Mapping in Algorithmic Composition
and Related Practices
Volume 1:
An essay integrating and discussing works by Paul Doornbusch
Paul Doornbusch
Doctor of Philosophy by Publication
2010
!RMIT
!
Mapping in Algorithmic Composition and Related Practices 1
Table of Contents
Included parts………………………………………………………………………. 4
Musical works……………………………………………………………… 4
Books………………………………………………………………………. 5
Book chapters………………………………………………………………. 5
Papers………………………………………………………………………. 5
Support material……………………………………………………………. 5
Abstract…………………………………………………………………………….. 6
Acknowledgements………………………………………………………………… 6
1. Introduction………………………………………………………………… 7
2. Definition of key terms and scope…………………………………………. 15
3. Historical context…………………………………………………………... 23
4. Mapping concepts and ideas in my music……...………………………….. 38
5. Exploring themes in my writings……………………………………...…...107
6. Conclusions………………………………………………………………...127
7. Reference list…………………………………………………...…..………133
Mapping in Algorithmic Composition and Related Practices 2
Typographical conventions:
Throughout this document several conventions are used to maintain clarity: Double
quotes (“ ”) are used to indicate a direct quote, and an extended direct quote is indicated
by indented text; Italics (italics) text is used to emphasise a word or phrase, and also as is
traditional, to indicate the title of a work; Single quotes (‘ ’) are used to indicate when a
word or phrase is a specialised term, or has a meaning beyond what might be
traditionally understood – for example, ‘mapping’ means a use of the word which is
beyond the traditional charting of land to paper maps; Times of musical pieces are
indicated in the convention of minutes and seconds with trailing single and double quotes
respectively, for example a musical work of length three minutes and thirty seconds is
indicated as 3’30”; Time positions within a musical work, or the length of sections, are
indicated by the numbers of minutes and seconds separated by a colon, for example, to
indicate a time of two minutes and twenty-five seconds in a piece is written as 2:25.
Mapping in Algorithmic Composition and Related Practices 3
Mapping in Algorithmic Composition and Related Practices 4
INCLUDED PARTS:
The scope of this submission will be limited to a critical appraisal (this essay) and the
submitted works as outlined below and shall not include other elements of my
compositional and written output or substantial media works that do not necessarily fit
the theme of the submission. Please refer to the included Curriculum Vitae for a full
listing of works.
The submission comprises the following components, in addition to this contextualising
essay:
Musical works:
• A CD of published musical works, containing the following pieces;
- Continuity 3 (15’ 08”) for percussion and live electronics, 2002. Recorded in
Melbourne, Australia, by !"#$%&'()&"**"+,-
- Continuity 2 (9’ 33”) for bass recorder quartet and electronics, 1999.
Recorded in The Hague, Netherlands, by the Malle Symen quartet.
- ACT 5 (10’ 01”) for amplified bassoon, 1998. Recorded in The Hague,
Netherlands, by ./#",&(0123"1&.
- G4 (11’ 41”) for computer generated fixed media, 1997. Recorded in The
Hague, Netherlands.
- Strepidus Somnus (26’ 33”) for vocal quartet and electronics, 1996. Recorded
in The Hague, Netherlands, by Randi Pontoppidan, Stephie Büttrich, Richard
Prada and Vim Hein Voorsluis.
• Scores and other documentation for the works as defined below:
- Score for Continuity 3.
- Preliminary sketches for Continuity 3.
- Score excerpts of Continuity 2.
- Score for Act 5.
Mapping in Algorithmic Composition and Related Practices 5
Book:
• The Music of CSIRAC: Australia’s First Computer Music. (Includes companion
CD/CDROM) Melbourne: Common Ground.
Book chapters:
• Early Hardware and Early Ideas in Computer Music: Their Development and
Their Current Forms. The Oxford Handbook of Computer Music (2009)
published by Oxford University Press.
• A Chronology of Computer Music. The Oxford Handbook of Computer Music
(2009) published by Oxford University Press. Also see
http://www.doornbusch.net/chronology for an updated version of this.
Papers:
• Computer Sound Synthesis in 1951- The Music of CSIRAC: Computer Music
Journal, MIT Press, Massachusetts, 2004.
• Pre-composition and Algorithmic Composition: Reflections on Disappearing
Lines in the Sand. Context Journal of Music Research, Vols. 29 and 30: pp. 47–
58.
• A Brief Survey of Mapping in Algorithmic Composition. In Proceedings of the
International Computer Music Conference, Gothenburg. 2002. San Francisco:
International Computer Music Association, pp. 205–210.
• Composers’ Views on Mapping in Algorithmic Composition. Organised Sound,
Cambridge University Press, Cambridge, 2002. Vol 7(2): pp. 145–156.
• The Application of Mapping in Composition and Design: in Proceedings of the
Australasian Computer Music Conference, Melbourne, 2002. Australasian
Computer Music Association.
Support material:
• Supplementary disks of musical excerpts (as sound files) and Max/MSP patches.
• My curriculum vitae.
Mapping in Algorithmic Composition and Related Practices 6
ABSTRACT:
This dissertation presents a new and expanded context for the process of
‘mapping’ in algorithmic composition, particularly with respect to electronic music
composition. In addition, through the selected publications (which it brings together and
reviews) it demonstrates how my published music and written work represents a unique
and significant contribution to the field of electronic music and algorithmic composition.
The integrating theme of this essay is the theoretical construct and application of
‘mapping in algorithmic composition and computer music’. This essay explores the
multiple ways in which this theme has been worked through and elaborated in my written
publications, and explored and applied in my musical compositions. The combination of
the dissertation and published works provides others in the field with a layered,
multimodal and nuanced appreciation of the musical and compositional significances of
mapping in electronic and computer music.
ACKNOWLEDGEMENTS:
I am deeply indebted to a number of people who have made this work possible.
Firstly, I would like to thank the Institute of Sonology in The Hague, Holland, and my
colleagues there, particularly Professor Paul Berg, for many years of being immersed in a
highly stimulating musical environment – this thesis would not have been possible, nor
much of my musical output, without the experience and my years there. Many people at
RMIT University have also been particularly supportive and helpful. Thanks are due to
my supervisor, Dr. Philip Samartzis, for his support, encouragement, and insightful
comments, and also Associate Professor Lesley Duxbury (Program Director Postgraduate
Research School of Art), Joy Hirst (Postgraduate Research Administrator School of Art)
and Jeremy Yuille (Senior Lecturer in Communication Design). I would like to thank
deeply my good friend Dr. Peter Burrows, whose long suffering job was to help me edit
my ramblings into the coherent thesis which follows – many heartfelt thanks. Also thanks
to my brother John who proofread this. Lastly, I would like to thank my full-time
companion Tomson, who, daily, sat waiting patiently (and sometimes not so patiently)
for a walk, through the writing of this thesis.
Mapping in Algorithmic Composition and Related Practices 7
1 – INTRODUCTION:
So beautiful and strange and new! Since it was to end so soon, I almost wish I had
never heard it. For it has roused a longing in me that is pain, and nothing seems
worthwhile but just to hear that sound once more and go on listening to it for ever.
– The Wind in the Willows. (Grahame, Rogers et al. 1908, pp. 150-151)
Algorithmic composition is the practice of using algorithms to generate musical
data for at least some part of a musical composition. This does not preclude direct
intervention on the part of the composer to achieve a desired aesthetic result. Algorithmic
composition has been far more prevalent with the development of computers and
software, which have made such practices less labour intensive, but algorithmic
compositions need not be computer based. Composers have used algorithmic approaches
to composition for a variety of reasons, from breaking free of the moulds of tradition and
previously learned or memorised patterns and ideas, to having an affinity with the
aesthetics of data and data patterns and wanting to express these in music and sound.
Mapping is that part of the process of algorithmic composition which determines
how the raw or original data is converted into musical parameters, such as pitch,
dynamics, density, timbre and so on. Traditionally, mapping has been linear with a direct,
sometimes semantic, correspondence between the original data and the musical
parameter output. However, with the development of more interactive computing
systems (hardware and software) allowing for the rapid audition of a sonic result,
mapping has come more into its own as a way of achieving the desired aesthetic outcome
as varying the approach to mapping is more flexible than varying the original data.
Mapping in various ways is one of the techniques that I have used to achieve the desired
aesthetic results in producing my music.
The following arguments represent a broad overview of the submitted
compositions, and serve as an introduction to how I have employed mapping techniques
in these works. Moreover, as an over-arching theme, my musical output should be
considered as a means of mapping concepts of form to the actuality of music. This
mapping is manifested in the following pieces in terms of how the concepts of continuity
Mapping in Algorithmic Composition and Related Practices 8
and fragmentation (as metaphors and a basis for musical form), and the transitions from
one ‘state’ to another in multiple musical dimensions, are mapped to musical parameters.
This can sometimes be recognised as a typical ‘opposed duality’ as the basis for musical
form, such as the more classically understood concept of tension and release, although
this is traditionally based on the tension and release in functional harmony, whereas the
concepts of fragmentation and continuity in musical dimensions are vastly different.
The use of an opposed duality is in some ways classical and convenient; you
cannot have one without the other, even conceptually. Thus, they are eternally bound
together, as William Blake once famously commented, “Opposition is true friendship,”
(Blake and Keynes 1975, p. xxv.). However, when working with sound itself as the
fundamental musical element, instead of harmony, there are many dimensions of sound,
such as timbre, spectrum, time, frequency and so on, which come into play. Composition
with sound itself is immediate, as an art form it has similarities to sculpture or painting
because the composer works directly with the medium itself, which is both pliable and
malleable. Electronic music composition extends the domain of music and composition
beyond the traditional note-based system to an open and infinite universe of sound
objects1. I have used sound-based algorithmic composition practice to create pieces with
traditional instruments and electronics, in the process creating new sounds and new
forms of expression.
Continuity 3 is a piece for percussion and electronics, which like many of my
other pieces, uses the dual opposition of continuity and fragmentation as both organising
idea and formal parameter to structure the piece, and as a way to map continuity and
fragmentation onto musical parameters. Continuity 3 explores the spectral structure of
percussion instruments through this mapping, with at one extreme a cracked China-
cymbal – which has an extremely fragmented overtone structure – and at the other a
circular metal plate from a mainframe computer hard disk, which has a very pure tone
and overtone structure. To bridge these two extremes I used a large tam-tam which has a
variable overtone structure, depending on how it is played. An electronic part of real-
time manipulation of the acoustic sounds fully articulates the main elements of the form,
((((((((((((((((((((((((((((((((((((((((((((((((((((((((1 Sometimes the term ‘sound objects’ may be used in this essay, but it is never a reference to Schaeffer and the ‘sonic object’ unless directly specified.
Mapping in Algorithmic Composition and Related Practices 9
both amplifying and causing continuity and fragmentation of the spectral components of
the instruments.
Continuity 2 also explores continuity and fragmentation. In this piece, with a
recorder quartet and electronics, much of the fragmentation and continuity is mapped to
the playing technique. The recorder fingering is notated separately to the embouchure
and tongue articulation – similar to Luciano Berio’s Gesti (Berio 1970) – giving an
extremely fragmented sonic result. This slowly transforms into standard playing
technique, giving the expected continuous sonic output. The electronic part similarly
flows through layers of continuity and fragmentation in the pitch, timbrel, density and
rhythmic domains, providing a counterpoint to the recorder part.
Act5 is a piece for solo bassoon and electronics which explores the concepts of
effort in performance, virtuosity, the intimate relationship between the performer and
their instrument, and vertical movement. These concepts are mapped to various musical
and performance parameters. Vertical movement is, quite directly, mapped to pitch in
this piece. This also mirrors the effort required to play, as the piece builds the higher
notes take increasing effort to play. There are four sections to the piece, and each is
articulated by an interruption – falling pots and pans, a falling glockenspiel and a falling
timpani – which also involves vertical movement and their release involves effort. The
electronics were, after some experimentation, specially amplified bassoon sounds in real
time – this required the positioning of contact microphones on the crook of the
instrument as this provided the sounds desired and the most intense sense of intimacy
with the instrument. The sound needed no further processing for the desired aesthetic
result.
G4 uses solely ‘Dynamic Stochastic Synthesis’(Xenakis 1992) as its sound
production technique. Dynamic stochastic synthesis is a type of instruction, non-standard
or waveform synthesis and these do not have an acoustical parallel in the real, physical
world. The synthesis algorithm uses controlled stochastic functions to generate the
vertices of the waveform for each voice. The type of random distribution used (Poisson,
Cauchy etc.) determines the nature and development of the waveform and sound. Also,
the formal structure of the piece is determined by random processes, such that the density
of the parts and their distribution can be determined by controlled random selections.
Mapping in Algorithmic Composition and Related Practices 10
What is being presented with this piece is the concept of ‘music from nothing’. This
piece is discussed in more detail later in section 4.4, however, the system used to create
the piece writes a sound file which is the piece. Each time the piece is generated it
produces a different sound file, because of the random processes involved. Clearly, such
an approach to composition – whereby each time the piece is generated it produces a
different sound file – opens up questions about the role of the algorithmic composer and
what exactly is it that is being 'composed'? Note, however, that standard composition
practice and notation offers the composer only limited means to control the sound of the
piece. This theme is also explored in section 4.4 as these questions are central to
understanding and grasping the ideas, and 'mapping', as exists in G4 and as applied in my
compositional practice.
Strepidus Somnus is a piece for voices and electronics, which also investigates
both continuity and fragmentation and how these concepts can be mapped to musical
material. Strepidus Somnus is a composition in six sections with each section exploring
transitions between different sonic states. Section one transitions from the sonic state of
not being able to make a (vocal) sound through making vowel sounds, fricatives, parts of
words, whole words, parts of sentences and whole sentences, in four languages
simultaneously and against a counterpoint of processed short-wave radio sounds – the
voice struggling from the Aether. The second section marks a transition from
conversation to the sounds of sex. The third transition is from sounds of grief to
singing. The fourth transition is from single notes to melody. The fifth transition is
from vocalised noises to conversation. The sixth and final transition is a lengthier
complex arrangement of sub-sections of whispered text, which are a progressively less
distorted and fragmented vocalisation of a passage from Lewis Carroll’s Alice in
Wonderland which has been distorted and fragmented to varying degrees with the
Travesty algorithm2. Thus it starts out heavily fragmented and distorted, sounding
nothing like English, and progresses through stages of greater continuity and ends up like
nonsense English. These sub-sections are separated with laughter of varying types, from
malicious and ironic to joyful. An electronic part based on short-wave radio sounds is
((((((((((((((((((((((((((((((((((((((((((((((((((((((((2 The Travesty algorithm makes a strange arrangement of made up words, or a parody of any text, by rearranging the letters or words based on the frequency with which sequences of letters appear. It is also sometimes named the “mangler”.
Mapping in Algorithmic Composition and Related Practices 11
interwoven with the vocal parts, providing a contrasting counterpoint to the voice. This
sometimes pre-empts the textures to come and sometimes follows them, excitedly
bubbling along with the vocals, and showing a tendency to fragment or coalesce into
continuity before or after them.
Despite the extreme difference between the voices and the electronics in this
composition, they have equal weight in the piece and where the vocal part moves in its
transitions the electronics will change in density and texture, in a form of counterpoint
which is in response to the vocals, or at other times leading them. Strepidus Somnus thus
provides an extended aural essay on fragmentation and continuity across various types of
musical space, using sources which are, in some ways opposed (voice and short-wave
radio sounds), and in other ways united (short-wave radio being a carrier for far-off
voices).
In addition to the above compositions, the submitted book and book chapters also
provide various ‘mappings’, not the least of which are a mapping of ideas onto
algorithmic composition and the mapping of the past onto the present. Further, the
historical writings on computer music offer a mapping of events, from a time in history
where the making of such music appeared haphazard, fragmented and without a
discernible future, to contemporary times, where with current knowledge and insights,
we can see computer music as an unfolding continuity of developments, practices and
experiences.
The Chronology of Computer Music clearly shows the relationship between
computer and electronic music and the technology available at the time. This work
provides the only tabulated chronology or timeline of the development of electronic and
computer music which relates the musical and artistic output directly with the
technological developments, both within the area and in general, at the same time. This
mapping provides a clearer understanding of several aspects of the discipline, from how
electronic music developments have been dependent on technological developments, to
how in recent years, as Paul Berg remarked almost fifteen years ago (Berg 1996),
technological developments have outstripped musical compositional developments.
Mapping in Algorithmic Composition and Related Practices 12
In the chapter titled Early Hardware and Early Ideas in Computer Music: Their
Development and Their Current Forms, I have taken a sub-set of the information
presented in the Chronology of Computer Music, specifically early hardware and
software developments, and show how these have influenced and map to the
development of computer music through to the present. This chapter takes a broad-brush
approach in terms of tracking trends, while discussing the finer details of developments
that were particularly influential. In addition, the chapter maps the developments in
specialised hardware, which generally have given way to software developments as
general-purpose hardware became faster and more capable. This meant that composers of
computer music became more interested in software and its aesthetic and aural
affordances. Thus there is a mapping of ideas and concepts in computer music which
were originally realised in hardware, but later realised in software or in a different
incarnation that may seem new initially, but which on closer inspection are revealed to be
somewhat older ideas repackaged.
The book The Music of CSIRAC makes several unique contributions to the field
of computer music and to its body of knowledge. Firstly, it charts the instrumental role I
played in leading the research team that reconstructed the first music played by a
computer, which had been lost for more than forty years. This represented the first ever
reconstruction of a body of historically significant computer music. Secondly, it
discusses how and why the development of this music took place and how and why it
failed to develop further, by mapping it both to the contemporary context of the day and
to the present day. The research into the music and its reconstruction required a team of
specialists as although CSIRAC may be the world’s best-documented first-generation
computer, there was not enough documentation to reconstruct the music without the aid
of some of the original personnel. The original coding of the music itself on CSIRAC
required particularly ingenious and cunning programming because of the characteristics
of the machine. The key to making a steady tone was sending pulses at a regular period
to the speaker. This may sound trivial, but in a machine in which the major cycle
frequency was only 1KHz and each memory access took a different time, it was the most
difficult of programming challenges.
Mapping in Algorithmic Composition and Related Practices 13
Pre-composition and Algorithmic Composition: Reflections on Disappearing
Lines in the Sand is a research paper which discusses whether and to what extent
algorithmic composers use pre-compositional techniques. The composer Chris Dench,
acting as guest editor of an edition of Context: Journal of Music Research devoted to the
concept of pre-composition, invited me to comment on this from the point of view of an
algorithmic composer. While pre-composition is not an issue that I find important, I
found the reflection on my practice, and that of others, very instructive. This exposition,
along with responses from such noted composers as Gottfried Michael Koenig, Richard
Barrett, Bernard Parmegiani and Gerard Pape, examines particularly algorithmic and
electronic music composition practice as compared with, or mapped to, instrumental
composition practice. As it turned out, the comparison was useful for examining my own
practice in such a light, but ultimately for many algorithmic and electronic composers the
formal act of pre-composition is rarely if ever necessary. When examining my own
compositional practice in this context, elements of mapping and how mapping techniques
are used in my work are exposed.
The three papers A Brief Survey Of Mapping In Algorithmic Composition,
Composers’ Views On Mapping In Algorithmic Composition and The Application Of
Mapping In Composition and Design will be outlined here together because of their
related themes and conceptual overlaps. These three papers, when taken together
represent the first clear indication that there is a distinct mapping process in algorithmic
composition which had previously been undocumented, ignored, or left un-named. The
three papers make the unique case that explicit mapping is a more recent development-
phenomenon (commensurate with advances in technology and tools) and that implicit,
linear, mapping was common in the early practice of algorithmic composition.
Chronologically, the first of these papers is The Application of Mapping in
Composition and Design wherein I discuss how mapping in algorithmic composition
may have parallels in the discipline of design. Some of the conclusions are that
algorithmic composers always use mapping of some sort and that it is often quite
complex. Designers (for example, architects) also seem to use mapping and sometimes in
similar ways to algorithmic composers.
Mapping in Algorithmic Composition and Related Practices 14
In Composers’ Views on Mapping in Algorithmic Composition and A Brief Survey
of Mapping in Algorithmic Composition I discuss the question of mapping techniques
with a number of composers of international standing, presenting different composers in
each paper. This includes general ideas of mapping and its detailed application in musical
pieces. The results of these research efforts reiterate some of the findings from the earlier
paper, this time framed in a more musical context, and without the focus on cross-
discipline dialogue. One result of this is that a greater discussion of the aesthetic
consequences of mapping was possible. For example, most composers say that they are
interested in a certain aesthetic result and will use changes in the mapping, rather than the
initial data, to achieve the desired musical expression. This is clearly a change in practice
as discussions in earlier texts (for example Xenakis’ Formalized Music (1992) when
discussing his works, and Dodge’s piece Earth’s Magnetic Field as discussed by Dodge
in his text (Dodge and Jerse 1997)) show no such tendencies as the mapping is implicitly
linear. These three papers, while necessarily covering some common ground for each
audience, make a strong and original statement on the use of mapping in algorithmic
composition and how such practices have changed and evolved during the last half
century.
Mapping in Algorithmic Composition and Related Practices 15
2 – DEFINITION OF KEY TERMS AND SCOPE:
For when we have explained the wonderful, unmasked the hidden pattern, a new
wonder arises at how complexity was woven out of simplicity. The aesthetics of
natural science and mathematics is at one with the aesthetics of music and
painting – both inhere in the discovery of a partially concealed pattern.
– The Sciences of the Artificial (Simon 1996, p. 4)
Mapping is a somewhat multiplicitous and sometimes ill-defined term, particularly
in the discipline of musical composition. Moreover, mapping just within the discipline of
music has a variety of definitions outside of musical composition, for example, when
used in relation to musical instruments it conveys how the physical gestures required to
play an instrument relate to the sonic output of that instrument. It is worth noting that
most instruments have nonlinear mappings that span multiple dimensions. Mapping is
often used as a means of analysing and looking for patterns in complex data sets, as a
way to make sense of and understand those data sets in some way. Mapping is a
technique often used, for example, in data visualisation. Looking at the general meaning
of the term, the Macquarie Dictionary (Delbridge and Yallop 2005, p. 1052) describes
mapping as (a section from ‘map’):
--verb (t) (mapped, mapping)
3. to represent or delineate in or as in a map.
4. Computers to translate (information) from one layer of organisation to another,
such as from a computer language to machine language or from an image stored in
memory to an image displayed on a screen.
chromosome mapping
noun the process by which the sequence of chromosomes in specific DNA is
described, in particular the location of unique, identifiable sections.
facial mapping
noun the identification of a person from a photograph, video footage, etc., by
comparing key features of the face in the image with those of the person.
The reader will note from these various definitions that ‘mapping’ infers the
representing or translating of a phenomenon that exists in one domain, for example the
Mapping in Algorithmic Composition and Related Practices 16
physical world of skin and bone, into another domain, such as a computer-generated or
conceptual realm. Perhaps a more recognisable illustration of the idea of mapping is a
mountain range in a landscape that becomes a series of concentric lines on a large flat
piece of paper on the kitchen table. Those small concentric lines may represent a
spectacular and breathtaking landscape. In the next section, I elaborate the idea of
mapping, as applied to my compositional practice, and contrast this conceptualisation
with more mimetic approaches.
I note that there are at least two types of mapping used in algorithmic composition,
linear mapping and nonlinear mapping. Linear mapping is a mapping where there is a
constant correspondence between one parameter or domain and the other. Nonlinear
mapping is one where this rate of change varies with the data or mapping, it might be a
logarithmic or exponential correspondence, or even chaotic. Thus nonlinear mapping
provides a potentially more complex result than a linear mapping given the same original
data, one which might highlight some aspect of the data or another which may be less
obvious with a linear mapping. I found nonlinear mappings most useful when adjusting a
process for the result I was seeking.
While mapping is often used here to describe how data or concepts are translated
into musical parameters, sometimes mapping is used in this essay to relate concepts to
music, or musically related information and ideas. Thus the term has a broad meaning
and its meaning can change because of the context of its use. This might be a limitation
of language and I have made an effort to be as clear as possible. There may be other
ways to describe this, such as to ‘correlate’ concepts, events or data, but the term
mapping best describes how my thought processes work in these and thus I have used
this term.
