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LOCATING RECURRING THEMES IN MUSICAL SEQUENCES
by Shyamala Doraisamy
A dissertation submitted in partial fulfilment of the requirements for the degree
of Master of Information Technology
Faculty of Information Technology UNIVERSITI MALAYSIA SARA W AK
July 1995
DECLARATION
No portion of the work referred to in this dissertation has been submitted in
support of an application for another degree or qualification of this or any other
university or institution of higher learning.
ii
ACKNOWLEDGEMENTS
I would like to thank my supervisor Professor Dr. Zahran Halim for the guidance
throughout this project.
I would also like to thank my external examiner Professor Dennis Longley and
co-supervisor Dr. Abdelhamid.
I wish to thank Associate Professor Dr. Zaidah Abdul Razak, Mr. K. Narayanan,
Mr. Leng Chee Kong, Ms. Beverly La Rock and Dr. Lloyd Smith. Thanks also to
the staff of the Faculty of Information Technology for all the assistance.
Thanks ,to my friends Yong Huan Loon, Ong Chooi Sim, Sih Yiak May and
Rueben Wee. A special thanks to Wong Pek Wan for the support. Also thanks to
my friends in Sarawak , namely: Alvin, Sita, Shakila, Shela and Hartinah.
Thanks to my family for their love and understanding. Thanks to Ann Perreau
for her support.
Finally thanks to the special person in my life - Suresh Singam.
Shyamala Doraisamy.
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~--
TABLE OF CONTENTS
Title 1
Declaration 11
Acknowledgement 111
Table Of Contents IV
List Of Figures VlV
List Of Tables Xl
Abstrak Xli
Abstract Xlll
CHAPTER 1 INTRODUCTION
1.1 Introduction 1
1.2 Computers And Music 1
1.3 Musical Sequence Comparison 3
1.4 Application Areas For Theme Location 5
1.4.1 Musical Forms Analysis 5 , 1.4.2 Index 6
1.4.3 Musicology 6
1.4.4 Copyright Issues 7
1.5 Research Objectives 7
1.6 Methodology 8
1.7 Scope Of Study 10
1.8 Outline Of Dissertation 11
IV
CHAPTER 2 SEQUENCE COMPARISON
2.1 Introduction
2.2 Sequence Comparison
2.3 Sequence Comparison In Music
2.4 Sequence Comparison Techniques
2.4.1 Template Matching
2.4.2 Statistical Methods
2.4.3 Structural Methods
2.5 Examples Of Sequence Comparison Techniques
2.5.1 Matching (Template Matching)
2.5.1.1 Exact Matching
2.5.1.2 Approximate Matching
2.5.2 Cluster Analysis And Decision Method
(Statistical Approach)
2.5.3 Rhythmic Patterns In Musical Lines
(Structural Methods)
2.5.3.1 Exact Matching
2.5.3.2 Rhythmic Elaboration
2.6 Summary
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CHAPTER 3 COMPUTER-ASSISTED MUSIC ANALYSIS
3.1 Introduction 40
3.2 Survey Of Comparison Methods 40
3.2.1 Template Matching 41
3.2.1.1 Automated Identification Of Melodic Variants In
Folk Music - Martin Dillon & Michael Hunter 41
3.2.1.2 A Computer-Assisted Approach To Micro-Analysis
Of Melodic Lines - David A.Stech 41
3.2.1.3 Comparison Of Musical Sequences-
Marcel Mongeau & David Sankof'f 42
3.2.2 Statistical Methods 44
3.2.2.1 Cluster Analysis For The Computer-
Assisted Statistical Analysis Of Melodies - Luigi
Logrippo & Bernard Stepien 44
3.2.2.2 Minimum Message Length Comparison Of
Musical Sequences - Shane Samuel Cook 44
3.2.3 Structural & Syntactic Methods 46
3.2.3.1 On Finding Rhythmic Patterns In Musical Lines -
Bernard Mont-Reynaud & Mark Goldstein 46
3.3 Rationale For Adopting Mongeau & Sankoffs Method 47
