbers), and the serial execution of instructions.

While EDVAC was never actually realized, in 1949 Maurice V. Wilkes'
“EDSAC” (Electronic Delay Storage Automatic Calculator) became the first full-
scale universal digital computer with saved programs based on John von
Neumann's principles. It used delay lines, reducing the number of vacuum tubes
by five-sixth compared to ENIAC. Because of its saved programs, software
design came into being with EDSAC. Eventually, programs were developed
which translated other programs into machine code and could, thus, be
understood by the hardware. ln1950, the developers of EDSAC started to
develop a “subroutine library,” i.e. a library of programs for solving common
problems, such as certain arithmetic calculations, etc. Even today, programming
continues to follow the principle of organizing subroutines.

In the second half of the 19403, IBM became the leading company in the
computer industry. The “Card Programmed Calculator” became—in the late

19403 and early 19503—the most often sold calculating tool. However, by the

170

end of the 19403, IBM had also developed several full-scale computers. IBM also
developed the magnetic drum for the main memory (instead of mercury delay
lines or electrostatic storage tubes). After setting up their own computer
business, J. P. Eckert and J. Mouchly developed similar devices. After being
taken over by Remington Rand, Eckert and Mouchly completed the development
of their UNIVAC (UNlVersaI Automatic Computer; 1951). It was the world's first
commercially available fully electronic computer, and it became a market leader
for its type. The UNIVAC was eventually the first computer the broader public
had been introduced to during election night 1952, when it accurately predicted
Eisenhower's win over Stevenson. After that, 'UNIVAC' became a generic name
for computers.

The prediction of the election outcome also showed the great potential for
computers in data processing for many business areas. Thus, in the early 19503,
there was a change of the main use of computers: a change from mathematical
calculations to data processing. The first music applications date from the mid-
19503. (See chapter 2.2.) Dozens of computer businesses—mainly in the United
States—emerged. Most of them were eventually acquired by bigger office-
machine firms. But IBM re-entered the market with its IBM model 701 in 1952.
The first real data processing computer was announced one year later: the IBM
702. This computer used a more reliable and faster tube technology (memory)
and a modular construction; but most important, its magnetic tape systems made
the UNIVAC's obsolete. IBM’s superior marketing and its customer service

helped gain the leadership in this area. The low-cost Magnetic Drum Computer

171

(IBM 650; 1953) was acquired by many institutions of higher learning. It reflected
IBM’s total-system view, i.e. the combination of computer development,
programming, field service, customer transition, and training, which led to the
eventual replacement of the electro-mechanic punched-card accounting machine
in the early 19603. IBM developed the 1401 model with transistors instead of
tubes and core memory instead of the magnetic drum; peripherals were new card
readers, punchers, high speed printers, and magnetic tape units. To avoid the
high cost of machine replacements, IBM developed the programming system
RPG (Report Program Generator), a business data processing language
designed for analysts familiar with punched-card machines. This programming
language is still in use today. Also, IBM itself developed software solutions.

Already by 1953, programming had become a serious research project at
IBM. There, John Backus proposed a higher-level programming code, called
Formula Translator (FORTRAN). His goal was to develop an automatic
programming system which could produce machine code as good as that written
by an experienced programmer with only short and logical commands. Finalized
in 1957, FORTRAN became the first'successful scientific programming language
and is still in use today in certain dialects. An improved version, FORTAN II,
followed in 1959. By the end of the 19503, several other languages had been
developed by other computer manufacturers or research groups: MAD, IT,
ALGOL, etc. However, FORTRAN continued to dominate scientific applications.
Last but not least, ‘standardizing' FORTRAN made it possible to exchange

programs, even if different makes of computers were used. ALGOL was, for

172

several years, more common in Europe; eventually, even there FORTRAN took
over a dominating position.

For business applications, the US. government initiated the development
of COBOL (COmmon Business Oriented Language). It came into life in 1960 as
“COBOL 60”. This language was based on Business English, rather than on
mathematical terms. This allowed non-programmers to understand the code,
even though they would not be able to write it themselves. Hundreds of other
programming languages were designed in the 19603, but most of them died out.
COBOL and FORTRAN dominated the programming world for the next twenty
years.

In the early 19603, IBM continued with a standardization process to
achieve compatibility among all their computer components as well as their
software components. The result was their System/360 (1964). However,
programming turned out to be more costly than the hardware itself. Further
developments were fully integrated circuits, giant number-crunching computers,
and time-sharing computer systems (which allowed more than one user to
execute programs concurrently).

The military had also played an important role in the emerging computer
industry since World-War II. For their needs, the idea of real-time computing for a
flight simulator at MIT was most important. For the purpose of real-time
computing, computers with a much higher speed and a much higher reliability
were needed than existing technology had to offer. Important developments were

the core-memory, printed circuits, mass-storage devices, and CRT-graphical

173

displays. Military projects also provided a ‘platform’ for further developments in
software engineering.

The first large civilian real-time project was the airline reservation system
SABRE (Semi-Automatic Business Research Environment) in the 19503 and
early 19603, and the Universal Product Code (UPC) in the early 19703. First
scanners were manufactured by IBM and NCR. These developments were of
great economic importance: the whole manufacturing-distribution network
became involved in electronic data tracking and automatic ordering, etc.