There is a large body of work on algorithmic composition for style imitation. This
approach to algorithmic composition generally seeks to imitate or replicate a particular
style of music via algorithmic means, using either a mechanical, or computerised,
application of rule-based music theory, or the application of mathematical or other
constructs. The aim of this approach is often to imitate or replicate a style such that an
experienced listener is unable to tell the difference between a machine composition and a
human composition. Sometimes this is used to examine human musical creativity and
Mapping in Algorithmic Composition and Related Practices 17
thus it seeks to model such creativity to better understand it. The mapping used for these
compositional and research practices is invariably linear (Kramer 1996; Nierhaus 2009).
As the purpose is usually imitation (sometimes for research) rather than innovation,
typically there is no room for the kinds of creative mappings which might achieve an
original aesthetic result or produce a distinctively new or unique work of art. While this
mapping must be liner to verify the validity of the models, and the research into musical
creativity may offer important insights for composers of original music, the necessary
use of linear mapping makes style imitation less relevant to this discussion.
I must make clear here, by way of contrast, that my practice in algorithmic
composition is artistically and philosophically opposed to the kind of algorithmic
composition and mapping applied in style imitation. Moreover, as a composer my
opinion is that I find such an approach to composition (and mapping) lacking in artistic
merit, aesthetic value or intellectual challenge – such approaches dilute the public
perception of the riches and creativity made possible through algorithmic means. It is
perhaps for this reason that style imitation practice faces some criticism from the musical
community and it has not succeeded in creating compelling pieces of music, but rather
more-or-less novel demonstrations. However, it is possible that style imitation research
could lead to insights into human creativity, and it is for that reason that I hope
researchers are engaged in the practice.
Creative algorithmic composition can be defined as a means of implementing
compositional strategies with the intent of creating a new piece of art which offers a
unique (and hopefully compelling) aesthetic musical experience. This is sometimes
referred to as ‘genuine composition’ or ‘genuine algorithmic composition’ in the
literature (Nierhaus 2009). While I always treat algorithmic composition as ‘genuine
algorithmic composition’, I will use these two terms throughout this thesis should I need
to more clearly indicate the creative approach to mapping in my compositional practice
as distinct from the mapping used for imitative purposes.
Mapping in Algorithmic Composition and Related Practices 18
I have explored the compositional concept and practice of mapping in my
previously published work. For example, the following is an extract from my conference
paper, A Brief Survey of Mapping in Algorithmic Composition:
Compositional structures and ideas can take many forms, but they are often abstract
in some way, to a greater or lesser degree, from the music that is composed.
Composers sometimes use visual ideas of shapes, mathematical functions, physical
processes or phenomena and so on as ideas for creating music. Mapping is the
process of taking the (possibly abstract) compositional structures and generating
musical parameters. (Doornbusch 2002b, p. 205)
Also, from Composers’ Views On Mapping in Algorithmic Composition:
The term ‘gesture’ has many meanings. Even a cursory reading of the literature
will show that the term is imbued with multiple, even contradictory, meanings
within single disciplines and a single context (Cadoz and Wanderley 1999). For the
purposes of this paper, gesture is a musical concept; it is not a physical movement.
A musical gesture is a planned change (randomness can be planned) in musical
parameters as part of a piece of music. The parameters could be, for example;
timbre, density, intensity, timing, pitch and so on. A compositional gesture is the
underlying conception, structure and planning of the musical gesture. As such, a
compositional gesture can be a kind of abstraction of a musical gesture or a group
of musical gestures. Thus, compositional gestures can be directly related to
(possibly complex) musical gestures, possibly as an abstraction.
[…] Further, organisation strategies in algorithmic composition may not fit a
definition of even a compositional gesture, but there can still be a mapping
requirement to move from the conceptual organisation of data to the required
musical parameters. (Doornbusch 2002c, p. 245)
There are clear historical examples of mapping which serve to highlight the
specific nature, function and significance of mapping in algorithmic composition, and
these are discussed in detail in the next section. The above papers on mapping analyse
two well known examples; Pithoprakta by Iannis Xenakis and Earth’s Magnetic Field by
Charles Dodge, which exemplify the mapping of phenomena from one domain to the
Mapping in Algorithmic Composition and Related Practices 19
sonic and musical. There are also two other examples analysed in detail in section 3,
including; Xenakis’ Metastasis, and Larry Austin’s Canadian Coastlines, which illustrate
the mapping practices of two algorithmic composers. These pieces demonstrate that for
‘mapping’ to exist, at some stage there must be a translation from the domain of data,
mathematics, functions or concepts, to musical or sonic parameters – from the conceptual
domain to the sonic domain. As defined in all of my mapping papers:
‘Conceptual domain’ is a term that will be used to cover the entire conceptual area
of compositional practice, which includes other organisation strategies as well as
compositional gesture. Further uses of the term ‘gesture’, unless otherwise
specified, will implicitly mean a compositional gesture.
My musical pieces and writings, and the noted historical examples above and in section
3, show that the concepts of musical composition, musical gestures, and mapping are
intimately linked.
There is another aspect of mapping which appears in the literature but which I have
not so far addressed. That is mapping in sound synthesis. This is intimately related to
mapping in composition, as sound synthesis is often considered (and I would concur) as
micro-composition. This is not a contentious position, as many other algorithmic
composers and researchers share it (Berg 2009; Di Scipio 1994; Di Scipio 1997; Harley
2005) and it is explored further in section 4.4. When digital sound synthesis from
equations was first undertaken, from the early experiments of Max Matthews and the
team at Bell Labs (Roads 1995), to the first experiments in physical modelling synthesis,
there needed to be a way to turn the output of equations into sound. This was usually
through a direct mapping. However, when experiments with using chaos equations for
sound synthesis were undertaken, there was sometimes a need for nonlinear mapping,
and so the mapping element of the compositional process became more important
(Pressing 1988).
Pressing (1988) discusses mostly direct linear mapping in Nonlinear Maps as
Generators of Musical Design, but he also discusses “Quantization to tempered (or other)
tuning norms …” and other mapping strategies such as, “Likewise dynamics were readily
applicable after multiplication by a scale factor …” (scaled mapping) and, “Envelope
attack time was computed by squaring the output of the logistic map equation”, (squared
Mapping in Algorithmic Composition and Related Practices 20
mapping) and so on (ibid). These are all examples of relatively linear mappings and
while Pressing implies that experimenting with the mapping of the data will be useful for
a composer, he stops short of recommending nonlinear mapping and creative mapping as
a feature of algorithmic composition.
There are a number of authors who discuss mapping in musical applications
(Arfib, Couturier et al. 2002; Cadoz and Wanderley 1999; Dabby 1996; Nierhaus 2009).
However, much of this theorising has to do with electronic instrument design, where the
mapping of physical gestures to sound production is an area of considerable research
effort. Dabby (1996), uniquely, discusses using nonlinear mapping based on chaos
functions to create variations on standard and well-known musical works such as those
by Bach. This is a use of mapping which is peripheral to the central discussion here and
is related to style imitation.
A wealth of literature exists on mapping and visualisation of data (Card,
Mackinlay et al. 1999; Chi 2000; Iswandy and Konig 2004), as this is an obvious area of
activity with computer graphics and visualisation, see also, for example, other papers in
the title Readings in Information Visualization: Using Vision to Think (Card, Mackinlay
et al. 1999). There is also a range of literature on mapping in the areas of design and
data-aesthetics, for example Manovich’s Making art of databases (Manovich 2003), The
Language of New Media (Manovich 2002a), ON MAPPING: Lev Manovich + Jenny
Marketou (Manovich 2002b) and Art Against Information: Case Studies in Data Practice
(Whitelaw 2007).
In some ways a musical score is a mapping of the composers intent and a way of
controlling and shaping musical output. However, a musical score is also a codification,
or language, that represents gestures to be made by performers, and hopefully these
gestures will make the sounds the composer intended. It need hardly be said that
sometimes the results are not as the composer intended. Therefore, the score is not
always the most effective of mapping devices. Acknowledging this point in relation to
the musical scores I have used in my music, I often go to great lengths to produce a score
which can be minimally misinterpreted.
Mapping in Algorithmic Composition and Related Practices 21
Such could be the importance of mapping in algorithmic composition that the
mapping (depending on the degree of innovation and creativity involved), in many ways
is the composition or piece. It could be theorised that the mapping – how things have
been mapped – determines the aesthetic character and quality of the piece. One could test
this theory by having several, controlled, data sets, and also a data set of random numbers
(noise), and pass them through different mappings. The effects of the mapping will be
most evident on the random data, but if other data sets are substituted and there is little
perceptual difference, then it is the mapping itself which is producing the character and
aesthetic quality of the composition rather than the data. I have not formally tested this
theory, and it is beyond the requirements of this thesis as commentary on my current
works, however I have noticed that this is at least partially true in relation to both my
own compositions and the works of others. For example, during my compositional work
on parts of both Strepidus Somnus and Continuity 3, I recall deliberately trying radically
different data for sections of these works. This was in an effort to generate new ideas for
those pieces, but to my surprise, the results were similar and I believe this was because it
was the mapping that was producing the dominant artistic character in the works. I
returned to the original data in both cases and adjusted the mapping to achieve my
aesthetic intent, as happened a number of times throughout the composition process. This
is an area of compositional practice worthy of further investigation and research.
Further areas of mapping exist, such as with the phenomenon of synaesthesia,
where, typically, the hearing of a particular sound will induces or stimulates the
visualisation of a particular colour. Thus there is some sort of mapping from sound to
vision, from the auditory to the visual cortex in the brain. This is a particular transmodal
mapping, and it is nonlinear in its nature. Research in this area (Dean, Whitelaw et al.
2006) discusses several modes of transmodal mappings, which are highly interesting, but
not part of my practice and they are not discussed as part of my investigations below.
From the examples following in section 3 on Historical Context, and the
definitions cited in my papers on mapping, it can be appreciated how strongly the
concepts of musical and algorithmic composition gestures, and mapping, are intimately
linked. These connections will be explored in more detail later in this thesis, particularly
in relation to my own musical works. In the section that deals in detail with my writings I
reveal how similar issues are faced by designers in their practice. The above discussion
Mapping in Algorithmic Composition and Related Practices 22
of the literature on mapping serves to situate and contextualise the concepts and theories
which I am proposing and indicates the lack of literature on creative mapping practice in
algorithmic composition.
Mapping in Algorithmic Composition and Related Practices 23
3 – HISTORICAL CONTEXT:
A map of the world that does not include Utopia is not worth even glancing at, for
it leaves out the one country at which Humanity is always landing… Progress is the
realization of Utopias.
– Oscar Wilde (Carter 1971, p. 83)
Algorithmic techniques for composition have been in use in western concert
music for several centuries. With these techniques there is always a system of mapping to
arrive at musical data. The earliest references to algorithmic composition go back to the
Medieval Benedictine monk Guido d’Arezzo who wrote Micrologus, a music treatise in
approximately 1026, in which he describes a system where text may be turned into music
by mapping vowels to pitches (Hucbald, Guido et al. 1978). This is usually cited as the
first known system for algorithmic composition (Roads 1995). Many other examples
exist, such as:
• The isorhythmic motets, where different melodic layer have a recurring
rhythmic, composed by Guillaume de Machaut and others from 1300 to
1450 (Roads 1995);
• The composing machine proposed by Anthanasius Kircher in his 1650
text Musurgia Universalis (Gardner 1974);
• William Hayes’ 1751 technique of splattering ink onto manuscript paper,
described in The Art of Composing Musick by a Method Entirely New,
Suited to the Meanest Capacity (Hiller and Isaacson 1959);
• Compositional dice games attributed to Wolfgang Amadeus Mozart in
1787 (Ibid);
• Arnold Schoenberg’s twelve-tone system from the early twentieth century
(Ibid); and,
• John Cage’s composition using aleatoric methods as demonstrated in his
1958 piece Music of Changes (Ibid).
All of these techniques used direct or linear mapping from the data or concept to,
typically, pitches. Thus, historically mapping in algorithmic composition has been a
Mapping in Algorithmic Composition and Related Practices 24
direct translation process from one realm to another, at least until the development of
cheap and powerful commodity computers. The famous pictures of part of Iannis
Xenakis’ Pithoprakta show a very direct mapping of data to musical parameters. There
are other approaches, also used historically, as described in my papers on mapping in
algorithmic composition. This is discussed below in the extended excerpt from
Composers’ Views on Mapping in Algorithmic Composition (Doornbusch 2002c);
A famous example of the mapping process is the part of Pithoprakta (1955-56) [by
Iannis Xenakis] as reproduced in Formalized Music pp. 18-21 (Xenakis 1992).
Xenakis used the Brownian motion of gas particles, combined with Bernoulli’s
Law of Large Numbers, as his basic model for the cloud pizzicato glissandi section.
After calculating, statistically, over 1000 velocities of gas particles at given instants
of time (as the measurement of this was impossible), he then graphed them on an
XY plane and directly mapped the straight lines of the velocities to glissandi for 46
string instruments. Xenakis divided his graph vertically into 15 pitched sections,
each corresponding to a major third. This was then mapped to the ranges of the
string instruments. The mapping was directly of pitch in the vertical direction. This
is a particularly direct and concrete example of mapping. All intensities and
durations are the same, but to ensure the sensation of a cloud of particles, Xenakis
used a complex temporal arrangement of overlapping timing subdivisions that are
factorially unrelated (that is, they do not have common divisors and thus the
rhythms created do not repeat). This is a complex mapping of linear time, designed
to represent the instantaneous nature of the movement of the gas particles. Along
with many other algorithmic composers, the mapping phase is implicit in much of
Mapping in Algorithmic Composition and Related Practices 25
Xenakis’ work. He often uses direct mapping as a result of the deliberate
organisation of one set of data in such a way that it maps directly to musical
parameters.
Another famous example of algorithmic composition and mapping is Charles
Dodge’s Earth’s Magnetic Field (1970). Here, Dodge uses data from the effects of
the radiation of the sun on the magnetic field of Earth. A Bartels diagram showed
fluctuations in the Earth’s magnetic field for 1961 and this data formed the basis
for the piece. Dodge mapped this data, the Kp index (a measure of the average
magnetic activity of the earth) to pitches and rhythms. From the program notes of
the recording of Earth’s Magnetic Field (Dodge, 1970), we may glean an insight
into the mapping used:
The succession of notes in the music corresponds to the natural succession of
the Kp indices for the year 1961. The musical interpretation consists of setting
up a correlation between the level of the Kp reading and the pitch of the note (in
a diatonic collection over four octaves), and compressing the 2,920 readings for
the year into just over eight minutes of musical time. (Dodge, 1970. LP notes)
While the pitches appear to be a fairly direct mapping from the Kp index, some
elements of the composition such as the timbres were chosen purely for aesthetic
effect. An arrangement of the data that plotted the length of sections of the data
against the maximum amplitude in the section was used to determine the speed and
direction of the sound spatialisation and also the rhythms. The data was also
sometimes read multiple times to generate the musical parameters. That, combined
with the similarity of the fluctuations in the Kp index to 1/f noise data, contributes
to the aspects of self-similarity in the piece.
The two previous examples contrast different approaches to mapping. It may be
linear and direct, but it may also be nonlinear and more complex. Both examples
use the data as a structural component and the music achieves some structural unity
for that. (Doornbusch 2002c, pp. 145-146)
As noted in the previous section, there are other historical examples of mapping
which illustrate how it has been used in the past. Xenakis’ Metastasis and Larry Austin’s
Canadian Coastlines will be examined here. Metastasis (1953-54) is Xenakis’ first major
Mapping in Algorithmic Composition and Related Practices 26
orchestral work, produced while he was still working as an architect and engineer in Le
Corbusier’s studio in Paris. It is composed for 60 instruments, and all players have
individual parts with individual rates of glissando, introduced for the first time in the
piece. The concept of the piece comes directly from Xenakis’ architectural work where
he was experimenting with hyperbolic paraboloid shapes, single ruled curves and double
ruled surfaces, made by drawing straight lines similar to figure 1:
Figure 1. Hyperbolic paraboloid curves created with ruled lines. Xenakis drew several such diagrams and later mapped the lines to sounds by setting a
scale on the X and Y axis such that pitch was graduated on the vertical (Y-axis) and time
was mapped to the horizontal (X-axis), as shown in figure 2, below:
Mapping in Algorithmic Composition and Related Practices 27
Figure 2. Xenakis’ sketch for Metastasis, clearly showing the pitches (vertical) and time (horizontal) graduations for mapping the lines to musical parameters. Image reprinted with the kind permission of the Bibliotèque nationale de France.
The resulting piece became the basis for the aesthetic and style for much of
Xenakis’ later work, with the concepts of massed sounds and textural sonic composition.
Xenakis’ notations for the mapping of pitch and time can be seen on the sketch above.
Later, when Xenakis designed the Philips Pavilion for the 1956 world’s fair, he used
similar drawings to define its structure. Another element of mapping in Metastasis is that
it is an attempt by Xenakis to represent, or at least engage with, Albert Einstein’s view of
time as a nonlinear function of acceleration and gravity rather than a linear imperative as
per Newtonian mechanics. Using this metaphor, Metastasis propels itself forward
through changes of musical mass and density. This conceptual mapping is similar to
some works by other algorithmic composers, and in my own works discussed later.
Mapping in Algorithmic Composition and Related Practices 28
Canadian Coastlines (1981) by Larry Austin is an eight-voice canon3, where four
of the voices are played by musicians and the other four voices are electronic and played
back from tape. Austin was inspired by the fractal, and self-similar nature of the
coastline, which gave him the idea to use a canon for this piece. He discusses this in an
interview:
Austin: Studying a map, it struck me that Canada and its coastlines were
beautifully complex. I started experimenting, concatenating the coastlines of
Canada, the various Great Lakes, the Atlantic coast, the Pacific coast, Hudson Bay,
and Lake Manitoba; and the time plot for Canadian Coastlines was fashioned
[below]. I was pleased that the Canadian Broadcasting Company had
commissioned an American composer, and in this way I could pay homage to that
great country. (Clark and Austin 1989, pp. 21-35)
((((((((((((((((((((((((((((((((((((((((((((((((((((((((3 A canon is a contrapuntal composition in which a melody is imitated, or is repeated, by one or more voices after a given duration, typically throughout the whole piece (e.g. the Australian children’s song Laugh Kookaburra).
Mapping in Algorithmic Composition and Related Practices 29
Figure 3. Austin’s parameter chart for Canadian Coastlines, showing the four (roughly
horizontal) coastlines and elements of the parameter mapping along the X and Y axes.
It is clear from figure 3 and the discussion below that Austin has used algorithmic
and mapping procedures to produce the piece. Austin chose tempo relationships for the
piece to ensure that there are five junctures where the voices all come briefly together
during the course of the piece, this making the canonic structure. Other aspects of the
piece were determined by stochastic processes4 applied to various parameters of the
music for short durations during the whole piece. The four coastlines illustrated in the
diagram above set the limits for musical elements such as rhythm, density, melodic
interval expansion and dynamic changes. Actually, the four coastlines shown are
composed of seven coastline fragments that have been freely concatenated by the
composer to obtain the pattern of change desired for the elements of the piece. As a
specific example of this, the uppermost coastline in the figure controls the dynamics
changes – not the absolute dynamic level, but the rate of dynamic change at a particular
point in the piece. This ensures that the piece will begin and end with relatively little
dynamic variation, while at the mid- point, there will be large changes of dynamic level.
When Thomas Clark interviewed Larry Austin about the piece, they discussed the
mapping:
Clark: There seems to be a reverse relationship between the fractal process of
mathematically generating artificial, nature-like patterns, and tracing actual
patterns from a map. Which feels more genuine to you in terms of musical results,
artificial fractal processes or actual mappings of nature? Or are they truly coequal
reverses of the same process?
Austin: While I extrapolated Mandelbrot's fractal concepts by actually using a real
map of a coastline, a pattern created by nature, the compositional algorithm I
created for Canadian Coastlines uses a 1/f mathematical procedure to create
((((((((((((((((((((((((((((((((((((((((((((((((((((((((4 A stochastic process is a random process, which is indeterminate in its outcome. A typical approach to stochastic processes treats them as functions of one or several deterministic arguments or inputs, whose outputs are random variables – non-deterministic numbers which have a particular probability distribution. They exist everywhere in nature and some typical examples of stochastic processes include stock market and currency exchange rate fluctuations and random movement such as Brownian motion.
Mapping in Algorithmic Composition and Related Practices 30
musical fractals, or what Mandelbrot in letters to me termed "fractalmusic." The
data used to generate the fractals for pitch, duration, event rate, density, dynamic
contours, etc., come from nature's fractals: coastlines. It's a kind of a double use of
Mandelbrot's concepts, coming at it from both ways.
Clark: Is it simply a kind of cloning of natural patterns, feeding them into a fractal
algorithm as seeds?
Austin: Many other patterns are generated through the fractal process, some quite
different than the original seeds. When the plot for Canadian Coastlines is first
seen, people sometimes get the wrong idea that I simply mapped melodic contours
directly to geographic coastal shapes so that when a shape on the map goes north,
the pitch goes high, or south, low. When the first performance of Canadian
Coastlines took place in May 1981, I heard there was a great deal of response from
Canadian geographical societies. They were fascinated that someone had used their
geography to make a piece. But I don't think they could find a melodic contour in
there that resembled the northern coast of Lake Erie, for instance.
Clark: The influence of the original coastal shapes is more submerged.
Austin: Yes. There are eight instruments and four channels of taped computer-
generated sound; more than anything else, you can feel the shape in the density of
the sounds and in how disjunct the lines are.
Clark: How direct is the mapping process? Did you try different conversion scales
to determine the ideal one for an adjusted mapping?
Austin: No, while there is concatenation of all the coastlines, their scale and
orientation were fixed precisely; once those data were extracted from a vector in
the plot and became a seed for the algorithm, the fractal result could not be
understood in terms of the map.
Clark: There is a general tendency to think of mapping natural phenomena into
music by such a literal process as an abrogation of the composer's responsibilities;
what is your response to that?
Austin: I don't have any qualms at all. I find creative pleasure in direct mapping of
information to my music, whatever kind of information it might be. I don't take
seriously observations about that technique being an abrogation of composerly
prerogatives for convenience or effect or some other superficial reason. I think that
Mapping in Algorithmic Composition and Related Practices 31
the same complaint really could be made about representational painting. We never
say, "That's representational-why did you paint it? Why didn't you just photograph
it?" Why wouldn't there be a kind of art in music that is representational, that takes
external models as the conceptual basis for a work? (Clark and Austin 1989, p. 22)
This last point of Austin’s is significant because it suggests a musical use for
sonification (more later), but it only works effectively with a complex data set. While
Canadian Coastlines uses a linear mapping of data to musical parameters, as with other
historical examples, it is worth noting that the data set is very complex and it has been
arranged (by freely selecting and concatenating sections of coastline) in a particular way
to determine the end result. Thus, Austin’s practice of algorithmic composition and
mapping has much in common with Xenakis’, who freely drew or plotted lines of
mathematical or natural phenomena. What is extraordinary about this process is that each
composer must have had some way of imagining the end result, the music, while freely
arranging the data. This raises many questions and suggests a rich avenue for further
investigation and analysis. However, maintaining a focus on the mapping theme, it is
reasonable to infer that a linear mapping would make this creative leap easier to manage.
This may be another reason for the proliferation of linear mappings in historical
algorithmic composition practice. Xenakis may be a special case amongst algorithmic
composers as he seemed to be adept at expressing his ideas equally in either musical or
spatial (architecture) forms (Kanach and Xenakis 2008), but always with linear mappings
(Sterken 2007; Xenakis 1992). With modern computer-based tools and their interactive
affordances, there is possibly less need for such leaps of the imagination on the part of
the composer, and therefore less need to rely on linear mapping to make algorithmic
composition possible.
Larry Polansky, during an email exchange and in a published document, defines
what he calls ‘the mapping problem’, as:
An idea in one domain is manifested in another. […] that phrase became a kind of
catch-all for everything from the digits of Pi piece [simple example] to musical
fractals to chaos equations pieces to the more sophisticated compositional
experiments of people like Tenney, Ames, Koenig, and Xenakis. (Doornbusch and
Polansky 2010; Polansky and Childs 2002).