3.4 Music Data Representation 50
3.4.1 Overview Of Repesentation Schemes
3.4.1.1 DARMS
3.4.1.2 MIDI Notelist
3.4.1.3 Digital-tradition
3.4.1.4 Humdrum
3.4.2 Review Of Representation Schemes
3.5 Conclusion
CHAPTER 4 PERFORMANCE ASSESSMENT
4.1 Introduction
4.2 Algorithm By Mongeau & Sankoff (1990)
4.3 Encoding & Parameters
4.4 Matching Experiments
4.4.1 Matching Of Sequences An Octave Apart
4.4.2 Matching Of Sequence A 5th Higher
4.4.3 Matching Of Sequence A 4th Lower
4.4.4 Tests For Passing Notes
4.4.5 Tests For Key Change
4.4.6 Tests For Rhythmic Change - Augmentation
4.4.7 Tests For Rhythmic Change - Diminution
4.5 Experiment Results
4.5.1 Sequences An Octave Apart
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4.5.2 Sequences A 5th Higher 68
4.5.3 Sequences A 4th Lower 68
4.5.4 Sequences With A Passing Note 68
4.5.5 Sequences With A Key Change 70
4.5.6 Sequences With Rhythmic Change - Augmentation 70
4.5.7 Sequences With Rhythmic Change - Diminution 70
4.6 Conclusion 71
CHAPTER 5 SYSTEM OVERVIEW & IMPLEMENTATION
5.1
5.2
5.3
5.4
5.5
Introduction
Theme Locater System
5.2.1 Approach
5.2.2 Requirements Of The System
Humdrum Format
Processes In TLS
5.4.1 Extraction
5.4.2 Conversion
5.4.3 Comparison
5.4.4 Analysis
Results
CHAPTER 6 ENHANCEMENT & APPLICATION
6.1
6.2
6.3
6.4
6.5
Introduction
Strengths And Weaknesses
Enhancement
6.3.1 Weight Change
6.3.2 Melodic Contour
6.3.3 Rhythmic Contour
Matching experiments
Experiment Results
6.5.1 Exact Pitch Contour
6.5.2 Rhythm Contour
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6.5.3 Passing Note
6.6 Application On Fugue
6.7 Results
6.8 Conclusion
CHAPTER 7 CONCLUSION & FUTURE WORKS
7.1 Introduction
7.2 Findings
7.2.1 Dynamic Programming
7.2.2 Data Encoding
7.2.3 Music Data Representation
7.2.4 Weight Tables ,,!
7.2.5 Pattern Recognition
7.3 Accomplishments
7.4 Limitations
7.4.1 Data Set
7.4.2 Variations
7.4.3 Threshold
7.5 Future Works
7.5.1 Variation
7.5.2 Dimensions For Comparison
7.5.3 Result Reporting Method
7.5.4 User Interface
7.5.5 Experiments
7.5.6 Other Possible Works
7.6 Concluding Remarks
BIBLIOGRAPHY
GLOSSARY
APPENDIX A - SCORES
APPENDIX B - PROGRAM LISTING
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LIST OF FIGURES
2.1 Modification with a passing note 16
2.2 Modification based on transposition 17
2.3 Modification based on augmentationldimunition 18
2.4 Pattern recognition using template matching 19
2.5 Pattern recognition using a statistical pattern recogniser 21
2.6 Examples of structural pattern representation 22
2.7 Pattern recognition JIBing a structural recogniser 23
2.8 Trace linking two sequences 24
2.9 Illustration of the principle of optimality 27
2.10 Dynamic programming array 28
2.11 Dynamic programming example 31
2.12 Optimal alignment with a dissimilarity measure of 2 32
2.13 Visualisation in 2-dimensional space 34
4.1 Alignment for sequences an octave apart 61
4.2 Alignment for sequence a 5th higher 62
4.3 Alignment for sequence a 4th lower 63
4.4 Alignment for sequence with a passing note 64 \
4.5 Alignment for sequence with key change 65
4.6 Alignment for sequence with rhythmic change - augmentation 66
4.7 Alignment for sequence with rhythmic change - dimunition 67
5.1 Theme locater system '76
5.2 A portion of Fugue I, Bk I in Humdrum format 78
5.3 A portion of Fugue I, Bk I after extraction 80