While in the early 19503 software was still supplied at no additional cost
by the computer manufacturer, ‘software contracting’ soon developed:
Corporations, such as the System Development Corporation (SDC), emerged. In
the early 19603, the software industry was booming. However, in the late 19603,
a software crisis emerged because of the much faster growing hardware industry
and the incapability of exploiting the new hardware effectively (since large
programs were needed). It took many years, before programming became a real
engineering discipline with its “structured design methodology” and its
development model as an organic process which would never really be ‘finished’.
The concept of ‘software packages’ emerged in the late 19603; these packages
were much more cost-effective than custom software. At the same time, large
computer manufacturers decided to price their software and hardware
separately.

The 19703 brought faster, and more reliable, integrated circuits, random-

access disk storage units, semiconductor memory, more effective time-sharing,

174

communication-based on-line computing, and virtual memory. In 1971, the 4004
microprocessor was announced by INTEL; it was the first “computer on a chip".
The microprocessor was initially used for simple control applications and for
(emerging) minicomputers, but soon it was used for full-scale computers. The
first personal computer came on the market in 1977: the Apple II. The personal
computer included a central processing unit, screen, keyboard, floppy disk
drives, and a printer. In 1981, IBM announced its entrance into this new market
with the IBM PC. Apple responded with the “Macintosh” (famous for its user-
friendly point-and-click-software).

Wlth the personal computer, new programming languages became
important. BASIC (Beginners All-purpose Symbolic Instruction Code) was
developed in 1964 by John Kemeny and Thomas E. Kurtz at Dartmouth College.
It superseded FORTRAN not only in its simplicity, but also in its speed (of
translation). It became the introductory language for many students, and in the
mid-19703, it became the first widely available programming language for the
new personal computers. Pascal (1971) as well as the systems programming
language C (1970; originally developed for the implementation of Unix) became
more sophisticated and are still two of the most commonly used higher level
programming languages. The Unix operating system, developed between 1969
and 1974 by Bell Laboratories, became the—to-date—most widely used
operating system for multi-user environments. And while LISP (LISt Processing)
was developed already in 1961, it became important decades later, especially in

artificial intelligence research.

175

However, as early as the 19603, the research of MIT psychologist and
computer scientist J. C. R. Licklider suggested that computers could be used to
augment the human intellect, but not to supercede it, as Al researchers at the
time hoped. Licklider argued that computers should enhance the every-day-work
of researchers, since computers spent most of the time not “thinking” but
calculating and referencing. Licklider’s theories promoted the development of
interactive computing with graphical user interfaces, software engineering, and,
years later, text processing (1980) and refined calculating software, etc.

During the last three decades, computer hardware costs have fallen
dramatically. Changes in the nature of data processing have generally occured
invisibly. More sophisticated applications are possible, and real-time systems as
well as time-sharing systems have become common in many areas. The IBM PC
has set the standard of personal computers up to the present, and Microsoft,
contracted by IBM in 1980 to produce of MS-DOS operating system, grew to be
the largest software company in the world, later producing Windows, Word,
Excel, and other high-quality software products. In the last decade, Microsoft has
become the symbol for a major shift from hardware to software. And the World
Wide Web is a logical continuation of the demand for universal information and

communication.

176

APPENDIX C

SELECTIONS OF W. A. MOZART'S FUNFUNDZWANZIG S TUCKE

(FUNF DIVERTIMENTI) FUR DRE! BASSETTHORNER (KV 439”)

The following pages reproduce the score of the W. A. Mozart pieces analyzed in
chapter 4, i.e. numbers 1, 2, 3, 4, 6, and 11 of Fiinfundzwanzig Stiicke (fi‘inf
Divertimenti) fiir drei Bassetthomer (KV 439”). The reproduced scores contain
page numbers that refer to Mozart 1975. © 1975 by Barenreiter Verlag.

Reprinted by Permission.

177

2. Fiinfundzwanzig Stficke (fiinf Divertimenti)” 67

fiir drei Bassetthbrncr”)
xv 439b ‘0

Divertimento 1

1. Komponiert angeblich zwischen 1783 und 1788‘?)
Allegro /"

A

    

00110 d:' Basset“ I
in Fa/F p

(Iona di’ Bassetto II
in Fall

Como dz’ Banana [1!
is Fri/F

 

178

68

 

179

 

180

70
107

 

113 ’ ‘

 

1“!

 

 

2. MENUE’I‘TO

 

181

 

Trio

 

Menuetto
d: dapo

 

182

A. ..l.._. . .

 

:
.___ ___ ___
.r: =—- __u-
n: m“ “we
. E ___.
m _= _=
=_ =_
=_ ___—
___ ___..
= __=
.= =—
- = =_
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= E.
=_ ___.
=_ =—
___ 5 w
=-
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0
4n

=
4 MENUETTO

 
 
 

.. I. _= an
From“ Il-l-u.“ I nu-_

183

73

 

184

 

185

Divertimento II

6.

Allegro

 

 

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__
.—
__u
=
on
3
=
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a
.—
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- - — n..--.-l—
-.—l-'-n-—--'_v—
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186

79

 

187

89
Divertimento III

11.
Allegro . , /—-\

 

188

90

 

 

____u____
_m__

I-IIIH“ “Him-l

 

189

Vi- ., 91

 

f p ° ' simile

 

190

 

© 1975 by Barenreiter Verlag. Reprinted by Permission.

191

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192

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