Mapping in Algorithmic Composition and Related Practices 32
However, Polansky does not mean that the idea in the first domain is somehow
perceptible as the same idea in the second domain after it is mapped. While such a
transference of features from one domain to another is true for the practice of
sonification, where the point is to illustrate the idea to better understand it, I would argue
that Polansky’s definition remains valid (perhaps with clarification) for music where the
intent is to provide a positive musical aesthetic experience. Polansky (Ibid) also states
that since it is an artistic problem, there may not be an answer in the traditional sense. I
contend that for musical purposes the mapping from one domain to another need not
show the original idea in the musical domain, or transfer the features from the first
domain to the musical, but perhaps only allow the listener to perceive that the sounds are
organised in some way; that is, that there is an idea or some sort of organisation, which
may or may not become clearer later or upon repeated listening. This is because it is a
characteristic of musical listening (at least for what is called ‘art music’) that the listener
typically ‘explores’ the piece for structure (Copland 2009; Levitin 2006). In addition,
listeners may not want anything too transparent and often desire something unexpected
(Levitin 2006), so a more exploratory or creative mapping than typical for sonification is
warranted.
In a pair of papers investigating the use of chaos theory for generating useful
musical data, Harley (1994; 1995) makes several observations about the use of mapping
and its importance for generating sophisticated and usable musical output (as opposed to
sonification). During this investigation, Harley observes that the scientific philosopher
Hans Reichenbach, who investigated the philosophical implications of Einstein’s
relativity theory (Reichenbach 1958), stated that the geometry of space and time was a
convention rather than a fact, and applied this principle to the representation of
mathematical equations in music:
However, it must be kept in mind that mathematical functions are distinct from
physical, or graphical, constructs. As the philosopher Hans Reichenbach put it,
"[mathematical] concepts are defined by implicit definitions and are not dependent
on a unique and specific kind of visualization. Whatever visual objects we wish to
coordinate to them is left to our choice" [Reichenbach, 1957]. […] Musical, or
auditory, spaces must also be defined on their own terms, and these tend to have
little in common with the visual domain. The importance of the distinctiveness of
Mapping in Algorithmic Composition and Related Practices 33
mathematical and musical spaces for composition will become clearer once we
examine in more detail the nature of nonlinear mathematical functions. (Harley
1994)
This supports the concept that mapping, from the data domain to the musical, may be
based on the choice of the person undertaking it and that there is no inherently correct
musical, or external, representation of the mathematical formula or data. Harley further
discusses the importance of quantising continuous data and functions, and how this may
change their character:
Researchers have discovered, though, that this filtering process, rather than just
affecting our perception of the function (in a similar way to changing lenses on a
microscope), actually influences the behaviour of the system [Ford, 1986]. […] It
follows then, that in using finite symbols to represent infinity, interesting patterns
(or perhaps distortions) arise which highlight both the order and disorder inherent
to this process. The details of these patterns are specific to the degree of restriction
(numerical resolution) placed upon the system. […] Viewing the output of a
chaotic function as a set of discrete elements is crucial to composition based on
such functions, given that music is usually viewed as being based on sets of
discrete elements as well. (Ibid)
As the quantisation of data is often part of the mapping, this points to mapping as being
more a function of the aesthetics of the composer (and potentially creative) rather than
providing a close representation of the detailed features of the initial data or
mathematical function. This point is made more explicitly at the end of the paper where
Harley proposes a complex and nested mapping procedure, and that this may ultimately
reflect the overall nature of the function or data more directly:
These kinds of nested processes, all of which are based on mappings from the
solution orbits of chaotic systems, have the effect of creating a complex, multi-
dimensional, multi-layered compositional "space," which exhibits similar
properties to the nonlinear system(s) used to generate the musical material. (Ibid)
Thus, to achieve a musical output that is non-trivial and also representative, in some way,
of the initial mathematical function or data, the mapping may need to be quite complex.
Here Harley would seem to be hinting at a musical output which has similarities to
sonification, and indeed there may be elements of this, but in my creative practice I have
Mapping in Algorithmic Composition and Related Practices 34
come to similar conclusions even though I am primarily concerned with achieving a
particular aesthetic result.
Harley (1995) supports the position that linear mapping of data to musical
information may not be sufficient for an aesthetically successful composition, and that
more creative mapping may be necessary. In a paper exploring the use of chaos functions
in generating musical data, Harley (Ibid p. 222) states:
To the extent that nonlinear functions exhibit self-similar characteristics similar
to the self-similarity found in music, numerical output can be translated directly
into musical values and be judged to be aesthetically pleasing or at least acceptable.
However, in moving beyond generating a series of notes as an experiment to
generating a complete composition, with all of the multi-layered temporal and
structural details and relationships that this usually entails, it is not evident that
such a direct mapping can be so easily made.
Later in the same paper (Ibid p. 223), he also states:
The other approach is to develop more sophisticated mapping processes and to
translate the generative numerical data into musical data in ways which take into
account the particular characteristics of each musical parameter or procedure.
The significance of these two points is that simple and linear mapping may be too limited
and not suitable to create an aesthetically acceptable piece of music, and that further
development of mapping techniques may be needed.
In addition, Harley (1995) discusses the role played by a software system titled
CHAOTICS, within which one of the modules is designed for mapping while another is
designed for reordering data within a range specified in the mapping, of which he says:
This reordering function is very important in that it allows the user a great deal of
control over the process of translating the numerical data into musical material. The
autocorrelational characteristics of the generative function are preserved, but the
output "space" is able to be defined in ways which may be more suited to a musical
context (the parameter of musical pitch, for example, contains strong relationships,
such as octave equivalence, which cannot be accounted for in a direct linear
transfer from the numerical domain). (Ibid, p. 223)
Mapping in Algorithmic Composition and Related Practices 35
This last quotation clearly outlines at least one further aspect of the limitations of
mapping data to musical parameters in a musically useful way – that some musical
parameters exhibit strong relationships which may not suit simple mapping – and points
to the possibility of creative mapping as part of the process of algorithmic composition
which can lead to non-trivial musical results. Harley’s two papers outlined above are the
only examples in the literature which explicitly point to mapping as being part of the
creative task of the composer and imply that such mapping is a separate step in the
process. While this last point is implicit rather than explicit, the two papers at least
provide a bridge between the linear mapping practices of the past and the more creative
nonlinear approaches to mapping which I, and others (see later discussions of my
research papers), practice.
The mappings in my pieces are part of the exploration of the work and part of the
compositional process, they are not fixed before the work is composed and might even
change during the duration of the piece, although this would be unusual. As such, the
mappings form part of the compositional process and are not divorced from any step.
This is in contrast to the way that, say, Charles Dodge or Iannis Xenakis worked, but it is
probably a development that is only possible because of the evolution of sophisticated
computer hardware and software which was not available to these earlier composers. It is
worth noting that in these older works of algorithmic composition, which most critics
would agree were aesthetically successful, the original data sets were typically very
complex and a linear mapping adequately translated these into musical results which
were also rich, complex and detailed – anything but pedestrian or boring. More modern
composition practice (such as my own) may use data sets which are not as complex, but
which achieve appropriate musical complexity and aesthetic character through nonlinear
mappings and via use of the mapping technique itself, which is central to the creative
process. Thus, the mappings evident in my own work and as identified in this thesis, are
integral to the process of composition, in some ways they are the composition or piece, at
least partially. How things have been mapped, or the mapping process, may produce
many of the defining characteristics of the piece.
There are potentially as many mapping strategies as there are algorithmic
compositions or at least composers, and this is the conclusion I reached in my mapping
Mapping in Algorithmic Composition and Related Practices 36
papers where I interviewed composers about how they used mapping as a stage or step in
their practice.
The published research papers on mapping investigate this step in the algorithmic
composition process. Since mappings were historically linear, it was not seen as part of
the creative act as strongly as it is now, and since computational power and tools were
primitive compared to today, there may not have been the same need to investigate this
step in the process as there is today, or perhaps it is a concept whose time has come. My
four papers Pre-composition and Algorithmic Composition: Reflections on Disappearing
Lines in the Sand, A Brief Survey Of Mapping In Algorithmic Composition, Composers’
Views On Mapping In Algorithmic Composition, and The Application Of Mapping in
Composition and Design all discuss mapping and how it applies to composition, design,
and features in the thoughts of prominent composers.
The historical writings in my research oeuvre consist of the book The Music of
CSIRAC: Australia’s First Computer Music (Doornbusch 2005a), the book chapters
Early Hardware and Early Ideas in Computer Music: Their Development and Their
Current Forms and A Chronology of Computer Music published in The Oxford
Handbook of Computer Music (Dean 2009) and the research paper Computer Sound
Synthesis in 1951- The Music of CSIRAC published in The Computer Music journal
(Doornbusch 2005a). This body of writing discuss a variety of historical topics such as
previously unknown developments in computer music, for example those with CSIRAC
(Council for Scientific and Industrial Research Automatic Computer), and new
understandings of the interplay of hardware and software developments. These, like
many modern historical analyses, can be seen as mapping, or re-mapping, the past with
knowledge of the present, as a way of mapping the past to the present. The CSIRAC
writing discusses the unique elements of how CSIRAC was programmed to play music,
and this research re-wrote early computer music history by proving that CSIRAC was the
first computer to play music, some five years earlier than had been known previously.
This is acknowledged now in all computer music history texts subsequently published or
revised. In addition, this research presented the world’s first reconstruction of lost
computer music, presenting a logical and verifiable method for accurately reconstructing
such artefacts.
Mapping in Algorithmic Composition and Related Practices 37
The chapters published in The Oxford Handbook for Computer Music (Dean
2009) present a new chronological mapping of musical and artistic developments against
technical developments, showing how developments in one area offer possibilities in
other areas. This is most easily seen in the chapter (appendix) A Chronology of Computer
Music and Related Events, where the table lays out the technological events along with
the chronologically appropriate musical events. The Chapter Early Hardware and Early
Ideas in Computer Music: Their Development and Their Current Forms provides a
detailed discussion of the technological developments in computers and technology, and
how these mapped to artistic developments in computer music. This chapter also
explores how the technology of specialised hardware developments today have been
transformed and mapped to specialised computer software developments running on
generalised computing hardware.
Individually, the research represented by these texts has made significant
contributions to the understanding of how computer music has developed. Collectively,
they have significantly extended the understanding of computer music developments. My
various works fit into an historical context as described above, complete with my
mapping practice, which can be seen as a further development and extension of historical
practice. In addition, the written texts extend the understanding of mapping, its breadth,
depth and practice. My texts on the history and development of computer music have
extended the understanding of its development and nature beyond what was previously
understood and accepted, for example showing the relationship between artistic and
technical developments and defining a new beginning for the use of computers to
compose and produce music.
Mapping in Algorithmic Composition and Related Practices 38
4 – MAPPING CONCEPTS AND IDEAS IN MY MUSIC:
Freed from tedious calculations, the composer is able to devote himself to the
general problems that new musical form poses and to explore the nooks and
crannies of this form while modifying the values of the input data. […] With the
aid of electronic computers the composer becomes a sort of pilot: he presses the
buttons, introduces coordinates, and supervises the controls of a cosmic vessel
sailing in the space of sound, across sonic constellations and galaxies that he could
formerly glimpse only as a distant dream. Now he can explore them at his ease,
seated in an armchair.
– Iannis Xenakis (1992, p. 144).
In this chapter I will discuss and elaborate the various mapping concepts and
practices evident in a number of my compositions.
• Continuity 3 (2002), for percussion and live electronics;
• Continuity 2 (1999), for bass recorder quartet and electronics;
• ACT 5 (1998), for amplified bassoon;
• G4 (1997), for computer generated fixed media;
• Strepidus Somnus (1996), for vocal quartet and electronics.
As the ideas in this chapter are central to my thesis, the reader should expect
greater analytical detail and depth as each composition is deconstructed and the
composition techniques (especially as related to form) and gestures therein are explored
and explained. Most of my works, as previously stated, use mapping in various ways;
from planning the overall form of a musical piece, through any sound synthesis
requirements to finessing the finest details of the score, and performance. Mapping has
become an essential aspect of my composition practice, and recently of electronic music
composition practice in general (Emmerson 2000). During the following discussions, it is
important to keep in mind that (in general) composition with sound itself is, today,
immediate (in the past it was not) and it is an art form somewhat similar to sculpture or
painting, because in all of these fields one works directly with the medium itself, which
is malleable and worked in a tactile manner. Electronic music composition extends the
domain of music and composition from the traditional note-based system to an open
Mapping in Algorithmic Composition and Related Practices 39
universe of sound objects5 that can be manipulated and organised in ways unimaginable
to earlier composers. The works described below use sound-based algorithmic
composition practice to create pieces with traditional instruments and electronics,
creating new sounds and new forms of expression, in a completely contemporary
compositional practice, displaying strong and original technique in instrumental as well
as electronic music creation.
The Continuity series of pieces, as discussed below, map concepts of continuity
and (through degrees) fragmentation to musical form, and reflective investigation of my
other works has revealed this as part of them as well. My compositions usually involve
various instruments and technology and my interest in this musical model is that it allows
me to investigate new possibilities for musical form and how that can be enhanced or
extended through the use of modern technology. As my composition technique is largely
algorithmic in nature, I am also interested in the use of mapping, from conceptual
structures to musical parameters, as a component of my compositional technique. In the
sections that follow, these compositional practices and mapping techniques are illustrated
and explained via five of my compositions, beginning with Continuity 3 and ending with
Strepidus Somnus.
The compositions analysed and deconstructed below are presented in the order
that they appear on the CD because it makes for a simplicity of listening and reading, and
it is a convenience for discussing how elements of continuity and fragmentation have
been used in different ways. This is merely a convenience for the purposes of this thesis
and the reader might decide to treat the following sub-sections (4.1 – 4.5) as relatively
autonomous, reading and listening to the relevant pieces in any order they may desire.
Further, each of these sections on the musical works starts out, by way of introduction,
with extracts from the CD notes for each piece, to provide an overview of the piece
before a more detailed examination is undertaken.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((5 This is not a reference to Schaeffer or l’objet sonore.
Mapping in Algorithmic Composition and Related Practices 40
4.1 Mapping in Continuity 3
The following excerpt, taken from the booklet which accompanies the CD
recording of a performance of Continuity 3, outlines the key elements of the composition:
Continuity 3 uses, as its instrumentation, a china cymbal; a flat, circular, metal
plate; and a tam-tam. This gives an idea of the direction of the piece. The china
cymbal has harmonics that are fragmented and unrelated to its fundamental note,
the metal plate has a pure pitch and the tam-tam can vary its overtone structure
completely depending on how it is struck, where it is struck and what it is struck
with. The china cymbal can also vary its timbre depending on what beaters are used
and how close to the centre or edge it is struck. The computer processes these
sounds in real time, transforming each instrument as it plays. The electronic
transformations range from spectral resynthesis with modifications, to pitch
shifting, ring modulation, spatialisation and various modulations. The performer
has the challenge of hearing the instruments change from second to second,
recognising the transformations occurring and playing with those changes in the
same way as they would play with any instrument.
What does ‘continuous’ mean when dealing with percussion? It could be a long
sustaining sound, but it could also be something repeated quickly enough - the
opening of Continuity 3 uses both of these approaches in juxtaposition, while the
electronics part variously moves around and somewhat fragments the sounds. The
instrumental part gradually becomes more fragmented, but in the rhythms and also
in the sounds. The notation specifies not only when and how, but also where each
note must be played on the instrument, controlling the variations in timbre and
overtones produced. As the instrumental part moves to and fro between the
fragmentation and continuous aspects of musical space, the electronics come into,
and out of, phase with this, sometimes accentuating the fragmentation and at other
times not. The piece settles for a while on the tam-tam, which becomes scraped and
‘sings’ a long note and has some of its harmonics picked out for intense
examination and transformation. The piece picks up energy again, becoming
increasingly fragmented, and ultimately becomes a continuous roll on the cymbal
with the sound fragmented by the electronics. (Doornbusch 2002d. EMF CD 043
Music CD and booklet)
Mapping in Algorithmic Composition and Related Practices 41
Continuity 3 (2002), for percussion and computer, is a prime example of the
embodiment of this philosophy and the techniques of algorithmic composition and
mapping as I practice them. Simplistically, the overall form of the piece is A-B-A; it
starts very fragmented, becomes continuous, and ends in a very fragmented way.
However, this is too simplistic and the concepts of fragmentation and continuity are
mapped very deeply into the piece and layered through many parts of it. The
instrumentation of Continuity 3 is; a broken china cymbal, a large tam-tam (1.5m), a
circular metal plate (450mm), and a computer. The china cymbal always has a particular
overtone structure which does not harmonically match the fundamental (pitch) of the
cymbal, and when the china cymbal is broken, or cracked, it will have overtones that are
even more inharmonious – I treat this as fragmentation in the spectral domain (more on
the significance of this later). The circular metal plate used is finely balanced and made
out of a particularly stable alloy. I used a disc platter from the first computer used at the
Sonology Institute in Utrecht (a PDP-15); it has a very pure sound and minimal
overtones. I treat this as continuity in the spectral domain. The large tam-tam can be
played in a wide variety of ways and can sound spectrally pure or fragmented. The
computer is used to process all of these sounds in real time, transforming them, providing
additional degrees of mostly spectral and pitch continuity and fragmentation. The
software tool AC Toolbox (Berg 2010) was used to create a ‘library’ or ‘palette’ of
rhythms for Continuity 3.
The structure of Continuity 3 is probably best described as many-layered. I will
occasionally refer to the document Continuity 3 Initial Sketch during this discussion
(included with the other documents with this thesis), and I will simply call it the Initial
Sketch. Additionally, the score will also be referred to in this analysis. At the top left of
the Initial Sketch, it can be seen that I have elected to map, against time, the following
parameters: General continuity, from hi to low (fragmentation); Time and rhythm, from
fast to slow and also from discontinuous to continuous; Pitch (including harmonic
content), also from continuous to fragmented; Electronic sounds and processing from
continuous to discontinuous. From this it can be seen that while the piece may have
continuity in one dimension, it can have fragmentation in others, simultaneously. This
produces a variety of rich, complex and multilayered gestures within the piece, with
sonic representations of continuity and fragmentation occurring differently and
Mapping in Algorithmic Composition and Related Practices 42
simultaneously in the aforementioned musical dimensions – general
continuity/fragmentation, rhythm and time, pitch and timbre, and computer processing.
In the Initial Sketch the length of sections and transitions was determined by ratios of
numbers from the Fibonacci series. I must confess to not holding strictly to this plan
when moving, or mapping, the piece from the Initial Sketch to the fully notated part, such
that I felt free to change the durations, and indeed even the degrees of fragmentation
based on aesthetic requirements. Thus, the Initial Sketch was used as a means of
organising and guiding the composition, providing a foundational mapping, while
aesthetic imperatives took precedence at all times.
One of the compositional details not evident here, but which is important for a
fuller understanding of the piece, is that the score notates where on the instrument the
player is to play or strike it. A China cymbal has more pure and regular harmonics when
it is played near the centre and, conversely, more irregular and discontinuous harmonics
when played at the outer edge, with different possibilities between these extremes. The
plate is somewhat similar in respect to playing position but with minor variations as it is
mostly very pure, whereas the tam-tam is complex and does not easily follow such
maxims. In addition, the type of beater or stick used to strike these instruments also has
an affect on the spectrum generated, so the playing position (where to hit), type of striker
and how to play are all carefully notated and specified to provide maximum articulation
of the concepts of fragmentation and continuity across multiple parameters.
The palette of rhythms created for Continuity 3 required special consideration,
because what does continuous or fragmented mean with rhythm and time for percussion
– how can these concepts be mapped to rhythm and time? Musically, unlike sustaining
instruments such as strings or winds, continuous time or rhythm for percussion can have
two meanings; it can mean a single event which is left to sustain (for example a tam-tam
or gong hit), or very rapidly repeating events which have a regular rhythm, such as a roll.
The opposite of this, a fragmented rhythm must be not so random that it sounds like long
sustained notes, nor so frequent that it seems like a drum roll, but perceptibly random.
To develop the rhythmic palette I treated the two extremes of continuity as the
endpoints of a continuum, or adjacent points on a circle, and I used AC Toolbox (Berg
2010) and Max/MSP (Zicarelli 2010) to generate rhythms with varying degrees of
Mapping in Algorithmic Composition and Related Practices 43
randomness and both types of continuity. Examples of the generated rhythms are shown
below in figures 4 – 7 (note that as these have been mechanically transcribed, there are a
number of ties and notation conventions which would be simplified in practice and which
can be seen in the score). These four examples range from somewhat fragmented on the
first example to very fragmented in the last example, and they represent some of the
rhythmic possibilities used in Continuity 3. Continuous rhythms in this context are trivial
and therefore examples have not been shown below.
Figure 4. Examples of the rhythms used in Continuity 3 – slightly fragmented.
Figure 5. Examples of the rhythms used in Continuity 3 – more fragmentation.
Figure 6. Examples of the rhythms used in Continuity 3 – still more fragmentation.
Figure 7. Examples of the rhythms used in Continuity 3 – heavily fragmented.
The score of Continuity 3 is divided into several sections, even though these often
seamlessly meet up and flow into one another, and are thus not always obvious when
listening. These sections are noted with a number in a triangle, for example the first
section is marked as 1 , which also corresponds with the stage of the computer
processing produced with the Max/MSP patch. I will mention sections by number here
and these can be found in the score by looking for the same number within a triangle.
The first minute of Continuity 3 is a brief prelude of things to come. Initially, the
opening statement begins with a continuous rhythm, but fragmented spectral information.
Mapping in Algorithmic Composition and Related Practices 44
This can be clearly heard in the first 30 seconds of the opening section. The playing
position on the cymbal is carefully notated on the score so that the spectral information
of the broken china cymbal starts less fragmented than it can be, by playing in the centre
of it, and ends very fragmented by playing at the edge. The spectral fragmentation is
further articulated by the computer processing which picks harmonics and after analysing
them creates resynthesised harmonics which are more fragmented spectrally as they
glissando and shift in the frequency domain along nonlinear and logarithmic paths, but
they are less fragmented in time. This is important because it articulates elements of the
form of the piece, which are explained below.
The compositional affordances of the Max/MSP patch which does the processing
will be explained later, but at this point the spatial information is also fragmented with a
delay-panner6 which pans the original and pitch-processed sound between the left and
right speakers in a fairly erratic manner providing a fragmentation of space. After the
cymbal has finished the roll, and after the computer has completed it’s processing and
fragmenting of the cymbal overtones, there is, after a pause, a single hit on the plate
(section two on the score). The plate sustains for twenty or more seconds, offering the
other extreme of temporal continuity, while similarly the computer selects and sustains
some of the harmonics. The sustaining plate sound is subtly disturbed by the player
waving his hand over it, as notated in the score, creating a slight spectral shift or vibrato,
which adds subtly to the computer processing of the sound. The computer processing is
slightly different for this gesture as the processed and reconstructed overtones are no
longer spatially fragmented but are reverberated, providing spatial continuity. Eventually,
from twelve seconds after the initial strike, the computer generated overtones abruptly
cut out one by one, further suggesting that there is more fragmentation to come while
leaving the pure plate tone to fade to silence.(
((((((((((((((((((((((((((((((((((((((((((((((((((((((((6 A delay-panner is also sometimes called a Haas panner because it is based on a psychoacoustic principle known as the Haas effect (after the work of Helmut Haas) or the precedence effect. This is a complex psychoacoustic effect where signals reaching the ears with equal loudness, but at different times, cause the perceived sound location to be determined by the sound that arrives first, within a certain time window. Thus, a delay-panner will delay either the left or right signal, while keeping the intensity the same, to achieve an apparent left-right spatial shift. A performance benefit of this approach is no loss of volume from either channel.
Mapping in Algorithmic Composition and Related Practices 45
After a pause of ten seconds (section three in the score), the piece begins properly
with a somewhat fragmented rhythmic figure on the China cymbal, repeated so that it is
not too random (1:02 – 1:10), but with each repetition, the computer processing becomes
more fragmented and extreme. This continues with some changes to the rhythmic figure
making it slightly more random and with less repetition. This is increasing the
fragmentation in the pitch and time/rhythm domains. This gesture continues until 1:25
(section four in the score) when some similar rhythmic figures on the plate begin the
conclusion of this section, which lasts for another 30 seconds. The plate has a purer and
more continuous harmonic output, but it is still fragmented by the computer
manipulation. Additional overtone variation occurs because subsequent hits on the plate
are with a hard rubber beater, and a steel triangle beater which is also used for rubbing
the plate. My intention with this combination of gestures is to express elements of the
form of the piece through continuity and fragmentation in the time and spectral domains.
This section concludes at 1:55.