5.4 Output from extraction of Fugue I, Bk I 81
5.5 Data encoding 82
5.6 Dissimilarity array 85
5.7 Results of analysis 86
6.1 Weight change 89
6.2 Two significantly different sequences 92
6.3 Pitch versus duration graph 94
viv
6.4 Modifications 96
6.5 Exact pitch contour for transposition 98
6.6 Exact rhythmic contour for augmentation and dimunition 99
6.7 To detect passing notes 100
6.8 Theme locater system - modified 101
6.9 Data encoding with contours 103
6.10 Dissimilarity array after change 104
6.11 Locations of theme~ 105
LIST OF TABLES
2.1 Example of note occurrence frequency 33
2.2 Distance table example 34
4.1 Weight assignment base~n difference in degrees 57
4.2 Weight assignment based on difference in semitones 58
4.3 Dynamic programming match 69
xi
ABSTRAK Penggunaan komputer pada masa kini dalam hampir semua subdisiplin
subdisiplin muzik semakin bertambah. Otomasi penggubahan lagu, sistem
pakar teori muzik, (acoustic' senibina adalah beberapa dari pelabgai bidang
muzik bagi penggunaan komputer.
Kerja yang dilapurkan di sini mengkaji kaedah-kaedah yang diguna dalam
pembezaan dua jujukan muzik (musical sequence). Dalam pembezaan dua
jujukan muzik, apa yang perlu dipertimbangkan ialah sujektiviti yang terlibat
dan penganalisaan yang diperlukan. Beberapa algoritma dalam pembezaan
jujukan muzik di mana teknik-teknik yang diguna dikaji berdasarkan teknik
teknik pengcaman corak (pattern recognition). Sistem-sistem pengwakilan notasi
muzik bagi komputer yang berlainan juga dikaji supaya muzik data boleh
diubahsuai dalam bentuk yang boleh dibaca oleh mesin.
Tujuan mengkaji algoritma-algoritma pembezaan jujukan muzik ialah untuk
memperolehi satu kaedah untuk menglokasi pengulangan tema utama dalam
sesuatu gubahan lagu walaupun tema tersebut diubahsuai oleh penggubah
untuk menjadikan pengulangan lebih menarik. Manusia boleh mengcam
pengulangan tema walaupun diubahsuai dengan senang tetapi jika kaedah
komputasi diguna, algoritma akan diperlukan.
Kaedah oleh Marcel Mongeau & David Sanko!! (1990) diguna sebagai algoritma
pembezaan jujukan muzik. Ujikaji-ujikaji dilakukan untuk menguji kebolehan
penggunaan algoritma ini untuk penglokasian tema. Satu sistem Penglokasian
Pengulangan Tema dibangunkan di mana kaedah terse but diguna untuk
mencari subjek fugue' yang berulang dalam dalam (suara-suara' lain dalam
sesutu fugue' Bach yang tertentu. Kelebihan-kelebihan dan kelemahan
kelemahan kaedah terse but dikaji. Perubahan dicadang dan diimplimentasikan
di mana corak melodi dan ritma diguna sebagai ciri pembezaan untuk
membolehkan subjek fugue' dikesan walaupun subjek tersebut diubahsuai
dengan penambahan nota laluan, (transposisi' melodi dan ogmentasi dan
dimunasi ritma.
ABSTRACT
Computers are now being used in almost all (sub)disciplines of music.
Automated composition, music theory expert systems, architectural acoustics are
just a few of these many areas.
This thesis looks into methods being used in comparing two musical sequences.
In comparing two musical sequences, the subjectivity and the reasoning required
for comparison needs to be considered. A few algorithms in musical sequence
companson and the different techniques used were studied based on pattern
recognition techniques. Apart from that, different musical representation
systems were also looked into for encoding music notation into machine-readable
form.