The following gesture, which begins at section five in the score, starts on the
china cymbal with a fragment of a moderately continuous rhythmic pattern that is
repeated. The computer processing in this section is somewhat more extreme than in the
initial sections, particularly with the left-right spatialisation. The rhythmic patterns are
frequently spread across the cymbal and the plate, accentuating the timbrel differences
and highlighting the spatial movements via the computer processing. This gesture is
completed by 2:25 or the point marked as six on the score, where the processing changes
to only send the pitch resynthesis through the panner and the reverberation. This further
accentuates the spatial fragmentation of the sound. The rhythmic figures, although of
lesser complexity, are structured to highlight the fragmentation of the cymbal and plate
overtones, and space, by the computer processing. Thus, this offers a slightly different
aspect of the fragmentation and continuity, which drives the form of this piece.
Section seven works as a bridge to the next part and starts (at 2:53) with a
continuous roll on the cymbal. The processing at this point is complex with two
harmonisers, reverberation and panning, often cross-mixed. As the cymbal roll grows
from very quiet to mezzo-forte, the computer processing is continuously lowering the
pitch, so the extra harmonics which emerge as the playing gets louder, and eventually
starts on the plate, are dropped in pitch and glissando down for 10.5 seconds, after which
Mapping in Algorithmic Composition and Related Practices 46
they glissando up briefly, and then when the playing on the plate becomes continuous, it
all glissandos down markedly. This makes the plate sound as if it is growing in size for
approximately eight seconds. The following sections with playing across the cymbal and
plate grow more fragmented, leading to the first use of the tam-tam at 3:40. The fifteen
second sustain of the tam-tam, with its deep resonances, concludes this section at 3:55
with the strongest sense of continuity yet in the piece, with some computer processing of
the sound to lower the pitch.
Section eight starts with a very brief tam-tam strike to a longer cymbal hit, and
the computer processing is complex with overtone resynthesis, three harmonisers across
different frequency bands, left-right spatial movement, and reverberation. The rhythmic
figures are repeated and extended over the 16 seconds of the section, with the primarily
cymbal figures progressively more punctuated and interrupted with loud hits on the plate,
which sustain. Against this rhythmic progression, the plate harmonics become
progressively more fragmented and distorted in their resynthesis.
The rhythmic figures of section nine (4:11) become progressively more
continuous and the playing, ending up with rolls, work across all three instruments. An
early single hit on the tam-tam provides a sustaining undercurrent for this section which
concludes with a roll across the cymbal and tam-tam with the tam-tam sustaining for
several seconds while the computer ring-modulates and harmonises the harmonics,
resulting in a slowly rising complexity of harmonics. My intention with this combination
of gestures is to provide a rich combination of both fragmentation and continuity at this
point in the piece through the complexity of the sound world, and ambiguity with respect
to the future direction of the piece.
At 4:33 (a completely accidental and serendipitous timing and not a reference to
John Cage’s famous piece) section ten starts with a quick cymbal figure, a sustained hit
on it, and scratching and a roll, while the computer processing re-engages the analysis-
resynthesis section with a complex arrangement of harmonisers, delay-panners, and
signal degradation. The processing and fragmentation of the spectrum is immediately
obvious as it contrasts with the preceding section. The rhythmic figures persist with
continuous rolls on the cymbal interrupted by the plate and its combination of continuous
harmonics and the fragmentation of the computer processing. This serves to extend the
Mapping in Algorithmic Composition and Related Practices 47
previous section with a variety of processing and instrumental sounds to maintain the
fragmentation through other means before it is released in sections thirteen and fourteen.
Section eleven opens with a slightly fragmented rhythmic figure on the plate and
cymbal which moves to a roll, slower and fragmented to begin with and fast and smooth
to end, across both instruments while the computer processing progressively more
strongly ring-modulates the sound. This gives the effect of simultaneous glissando up
and down from the centre pitch, although the upper glissando is mostly lost in the
instrument harmonics. After a pause for the computer to process the ringing harmonics,
the section continues with rolls across the plate and tam-tam, which are punctuated by
tam-tam-strikes. These are quite low in volume so as not to excite too many harmonics.
The complex overtones created by the ring-modulation of the harmonics are
complemented at the end of the section by a scratching figure on the cymbal with its very
complex harmonic structure, and a single hit on it, while the tam-tam sustains
underneath. At 6:42, section twelve makes a bridge to section thirteen with short
rhythmic figures on the cymbal and later on the plate, culminating in a single plate hit.
All of this is with minimal processing, beginning the relaxation of the fragmentation
accrued in earlier sections.
A short figure on the cymbal which quickly moves to a complex rhythmic
structure played on the tam-tam begins section thirteen, with the moderately complex
rhythms quickly moving across all three instruments. The processing for this section is a
harmoniser, ring-modulation and delay-panning. This gives a moderately constant
movement to all of the harmonics. The rapid rhythms slow and combined hits on
multiple couplings of instruments, sustained sometimes for many seconds, and at varying
intensities, gives strong and continuous low frequency content with fairly continuous
high frequency content. This leads the way to section fourteen where there is the
strongest sense of continuity.
Scraping the head of a drumstick around the tam-tam opens section fourteen with
the most continuous sound possible on these instruments. Initially this is relatively
unprocessed by the computer, but several seconds into the piece a combination of
harmoniser and level-dependent analysis-resynthesis starts to distort and fragment the
sounds with accentuated harmonics. These eventually ‘fly off’ in several directions as
Mapping in Algorithmic Composition and Related Practices 48
they are mapped along steep logarithmic paths, signalling that this continuous state is not
one of rest but one which will eventually again become excited, as if the tam-tam is
exciting the virtual resonances of the machine. A very strong hit on the plate (the
instrument with the most continuous harmonics) ends the section with sustaining,
processed, harmonics.
Section fifteen continues with the same hit on the plate, but now the processing is
ring-modulation and uses two harmonisers. The section continues with a sustaining hit on
the cymbal and also on the tam-tam to end the section, the cymbal having discontinuous
overtones. This ends the most continuous section of the piece, where most of the
elements are as continuous as they will become – continuous rhythms, mostly continuous
overtones, spatialisation and processing. This means that the piece is at its most extreme
point in the form, and the only way forward is through further fragmentation, which is
prefigured by some of the processing employed here and the cymbal hit.
In section sixteen, some slightly fragmented rhythmic figures on the plate leads to
scratching on the cymbal, plate and tam-tam, which have their harmonics somewhat
further fragmented by the analysis-resynthesis section of the processing. This is the
beginning of the further fragmentation of the sound world. More scrapes and rhythmic
figures across the instruments make up section seventeen, with simple processing,
leading to section eighteen (at 11:13) where the rhythms fragment more and the
processing becomes more energetic. This section ends with some fairly extreme
processing in pitch and space of the tam-tam which, offers a range of overtones to
process, and a single strike on the plate.
Ring-modulation offers moderate processing of the overtones of section nineteen,
which starts with some moderately fragmented rhythmic figures on the plate and ends
with some fragmented playing on the cymbal. The ‘scraping stick’ technique used on the
tam-tam in section fourteen is now used on the cymbal in section twenty, with processing
used to fragment the harmonics significantly through analysis and (distorted) resynthesis.
Fragmented rhythmic playing continues on the cymbal, which moves to the plate and
eventually single sustained strikes on the tam-tam, plate and cymbal to end all with the
aurally obvious processing.
Mapping in Algorithmic Composition and Related Practices 49
Section twenty-one concludes the piece, similarly to how it began. A combination
of fragmented rhythms on the cymbal are processed with techniques to provide the most
fragmentation. The playing becomes more frenetic across dynamics and instruments as
all combinations of instruments are involved in the heavily fragmented and frantic
rhythms, until various kinds of rolls are performed on combinations of the three
instruments. The piece ends with a roll on the cymbal, with the processing continuing to
drag out the harmonics of the cymbal and tam-tam, suggesting the continuous cycle of
fragmentation and continuity, and the tension that comes from that opposed duality.
All of these sections may be listened to individually on the accompanying
supplementary disk 1, and the Max/MSP patch may also be examined on supplementary
disk 2. Because of some Max/MSP third-party object limitations, the supplied patch is
only viewable on Apple Macintosh computers and a full install of Max/MSP7 is required
for full functionality.
The Max/MSP patch is crucial in this composition because it performs the
processing of the sounds in Continuity 3, and manages many digital signal processing
(DSP) processes and routines that were developed specifically for this piece. In the
commentary below my aim is to provide the reader with a deeper understanding of the
role played by this important piece of software in affording the complex mapping
practices and techniques that are central to this composition. Moreover, it is hoped that
the reader will have some insight into the role played by the composer in making use of
such software affordances. Figure 8 below is a picture of the main screen for the
Max/MSP patch.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((7 A time-limited but fully functional demonstration version of Max/MSP is available from the Cycling74 website: http://cycling74.com.
Mapping in Algorithmic Composition and Related Practices 50
Figure 8. The main window of the MaxMSP patch used in Continuity 3.
All of the separate DSP modules can be found through the sub-patch named
‘guts’, and objects and sub-patches in Max/MSP are noted by square brackets. Figure 9 is
a picture of the [guts] sub-patch:
Figure 9. The DSP sub-patch ([guts]) of the MaxMSP patch used in Continuity 3.
The [guts] sub-patch contains all of the DSP modules; the pitch tracking and
resynthesis module [ptrack5~], the harmonisers [harm~], [harm2~] and [harmH~] (this is
Mapping in Algorithmic Composition and Related Practices 51
optimised for high frequency harmonising), a ‘flanging8’ phase effect [flange~], a
reverberation module [rev2~], a signal degrader [deg~] (reduces the sample rate and bit
depth), a delay or ‘Haas’ panner [haas-pan~], and a ring modulator [ring-mod~]. These
modules are interconnected in various ways through the large (20 input and 16 output)
cross-matrix switcher in the main patch window, as can be seen above.
A system of presets (preset configurations) has been established which runs
through to the depths of each sub-patch and sub-sub-patch and so on, so that when the
space-bar is pressed, or a MIDI footswitch is depressed, the processing configuration and
interconnection of modules all change for that part of the piece. Sometimes it is possible
that only the interconnections change, but often the internal configuration of the DSP
sub-patches also change. In addition, with many preset configurations pre-programmed,
time-dependent changes occur within the DSP sub-patches, such as the constant
glissando down in the harmoniser modules as used in several sections of the piece, or the
resynthesis of partials in [ptrack5~], and these often map the parameters along non-linear
or logarithmic paths to accentuate elements in the piece (usually the fragmentation).
Figure 10, below, is a picture of [ptrack5~] sub-patch.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((8 Flanging is a comb-filtering effect caused by mixing a signal with a slightly delayed version of itself. The comb-filtering typically sweeps the audio spectrum such that the notches in the spectrum vary with frequency in time.
Mapping in Algorithmic Composition and Related Practices 52
Figure 10. The pitch tracking MaxMSP sub-patch used in Continuity 3.
Other changes which occur are responsive to the input; for example, threshold changes
such that when the player goes above or below a certain threshold, then different DSP
processing occurs. This is shown in the right hand edge of figure 10 and it makes for a
highly dynamic and responsive performance environment for the musicians, and in
reality it extends the instruments in ways that were previously impossible. Figure 10 also
illustrates some of the complex mappings present in the composition.
The foregoing detailed deconstruction and analysis of Continuity 3 shows how
mapping the concept of continuity and fragmentation in multiple musical dimensions
(time, spectrum and overtones, instrumentation) has been used to structure the piece,
from the overall narrative arch to the moment-to-moment details of what is going on at
any one time. In some ways it offers a combinatorial study of how fragmentation in one
or more domains, including the player’s technique, may exist while continuity may exist
in others. This offers a new way of structuring music (as discussed in 4.7) which can be
Mapping in Algorithmic Composition and Related Practices 53
rigorous, yet does not rely on romantic concepts of musical form (for example sonata
form or sentimentality), and which may be more in touch with the complex milieu in
which we find ourselves today. Indeed, while continuity and fragmentation in spectral
and other domains may be straightforward, time has often been seen as purely
continuous, as in Newtonian physics.
The human experience of time is often at variance with the linear passage of time
as measured on a day-to-day basis (Kern 2003). Our recollection of time and our memory
is even more fragmented than the steady measure of everyday time. Time itself is still a
mystery, as St. Augustine famously commented late in the 4th century, “What, then is
time? If no one asks me, I know what time is; if someone asks and I want to explain it, I
do not know” (Melia 2003, p. 73). Indeed, as noted earlier, Newtonian universal, linear
and absolute time was replaced by Einstein with multiple correct times in each gravity
centre, such that there is no absolute time (Hawking 1988). In addition, it has recently
been postulated that the unification of quantum mechanics with general relativity may
result in the elimination, or end, of time – meaning that time will no longer have a
function in the foundation of physics (Barbour 2000). I do not know how philosophers
would view such an occurrence. More recent research into how the brain processes time
indicates that the perception of time is indeed fragmented, discrete and ‘sampled’ (Fox
2009) , and that this fragmentation may vary depending on the surrounding stimulus.
Some knowledge (however limited) of this more modern understanding of time may be
used to shape elements of a composition which is concerned with fragmentation and
continuity, our place in the universe and our perceptual understanding of it. I believe that
for myself, part of a composer’s responsibility is to have a genuine aesthetic response
(but not a sentimental response9) to the world and period in which they live. However,
this may not be a position everybody would want to have.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((9 By ‘sentimental response’ I mean the sort of responses typically sought in popular music, such as feelings of ‘happiness’ or ‘sadness’ and so on. I believe that music as works of art can be structured beyond such sentimental responses to provide more insight into the human condition and how we negotiate our understanding of our place and humanity in a complex universe.
Mapping in Algorithmic Composition and Related Practices 54
We live in an era in which we understand that we are but a small planet in orbit
around an insignificant star, in a medium sized galaxy, amongst billions of such galaxies,
and at the time of writing we are presently looking for the Higgs boson10 (subatomic
particle) in the Large Hadron Collider to (hopefully) finally understand the nature of
matter. In such circumstances, the approach to music illustrated in my compositions
seems to be both authentic and appropriate. While traditionalists will view this as a
radical departure from the past, there was a time, in the Aristotelian world, where the
seven notes were a parallel to the seven known planets, and music was as much science
as art. Thus, my approach to music can be seen not necessarily as new (indeed Varèse
and Xenakis may share it), but rather an updated and contemporary view without the
sentimental ‘baggage’ and weight of the past. These ideas are expanded upon later in this
section.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((10 The Higgs boson is a hypothetical sub-atomic particle which, it is theorised, will provide the answer to inconsistencies in the mass of atomic particles.
Mapping in Algorithmic Composition and Related Practices 55
4.2 Mapping in Continuity 2
Again, I have elected to begin this section with an excerpt from the booklet that
accompanied the CD recording of Continuity 2:
The recorder notation, and only the notation, of Continuity 2 borrows heavily
from Berio’s Gesti for solo recorder – the fingering, and the embouchure and
breath, are separated in such a way to create a great discontinuity and schism for
the performers’ technique and the sonic result. This is most evident in the opening
minute or two of the recorder part. The overall shape was based on graphs of
various chaotic functions - bifurcation functions, for example, and their mirror
image. Doornbusch liked the way these illustrated processes of nature, which cause
things to come together and fly apart. The piece is concerned with the way the
continuous can become the fragmented, how one can lead to another, and how our
perception of continuity and fragmentation can change depending on how we
choose to relate to something. For example, continuous polished surfaces may look
very discontinuous and irregular under intense magnification.
The opening of this piece is dramatic and piercing. A high pitched tone, which is
a middle-G of the bass recorder, electronically transposed four octaves higher. This
is slowly, electronically transformed into the tearing of corrugated cardboard (a
transformation from continuous to fragmented). Then the four bass recorders enter,
taking up the fragmentation and moving it between them as the electronic part
returns, initially continuous, but this also soon fragments into a frenzy of activity
The electronic part is made with 3 main sound sources; recorder samples
(continuous - a sustained G in middle of treble staff, played on bass recorder
sounding 8ve lower), samples of scraping/tearing corrugated cardboard
(discontinuous), and about 40 streams of dynamic-stochastic synthesis sounds that
often have varying parameters, moving from the very unstable and discontinuous to
more stable and continuous, and back. As the piece progresses these sounds slowly
become more continuous, although there are many energetic disturbances and
interruptions, until they come together on the recorder sample (this time not
transposed, but stretched). The recorders slowly settle on this G, although this
continuity is disturbed by some energetic electronic interruptions. The recorders are
stimulated by this disruption and begin to deviate, ultimately moving through
Mapping in Algorithmic Composition and Related Practices 56
multiple octaves of smooth glissando (with circular breathing), until they excite the
material again into a frenzy of activity where the piece explodes again into a state
of complete fragmentation. (Doornbusch 2002d. EMF CD 043 Music CD and
booklet)
Continuity 2 (1999) is a piece for bass recorder quartet and pre-recorded
electronics. The piece is more monolithic in structure than Continuity 3, partly as an
aesthetic and technical challenge played out in the composition, but also as a
consequence of the characteristics of the instrumentation. By monolithic I mean that
there are fewer discrete and clearly delineated sections, as there are in my other works
(for example Continuity 3 and Act 5). Despite this monolithic structure, the work still has
sections, and certainly musical gestures that are that are evident, and I will use this
framework to deconstruct and discuss the piece.
The overall, ‘broad-brush’ structure is one that basically shifts from
fragmentation, to continuity and back to fragmentation. As the electronics are pre-
recorded, the performers have less freedom of expression than with an interactive piece
such as Continuity 3, but at the time of its making, interactive systems were not available
that could manage this. The performers listen to a click-track via earpieces to keep them
synchronised with the electronic part, and the score is marked in places where the players
must synchronise with the tape. Thus, there are degrees of freedom for the players, but
not as much agency as there would be in an interactive piece.
Section one, from the start until 1:38, is a brief electronic prelude. It starts with an
insistent high-frequency tone that is continuous, but it has a fragile nature which suggests
its vulnerability and later fragmentation. This was made from a recording of a bass
recorder playing the note middle-G, which is transposed four octaves higher and I also
stretched it several times longer with a phase-vocoder. This is mixed with a slightly
pitch-altered version of the same sound, resulting in ‘beating’ and difference tones which
provides the first hint of fragmentation, with some very quiet lower frequency sounds
imitating a typical recorder performance gesture. At 1:07 a new sound enters, which is
the same recording of the recorder playing middle-G, but this time transposed only, two
octaves higher, and this sound is slowly spectrally transformed into the sound of tearing
corrugated cardboard while the higher frequency sound fades out. A processed version of
Mapping in Algorithmic Composition and Related Practices 57
the corrugated cardboard sound, offering a high degree of fragmentation from the initial
continuous tone, ends this section.
The recorders enter at 1:40 (section 2) by simply playing solely with slapping
fingers on the recorder finger-holes, giving a bubbling and discontinuous texture before
they play a sharp multiphonic to signal their arrival. The playing technique for the
recorder is extremely fragmented for a good part of the piece because the fingering is
notated differently from the embouchure and breathing. Forcing the player to separate
intimately connected parts of their technique is not unprecedented, as Luciano Berio did
this in his piece Gesti. In an acknowledgement of Berio’s piece, which is well-known
amongst recorder players, I thought it best to build on this established technique rather
than invent something new for the sake of it, so I used similar notation. The directions on
the first page of the score are as below:
Embouchure and mouth tension is indicated relatively:
- So as to produce a high pitch.
- So as to produce a sound in the middle register.
- So to produce a low pitch.
- Indicates an instrumental sound.
- Indicates a vocal sound.
- Indicates a instrumental pitch coloured with the same vocal pitch.
- As short as possible, vocal and instrumental respectively.
- Breathy flutter tongue.
- Throat flutter tongue.
- Inhaling on this note.
- Numbers in boxes indicate dynamics, 7 is loudest, 1 is softest.
Figure 11. Score annotations used in Continuity 2.
7( >(
1(
Mapping in Algorithmic Composition and Related Practices 58
An example of the notation, to indicate its use, is shown in figure 12, below, and a larger
sample is provided in the scores and supplementary materials section:
Figure 12. Score fragment from Continuity 2.
The notation starts out extremely fragmented, along with the playing technique,
and slowly (over several minutes) these two aspects of the piece are brought to a point of
continuity, as can be heard later in the piece (from about 5:30), then they start to become
fragmented again. The recorder entrance beginning at 1:40 continues in a highly
fragmented manner, with bubbling and outbursts, through this first gesture to
approximately 2:51. Both the electronic and the instrumental parts build through this
section, with the electronics having a complex amalgam of continuous high-frequency
sounds and noisy, tearing, sounds with the instrumental part progressively building
Mapping in Algorithmic Composition and Related Practices 59
through bubbling sounds, noises and multiphonic outbursts with a release of descending
vocal sounds.
A brief electronic section bridges to the next part (section three, 2:51 – 3:09),
which starts with vocalisations and multiphonic bursts from the instrumentalists. After
another short electronic bridge, the substantial section four begins at 3:09. Highly
fragmented bass-recorder playing provides occasional bubbles and multiphonics in
waves as flutter-tongue techniques (both throat and tongue versions) are introduced,
signalling the beginning of continuity. The rapid undulations start to hint at notes as the
fingering is directed to be smoother and more like playing glissando. However, this is
interrupted by multiphonics and staccato playing as the electronic part continues to
writhe with energy and noisy bursts in a counterpoint to the instrumentalists’ sounds.
This section, ending at approximately 4:10, is documented in the extract of the score11
and the change in playing technique from highly fragmented to more continuous is
evident there. This tightly scripted combination of gestures indicates the start of the
transition from fragmentation to continuity in the playing technique and sounds of the
recorders, articulating the form of the piece during this section.
Section five begins seamlessly from the previous section with strong flutter-
tongue at approximately 4:10. This is a midpoint in the piece and the tendency to
continuity is clear here, compared to the beginning, although the electronic part continues
to resist the continuity of the instrumentalists at this time, providing a counterpoint to the
instrumental part. From 5:10 the series of preceding compositional gestures leads into a
long sustained electronic note which becomes prominent from about 5:14 while the
recorders seem to be struggling to achieve a continuity. The electronic low frequency
note is not only longer but is also less noisy, although it recedes to leave noisy sounds in
its wake. The section ends at 5:28 with noisy electronic sounds fading out.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((11 Unfortunately, the original full score has been destroyed in flood damage and cannot be presented. I have asked the performers to look for copies in their archives and I am still hopeful that this will bring results, but as yet there has been only the three-page excerpt of a draft score returned, as presented with the scores and supplementary material. The presented digitised page of the score is the only part which remains because the performers thought the score so beautiful they selected a page, made a high quality copy, and had it framed for me as a gift.
Mapping in Algorithmic Composition and Related Practices 60
Section six (5:28) starts with flutter tongue glissando on the bass recorders, which
individually glide down to and around a central note (a G) while the flutter tongue gives
way to regular sustained notes. The bass recorders drift up and down in pitch smoothly
while the dynamics of their playing is still sometimes changing, but the tendency to a
continuous sound is clear. During this time the electronics are also starting to become
more continuous with a high-pitched continuous sound added to the noisy tearing
textures which are becoming less common, and another continuous, electronic and
processed, low-frequency sound is also usually present. By approximately 6:14, the
recorders are all close to the middle-G that they have been drifting to, and the electronics
gives way to more continuous sounds. The recorders now express their discontinuity
through the ‘beating’ of the notes that are (microtonally) close in pitch to each other12.
The piece briefly manages to be fully continuous at 6:53, which is the beginning of
section seven. A high frequency note in the electronics, with a corresponding low
frequency note (both created my manipulating the G being played on the recorder),
makes for a fully continuous moment of approximately six seconds, before the low
frequency electronic sound starts to rumble and fragment and the high electronic sound
also starts to become energised and slowly fragment. This energises the recorders, which
again start to drift away from the note and the combined sound starts beating again. By
7:30, it is clear that this will fragment again as the recorders drift more and the electronic
sounds become more agitated. The electronic sounds become more fragmented by 8:00
and the recorders are performing glissandi by almost an octave in their effort to get away
from each other.
A momentary lull from 8:21 allows the sustained low frequency electronic sounds
to dissipate and the fragmented noisy sounds to take over as section eight begins at
approximately 8:24. The recorder technique used in section eight uses more vocalisations
and re-introduces flutter tongue as the recorders glissando further and further away from
each other. While section nine is heralded by recorder overblown multiphonics,
((((((((((((((((((((((((((((((((((((((((((((((((((((((((12 Tribute must be paid here to the performers who were not only able to easily manage three octaves of smooth glissando on F-bass recorder, an extraordinary feat in itself, but they could also microtonally control their pitch to slowly bring themselves to the note and drift off by precise amounts to cause the beating. After the recorder has become very wet with extreme amounts of flutter tongue, this is something that only a handful of performers in the world can manage, such is the virtuosity required.
Mapping in Algorithmic Composition and Related Practices 61
fragmenting more completely the recorder sounds, the electronics build to a rage of
activity. The recorders still possess some ability to glissando but the energy is increasing
and it is fragmenting with more overblown-multiphonics. The piece ends at 9:26 with
extreme overblown multiphonics and the electronics in a superheated writhing of
fragmented activity.
In the context of this thesis, Continuity 2 illustrates the mapping of the concepts
of continuity and fragmentation into the musical domain of timbre, time (to a more
limited degree than Continuity 3), playing technique and so on. The piece is quite
different from Continuity 3 as it uses sustaining instruments instead of percussion and a
fixed electronic part instead of a responsive and reactive one. However, mapping plays a
central role in how the piece was both composed and performed. Moreover, the
electronic part uses elements of continuity and fragmentation in the sound synthesis and
transformations, to act as a counterpoint to the instrumental part. It is a unique piece in
terms of its instrumentation, complexity and compositional goals, which it successfully
achieves. Essentially these goals are, as previously outlined, to map continuity and
fragmentation of as many parameters and dimensions as possible, and in combinations, to
provide a unique aesthetic experience.
Mapping in Algorithmic Composition and Related Practices 62
4.3 Mapping in Act 5
The notes from the CD booklet provide an appropriate and convenient introduction
to Act 5 and an extract appears here:
ACT 5 takes its name from the software used to create it – Algorithmic
Composition Toolbox and it is the fifth piece made with this tool. The main
concept of the piece is the struggle to gain height and the attendant metaphors this
evokes. Act 5 is in four sections of increasing pitch range and rate of pitch change.
The four sections are punctuated with interruptions. These three interruptions are
percussion instruments, which are suspended above the stage behind the performer,
falling to the stage. The staging had the performer at the front, to the right was
suspended some pots and pans several meters above the stage, to the left was an old
glockenspiel and several meters behind the performer was a tympani. The
suspended instruments thus making a triangle, with the ropes holding them looped
to hooks near them on the stage. It is a requirement of the performer that they put
down their instrument and sprint across the stage to a rope that holds one of the
instruments aloft, release it, sprint back to the playing position and continue. This
is an athletic performance. Not only does the music take the listener into the body
of the instrument, the intimacy of sound that is usually the province of the
performer, but the listener is also exposed to the breathing and strenuous effort that
this piece requires. ACT 5 must be performed on a large stage (the premiere was on
a stage 12m by 18m). The suspended instruments can be anything deemed suitable,
on the recording there was a collection of half a dozen pots and pans, an old
xylophone, and lastly an old timpani. In line with this piece’s struggle to gain
altitude (like getting out of bed, an improvement in ‘quality’, and so on) and its
athletic nature, it is required that the performer wear clothing similar to a dancer.
On the premiere the performer was dressed in a singlet and boxer shorts, it made
for a memorable performance. No instruments were seriously injured in the
performance of this piece. (Doornbusch 2002d. EMF CD 043 Music CD and
booklet)
Act 5 (1998) is a piece for amplified solo bassoon, which was written using the
algorithmic composition software AC Toolbox (thus, ACT). The piece maps concepts of
height and struggle mostly against pitch, timbre, and playing technique. I chose ‘height’
Mapping in Algorithmic Composition and Related Practices 63
and ‘struggle’ as I was thinking of gravity, and gaining height always requires work, or
struggling, against the force of gravity – the working title for the piece was ‘gravity’.
However, I decided that gravity was too imbued with direct meaning to be used as the
title and the piece needed to speak in more abstract terms, so I decided on the more
ambiguous title of Act 5, perhaps implying that there were acts prior to and following this
one. There were also the attendant metaphors of ‘height’ and ‘struggle’, which referenced
the struggle to attain order ,‘quality’ and optimism against entropy and the tendencies to
disorder. It was originally intended that there should be an electronic part to the piece,
but in the end I decided to use close amplification of the instrument through contact
microphones carefully positioned on the bassoon’s crook, which heightens the raw
physicality of the piece. Giving the listener a performer’s close-up experience of the
instrument was also a consideration and part of the conceptual intent of the piece. The
shape of the piece, being basically from low to high, is shown in a plot from AC Toolbox
of the notes as MIDI data for the entire piece, as shown in figure 13, below:
Figure 13. MIDI plot (piano roll) of Act 5, showing its overall shape.
The above MIDI plot shows the general shape of Act 5, and the many falls as the piece
struggles to its highest point at the end, and it closely follows the initial sketch of the
shape for the piece as can be seen in the CD booklet.
Mapping in Algorithmic Composition and Related Practices 64
As noted above, the piece is in four parts. A virtuosic prelude begins the piece
and this uses 23 multiphonics on the bassoon, out of 24 possible multiphonics as
described in the seminal work by Bruno Bortolozzi, New sounds for woodwind
(Bartolozzi 1982) and those found by Hamish McKeich (the performer). The
multiphonics work as clouds of notes, with great spectral richness, and show off the
virtuosity of the performer. The note clouds offer a hint of what is to come and introduce
the extreme physicality of the piece, as this requires a high degree of energy to play, even
though it only takes just under a minute. The prelude ends with the performer pulling the
double-reed off the crook of the instrument and playing just that, so it mirrors the low-to-
high overall shape of the entire piece. This is a somewhat provocative performance and
musical gesture. It fragments the piece and the performance, ‘breaking through’ what
might be reasonably expected in performance, and prefigures the later bolder gestures.
Additionally, in fragmenting the performance technique (not unlike the interruptions to
follow) it takes the performer, and audience, into new and unfamiliar territory.
The first part lasts for 3:36, from the first note at 0:58 to the first interruption at
4:34. The beginning of this section resolves on the lowest note of the bassoon. The
performer is instructed to breathe heavily and grunt as if lifting something, and there are
several key slaps which are notated, hinting at the ‘thump’ of something falling and
hitting the ground, struggling and falling. The rhythmic figures begin quite slowly and
lazily, but as the energy increases in the first part, they generally become faster and more
energetic, although like the pitch changes, this is by no means a linear progression and
there are many retrograde steps, which contribute to the sense of struggle. In AC
Toolbox, the piece is modelled via seventy-four separate sections and approximately
thirty ‘tendency masks’ - a tendency mask is a concept developed by G. M. Koenig
(1970a) and it describes upper and lower limits which bound a random or stochastic
selection. The concept of ‘tendency’ is one of the most influential developed by Koenig,
as explained by Berg (2009) because, “… it provided a way to use random numbers to
generate transitions.” Figure 14, below, shows an illustrative selection of the tendency
masks used.
Mapping in Algorithmic Composition and Related Practices 65
Figure 14. Tendency masks M1, M16 and M22, as used in Act 5, showing their shapes.
These are obviously hand-drawn, although they could have been computer
generated, and are used to shape the selection of notes from a list or ‘stockpile’ as AC
Toolbox names these items. The thirty tendency masks cover all of the shapes used in the
piece, and as the range and domain of each is set programmatically each time it is used,
this makes the small imperfections in the hand-drawing of the masks inconsequential.
These are used in the seventy-four fragments from which the piece is constructed. The
example in figure 15 below shows this, where the mask is named m16.
(Figure 15. An AC Toolbox ‘data section’ dialog, as used in Act 5.
The dialog in figure 15 generates notes for the eight second part from 2:24 – 2:32
seconds. The duration of each note is a random choice of 1, 2 or 4 time units (1/100 of a
second, set in the ‘clock’ field) and the pitches are selected with a random value from
between the 30% and 60% points of the ‘bf-melodic-minor-bn’ stockpile (this is a B flat
melodic minor scale over the range of the bassoon), upon which the m16 mask is applied.
The plotted output of this data section is shown below in figure 16:
Mapping in Algorithmic Composition and Related Practices 66
Figure 16. A plot of the AC Toolbox note output for the ‘data section’ dialog of figure
15, above.
It can be seen here that the shape of the plotted output matches the shape of the
m16 mask above. In this way, the initial sketch was entered moment by moment into AC
Toolbox as tendency masks, so that each section could be generated. It must be noted
that there are many random selections being made for each small section, and each one
was auditioned. If a section did not fit aesthetically, I would re-generate the notes and
listen again until I had something with which I was satisfied. This re-generating of the
notes was merely telling AC Toolbox to re-make the section, involving a single button
click and then listening again. The feedback process is important, or indeed vital, in the
process to achieve the intended aesthetic result.
Moving up a degree in the structure, the small sections were added together to
create each of the four main parts of the piece. The shape of the first part, plotted as
MIDI information, is shown below in figure 17:
Mapping in Algorithmic Composition and Related Practices 67
Figure 17. MIDI plot (piano roll) of part one of Act 5, showing its overall shape.
The contours of the plot clearly show the range of the first part, up to almost
MIDI note 50, and the rate of climbing and falling. The duration of the plotted first part
is 173 seconds, which is not too far away from the 216 seconds of the performance of the
first part, especially as I made notational changes to the part when transcribing it from
the MIDI information to musical notation, and the recorded timing includes the time for
the performer to put down the instrument, sprint across the stage and release the hanging
pots-and-pans to crash to the stage. This first interruption ends the first part and palpably
underlines the conceptual intent of the piece as referencing vertical motion and the
struggle to gain ‘altitude’ or ‘height’ against forces and entropy pulling in the opposite
direction.
Part two begins with a faster rhythmic structure than the first part, and rapidly (in
approximately twenty seconds) goes beyond the range of the first part, as shown in the
plot of part two below. This part continues to gain in energy and eventually climbs again
before the second interruption, which is a hanging glockenspiel that is released and
crashes to the stage floor. By this time in the piece, the performer really is struggling
with the physicality of it and the panting and breathing does not need to be acted.
(Musicians are often not the fittest they could be!) This is also part of the piece, it makes
palpable the physicality of the piece and the effort of the performer for the audience, in a
similar way to watching a sports person struggling the utmost to achieve their goal.
Mapping in Algorithmic Composition and Related Practices 68
The recorded time of the second part is 2:16, or 136 seconds, which is in fair
agreement with the MIDI timing on the plot below of 98 seconds, as again this does not
include the interruption. It is clear by now when listening to the piece that there is an
increasing range, and increasing rate of change of the range, as the piece is progressing.
The MIDI plot of the second part is shown below in figure 18, and as well as graphically
illustrating the above points, it also clearly showing signs of the shapes used in the masks
to define the sections. It can be seen from the foregoing that shapes are important in this
piece and my compositional practice in creating it. It was the ‘shape’ of the piece which
first occurred conceptually to me, and that was the point of departure, as explained
above, for composing it. The mapping of the various shapes to musical data became part
of the composition process.
Figure 18. MIDI plot (piano roll) of part two of Act 5, showing its overall shape.
Part three (MIDI plot below in figure 19) continues with the progression of the
piece, the range is again greater with a higher top note (approximately MIDI note 65) and
the rate of change is again greater with the recorded time of 1:20, 80s (again including
interruption) and the time of the MIDI plot is 77 seconds. This illustrates the accelerating
nature of the piece, the greater rate of change, and the higher top note, are both
illustrative of greater energy being involved and input into the ‘system’, as might be
expected in experiments to launch something into orbit.
Mapping in Algorithmic Composition and Related Practices 69
Figure 19. MIDI plot (piano roll) of part three of Act 5, showing its overall shape.
Part four, the final part, again continues with the progression of the piece and
concludes it. The range is again greater, in fact the greatest possible for the bassoon and
performer, with a higher top note (approximately MIDI note 75), and the rate of change
is again greater. The recorded duration of 1:20, 80 seconds, for this section does not
include an interruption, but it does include a prolonged final gesture, which is the top
note possible on the bassoon. The MIDI plot time (see below, figure 20) for part four is
77s, but this does not include the final gesture, so it is closely aligned with the timing of
the recording. The rapidly ascending notes in the MIDI plot at the beginning are actually
replaced with a long ascending glissando in the piece. There are many glissandi in the
piece, ascending and falling, which are represented this way. The glissandi quite directly
represent vertical motion, one of the main themes of the piece, and the longest and most
rapid glissando in the piece is the last one. The piece ends on the top note of the bassoon,
as the highest point in the piece, and I find it an optimistic ending as it does not, again,
crash to the ground but maintains its elevation.
Mapping in Algorithmic Composition and Related Practices 70
Figure 20. MIDI plot (piano roll) of part four of Act 5, to show its overall shape.
The electronic component of Act 5 brings the audience into intimate range of the
instrument and performer so that the physicality of the performance is accentuated.
Amplification of piezo contact microphones, which are carefully positioned on the crook
of the instrument so as to highlight various overtones, remaps the timbre of the
instrument as it is amplified. This emphasises the shape of the piece as it develops,
making it clearer. The piezo microphones on the crook were mixed to achieve a balance
with the acoustic output of the instrument. The relationship between acoustic and
amplified sound was considered important for the articulation of the shapes and drama of
the piece, and this was experimented with in rehearsals. This relationship between
acoustic and amplified sound is part of the performance practice and depends upon the
performance space and speakers used, so it changes in different performance settings.
Act 5 maps the concepts of height and struggle (and the aforementioned
metaphors), to pitch and performance effort. The interruptions remind the listener of the
ever-present tendency to entropy and the potential to fall. The shapes and visual gestures
in the initial sketch were transformed into a number of tendency masks, which were used
to control the mapping of random functions to generate the notes. Thus, mapping
practices in Act 5 are used somewhat differently to the ways in which they are used in the
Continuity series. There is a very direct mapping in Act 5 from the initial sketch to the
generation of notes, and it is much more linear than in my other works. This more linear
Mapping in Algorithmic Composition and Related Practices 71
translation and mapping of shapes into sounds may be the cause of Richard Barrett’s
criticism of the piece (Barrett 2006) in the included review, as being a little too obvious.
However, the piece was critically acclaimed by Barrett and by newspaper and personal
reports at its debut in Holland, and it is a worthy illustration of my use of mapping
techniques in compositional practice.
Mapping in Algorithmic Composition and Related Practices 72
4.4 Mapping in G4
The notes from the CD booklet for G4 (1997) take on a somewhat distant,
technical, character as they describe the armature behind the work for the prospective
listener, barely hinting in the final few sentences at its compositional intent and
significance:
G4 is a piece that uses solely ‘dynamic stochastic synthesis’, which was developed
by Xenakis and embodied in his GENDYN program of 1991. Monolithic and
relentless in nature, G4 also has streams of activity come and go. The sound
synthesis technique can be described as a number of points on an XY grid and each
of these points does a random walk, based on specified random distributions, in
both the X and Y directions and values are linearly interpolated from one point to
the next. These values are sent directly to the digital to analogue converter of the
computer. To account for the random walks going out-of-bounds, barriers are put
in place to reflect out of range values back into the defined space. Additional
complexity is added to the sound through random modulation of the mirrors† and
repetition of the frames before another is computed. These parameters, and others,
are set to specify the evolution of each voice in the piece. A higher level structure
is determined by setting parameters for each voice, such as the density and duration
parameters. The program will then generate a structure for all of the specified
voices, but the composer can always intervene unconditionally‡. This is music that
can emerge from the minimum number of assumptions and initial conditions, like
the big bang. It is perfectly idiomatic computer music. (Doornbusch 2002d)
The following discussion will take many paths in its exploration of the unusual
synthesis and composition techniques used in G4. The multitude of paths required to
fully express my thoughts in and about this piece make it difficult to write about – which
path to take at what time? After much consideration, the following order seems to me to ((((((((((((((((((((((((((((((((((((((((((((((((((((((((† This is not true and is an error in the original program notes. The version of GENDYN that I used was strictly like Xenakis’ early version that did not have this feature. Xenakis added modulation of the mirrors to the version of GENDYN used for his piece S709. ‡ This was not possible for Xenakis, it was an enhancement added by Hoffmann to his reconstruction of the GENDYN program.
Mapping in Algorithmic Composition and Related Practices 73
be the most logical progression to bring clarity and cohesion to the various strands of
thought. I will discuss initially the characteristics and history of Dynamic Stochastic
Synthesis as this provides the compositional impetus for the piece and it is unusual, after
which I will discuss briefly the software used to compose this piece before I deconstruct
and analyse the various parts, streams and sections. Following this descriptive analysis I
will discuss concepts of composition with random processes, which are embodied within
G4, and which necessarily bring with them a perceived ‘lack of control’ over the process
of composing it – something that initially seems at odds with the requirements of
composition, which often seems to be about imposing order and ‘form’ on material.
Finally, I introduce and discuss three important ideas which effectively work in parallel,
as they provide different approaches to explaining a similar phenomenon:
• That form in music may arise secondarily from the rule-based generation of
sound material;
• That understanding and finding clarity in the ‘mess of sound’ has similarities to
psychoanalytic practice, which usually seeks to clarify the messes in our heads or
lives;
• That radical constructivism13 offers a further explanation of finding form in music
as it contends that we construct meaning (and thus musical form) through the
self-organising cognitive processes of our minds. (Glasersfeld 1995)
I believe that there are elements of these ideas exhibited in all of my pieces, and it has
been my experience that people almost always find form in music, regardless of the
intent of the composer14. However, I find the concepts mentioned above are embodied
most prominently within G4, and thus it is most appropriate to discuss them at this stage.
((((((((((((((((((((((((((((((((((((((((((((((((((((((((13 Radical constructivism was coined by Ernst von Glasersfeld in 1974. It is an unusual approach to the problem of knowledge and knowing, starting from the assumption that knowledge, regardless how it is defined, is in the heads of people, and that the thinking subject has no alternative but to construct what they know on the basis of their own experience. How we understand experiences constitutes the only world we consciously live in. Heinz von Foerster had a slightly different approach to the topic, based on second order cybernetics. It concentrates on self-referential systems for the explanation of complex phenomena. Ultimately, from this would emerge the concept of ‘operational closure’: where any cognitive system is semantically independent (and impenetrable). (Glasersfeld 1995) 14 John Cage, famously, wanted to remove all elements of himself, from the composition process and his compositions, through the use of the I-Ching. However, people still have
Mapping in Algorithmic Composition and Related Practices 74
At the conclusion of this section I bring these ideas together in the examination of G4,
discussing the potential roles they have played, and their influences upon my work, how
they are ‘mapped’ into the music, in both its construction and listening.
The name G4 is derived from the software used to create it – GENDYN – and it
was my fourth attempt at using this software to create a musical work. As mentioned in
the CD notes, G4 is a piece made entirely with Dynamic Stochastic Synthesis, which is a
type of sound synthesis developed by Iannis Xenakis (1992) and investigated most fully
by Peter Hoffmann (2000; 2009). Xenakis created two pieces with Dynamic Stochastic
Synthesis; GENDY3 in 1991 (Xenakis 1995) and S.709 in 1994 (Xenakis 2000), apart
from one other which was withdrawn (Harley 2004), and he also used an early prototype
of stochastic synthesis in parts of La Lègende d’Eer (Brown 2005; Di Scipio 2005;
Hoffmann 1996; Luque 2009; Xenakis 2005). I, and some others, treat Dynamic
Stochastic Synthesis as a particular type of instruction synthesis, although it works at a
much higher level than computer instructions (that is, it is about waveform segments and
not directly about computer instructions) and Hoffman describes it as a type of ‘abstract
synthesis’ (Doornbusch and Hoffmann 2010), however the distinctions are fine. This
class of synthesis is also sometimes called ‘non standard synthesis’ (Luque 2009).
Instruction synthesis is a type of synthesis that generates sound through
mathematical functions or direct computer instructions, and it has no relationship with
the real world physics of sound or synthesis (Roads 1995). Thus, instruction or non-
standard synthesis generates sounds which are idiomatic to the computer (Berg 2009),
which cannot be generated in another way, and which are not related to the real world or
physically generated sounds, as Berg explains (1979b, p. 30), “… computers produce and
manipulate numbers and other symbolic data very quickly. This could be considered the
idiom of the computer and used as a basis for musical work with the computer.” The
sounds created by instruction synthesis are fundamentally different in character than
those created with rule-based synthesis; it is a highly abstract approach to sound
synthesis and may be highly unpredictable. As Curtis Roads elegantly states, “the point
((((((((((((((((((((((((((((((((((((((((((((((((((((((((no problems finding structure in his works through a “composed attitude to listening” (Brün 2004, p. 36).
Mapping in Algorithmic Composition and Related Practices 75
of instruction synthesis is that the sound is specified exclusively in terms of logical
instructions, rather than in terms of traditional acoustical or signal-processing concepts,”
(Roads 1995, p. 328). This is significant because it forces the synthesis technique to be
separated from physical concepts of sound production, such as the vibration of air
columns, strings and wood, and brought into the realm of the abstract, without any
concept of the physical world external to the computer, and thus the composer is free to
indulge their creative will in sounds hitherto impossible to create.
There are several other varieties of instruction or, non-standard, synthesis, most
notably from the Institute of Sonology; SSP (Sound Synthesis Program) (Berg 1978b;
Berg 1979a), ASP (Automated Synthesis Program) (Berg 1975), and PILE (Berg 1978a;
Berg 1979b). Herbert Brün also developed an instruction synthesis program named
SAWDUST (Roads 1995), which had similarities with Koenig’s SSP. Some of these,
particularly SSP and SAWDUST, are considered abstract synthesis by Hoffmann
(Doornbusch and Hoffmann 2010), as a fine differentiation from instruction synthesis,
but I will not make that fine distinction here. Peter Hoffmann, from 1995 to 1997,
conducted a research program around the working of Xenakis’ GENDYN program (in
Paris and with Xenakis’ blessing) and developed a working version that would run on
modern computers (Hoffmann 1996; Hoffmann 2009).
I obtained a copy of this program from Hoffmann late in 1997 (for which I owe a
debt of thanks), and spent several months familiarising myself with it to the point where I
could begin experimenting with ideas for a new piece. I was very conscious, when
working with Hoffmann’s version of Xenakis’ program that I wished to do something
original with it. I had first heard Xenakis’ GENDY3 in the early to mid 1990s and it was
a revelation. I was immediately attracted to that sonic world, that synthesis technique
which bore no relationship with the physical world, and that seamless integration of
sound synthesis and musical form. Musical composition is traditionally seen as
constructing musical form, but in electronic and computer music, sound synthesis is as
much composition (on the micro scale) as is constructing the narrative arch and form of
the piece – the sound of the work is the music. So while I did not want to imitate
Xenakis’ work, I did want to engage with the same ideas and synthesis technique at least.
I am not alone in this of course, and many other composers, some mentioned above, have
built non-standard synthesis systems for their own use, but here was an opportunity to
Mapping in Algorithmic Composition and Related Practices 76
use something that I did not have to spend time building – it was an irresistible
opportunity. It took many months of experimentation and research to understand how
various parameters affect the sound and output, to reach a point of familiarity such that I
could construct a piece which reflects my aesthetic and ideas.
There are ten different layers (or ‘tracks’ as they are called in the GENDYN
software) in G4, each with a different individual sound. Each of the ten sounds on the
tracks were chosen with much care and an arduous amount of trial-and-error
experimentation, to discover and determine sounds which match both the aesthetic and
mapping functionality I desired. These sounds come and go at random times, as is
(randomly) determined by the structural aspects of the software. The individual tracks
have sounds as described below, and there is a CD, titled G4 Samples, included with
approximately thirty second examples of each sound:
• Track 01: Low frequency noisy sound, slightly muffled and with a slight buzz to
it.
• Track 02: Low frequency, slightly noisy and more muffled than track 01, and
buzzier.
• Track 03: Mid frequency, slightly buzzy or sounding like a square wave (many
harmonics), the main pitch changes a little and there is some modulation.
• Track 04: This is a complex sound; there is a low frequency sound like a distant
motor but with a higher frequency modulated noise, and there is also a high
frequency noisy and highly modulated sound (this is not unlike track 07).
• Track 05: This is somewhat like track 02, but quieter and this is less muffled and
with less low frequency, but it still sounds somewhat like a motor with the sound
modulated by a low frequency (lower than track 02).
• Track 06: A noisy sound with a frantic-sounding, frequency and amplitude
modulated mid-to-high pitch. It is highly recognisable in the piece and it often
disappears for long periods (low density in the track). Almost all of the silences
have been shortened in the example on the CD.
Mapping in Algorithmic Composition and Related Practices 77
• Track 07: High frequency sound, somewhat noisy, and highly modulated mostly
in the frequency domain, so that it sounds like frantic whistling. It is also highly
recognisable as the opening sound of the piece.