The purpose of surveying musical sequence comparison algorithms was to be
able to find a method to reliably locate recurring themes in a given score as the
theme can be varied by the composer to add variety to the composition. Humans
might have little difficulty identifying the theme despite it being varied whereas
algorithms will be needed if computational methods are to be used in locating
recurring themes.
The method by Marcel Mongeau & David Sankoff (1990) was selected as the
comparison algorithm. Experiments were done to test its usability in locating
recurring themes. A Theme Locater System was developed and this comparison
method was used in finding the recurring fugue subject in the different voices in
a particular Bach's fugue. Its strengths and weaknesses were studied.
Enhancements where melodic and rhythmic patterns were used as the basis for
comparison to be able to detect the fugue subject even when some basic
modifications such addition of passing notes, transposition of the melody and
augmentation and diminution of the rhythm had transformed this fugue subject.
XUl
1 INTRODUCTION
1.1 Introduction
This chapter first gives a discussion of combining two contrasting fields of study:
computers and music. Next, it presents the significance of the task undertaken
for this study in comparing musical sequences to locate recurring themes. Then
it discusses why this study was undertaken by presenting the application areas
for locating recurring themes. Following that, the objectives of this study are
given before the methodology taken to achieve the objective stated is described.
The scope of the study is then outlined. Finally, an outline of this dissertation is
presented.
1.2 Computers And Music
Music intelligence is research into methods of making the computer more
cognizant of and powerful over the manipulation and organisation of musical
materials, structures and systems.
- Phil Winsor and Gene DeLisa, 1991
Computers are used in almost every field now and music is no exception. One
might ask how can computers contribute to the musical arts which involve
creative thinking?
Real creative thinking takes practice and involves carefully following
principles and effective techniques. [JF90]
By analysing these principles and techniques, computational methods can be
applied to almost every domain in music.
For mUSIC researchers pursumg systematic investigations of musical
information, systems in posing and answering research questions are being
developed. This includes the posing of factual questions of use to music theorists,
musIc analysts, ethnomusicologists, historical musicologists,
psychomusicologists, music librarians and others.
Apart from the use of computers in systematic investigations of precomposed
music, computers are also being used extensively in music performance
(generating the sounds, including timbre, dynamics, synthesis/simulation of
orchestral and new instruments, etc.) and in music creation (generation of
rhythm, melody, harmony, orchestration, etc.). Music performed or created this
way is referred to as computer music.
Previously, both sound production and compositional processes were carried out
with the mainframe computer in a single environment. The scenario today is
that the personal computer often fills the role of composer/performer while the
synthesizer acts as the instrument of performance, in the same way that people
have traditionally played acoustic instruments. The development of MIDI
(Musical Instrument Digital Interface), is a primary reason for this advancement
where MIDI IS a communications protocol that allows electronic musical
instruments to interact with each other and with a general-purpose
computer[CA86]. With this, electronic musicians are now creating new and
different sounds.
Researchers in every music (sub)discipline are finding ways to use the computer
to help solve musical problems. Some of the major research areas are:[WD91]
Algorithmic and Automated Composition, Music Theory Expert Systems,
Computer-Aided Instruction / Music Education, Musicology & Ethnomusicology,
Performance, Psychoacoustic Phenomena (Cognition), Physics of Sound,
Architectural Acoustics, Performance Environment Simulation, Ecological (sonic
environment) Acoustics, Esthetic Perception Theory, General System Theory :
Information Theory, Intermedia Explorations (multidisciplinary events
comprised of multiple information media, such as choreography, video, film,
laser imagery, light sculpture, and music), Music representation systems,
2
Information retrieval systems for musical scores, Music Printing and Music
Analysis.
The focus of this thesis is in the usage of computers in music research where
methods of comparing two musical sequences encoded in machine readable
format is studied.
1.3 Musical Sequence Comparison
The purpose of this study is to identify a method to locate recurring themes in a
given music score. The theme here is referring to the main melody or musical
idea that forms the basis of the composition. Composers usually repeat this
theme throughout the composition and upon repetition, this theme is usually
varied or modified to add variety to their composition. Therefore, a method is
required to identify these reoccurrences despite it being varied.