• Track 08: This is a low frequency sound, very rich in harmonic content, it is very
buzzy and there is some frequency modulation but little amplitude modulation.
• Track 09: An intense low frequency buzzy sound with many harmonics. There is
a small amount of modulation.
• Track 10: This is another high frequency, slightly noisy sound, and it is frequency
modulated to frantic extremes making it sound like mad whistling. There are
some additional sounds there too, somewhat like short wave radio ‘static’.
The overall structure of G4 can be seen graphically in the screen shot of the software
below in figure 21. The density of activity of the beginning, middle and end of the piece
can clearly be seen, as can the overall timing, the changes in overall density over time
and so on.
Figure 21. Screenshot of the structure of G4, showing its density and part changes.
Mapping in Algorithmic Composition and Related Practices 78
The aesthetic of G4, as per most pieces using instruction or non-standard
synthesis, is more exploratory in nature than my other pieces. While I use randomness in
all of my compositions (a few obvious examples; in the signal processing in Continuity 3,
in details of the instrumental part in Continuity 2 and ACT 5, and in the vocal part of
Strepidus Somnus), G4 is the only piece in which elements of the form are controlled by
random processes. At 11:35 in length, G4 is neither a very long nor a very short piece,
and on first listening it sounds rather monolithic in structure, but there are ten sections,
largely delineated by when a prominent sound starts or stops. The sections are as
summarised in table 1 below, with timings to the closest second:
Time Dur. Name Description 00:00 – 00:21 00:21 Section 1 Introduction: High-frequency, modulated, noisy sounds
only for the first half (track 07), then low-frequency noisy sound (track 01) at several amplitude levels and with some modulation, along with modulated high-frequency whistling sounds (track 06) and a modulated midrange noisy sound. A stronger low-frequency buzzy sound (track 09) enters just before the section ends, with a half second silence.
00:21 – 02:22 02:01 Section 2 All of the sounds from Section 1 continue, but at 00:21 the dominant low-frequency sounds of tracks 02 and 09 along with the whistling sound of track 10 are added. At 00:36 (14” into the section) the piercing sound of track 03 enters. A few seconds later, all of the sounds are in play, and the piece becomes a writhing maelstrom of sound. Now that all of the sounds, or tracks, are playing, they randomly enter and depart according to the parameters (number of fields, density and activity) that set the structure or architecture of the piece.
02:22 – 02:51 00:29 Section 3 Several of the sounds drop out for this section, and the amplitude of most sounds reduces significantly, sometimes to almost being inaudible. The sounds most prominent, initially, are; track 06, track 09 and track 07. Later, other sounds enter, but all at reduced level.
02:51 – 03:44 00:53 Section 4 This section is at a louder level than the last, and again the piercing sound of track 03 is prominent as the other sounds come and go and the piece again turns into a turbulent torrent of sound.
03:44 – 04:52 01:08 Section 5 Most of the upper-frequency sounds drop away leaving a low-frequency basis for the start of section 3, which is mostly track 08 and track 10. Tracks 05 and 06 also enter later, and later still tracks 02 and 10 are again prominent. Tracks 10, 06 and 05 end the section, with a moderate volume reduction in the tension and energy in the sound world.
04:52 – 07:08 02:14 Section 6 Track 03, the piercing one, and several low-frequency sounds, which also provide low difference tones, make a sudden and prominent start to section 6. Most of the other sounds re-enter and it is similar to section 2.
Mapping in Algorithmic Composition and Related Practices 79
Time Dur. Name Description 07:08 – 08:36 01:28 Section 7 After most tracks from the previous section drop out, this
section starts with a combination of sounds like the second half of section 1. This continues for approximately 22” and it becomes much like section 4 with another frenzy of activity and track 03 prominent. Most sounds drop out to end the section.
08:36 – 09:35 00:59 Section 8 This section is much like section 5, with a little less activity. The piece ends with some short and prominent blasts of the low-frequency sound of track 05.
09:35 – 10:38 01:03 Section 9 An apparent recapitulation of section 1 starts section 9. Half way through the section track 09 enters prominently and it dominates until the end as most other sounds drop out.
10:38 – 11:35 00:57 Section 10 Silence, only the second one in the piece, starts section 10, but only for half a second. The beginning is dominated by the sound of tracks 06 and 01, quietly, and track 07 (energetic high-frequency sounds). Most sounds drop out later, leaving track one, with track 06 making a couple of appearances before track 01 alone, with increasing silences, conclude the piece as it splutters to an end.
Table1. Details of the sections and structure of G4.
This primarily descriptive deconstruction of G4 is offered to the reader as a
mapping of that which is intrinsically and inherently sonic and intensely experiential into
words – words which are chronically inadequate to the task of translating a complex
aural experience into a, potentially inelegant, understanding. However, this simple
tabular deconstruction is also meant to provide the reader with insights, and reference
points, for listening to the piece and into the compositional process of using sound itself,
in ways more commonly associated with how a painter uses paint or a sculptor shapes
materials, to express an artistic intent. In this illustration a palette of distinctive sounds,
some with variations, was specifically created with which to work in pursuit of the
compositional intent – which was to create a fresh, unusual and compelling work of aural
art, a piece of music which arises from the minimum number of assumptions and
instructions, using unusual sounds which are idiomatic to the computer.
This rather distinctive way of working, where not only the sounds but the
boundaries of the sound sections and timings are determined through stochastic
processes, gives rise to questions of compositional intent and form. There are concepts of
musical thought in which form emerges, or arises, secondarily from the rule-based
generation of material (Berg 2009) or during the act of listening (Koenig 1987, p. 171),
and the concept of form in G4 fits into this category. This is a characteristic of most of
Mapping in Algorithmic Composition and Related Practices 80
the output from non-standard synthesis systems, and it was investigated intensely at the
Institute of Sonology during the 1960s and 70s (Berg 2009; Koenig 1987), when much
successful research into non-standard synthesis was undertaken. This is an aesthetic
position of many of the researchers at that institution, and one which influenced me
greatly during my years there as I found it refreshing, liberating, and in congruence with
my (then) largely unformed thoughts on this. Koenig (ex collaborator with Stockhausen
and Director of the Sonology Institute) held this view, which pervaded the Institute of
Sonology and he expressed it in writing:
Form as I see it – especially in the post-1945 New Music – is not the result of an
auditory process, like feeling full after a meal. It is, rather, the way in which music
is experienced in time; a piece of music may seem to have more or less form
according to the listener’s mood, concentration and susceptibility to form, and may
also appear as a different kind of form – except of course for pieces which are well-
known and already classified. (Such classification, however, tends to impede an
open-minded new evaluation or new experience). I experience form as a process as
soon as I start working in the studio or at my desk; every bar on paper, every sound
on tape changes its formal function every time I look at it, like the light in a
landscape under scudding clouds. I rarely hear a work twice in exactly the same
way, as identical. (Koenig 1987, p. 171)
Later, Koenig adds:
“…[form] also emerges when musicians improvise, form always being both desired
and born, desired by the composer, born during the performance” (Ibid, p. 172).
Thus, as explained by Berg (2009, p. 77), form appears or, “… emerges during
planning and realization”. I was clearly influenced by these ideas during my years at the
Institute of Sonology and while elements of this pervade my musical output, G4 offered
the chance to work with, investigate, and enjoy these ideas of form to their fullest.
Another influence from the aesthetics of the Institute of Sonology, which I acknowledge
in my work, and which is prevalent in G4, is that it has a, “crunchy surface structure
common with many sonological activities” (Ibid, p. 85). Non-standard synthesis is
known for having noisy, sometimes chaotic and ‘crisp’ or ‘brittle’ sounds, however this
was also part of the aesthetic of the Institute of Sonology during my time there.
Mapping in Algorithmic Composition and Related Practices 81
This prevalence of ‘crunchy’ sounds at the Institute was the result of a confluence
of several factors. The Dutch electronic music scene wanted to distinguish itself from the
two main European forces in the field, France and Germany, and there were, at least
initially, regional characteristics to the sounds coming from them – the German studios
pioneered a purist approach to synthesising sounds from fundamental principles, and the
French studios were known for the quality of their productions with pristine, clear and
sometimes glass-like sounds. While these distinctions had decayed somewhat by the
1960s and 70s, there were still elements of their original characteristics in French and
German compositions. In addition, American studios were predominantly practicing
offline synthesis with digital models (typically with MUSIC V and derivatives) on large
computers. The Institute of Sonology under Koenig in the late 1960s and 1970s wanted
to distinguish itself from the French, German and American studios. Firstly it established
a different aesthetic based on Koenig’s algorithmic composition work, in which he
abstracted his composition process and made programs (PR1 and PR2) which translated
this process into compositions, so that he had rule-based generation of musical structures
with a variety of compositional and musical approaches. Koenig also started to develop a
sound synthesis program (SSP) in which shapes were concatenated as waveform
segments in real time, because the computer at the Institute had very little memory to
store or process digital data and this was the most viable and efficient synthesis technique
on such a computer. As explained in one of my book chapters, “SSP used compositional
selection principles to assemble individual elements of waveforms and larger-scale
composition structures” (Doornbusch 2009c, p. 60), and these compositional selection
principles were not unlike those in PR1 and PR2. SSP was one of the first non-standard
synthesis programs, and others were developed subsequently, for example ASP and
PILE, as previously outlined. Thus, the rule-based generation of musical structures had
moved from the macro level (form, phrases and gestures in musical pieces) to the micro
level where it became the rule-based generation of sound structures (sound synthesis). A
characteristic of non-standard synthesis is a crisp and ‘crunchy’ sound, as mentioned
previously, and this was accentuated by the details of the synthesis system which used a
12-bit DAC15, where often the smoothing-filter, which is on the output of the DAC to
((((((((((((((((((((((((((((((((((((((((((((((((((((((((15 The smaller the bit-depth of the digital-to-analogue converter (DAC), the less ‘fidelity’, noisier and ‘crunchier’ is the sound. CDs use a 16-bit encoding and playback system, which is very common on computers now.
Mapping in Algorithmic Composition and Related Practices 82
smooth out the square, digital, waveforms, was disconnected. Clearly, “smooth was not
part of the concept” (Berg 2009, p. 81). It can be appreciated how being immersed in the
compositional milieu of such an institution, even a decade or more after these events
were new, might influence a composer such as myself who was hungry for new and
original ideas and knowledge.
In the previous paragraphs I have mentioned ‘compositional process’ without
defining it. However, there are varying attitudes as to what constitutes the ‘composition
process’, and understanding this is obviously important in such a piece which uses
randomness. Koenig, engaging with the same issues, investigated this:
Opinions differ as to what a composing process is, there being all gradations
between constructive and intuitive composers. Investigations in the field of
programmed music can only be expected from composers who already have highly
constructive inclinations or previous knowledge or, although keener on free
expression, want to discover a new realm of experience. (Koenig 1978, p. 111)
In addition, Koenig discusses the elements of a composer interacting with a computer
program during the process of composition:
… even in composing programs the composer is still chiefly responsible because
he must at least prepare the data on which the composition process basically
depends, if he does not in fact also write the program himself. (Ibid, p. 110)
Thus, even though many elements of the piece G4 are produced by stochastic processes,
or controlled randomness, I decided on all of the input parameters, and in conjunction
with a feedback process I was able to select these to achieve the aesthetic result I desired.
The concepts of mapping in G4 relate strongly to Xenakis’ ideas of music out of
nothing, how things may come into existence from nothing by the random fluctuation of
a few points, and how this is a model for the ‘big bang’ of astrophysics or other theories
for the origin of the universe. As Xenakis explains (1992, p. 260), “What is extraordinary
is that both propositions, Big Bang or not, admit a beginning, an origin from nothing, or
nearly nothing with, however, cycles of re-creation!”
Mapping in Algorithmic Composition and Related Practices 83
Engaging with the tools of another composer, I found, put me in a difficult
psychological position. For example, I wondered, how much of this work is my
composition and how much is Xenakis’? Hoffmann notes (2009) that G4 is only the third
piece, and the first since Xenakis, to be made with pure dynamic stochastic synthesis.
Perhaps the issue of engaging with another composer’s tools has also disturbed others, or
perhaps other composers find it difficult to engage with a process where they relinquish
so much control (more on this later).
However, after careful consideration, I believe the composition G4 is much more
a reflection of my artistic intent than it is a mere product of the creator of the tool, or the
ideas and system behind it, as I had to very carefully choose the type of stochastic
distributions and parameters for the sound synthesis of each track, and then equally
carefully choose the overall formal parameters for these tracks to create an acceptable
aesthetic result. Essentially, I took advantage of the affordances of Xenakis’ tool
(through Hoffmann’s reconstruction of it) to express this intent – to create a sonic
representation (mapping) of what might best be described as the birth and death of an
imaginary universe in miniature. In addition – I feel that if one wishes to engage with
these ideas, ideas which might bring about ‘music out of nothing’ and ‘music from the
minimum of assumptions’ – then one must relinquish some of the desire to control every
miniscule parameter. While the same may be said of all algorithmic composition
practice, and it is true for all of my pieces in one way or another, I found it most obvious
when working on the construction of G4. One aspect of relinquishing control with
Gendyn which feels more acceptable, is if it is approached as an instrument which might
be mastered to a greater or lesser degree. In this way the tool may be approached as an
opportunity to investigate its sound world, possibilities, and to explore its limits
Relinquishing control over many parameters in the construction of a piece of
music is, in some ways, anathema to the way many people imagine the act of
composition. How can the composer communicate their intentions if they do not have
complete control? Herbert Brün notes just this point in an essay on Schoenberg:
The composer wishes to bring about that which without him and without human
intent would not happen. In particular, he wishes to construct systems, contents,
stipulated universes, wherein selected objects and statements manifest not only
Mapping in Algorithmic Composition and Related Practices 84
more than their mere existence but have a function or value or sense or meaning
which without his construction they would not have.
Occasionally a composer brings about that which without him and without human
intent could not have happened. (Brün 1973, p. 37)
There have been many others who have already investigated this idea of
relinquishing control over elements of the composition, and using chance – most
famously by John Cage (Apel 1969), but also others to varying degrees such as G. M.
Koenig (Roads 1995), Iannis Xenakis (Ibid), Herbert Brün (2004), Henry Cowell (Apel
1969) and even earlier composers such as Mozart (Hiller and Isaacson 1959) and more.
So it is certainly not a new development, but the act of musical composition usually
contains the idea of closely delimited organisation and control. With instrumental music,
this level of organisation is of course an illusion as part of the pleasure of such music is
that each performance is, however subtly or radically, different as the performers or
conductor interprets the score and the artistic intent of the composer. This means such
controlled ideas of composing instrumental music are also illusory, although electronic
music may come close to this dogged demand for complete control, but even then the
playback space and circumstances may dramatically influence the result. Note also that
‘perfect’ renditions of classical music by computers, while technically possible, are not
interesting or popular amongst audiences, as it would seem the deviations from
‘perfection’ are somehow interesting16. However, organisation implies, and is
accompanied by, meaning and meaning making. It is the desire for meaning, and the
perceived or potential mess resulting from the relaxation of control, that seems to be
contradictory because mess and disorder resists meaning. As previously mentioned, there
is a line of musical thought which contends that musical form (and thus meaning) can
arise from the rule-based generation of material, and this obviously creates order from
chaos. There are interesting parallels here between music, psychoanalysis, and radical
constructivism. In psychoanalysis, the analyst attempts to make order and meaning out of
((((((((((((((((((((((((((((((((((((((((((((((((((((((((16 Despite this and as a side issue, Derek Bailey’s (1992) BBC documentary on improvisation conversely suggests that modern audiences have an expectation based on specific, known, recordings and this undermines the acceptability of improvisation even when the score calls for it. It might be possible that the audience might be hoping for a performance to exceed their prior experience, but this is not explored by Bailey.
Mapping in Algorithmic Composition and Related Practices 85
the mess and disorder presented by the analysand. Phillips discusses this in relation to
literature:
All psychoanalyses are about mess and meaning, and the links between them; about
the patient's and the analyst's relationship to disorder, and their mostly unconscious
fantasies of what disorder might entail, something orgiastic, something violent,
something inchoate, something longed for and feared. If our lives have a tendency
to get cluttered, apparently by themselves but usually by ourselves, most accounts
of psychoanalysis have an inclination to sort things out. A kind of pragmatic
clarity is considered a virtue in psychoanalytic writing; it always has a how-to
ingredient as though its genre was the instruction manual. The raw material of
psychoanalysis — the unconscious desire that is personal history — may be wildly
unreasonable, but there are eminently sensible vocabularies for summing it up.
Psychoanalysis […] aims to clarify things; it is impressed by the lucidity it
promotes without acknowledging that this supposed lucidity is itself an effect of
language. Psychoanalytic theory — and indeed, its highly ritualized practice — has
an aversion to clutter. […] And yet, in all its versions, it promotes the intelligibility
of system; it repudiates chaos.
So, in the inevitable to and fro we might prefer between idealizing order and
idealizing disorder, clutter has rather an ambiguous status. It has the paradoxical
implication of being something which may have no intrinsic or discernable order or
pattern, and yet of being something that people make, wittingly or unwittingly,
determinedly or helplessly. It invites us, in other words, to do something puzzling,
or even uncanny; that is to make meaning […]. (Phillips 2002, pp. 59 - 60)
That last statement by Phillips, that clutter, mess or disorder invites us to make
order and meaning, has several resonances with constructing musical form through
listening. It has been documented that musical works which are too obvious can be
perceived to be boring because it is a characteristic of musical listening (at least for what
is called ‘art music’) that the listener typically ‘explores’ the piece for structure (Copland
2009; Levitin 2006). So it would appear that at least some disorder or mess is required
within a piece because, as humans, we want some complexity and often desire something
unexpected (Levitin 2006). This is also supported by Simon comparing the aesthetics of
Mapping in Algorithmic Composition and Related Practices 86
mathematics and music, “The aesthetics of natural science and mathematics is at one
with the aesthetics of music and painting – both inhere in the discovery of a partially
concealed pattern,” (Simon 1996, p. 4), so uncovering a hidden pattern reveals the
unexpected. This may raise a question about the reaction to such a piece by a lay
audience, and for G4 this is a valid point as it may be impenetrable to an average listener.
I have not found this a problem with my other pieces, as non-music-educated listeners
have thoroughly enjoyed them, but G4 may superficially appear to have so much disorder
that an average listener has difficulty appreciating it without uncharacteristic
concentration.
Clarity and lucidity are typically regarded as positive attributes in musical
composition. Much of this thesis has been tied up with explaining and clarifying my
musical thinking in the act of algorithmic composition, and the part that mapping plays in
that process – implying an overarching intellectual and cognitive orderliness, which
perhaps camouflages and hides a more chaotic substrata of compositional effort. While
these ideas on psychoanalytic thinking about chaos and mess, and those on radical
constructivism that follow shortly, may apply to all of my works, G4 is perhaps the most
opaque, messy and difficult piece (of those analysed in this thesis) to explain for a
number of reasons as already outlined. In many respects the piece must speak for itself in
the language of its making, as written words and the English language are inadequate –
as noted by Hayakawa, “Every language, like the language of the thermometer, leaves
work undone for other languages to do” (Hayakawa 1995, p. 9).
In the extended quote from Phillips above, he notes that while psychoanalysis is
impressed by the lucidity it promotes, that it does so, “… without acknowledging that
this supposed lucidity is itself an effect of language,” (Phillips 2002, p. 59). As much as
language is a function of cognitive processes in the brain, it can be argued that the
lucidity is an effect of the brain’s self-organising cognitive processes. Just this point is
argued by Heinz von Foerster (2003, p. 225):
The environment as we perceive it is our invention, [… because] the nervous
system is organized (or organizes itself) so that it computes a stable reality.
Mapping in Algorithmic Composition and Related Practices 87
Foerster was influential in the disciplines of second-order cybernetics and radical
constructivism. He was also a colleague and long-time friend of Herbert Brün. According
to Foerster, we tend to construct our own realities and acquire knowledge through
recursive computations and original input, which is regulated by our own interests. More
directly, Foerster (2003, p. 213) states, “Perceiving is doing!” Thus, from the perspective
of radical constructivism, when in the act of listening, the listener makes order, clarity
and connections in a ‘messy’ piece of music they are engaging in radical constructivism,
demonstrating that we make our own reality in our head. This aligns with Koenig’s ideas
as outlined above (Koenig 1987), that form emerges while in the act of creation or
listening.
The connection between radical constructivism and non-standard synthesis has
been made previously by others (Brün 2004; Di Scipio 2002; Döbereiner 2009; Supper
1997), and this same connection is also valid for G4. Nothing present in G4, neither the
sounds nor the structure of the work, had any prior existence before I composed the
piece, which sought musical organising principles and production techniques that were
unified. It is certainly an artificial and invented model, and in that way it is exploratory in
nature, investigating sound synthesis and compositional techniques in a unified manner,
being unique and idiomatic to the computer, such that relationships can be constructed
and discovered.
While the connections between radical constructivism and listening to create
order or form seem direct, I believe the connections made here between compositional
practice and psychoanalytic practice have not been recognised previously. However, it
seems reasonable to infer that the characteristics of psychoanalytic practice, as outlined
by Phillips, are congruent with the philosophy of radical constructivism, and thus
applicable to music in the ways mentioned in this chapter. Perhaps, for composers, a
psychoanalytic take on this concept of making meaning from mess or chaos is of more
potential use, as often the practice of composition is cathartic for those involved. The
product of such practices would, as noted by Phillips (2002, p. 60), invite us “to do
something puzzling, or even uncanny; that is to make meaning.”
Further research revealed that connections between psychoanalytic practice and
radical constructivism have been noted previously by practitioners in those two fields
Mapping in Algorithmic Composition and Related Practices 88
(Aron 1996; Brodbeck 1995; Gill 1994), however, it does not appear that anyone has
identified a similar connection to the discipline of music or composition. Berg’s assertion
that form can arise from rule-based generation of material (Berg 2009) is also consistent
with the position of radical constructivism. Taking these various threads into account, I
would contend that the elements of mapping in G4 occur in two areas. First, there is the
mapping of artistic and aesthetic intent to sound, and this is arrived at via the process of
adjusting the initial formal and sonic parameters, examining and iteratively adjusting and
readjusting the result. The difficulty of working with such a system was noted by Berg in
relation to PILE, “A more challenging aspect was the heuristic nature of the working
process” (2009, p. 83) – that is, Berg was implying that the composer has insights into
the work that are quite literally a product of the work itself. This somewhat recursive and
tautological idea of creative work being the product of creative work is consistent with
my own compositional practice. I found the feedback process afforded by such an
approach completely necessary due to the stochastic and heuristic nature of the system.
The secondary mapping occurs in listening to the work, where there is a cognitive
mapping for meaning, order and constructing form, as well as an embodied meaning,
which is the product of the listening experience.
When working on the basic sounds of G4, I can confidently say that form was
apparent when listening to the individual tracks as I generated various sounds for
potential use. Thus, while engaged in the process of generating sounds for an aesthetic
intent, form was apparent, or emerged. This parallels Berg’s (2009) and Koenig’s (1987)
claims about form as outlined above. However, at this distance in time from the
composition of G4, I cannot tell if I found form cognitively in the generated material,
through psychologically wanting to find order amongst the ‘mess’, or by some other
means. It appears likely that the parallels I am drawing between psychoanalysis and
radical constructivism represent different ways of understanding the same phenomena –
so perhaps we need yet another discipline to emerge, or disciplines to converge, to
properly understand these phenomena.
The second mapping in G4, as mentioned above, occurs when listening to the
work. I am listening to the piece as I write this now, and must admit that I am still
fascinated by the sounds and their interplay. I am delighted and surprised when I notice
particularly interesting or engaging juxtapositions of sounds. I can easily imagine that I
Mapping in Algorithmic Composition and Related Practices 89
am constructing form at this moment, I am listening to a rather sustained, ‘nasally’
sound, and then it disappears leaving a writhing and rustling in its wake. I can also,
without difficulty, imagine that this is different for each listener and perhaps different for
an individual at different times of the day, or moments in their life. As I continue
listening, I am struck by the forcefulness and relentlessness of the piece – a mapping of
the inevitability of the progression of the (perhaps micro and artificially modelled or
constructed) universe; the expansion of space and time (at least to me). Berg mentions at
the end of his paper that, “The awareness of the compositional significance of
programming material, in particular as part of the process which creates musical form, is
deserving of continued attention,” (Berg 2009, p. 86) a claim with which I can only
concur. This last aspect of the piece does not occur when I listen to some other aleatoric
works, for example Cage’s Williams Mix (Cage, Carmen et al. 1959), which is so
aleatoric as to eschew form – yet when I listen to it I always hear some sort of form,
although not the relentlessness and inevitable progression I noted above in G4. So, while
form may be an emergent property from the act of listening to music, it is clearly
different for different pieces. I cannot say definitively what process is occurring within
my own mind when I listen to G4 (or experience any other artistic work), but at the
moment, while listening to G4, I certainly seem to be internally constructing form (or it is
emerging from the sounds), untangling the ‘mess’ of sounds which impinge upon my
aural senses, and making maps within my mind for meaning. Perhaps this is the only
response humans are capable of when confronted with music that emerges from the
minimum number of assumptions.