The method needed is a musical sequence comparison method where two musical
sequences encoded in machine-readable format is compared. Different musical
sequence comparison methods are studied using pattern recognition techniques
as a basis for the study since musical sequence comparison can be viewed as an
application area of pattern recognition.
Sequence comparIson IS sometimes referred to as approximate string
matching[Sl-94]. Sequences are often different lengths. In speech, for example,
the length of a word or syllable changes with context and speaker.
In music, the complexity of sequence comparison is best described by [Stech81]:
Analysing and defining the factors affecting the succession of tonal events
ut a musical composition is a complex task. It requires evaluating particular
musical events within the context of the prevailing musical style and abstracting
those elements which appear to affect significantly the aural logic of the
composition. Through such a method, the analyst hopes to define more clearly, in
his own mind, how successfully the composer develops his musical material
without violating the composer's own sense of musical logic of order.
3
The difficulty lies in locating a recurring theme as the theme might have been
modified. Humans, normally, will find little difficulty recognising slightly
modified or decorated themes. Computers, on the other hand, do very well with
exact matching but struggles somewhat (i.e., it is difficult to define 'good'
algorithms) with approximate matching. Central to the problem is our ability (or
inability) to define 'similarity' - when are two sequences similar enough to be
considered variations of the same theme? There is an element of subjectivity in
such judgements which is difficult to capture algorithmically.
Apart from that, when the musical score being analysed is "full of notes", the
naked eye sometimes misses the recurrence of a melody as it is "hidden"
somewhere in the web of the notes. For large works, it can be tedious locating
the recurrences especially when modifications have happened. It is here that if
"sufficiently good" sequence comparison algorithms exist, computers can perhaps
do better - computers do not get tired or bored of tedious tasks.
Up till now, all these analysis has been based on experience and knowledge of
the listener and music has been looked upon as an art where it has been
impossible to apply computational methods. With systematic study as much as
possible of the processes possible in compositional works, it can move towards
automating analysis of music. Computers are now being introduced in assisting
or even acting as the expert in analysing this creative process. The need for
development of techniques which utilise melodic pattern analysis is necessary
towards this change.
The method used in this thesis to locate recurring themes can serve as a basis
for the future work in locating recurring themes or incorporated as modules for
automated musical forms analysis, copyright issues, recognising themes which
can prove to be an index for looking up a theme dictionary or even in expert
systems for some of the subdisciplines of music which requires comparison of
musical sequences.
4
1.4 Application Areas For Theme Location
The main purpose of studying methods in musical sequence comparison in this
thesis is in locating recurring themes. In this section, some of the areas in music
where locating recurring themes can be useful are discussed.
1.4.1 Musical Forms Analysis
Musical forms analysis is an important aspect of performing, listening and
studying music. Every piece of music, from the simplest song to the most
elaborate symphony, needs to have some kind of organisation, or form, if it is to
be coherent to the listener. [SS93]
Western music incorporates some aspects of departure and return. A departure
suggests a musical idea that is different from that which has already been
presented - a point of contrast. A return is either an exact or modified
repetition of the original idea. Patterns of departures and returns, contrasts and
repetitions and key relationships are determining factors in establishing the
form of a piece of music. To identify these contrasts between departure and
returns, the different elements of music are used as the basis for comparison.
The basic elements in music are pitch, rhythm (duration), intensity (dynamics)
and timbre ( tone quality - a flute sounds different from a clarinet ).
Whether listening to music or performing a piece, analysing and understanding
the form of the music is important. This process is called musical forms analysis
and is an important activity for those doing musical studies, research,
performance and so on. Musical analysis results in a higher level of musical
understanding, and this in turn leads to improved music performance and fuller
music appreciation.
The listening process is a communication of compositional ideas between the
composer and the listener. Awareness of musical patterns and musical forms is
an important aspect in this regard. The performer on the other hand has the
duty of presenting these ideas to the listener. Thus, understanding the form is
just as important if not more so. For example, the player might need to end the
first theme softly and begin the second theme louder in order to make it clear to
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the listener that the second theme is being introduced. This process is called
musical interpretation. By knowing form, one will know where to expect
changes and the likely type of change.
The first step one might take in analysing musical forms is to look at musical
sequences. Intuitively, a phrase will be characterised by its sequence of notes, in
both pitch and rhythm. The recognition of a recurring sequence and its location
would be a starting point in determining the form. Sequence comparison is
clearly central to the detection of recurring themes.
1.4.2 Index
For a musical theme dictionary or a musical score database to be constructed, an
index will be needed for retrieval. Another application of musical sequence
comparison is the retrieval of a musical work based on themes acting as indexes
like in Barlow and Morgenstern's Dictionary of Musical Themes or a score
database. A sequence that is found to be repeating very frequently might be as
the theme which is then extracted and used as a search index.
1.4.3 Musicology
Research into melodic pattern relationships provides insights into the mental
processes of both the listener and the composer [Stech81]. Musicologists
analysing particular compositional styles of a composer or works of a particular
period will need to analyse the recurrences of musical sequences in the scores
being studied. This does not necessarily mean that most composers consciously
attempt to construct their thematic or rhythmic variants, although such an
approach may have been used by a few composers.
Musicologists and anthropologists study folk songs as an indicator of population
migration. [Sl-94] This is done principally through comparing and detecting
similarities in melody lines of songs from different regions. Methods to compare
musical sequences are therefore of direct value in such efforts.
Ethnomusicology is another area of application. Ethnomusicology includes the
study of folk music, Eastern art music and contemporary music in oral tradition
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as well as conceptual issues such as the origins of music, musical change, music
as a symbol, universals of music, the function of music in society, the comparison
of musical systems and the biological basis of music and dance. [HM92].
Ethnomusicology formerly known as comparative musicology has been described
as:
"Comparative musicology has as its task the comparison of the musical
works - especially the folksongs - of the various peoples of the earth for
ethnographical purposes, and the classification of them according to their various
forms. "[HM92]
Musical sequence comparison methods to locate themes reoccurring can be used
in helping in this classification processes.
1.4.4 Copyright Issues
In automating the process of detecting if melodies have been copied, musical
sequence comparison forms the basis. Maybe one way is setting a limit to the
degree of variance allowed - anything below that figure is considered to have
been copied.
1.5 Research Objectives
The main aim is to be able to find a method in locating repeating themes in a
given music score. In achieving this aim, the objectives set are:
• to identify a sequence comparison method which can be used to locate a
recurring theme.
• to identify a music data representation system which can act as input for
music scores in machine-readable format.
• to design experiments that would test the usability of the algorithm m
identifying recurring themes.
• to develop a system that would locate a recurring theme automatically from a
given music score.
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1.6 Methodology
The methodology used for this study to achieve the aim of developing a system
which can locate a recurring theme in a given score is described below.
• Review sequence comparison techniques
To study sequence comparison in the context of music based on the different
categories of pattern recognition techniques. This will be the first step in trying
to identify a method to compare musical sequences for locating recurring themes.
What is to be obtained is an overview of the different categories for a
comparative study of the different techniques to be done before a decision can be
made as to the choice of the algorithm required for the study.
• Review studies done on computer-assisted music analysis
To look at works done in the different categories of sequence comparison with
the aim of obtaining a method that can be used as the comparison method
required to locate recurring themes. The works reviewed are:
- "A computer-assisted approach to micro-analysis of melodic lines", David
A.Stech (1981)
- "Automated identification of melodic variants in folk music" by Martin
Dillon & Michael Hunter (1982)
- "On Finding Rhythmic Patterns in Musical Lines" ,Bernard Mont
Reynaud& Mark Goldstein (1985)
- "Cluster analysis for the computer-assisted statistical analysis of
melodies", Luigi Logrippo & Bernard Stepien (1986)
- "Comparison of musical sequences" by Marcel Mongeau & David Sankoff
(1990)
- "Minimum Message Length comparison of musical sequences" -Shane
Samuel Cook (1994)
• Comparative study
An algorithm is to be chosen based on a comparative analysis of the different
categories of sequence comparison and the different techniques used in the
works surveyed. One of these methods would be used as the comparison method
in this study to locate recurring themes.