Mapping in Algorithmic Composition and Related Practices 90
4.5 Mapping in Strepidus Somnus
The note below from the CD booklet for Strepidus Somnus outlines the gist of a
somewhat surrealist composition and performance – the performance although briefly
described in the note remains invisible to listeners of the CD, although the picture in the
CD booklet, and later in this essay, gives some idea of the impact of the piece live:
Strepidus Somnus (noisy dreams) is a journey through a vocal and electronic
foreign landscape. Scored for four singers (SATB) and short-wave radio based
electronics, each section is a transition from one state to another. The vocal
sections occur in four languages simultaneously (Dutch, English, German,
Portuguese) and they are [here listed for clarity]:
1 - No sound, to some sounds, half vowels, vowels, fricatives, parts of words,
whole words parts of sentences, whole sentences;
2 – Conversation to sex;
3 – Grief to singing;
4 – Single notes to melody;
5 - Vocalised noises to conversation;
6 - Interspersed whispered text and laughter, where the text becomes
progressively more intelligible but nonsense English.
Interwoven with the vocal part, the electronic part is based on and sourced from
short-wave radio sounds. It sometimes pre-empts the textures to come and
sometimes follows them, excitedly bubbling along with the vocals. Despite the
extreme difference between the voices and the electronics, they have equal weight
in the piece and where the vocal part moves in its transitions the electronics will
change in density and texture, in a form of counterpoint which is in response to, or
leading, the vocals. The beginning of each of the whispered sections of text is
below:
waschedge ad fathttcrry he o parer? ter ce ralo ts Rane grsthado wsoing
He, Landolf me I’ttt!
ng side and gethe roof lips. I the went of lying in a Jack-in-the her was
voice alled that’s Bill she fanned thing.
By that the was quite othey’d one of what it it she one outside a came ther
up at a, any make it said turned a grow support.
Mapping in Algorithmic Composition and Related Practices 91
hat’s that !” “But the chimney, and now about like a Jack-in-the-box, and
stop to ready for the began shriek and the trembled
Alas! it was a bright idea came rattling messages for a Bandy now had lost
something, and so indeed, as sure to herself . . . (end) Whenever I eat her
without knocking, but nevertheless she cakes, she was it, trotting together.
The piece finishes with laughter, a celebration of the voice and the playfulness of
the piece. In performance, the four singers are spread across the front of stage, two
metres apart, and they receive directions through hidden earpieces. They wear
costumes of black rubber butcher’s aprons, beneath which they appear naked. In
bare feet, on a red swatch and bathed in red light they have an unsettling
appearance. At times the voices sound surreal and the electronics sound familiar,
an unexpected interchange amongst many others.
Strepidus Somnus (1996) is Latin for ‘noisy dreams’, which is one of the themes of
this piece along with mapping vocal transitions from one, sometimes extreme, point to
another. There is a long tradition of works with voice and electronics. Stockhausen’s
Gesang der Jünglinge of 1956 (Stockhausen 1991), Berio’s Visage of 1960 (Berio,
Berberian et al. 1970), and Luigi Nono’s Contrappunto dialettico alla mente from 1968
(Nono, Guevara et al. 2006) are three notable examples of pieces for voice and
electronics, but these are all tape works and cannot be performed live in the manner I
wished for with Strepidus Somnus. From earlier vocal writing, I wanted to compose
something for this combination of sonic possibilities (vocals and electronics). Voice is
perhaps the first and most natural musical instrument, and it is certainly the most human.
Electronic sounds could be considered the least natural and the antithesis of a musical
instrument, and particularly shortwave radio ‘static’, which suggests nostalgia and can be
related to the earliest practice of electronic music. I wanted to unify these two extremes
of musical expression in my composition, and there is a link as radio is a carrier of voice.
The vocal structure of Strepidus Somnus is broken into six main sections (see table
2 below), with short silences between them, and the last section is in six sub-sections.
Mapping in Algorithmic Composition and Related Practices 92
Section Time Dur. Transition description
1 00:00 – 03:49 03:49 No sound, to some sounds, half vowels, vowels, fricatives, parts of words, whole words parts of sentences, whole sentences.
2 03:49 – 05:25 01:36 Conversation to sex.
3 05:25 – 07:38 02:13 Grief to singing.
4 07:38 – 12:52 05:14 Single notes to melody.
5 12:52 – 15:37 02:41 Vocalised noises to fractured conversation.
6 15:37 – 19:04 19:04 – 20:30 20:30 – 22:05 22:05 – 23:11 23:11 – 26:33
10:56 Interspersed whispered, heavily distorted text, and laughter, where the text becomes progressively more intelligible but nonsense English, over 5 sub-sections.
Table 2. Structure and vocal parts of Strepidus Somnus.
The electronic part functions as a counterpoint to the vocal part, but it is a
counterpoint of tonal dimensions, of transformations and shifting timbre. It has been
understood for many years that electronic music articulates form through timbral
variation (Licata 2002; McHard 2006), and the counterpoint of timbral variation in
Strepidus Somnus also contributes to the articulation of form along with the vocal
transformations. Thus, the electronic part functions with equal importance with the
vocals and sometimes overwhelms the vocal part such that it disappears under a
turbulence of electronic sounds and re-emerges again later. One sometimes strains to
hear the vocals, buried under the electronics. The listener tries to hear snatches of what
the voices are saying, similar to a dream, or when waking from a dream and struggling to
remember what was said or what happened.
There was a notation challenge with the vocal part as there is no notation with the
facility to adequately cover the range of vocal expression. I investigated the very
advanced notation used by Ligeti in Aventures (Ligeti, Leonard et al. 2004; Ligeti,
Maderna et al. 1970) and Wishart for the Vox cycle (Wishart 1993; Wishart and Electric
Phoenix (Musical group) 1990; Wishart and Emmerson 1996), but neither was precise
enough or covered what I needed to notate. Eventually I settled on a procedure whereby I
recorded the performers onto tape speaking, vocalising and singing, and later assembling
Mapping in Algorithmic Composition and Related Practices 93
sounds from the recordings into a part for each singer. This was played back from a
multi-track tape and each singer would hear their own voice in their left ear and copy it17.
This proved to be particularly effective at keeping the singers in time and getting the
vocal utterances as coordinated as I wanted them to be in live performance. It should be
noted that the vocal part is in four of five languages simultaneously, as a way to
concentrate on the sound of the voices instead of the semantics of the utterances. The five
languages are; English, Dutch, German, Portuguese, and Danish, because these were the
languages other than English known to the singers. I wanted to use the vocal sounds
themselves, and to avoid the audience listening for meaning, I used a melange of
languages to achieve this.
The main components of the electronic part are shortwave radio sounds; often
recorded and manipulated to create transformations that were not possible in real time.
The transformations typically make sonic gestures with an expressive arch, often over
many seconds, which form a natural balance and counterpoint with the high-frequency
crackly sounds from short wave radio static. There are also moments of voice over the
radio, and while much of this is transformed, not all of it is, and the snippets add a level
of coherence between the electronic sounds and the vocals.
Strepidus Somnus is a significant work at just over twenty-six minutes in length.
While not initially intended to be a study in continuity and fragmentation, upon reflection
there is a significant degree of this opposition in the work and this realisation led to it
becoming a major focus in my later works. Deconstructing in detail such a work may be
interesting and potentially revealing, but is unlikely to lend much to the discussion of
mapping, which will be better served by a description and brief analysis of each section
which appears below:
Section one (duration 3’49”) starts with electronic sounds which build and pulse
slowly before the voices come in with some random noises some seventeen seconds into
the section. The vocals soon start practicing vowel sounds, and fricatives, gurgles and so
on, as if for the first time ever, exploring what sounds are possible with these ‘new’
voices. The electronics now become layers of overlapping gestures, some short and some ((((((((((((((((((((((((((((((((((((((((((((((((((((((((17 I had seen this idea used earlier in a piece by Robert Ashley titled eL/Aficionado.
Mapping in Algorithmic Composition and Related Practices 94
long (like fricatives and vowels), along with unprocessed shortwave radio sounds. The
four vocal parts operate at different rates of development (forming a kind of counterpoint
amongst themselves) and a few seconds later one of the voices is making parts of words
while others are still trying to master the sounds. At 1:57 there is an event in the
electronics, a long low-frequency gesture, which results in most of the voices being able
to make parts of words (in four languages simultaneously). Shortly after this gesture,
there is an interplay of similar gestures and frequencies between one of the voices and
the electronics, as if mimicking each other. By 2:49, most of the voices are able to make
whole words and parts of sentences. As the vocal ability develops there is suddenly a
radio voice heard through the electronic part at 3:13, and this spurs another development
in the vocal part such that over the next 33 seconds to the sudden end of the section, the
voices develop to the point that they can articulate complete sentences. The sudden stop
at the end of this first section, in performance, is an event that immediately shocks the
audience and demands their attention. My purpose with this combination of gestures was
to introduce the ideas of primal and rudimentary vocal sounds, and how they may be
combined. The counterpoint between the voices bubbles along like a group of
conversations, from primal sounds to conversation, where some parts reinforce each
other and others oppose. Electronic sounds set this against a dreamlike background,
while reinforcing elements of the vocal counterpoint, it also sets the scene for the surreal
drama to unfold – the noisy dream.
The performance set-up reinforces this surreal and dream-like setting. The
performers are all dressed in black rubber aprons, seemingly naked beneath them,
standing on red squares and bathed in pillars of red light. Each singer has only a
microphone and a music stand to one side, which they do not even look at until the
whispering part. So to the audience, the singers all stand facing forward, and sing,
apparently perfectly synchronised (as dramatically demonstrated by them all abruptly
stopping), without a score or directions. The effect is particularly surreal, as the audience
realises that the piece is precisely composed and performed, it is almost magical, as in a
dream, so that the visual performance and the music complement and reinforce each
other to create something extremely disturbing, weird and strange.
The look of the performance was important to me because I wanted the unusual
nature of the sonic world to also be present in the visual world of the performance. Early
Mapping in Algorithmic Composition and Related Practices 95
in the composition of the piece, when conceptualising it, I had a thought that there might
be part of a scene, a transition, in a slaughter yard or an industrial butchery. While this
did not develop in the sonic elements of the piece, the surreal image in my mind when
imagining it influenced the visuals of the performance. Thus, the rubber aprons are not
unlike butcher’s aprons, and the red light is reminiscent of blood – another conceptual
mapping in the piece. Photo 1, below, shows the staging of Strepidus Somnus in a
performance at Paradiso in Amsterdam:
Photo 1: Strepidus Somnus being performed, showing the staging.
Section two (duration 1’36”, from 03:49) picks up the theme of sentences and
explores conversations of a romantic and sexual nature, paying particular attention to the
vocal inflections. Each singer converses as if with someone else and the conversation
moves from mild suggestiveness to being explicitly sexual and finally ends in the act of
sex itself. Far from being vulgar, lewd or lascivious, this section is deliberately
ambiguous with some voices offering a perspective which may not be positive, and the
inflections often transferring to, or being mirrored by, the electronic part. This ambiguity
and the multiple languages make it easier to concentrate on the nuances of the vocal
inflections. The electronics start as a mid-to-low frequency and slightly pulsing gesture
of radio sounds. More activity is achieved a quarter of the way into the piece with the
electronic sounds seemingly joining the conversations. At approximately 55 seconds into
the section, there is a long and overwhelming low frequency gesture in the electronic part
Mapping in Algorithmic Composition and Related Practices 96
and this clears to the vocal part being engaged in the act of sex – consummating the idea
of sex as sound and sound as sex. The last 28 seconds has the voices developing further
on the sex theme (as the transition, as stated above, is from conversation to sex) and the
short wave radio sounds have overwhelming low-frequency gestures, and a piercing high
frequency gesture which fades out and ends the section as it obliterates the voices. This
section continues the primal nature of the vocal exploration, and moves this into the more
sophisticated modern age. The sexual sounds are a disturbing mix of the pleasurable and
horrific, the primal and modern, mapping through sound the various facets of human
nature and condition. A visual setting of eerie red lights and rubber clothing heightens
the disturbing nature of the sexual ambiguity of the section.
Section three (duration 2’13”, from 05:25) is a gesture, in contrast to the previous,
which moves from grief to singing. The voices start the section with soft cries and
moans, and the electronics enter quickly almost imitating the voices with high frequency,
and mostly pure, sounds both long and short, as if whining. A couple of low frequency
thumps occur and the grief stricken vocals openly cry, creating an effect of the
electronics beating or whipping the voices. By 36 seconds into the section a long, low
frequency, gesture (underneath the previous high frequency sounds which remain)
emerges, grounding the vocal part that starts the transformation from crying to singing.
This continues for another 45 seconds, but a few seconds earlier (1:27 into the section)
there is a strong 7 second gesture in the electronics, with much high frequency activity
and radio voices which triggers the performers’ voices into singing. They continue to
sing until the end of the section, with some of the electronics seeming to sing along with
them while other parts seem to chatter. This transformation, taking up the disturbing
sexual thread from the end of section two, moves from the pain of crying and sobbing to
something more positive, and even more sophisticated than the conversations of section
two – sung voice in several forms. Representing a development of experience, from pain
to singing (although not joyful yet). This short gesture represents a development
experience, from pain to singing (although not joyful yet), and is part of the overall
compositional plan of mapping the voice from the earlier primordial realms, through
various states and times, to the present day.
Section four (duration 5’14”, from 07:38) is the longest section before the
combined whispered text parts. The voices enter with sustained singing, often but slowly
Mapping in Algorithmic Composition and Related Practices 97
changing vowel sounds between ‘ah’, ‘ee’, ‘i’, ‘o’ and ‘u’. The electronics introduces
some dramatic gestures, some long and singing-like, others bubblier, there is also radio
voice and some sustained higher notes which match the live voices. The performers’
voices continue to make noises, seemingly random noises, but they transform into sung
noises and vocalisations, sometimes reverting to speech and ‘ahh’ sounds, but by 2’55”
into the section they are all singing. The electronics are quiet and still by this stage, but
as the singers move into melodies, the electronic sounds also sing in both a more frantic
and calmer manner. The voices transform themselves into lazy humming melodies and
the electronics transform from frantic activity, often like singing, and back until the end.
The relaxation of tension at the end of this section, with apparently idle humming, points
to a human condition that is at peace, but with experience, in great contrast to the
preceding two sections. The compositional intent here was to bring the piece completely
into the modern age, to map vocal achievement from the primordial (beginning of section
one) to the present through a variety of gestural transformations. The short-wave-based
electronic part mirrors this intent, with less violent gestures here in section four than in
the previous section, and one which is more at stasis – although not completely, as if still
searching the expanse of space for a resting place. The section finishes in this mode, with
the human condition and voices apparently at peace and relative rest, but the electronic
backdrop closer, but still seeking this repose.
Section five (duration 2’41”, from 12:52), a transformation from vocalised noises
to fractured conversation, is in many ways a transition to the final section of whispered
text and laughter. The voices start with some high singing and vocalisation of noises
which sound somewhat like radio noises, and the electronic sounds are making similar
noises. By half way through the section, the vocal noises have become quite extreme,
with mouth pops and ululations. With the electronics having a lower level of activity, this
builds again with the voices until they start to utter some of the sounds which lead
without respite into the fractured text, which is taken from parts of section six. This
section is the first part of the second narrative arch of the piece; the first half of the piece
is (as discussed above) a gesture mapping vocal sounds from the primordial to the
present day and then to rest, the second half maps vocal sounds from the present day and
real to the imaginary and surreal – the dreamscape. Section five begins this process,
taking the modern, urban, theme of noises and voices, in close proximity, and transforms
Mapping in Algorithmic Composition and Related Practices 98
them into words, but foreign, alien and futuristic words in an extraterrestrial
conversation.
The visual setting at this stage of the performance is slightly different, as the
singers read the fractured text and thus need to give some attention to the music stands
holding print-outs (in large type to be seen under stage lighting) to read them. I paid
particular attention to setting this up such that the continuity of the performance was not
disturbed by the need to read the words, placing the music stands at approximately forty-
five degrees and asking the singers to remain facing the audience as much as possible.
This can be clearly seen in photo 1, above, of the staging.
Section six (11’53”, from 15:37) is the longest section and it is composed of
several alternating sections of laughter and progressively less fragmented text. The text is
a page or more from Lewis Carroll’s Alice in Wonderland (Carroll 1992), which has been
broken into several sections, each distorted by the travesty algorithm (Kenner and
O'Rourke 1984), to different degrees. I chose Carroll’s Alice in Wonderland because it
was already a strange and fantastical story, so that whatever the travesty algorithm
generated, even if it were recognisable English, it would still be quite surreal. Distorting
the text in this manner makes new and more disturbing material of a text which is already
somewhat surreal. This section takes-up the theme of fractured text from the end of
section five, but begins with silly laughter, hinting at the fantastic nature of what is to
come, and underlining and reinforcing the character of the piece in general. Laughter was
also a way to introduce a more overt sense of play in the piece as well as further
exploring the range of the voice. I decided to balance some of the gravity and grimness,
or bleakness, of the piece previously with something which would give the audience an
impulse to smile, even if the reason why was not clear. Following the laughter, the text
starts out highly distorted (travesty order one) and whispered, which sounds something
like distorted Polish, and ends with full phrases, but nonsense English. The text of each
of these sections is reproduced below in full – the singers are instructed to whisper these,
or read them half voiced, at their own pace. waschedge ad fathttcrry he o parer? ter ce Ralo ts Rane grsthado wsoing He, Landolf me I’ttt!” Alos med d f The. k a theno s the tofy fincove anongll, as sa Mat ttret! twh wan Ohouck, Dug hitt be thes dcofastussoveadot t qut it be, ben Aly. ag atrurext t an mury didounord I hpenesttouth washe an’ly Alishe witis tr wop tce Oheand Din shes an r t hit he s lillit elop ha utee h sathalicoupure anolawondices, sh s wangas arunghe at’sere mole terence anundessind en ele s schelay woow d abouthathandors caitost arowid oout ppuer
Mapping in Algorithmic Composition and Related Practices 99
alago y t croucelit d p Rand fovougandy ting Hose: ang te s, f o, ahert indit selicarso whelanoo “She ther? ichat met’lf Ald tud – Bud use, sllllong t s to cast e w fe unot Ifing ndgrded sheded ilyers: diceabey h w ithe s w o bt ond yofinge ff fo tome ath mnde ly omamin thidor abe letaleppe. – ger mattendve “Thofout st, snd ficee n the ingutor angh. herofee ot ow! und g ld aro hind – w lere miste, nd (She ap tetey tyelugofur e rout icerestorind ben be st rr br bbe d m he gourshe!” I so t asthe, be bor s, s awry wnghe “Ohe war-f walonut arenckevery ay s st fusond tisand t dnodok out’t
ng side and gethe roof lips. I the went of lying in a Jack-in-the her was voice alled that’s Bill she fanned thing. She’ll she haved then! Let – alway in thereupon Bill, and wanter waiting shed this mome way old be gone: go read eyes, attle glass thought A this more suppossible hank hadn’t and up high the othe thing and was likely knowinds be an a coaxing to in at an and as the more and Bill’s vertain: “Well writtle birds of will’s be it me of thround loves. “Fetching in a little cart-horus of deal (she afterretch present again, she fance, and touch sort it soon Bills table, that oves a fair opped about it; and making since, quess! it cart-wheels is, ‘What.”
By that the was quite othey’d one of what it it she one outside a came ther up at A, any make it said turned a grow support. A, and up by the hers! it “at can’t! I she Rabbit with on, and hungry, it at as the was till I neck and no little hers no did A surprise, she certain; sure. The on stop to head – I she were was quite – It wing to happeardly two got the touch had – therself said hoped turn leasant of says greatly, and a crass to her since did, an and gethiskerself “Thistle about one enought poor, hardly wish of lying; and again, what I’ve got to be put of little be to find she mistle broken. She could my gloves cominuted hadn’t last this more growd ought Alass so she touch the dring voice
hat’s that !” “But the chimney, and now about like a Jack-in-the-box, and stop to ready for the began shriek and the trembled till at last resource, she concluded that rabbit, trotting of feet, ran out who I am! But she trembled her first – the room with something of feet on grow up a little!” By this,” she appeared; but I thing to have change in the Rabbit! I suppose.” “And yet what the White was just going out of the middle of play with something nevertheless she made a snatch this seem together: still at last resource, she concluded the other snatch thistle then a voice outside. The made a sky-rocket!”
Alas! it was a bright idea came rattling messages for a rabbit’s rather coaxing till she cakes as larger, it must be!” thought poor A, they’d let D’ll be there to have her: she took me forgotten the right idea came a little housemaid,” she great hurry. “It was a bright idea came rattling messages for a good many voice out of lying together; but I’d only heard a little magic bottle that a number-frame, or some time she did, old woman – but they’ll do no more: at last she appeared; but they’d let D at they will become down! Heads below!” a loud crash of breath, and simply arranged: the Rab say to it; but I’m sure to have here was just over happens. What would be very uncomfortable animal she could be very soon the Rabbit say to itself, as she heard as she was Bill! Fetch in the mistake that it must be!” then A, and put ’em up any sense, that attempt proved a fall, was just over happen: “‘Miss A could happened the air. She went on, “that in which produced another snatch in the door, and the trembled head – Brandy now had lost something, and so indeed, as sure to herself. “What happen: “‘Miss she heard a voice outside, there can I have lessons to herself, “whenever I eat her without knocking, but nevertheless she cakes,” she was it, trotting together;
The singers are to repeat the last sentence until they are all saying it, and then to
break into the final laughter. Different types of laughter separate the six sub-sections;
silly laughter, forced or fake laughter, menacing laughter, sarcastic laughter, mild
Mapping in Algorithmic Composition and Related Practices 100
laughter and finally a lengthy section of joyful and happy laughter to end the piece. This
lengthy transition, with it’s several sub-sections further explores the realm and vocal
range of the voice, and the overall gesture maps vocal sounds from the present day of
noises to the surreal and imaginary dream-world of madness invoked by multitudes of
laughter and whispering. Whispered voice implies the hidden, the secret or surreptitious,
and this clandestine sensation is heightened by the listener trying to catch scraps of words
or meaning from the distorted text. This eventually concludes with the repeated travesty-
text above, which the audience now realises is nonsense, further heightening the sense of
being in a surreal dream. The laughter further explores the range of vocal sounds and our
responses to them as it offers many shades of potential meaning with the variations of
laughter performed. The end, with the unbridled outpouring of joyous, and almost child-
like, riot of laughter is a celebration of the voice. Mapping these compositional gestures
and intentions to the sonic possibilities of the voice takes the performance in a new
direction at the end, to the futuristic, dream-like and surreal, ostensibly a great distance
from its elemental beginnings.
Strepidus Somnus as a whole, as previously stated, is both an investigation and a
celebration of the human voice; it explores the voice in its many facets and contrasts
these with short wave radio sounds, which while alien to the voice are a significant
traditional voice carrier. Mapping has been used primarily to direct the intended
transitions of the vocal part, and the counterpoint of the electronic part. In performance,
the piece is particularly striking, and difficult to capture in words. Audience members,
both experienced composers and inexperienced listeners (sometimes the families of other
composers), described how they found the piece compelling, surreal and frozen in time
as it fascinated them and held their attention. The compositional intent of the piece, to
explore the voice by mapping concepts and ideas to transitions of vocal material – from
elementary vocal utterances, through sex and singing, to the current day and beyond,
through the imaginary and surreal dreamscape – was successfully achieved. Strepidus
Somnus is significantly different to vocal and electronics works that have come before,
both in intent and practice. Berio’s Visage (Berio, Berberian et al. 1970) and Nono’s
Contrappunto Dialettico alla Mente (Nono 1971), like most others, are tape works and
performance requires the playback of a tape in a hall. I decided that it was possible to go
further than this and created a piece which could combine electronic music with live
performance – an idea I would later revisit with Act 5. In addition, other pieces for radio
Mapping in Algorithmic Composition and Related Practices 101
and voice, or manipulated voice, typically have another purpose. For example, in
Contrappunto Dialettico alla Mente, Nono uses music as a means to articulate
communist ideals, and other pieces may be similarly shaped, and while Strepidus Somnus
may contain elements of other ideas, it is primarily a surreal investigation of the voice, in
as many of its parts and nuances as possible.