8
• Review music data representations
Different music data representation methods used to encode mUSIC data into
machine readable format is surveyed with the aim of obtaining and using one of
these different methods. A study of the format used must be done.
• Experiment design and implementation
The algorithm to be used IS to be coded and tested on experiments set.
Experiments are designed to test its usability in comparing two musical
sequences where the sequence has been varied with some basic modifications.
Assessment is based on whether it compares two musical sequences that had
been varied with some frequently used techniques of varying a melody as similar
just as how a human might consider it as two musically similar sequences. An
assessment of the results and an analysis of strengths and weaknesses in
locating recurring themes would be done.
• Theme locater system
To locate recurring themes, a theme locater system needs to be implemented.
The main feature of the system would be that the theme and its recurrences
would be detected without any human intervention. Given a score, its theme
and its recurrences are to be identified. Bach's 48 Preludes and Fugues are the
scores studied where its subject and its recurrences in the different voices are
located. Data needs to be converted to the input format necessary for this
system. The theme and sequences from the score need to be extracted for
comparison. The algorithm tested is to be incorporated into the system as the
comparison method for comparing the theme of the score with sequences
extracted from the score to see if it is able to detect recurring themes
benchmarked on human analysis.
• Algorithm enhancements
Enhancements are to be suggested based on successes and failures of the
experiments and its performance in the Theme locater system.
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• Test of enhanced algorithms
The enhanced algorithm is tested to see if the weaknesses encountered earlier
are overcome and the enhancement is incorporated into the Theme locater
system.
1.7 Scope Of Study
• Elements in music
The different elements of music which are pitch, duration, timbre and dynamics
can act as a basis for comparison. For this thesis, only two dimensions are
considered which are pitch and duration. Timbre might need to be considered if
an analysis of orchestral scores are done where musical sequences might be
repeated by the different instruments or in the study of acoustics where musical
sequences based on sounds produced by different instruments are analysed.
Dynamics can be considered if more detailed study of a particular work where
repetition of a musical sequence with different dynamic level needs to be
considered. But for this study, we assume that pitch and duration is sufficient
basis for comparison of two musical sequences.
• Melody line
For this thesis, the sequences compared are a single melodic line, i.e. sequences
of chords or harmony are not considered.
• Variations
There are many types of variations or modifications that can happen to a theme
every time it recurs. Sequences comparison methods are applied to detect the
recurrence of a theme despite these modifications. In this thesis, the variations
of the melody that are taken into account are transpositions and changes where
passing notes are added, and for variations of rhythms that are looked into are
augmentation and diminution. Other modifications such as inversion (notes are
inverted), retrograde(upside-down) and so on are not looked into.
10
• Algorithm and data
Only one algorithm was chosen for detailed implementation and testing out of
several reviewed due to the lack of time. The algorithm was chosen based on the
study done$1 different comparison methods. Music data from one database only
was used also due to a lack of time to obtain and convert data from different
databases in different music data representation formats.
1.8 Outline Of Dissertation
This thesis comprises 7 chapters:
CHAPTER 1 gives an introduction to the area of research which is the usage of
computers in the music field, the scope of study, the significance of the task
undertaken and the research objectives.
CHAPTER 2 surveys techniques used in musical sequence comparison.
CHAPTER 3 presents works done on computer-assisted musical analysis where
techniques in musical sequence comparison are used. It also presents some of
the music data representations that can be used before reasons for adopting the \
algorithm by [M&S90] is given.
CHAPTER 4 provides details of experiments for testing if sequences are
detected as similar even with certain modifications done to the melody. Details
on the implementation of the algorithm, data used and the results obtained are
also given.
CHAPTER 5 provides details of the theme locater system where the algorithm
tested is incorporated into the system as the sequence algorithm needed for
locating recurring themes. The results of its performance in the system is
discussed.
CHAPTER 6 provides a discussion of strengths and weaknesses based on
experiments and analysis. Enhancement suggestions and results are given.
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