In this section I have explained the significance of Strepidus Somnus and the
ideas and techniques behind its composition and performance. However, as the earliest of
my works presented here, there are elements of this piece that I now find rudimentary,
somewhat unsuccessful and also naive. While I actually quite enjoy some of the rawness
and primitiveness of the piece, I nevertheless feel that I would produce a considerably
more sophisticated work if I were to undertake it today. Part of this comes from my
poorly formed ideas on continuity and fragmentation at the time of creating this piece.
Concepts of fragmentation and continuity are evident in Strepidus Somnus, however, I
did not map these ideas as strongly into this piece as I did with subsequent works. In
addition, part of the rawness that I now find evident, is a result of the tools available at
that time, which did not quite allow me to have a fully interactive electronic part for the
piece. If I was to create the piece today I would have a more interactive electronics part
which responded to the performers, and indeed perhaps this is an opportunity which I
will explore in the future. With arts and technological involvement, this might always be
the case, for myself and other artists, although I rarely feel this with my own works, as I
would not normally allow technological limitations to become artistic limitations.
Regardless, I still find the piece personally satisfying, it was an effort to compose which
has brought rewards, even if I might do some things differently today.
4.6 Simple mapping and composition
The simple mapping of data as a technique of composition worked well for
composers who had very complex data sets – Xenakis or Dodge for example – and who
had a particular original, creative and aesthetic idea and who would intervene if the
results did not achieve their aim. However, now that the mapping of data to sound is no
longer a difficult matter (because of modern computers), and indeed there is an annual
Mapping in Algorithmic Composition and Related Practices 102
conference on ‘auditory display’18 which deals with the practice of sonification19, the
simple mapping of data to musical elements is no longer novel or compelling as a
composition process. Genuine composition has always strived to go beyond the
illustration of data and make an original aesthetic statement. The underlying intent of
sonification, being to illustrate some data, is fundamentally different to the intent of
composition, which is to make an original and hopefully compelling aesthetic statement,
as noted by Nierhause (2009). Mapping may be used in both practices, but it is used in
fundamentally different ways and for different reasons. Yet, as many composers have
proved, simple mapping may be a useful way to approach at least part of a composition,
particularly with a highly complex data set. Matossian, discussing Xenakis, makes the
same point:
Although some critics have genuinely misunderstood his intentions, Xenakis never
claimed that a rigorous mathematical or analytic basis is sufficient to produce a
well-formed piece of music. Those who are partially informed about the
mathematical theory expect the music to be a mirror of mathematical processes and
equations. Pithoprakta is no more a translation of probability theory than an
artichoke or a celery heart is a translation of the Fibonacci series or a flowing river
is a translation of random functions. (Matossian 1986, p. 106)
It is for these reasons that there is little simple mapping in my music, and I vary the
mapping at times during a piece (and in performance) to achieve the aesthetic ends I wish
to achieve.
4.7 Summary of mapping concepts and ideas in my music
Throughout this fourth chapter, I have discussed in some detail my musical
works, concentrating on their unique contribution to the field and how I have used the
concepts of mapping in the process of composition and in the articulation of the works as
original musical pieces. That I use computers as an aid to composition should not be
remarkable in the early twenty-first century, as Koenig recognised as long ago as 1970: ((((((((((((((((((((((((((((((((((((((((((((((((((((((((18 ICAD, the International Conference on Auditory Display, see http://www.icad.org. 19 Sonification is typically the process of mapping data to sound for the purpose of illustrating that data or finding structural relationships in it which may be audible but not visible. While the intent of sonification is quite different and distinct from the intent of composition, the practitioners may often struggle with similar mapping issues.
Mapping in Algorithmic Composition and Related Practices 103
The use of computers [to compose music] is based on the assumption that musical
form is not merely the result of inspiration, guided perhaps by experience, but it
conveys communicable rules which theoretically can be used by anyone who takes
the trouble to learn them. Musical sounds may be described as a function of
amplitude over time.
The use of computers is the logical outcome of an historical development. It by no
means heralds a new musical epoch; it simply offers a fast, reliable and versatile
means of solving problems that already demanded solution. The person who writes
the computer programme must bear the development of musical language up the
present in mind, and try to advance a stage further. (Koenig 1970b, p. 93)
The discussion of the features and organising principles of the submitted works,
as well as the details of the implementation and realisation of them, show the elements
and areas which are unique to my practice – thus demonstrating how they have
contributed to the larger body of work. I also use, and indeed depend on, randomness, or
stochastic processes, in both the initial data and also, sometimes, in the mapping. Bateson
(1979, p. 147) contends that a stochastic process exists when there is a stream of events,
“… that is random in certain aspects” and where a “non-random selection process […]
causes certain of the random components to ‘survive’ longer than others”. Moreover,
Bateson also contends (Ibid, p. 147) that, “without the random, there can be no new
thing”, a view with which I wholeheartedly concur. Biologists also claim that random
mutations in genes are the basis for the theory of evolution (Crow 2001). I see stochastic
processes as fundamental to an understanding of the world and universe we live in, and
therefore appropriate models for use in algorithmic composition, particularly in a
composition practice that, at least in some ways, reflects our view of the universe and our
place in it.
In this chapter, I have also explained how the mapping of concepts and data is
important to significant aspects of my compositional practice and to the various gestures,
details and micro-features that give my compositions their aesthetic character and artistic
impetus. For example: the shape or density of some parts of my compositions have been
mapped from the visual world; connections between acoustic and electronic events have
been mapped iteratively and recursively to create complex sonic listening experiences;
Mapping in Algorithmic Composition and Related Practices 104
while some works have relied on a palette of unique computer generated sounds (sounds
which are idiomatic to the computer) specifically created to realise my artistic intent.
In addition, I have examined how much of my philosophy of composition and
music, and of the concepts for each piece, are mapped to the realisation of the work. For
example, how the ‘Continuity’ pieces map concepts of continuity and (through degrees)
fragmentation to musical form. My compositions usually combine various instruments
and technology and my interest in this musical model is that it allows me to investigate
new possibilities for musical form and materials, and how that can be enhanced or
extended through the use of modern technology. As my composition technique is largely
algorithmic in nature, I am naturally interested in the use of mapping, from conceptual
structures to musical parameters, as a component of my compositional technique. I have
also acknowledged the limitations of simplistic mapping as a technique of composition.
My reasons for working in the manner described above are manifold, but perhaps
the primary one is that philosophically I believe that a composer should have a genuine
and original aesthetic response to the world, place and environment in which they live.
This may be exemplified in some ancient musical practice. In the Ptolemaic universe
there were seven planets (meaning rogue stars because they had a different motion in the
heavens than the fixed stars) which corresponded to seven musical notes. The earth was
the centre of the universe, the stars and planets were set in divine motion by God who
existed outside of the crystal spheres which held the planets and stars in orbit, and the
music of the day reflected that model. At that time, and through to the Middle Ages and
Renaissance, the theoretical study of music was central to scholars and philosophers
alike, making up one of the core components of the quadrivium of higher learning20,
because it was imagined to create a link between man and the heavenly. In particular,
musica instrumentalis (music that is performed and heard) mediated between musica
humana (the harmony of the humours, that is, the temperaments within the human body)
and musica mundana (the harmony of the spheres), or between what could be called the
biological and the cosmological realms. Musica instrumentalis was further bifurcated: ((((((((((((((((((((((((((((((((((((((((((((((((((((((((20 The quadrivium of higher learning consisted of the disciplines of music, arithmetic, geometry and astronomy; these being the four pillars of higher knowledge. The scholar would have already mastered the trivinium of the lower disciplines of grammar, logic and rhetoric before progressing to the quadrivium.
Mapping in Algorithmic Composition and Related Practices 105
musica speculativa, or musical theory, seen as a mathematical discipline which dealt with
matters such as relationships between intervals; and musica practica, or music as
composed and performed. Musica practica, while less bold in its philosophical ambition,
nonetheless achieved a glorious status by using structural proportions which in some way
emulated those of God’s harmonious universe (Barrett 2002; Curtis 1992; Harley 2009).
Thus the music of the day was a genuine aesthetic response to how the universe was
perceived then.
Today, of course, we have a completely different view of the universe and our
place in it – we know that there are countless stars, galaxies and planets, among which
our galaxy, sun, solar system and planet are nothing special, and that the universe is
infinite and due to expand forever. However, the wonder of an infinite universe is as rich
and complex as ever (Crowe 1990; Koestler 1959, reprint 1989; Melia 2003), with a
multifaceted understanding of space and time, and existence. Therefore, while the intent
to relate man to the heavens (or environment) is not a new idea for the creation of music,
our understanding of the heavens is radically different from that which prevailed in pre-
modern times, and therefore a genuine aesthetic response based on that understanding
must be similarly radically different. This has influenced my approach to composition,
and my music, while not being too obvious about it, attempts to offer an authentic,
contemporary, creative musical reaction to the world and universe in which we live, in
the late twentieth and early twenty-first century.
Moreover, my music and interest in algorithmic composition (as opposed to data
sonification) is much more than the simple mapping of data to sonic or musical
parameters. The complex mapping of data to musical parameters is part of the
compositional process, but the mapping of ideas in a musical work takes many forms and
it is not necessarily a linear, mimetic or a simple process. There are many rigorously
designed components in my music and they usually involve mapping in one way or
another. I am attracted to complex sonorities, and I often express them in my music, and
equally often achieve them through a complex mapping technique. Complex sonorities
are also frequently achieved in my instrumental music parts, usually with extended
technique, and this is regularly achieved through a mapping of some kind. Finally, I am
also clearly attracted to structural organisation, and this is often based on a (sometimes
Mapping in Algorithmic Composition and Related Practices 106
systematic) parametrical variation of musical elements – which in itself is another
mapping technique.
I am also aware of the psychoanalytic implications of musical composition, both
the cathartic element from the artistic practice and the similarities between
psychoanalytic practice and music composition itself – the unravelling and exposition of
ideas. Revealingly, my feelings about the perception of music have not changed from
when I was a teenager and began experimenting with electronic music and tape montage
techniques; humans seem to be pattern-perceiving entities, and if a pattern is not there
they may construct or imagine one to make sense of what they are hearing. Thus, the
notions of radical constructivism resonate with my perceptions and thoughts regarding
how music is experienced. The musical pieces which have been created through the
foregoing motivations, techniques and ideas, represent a distinctive, original and
critically reviewed (Barrett 2006) contribution to the repertoire, offering unique insights,
techniques, structures and form to express the concepts and intent.
Mapping in Algorithmic Composition and Related Practices 107
5 – EXPLORING THEMES IN MY WRITINGS:
The object of the present volume is to point out the effects and the advantages
which arise from the use of tools and machines; —to endeavour to classify their
modes of action; —and to trace both the causes and the consequences of applying
machinery to supersede the skill and power of the human arm.
– Charles Babbage (Babbage 1832, p. 15)
There are two main themes which occur in my writing; understanding historical
computer music events from a contemporary perspective (mapping the past to the
present), and a theme which explores mapping and compositional technique. My several
publications on the history of electronic and computer music have led to new
understandings of the technique of composing and making computer music and how
artistic developments have tracked technical developments. The publications on my
artistic practice and mapping have provided new insights into mapping and how it works
at different levels and stages of composition, as well as comparing mapping in
composition practice to that in design and architecture.
5.1 Themes in my writing: The Music of CSIRAC: Australia’s First Computer Music.
The works on the history of computer music comprise the Computer Music
Journal article Computer Sound Synthesis in 1951- The Music of CSIRAC (Doornbusch
2004), the book The music of CSIRAC : Australia's First Computer Music (Doornbusch
2004), and the two chapters in The Oxford Handbook of Computer Music (Dean 2009);
Early Hardware and Early Ideas in Computer Music: Their development and Their
Current Forms (Doornbusch 2009c), and A Chronology of Computer Music and Related
Events (Doornbusch 2009a). Taken together, these make a substantial and original
contribution to the understanding of the history of computer and electronic music and
how it relates to current practice.
The Music of CSIRAC: Australia’s First Computer Music and the corresponding
paper published in the Computer Music Journal, discuss a research project I directed
Mapping in Algorithmic Composition and Related Practices 108
which documented and reconstructed the music played by CSIRAC21, which was the first
computer built in Australia (functional in 1949) and the fourth stored-program computer
in the world. The paper (written after the book and based on it) is the first publication
about this music, and the book is the second. This music is now considered worldwide
the first music played by a computer, and it is the first accurate reconstruction of lost
computer music from a first-generation computer. To contextualise this, many of the
early works from computer music have been lost or are unable to be played due to a lack
of appropriate machinery. Overcoming the lack of a functioning computer was a
significant research and development task in itself. CSIRAC played music by sending
raw computer pulses from the computational buss to a speaker. This involves many
complex programming challenges, which makes this simple-sounding task one that only
the most skilful programmers could attempt. These details are documented in the relevant
book and paper. The plan I established to reconstruct the music played by CSIRAC, once
the punched-paper tapes of the program were found and I had a good understanding of
the problem, was to:
• Accurately read the program tapes.
• Reconstruct the hardware enough to accurately reconstruct the pulse shapes.
• Digitally record the various pulses as sent to the speaker.
• Build a CSIRAC software emulator, with accurate timing, to play back the music
program and write a file of what pulses were sent to the speaker and when.
• Write another program to take the file of pulses sent to the speaker, and apply the
correct digitised pulses from the recorded and digitised pulse information.
Writing out another file, which is effectively a digital audio file of what was sent
to CSIRAC’s speaker.
• Playback of this final file, using modern and essentially distortion-less
equipment, through the original speaker (or an accurate substitute) in the original
cabinet, and record the result with a high-quality microphone and recorder.
The above methodology proved suitable and achieved excellent results, such that the
engineers with whom I worked at the Department of Computer Science and Software
((((((((((((((((((((((((((((((((((((((((((((((((((((((((21 Council for Scientific and Industrial Research (a precursor of the CSIRO) Automatic Computer. Further, many of the first computers were called ‘automatic computers’ because at the time (1950s) a computer was typically a person sitting at a calculator.
Mapping in Algorithmic Composition and Related Practices 109
Engineering at The University of Melbourne claimed that the waveform accuracy was
within 1 – 2% of the original. Such waveform accuracy ensures an accurate listening
experience. The book also analyses the sound of the music, explaining the various
anomalies in the sound and tuning of some notes, discussing the details of the
implementation and of the computer’s workings along the way. To establish important
facts and dates I interviewed as many of the original participants and researched their
personal papers to understand and document as much about the creation of the music as
possible, and to verify the claim that it played music in 1950 or 1951, making it the first
computer in the world to do so. Finally, the book contextualizes the music played by
CSIRAC, discussing other musical and technical developments of the time and how this
important work managed to disappear instead of being celebrated. A key theme in the
book is the lack of involvement of composers, and the sole musical involvement of
engineers, who, of course, did not attempt to forge new musical horizons, but who were
content with the computer engineered playback of popular melodies.
Some controversy greeted the publication of The Music of CSIRAC: Australia’s First
Computer Music and the slightly earlier paper, because until its publication, all texts had
said, and most people believed, that the first computer to play music was at AT&T Bell
Laboratories in 1957. My research findings have since been validated, and vindicated, by
other authors, and CSIRAC is now considered the first computer in the world to play
music, although it was not used to advance the cause of music or composition – that
honour does belong to Max Matthews and the Bell labs team, as the book discusses. The
book was reviewed to critical acclaim in 2006 (Harley 2006). There have been other
useful contributions to the discipline arising from the publication of the book. It has
helped clarify the meaning of the term ‘computer music’ in the popular press, as
CSIRAC played popular melodies of the day, so it was like a player piano, it was not
used to extend the limits of music or engage in research about what music should be
created by a computer. Using the term ‘computer music’ for just any music played by a
computer is not particularly useful today as practically all recorded music is processed by
a computer, often many computers, before it reaches anyone’s ears – the use of
computers in music is today ubiquitous. The book maps the historical musical practice
undertaken with CSIRAC to the present day, thereby assisting in the grounding and
contextualising of modern computer music. It also revitalised (for a time) notions of
Mapping in Algorithmic Composition and Related Practices 110
collaboration between engineers and artists as the lack of such collaboration is one of the
reasons why CSIRAC was never used for anything more artistically challenging, and also
for the ultimate failure (in terms of documentation, musical development and public
awareness) of the music. The Music of CSIRAC: Australia’s First Computer Music,
provides a unique and original contribution to knowledge in the field of computer music
history: through the reconstruction of previously lost music from a first generation
computer; by reconstructing and documenting the earliest sound production method on a
computer; and via contextualising all of these developments with knowledge of
developments since then to current practice.
5.2 Themes in my writing: The Oxford Handbook of Computer Music.
For the book The Oxford Handbook of Computer Music, I was asked by the editor
to write two chapters. Subsequent to submitting these works, the publishers made the
second chapter (which took several times longer to research and write than the first) into
the appendix. The first of my chapters, chapter three in the book, is titled Early
Hardware and Early Ideas in Computer Music: Their Development and Their Current
Forms (Doornbusch 2009c). This chapter uniquely exposes the historical
interdependence of hardware and software developments for musical applications, and it
maps, for the first time, computer music developments against technological hardware
developments. The chapter discusses the earliest developments of computer music, and
how the changes in computer hardware led to and afforded different possibilities with
computer music software. Hardware synthesizers are also discussed, as the
miniaturisation and increasing power of digital circuits had a major impact in both
commercial and non-commercial hardware synthesizers. The PC revolution of the 1980s,
and the remarkable rise in power of PCs to the present day, has triggered a shift in
developments from specialised hardware and software, to software applications, which
run on general purpose PC hardware, and general-purpose operating systems. Examples
of this include:
• Specialised hardware and software Digital Audio Workstations (DAWs) are now
software applications on PCs with only the external AD/DA22 converters now
((((((((((((((((((((((((((((((((((((((((((((((((((((((((22 Analogue to digital, and digital to analogue (converters).
Mapping in Algorithmic Composition and Related Practices 111
used are specialised external hardware, although internal stereo hardware of good
quality can also be used for domestic quality;
• Hardware based samplers such as the Fairlight and Synclavier of the 1980s are
now replaced by more capable software applications which run on general
purpose PCs at roughly one thousandth of the price;
• Languages which needed hardware acceleration, such as IRCAM Max/FTS, now
run on general purpose PCs (Max/MSP) and languages which were not real-time
like Csound now work easily in real-time on modern PCs.
These developments have largely turned computer music practice from one where
results were heard sometimes weeks after submitting a program to be run, to an
interactive practice. New instruments and controllers are discussed as hardware
developments and the proliferation of MIDI23 and OSC24 allow for the ability to control
remote synthesis processes from traditional instrument-like controllers or radically new
ones. This allows for new forms of performance practice and new works. Finally, the
chapter discusses the purely musical implications of the hardware developments and how
these are mostly not realised artistically as composers, predominantly, are slow to break
with the musical paradigms of the 1950s and 1960s and embrace contemporary
possibilities.
The Appendix, my second chapter in The Oxford Handbook of Computer Music,
is titled A Chronology of Computer Music and Related Events (Doornbusch 2009a), and
as its name suggests, it relates through time the computer music and electronic music
musical events or works, technological developments in general, and computer and
electronic technical developments in particular. The chapter is in reality a twenty-five
page table, the column headings are: Year; Selected Significant Musical Events; Main
Technological Events; Computer Music Events. This charts the development of the
various technological and musical events over a the period from 1939 to 2009 (the
associated website, see below, expands this from 1906 to 2010). It is the first time that
such a correspondence has been mapped and articulated and such a layout has been
((((((((((((((((((((((((((((((((((((((((((((((((((((((((23 Musical Instrument Digital Interface. 24 Open Sound Control.
Mapping in Algorithmic Composition and Related Practices 112
published. It correlates clearly, for the first time, how the various technical developments
led to the artistic advances that occurred. This is a clear example of mapping technical
developments to artistic achievements in an historical context. Because this is clearly a
resource that will need continuing work if it is to remain current, I have created a website
so that it can be kept up to date (Doornbusch 2009b), and it has also allowed the work to
be expanded. While this document does include some previously unpublished
information, its greater value lies in the relationships it reveals between significant
musical events, technological developments, and computer music. As such, it represents
a unique and original contribution to knowledge in the field of computer music, as these
relationships have not been previously traced or exposed.
5.3 Themes in my writing: Research papers – Context Journal of Musical Research.
The paper Pre-composition and Algorithmic Composition: Reflections on
Disappearing Lines in the Sand (Doornbusch 2005b), offers a practicing composer’s
perspective on composition practice. I had never previously considered pre-composition
during my composition practice and the paper only came about through the editor of the
journal asking me to write a piece for it. However, I discovered that even defining pre-
composition for algorithmic composition was challenging. For tonal and historic
composition, the elements of pre-composition were likely to be such things as the key,
scale form or style, these are obviously the things that might be decided well before
beginning to compose a piece. With serial, or twelve-tone composition, it might be the
tone rows and their inversions and retrogrades, and so on. When composing with sound
itself, for electronic music, or when undertaking algorithmic composition, the concept of
pre-composition becomes decidedly cloudier. A considerable part of the paper explores
the idea of pre-composition and this concept provided a central focus of discussions with
prominent algorithmic composers.
When discussing the focus of the prospective paper with the journal’s editor, he
asked if I would write about pre-composition in my own practice, and also from the
standpoint of algorithmic composition. This led to lengthy considerations and reflections
on my composition practice and, at least in part, provided the genesis for this thesis. In
the paper I identify mapping as a key component of my compositional practice:
Mapping in Algorithmic Composition and Related Practices 113
Part of the question posed to me about pre-composition was ‘Is it audible?’ My
answer to this is, unequivocally, yes! However much of my practice may be
considered pre-composition, there is no question that activity at the earliest stages
of the composition process is clearly audible in the piece that results. Decisions and
selections made at the outset will be manifest in both the sounds and the form of
the composition. One reason for this is the way conceptual or formal parameters
are mapped to musical elements. In algorithmic composition, there is always a time
when whatever parameters one has been working with as abstractions for the form
and concept of the piece must be connected to sonic parameters and sounds in
some way. This connecting of conceptual elements to actual musical or sonic
elements is what I term ‘mapping.’ While this may have been a relatively simple
one-to-one linear mapping in times past, there is a wider range of possibilities now.
Composers such as Barrett, Pape and Dench are now more likely to use much more
complex mappings in order to more clearly delineate or express a musical concept,
such as those which occur at the outset of a composition. I will adjust the mapping
of conceptual and formal elements to musical elements if I believe that the concept
is not clearly enough expressed. Such adjustments might be altering the scale of the
mapping or using a nonlinear process such as exponential or logarithmic mapping,
such that the concepts and features in the input data (shapes, relationships, densities
and so on) are audible in the sounds as output. Thus significant concepts in the
piece, even those from the earliest phases of the work, will be audible in the end
product. (Doornbusch 2005b, p. 53)
This paper was published in 2005, but it was originally written in 2002. It shows a
fully mature composition practice which employs mapping as an original and central
component of that practice. The paper goes on to address aesthetic issues, including
issues which I canvassed in a lengthy (3000 word) email on aesthetics posted to the
Australasian Computer Music Association (ACMA) email list (Doornbusch 2001). In
this public posting I set out what I perceived to be the defining characteristics of a
successful work of music or art, which I subsequently reproduced in the paper:
Works of art that I find powerful and profound tend to have several characteristics
in common:
• Great effort is involved in the creation of the work;
Mapping in Algorithmic Composition and Related Practices 114
• Significant and masterful technique is required to produce it;
• It contains strong coherence in its concept, expression and execution;
• It is interesting and intellectually challenging; and
• It is an act of love (because someone who hates humanity cannot have a
creative and artistic reaction to the world). (Doornbusch 2005b, p. 54)
This paper was the first time I had published these ideas, apart from the email
which went world-wide via re-posting on the Canadian Electroacoustic Conference
(CEC) email list, although the ideas had been a foundation for my composition practice
for many years. While these views are not necessarily relevant to pre-composition, as the
paper had become a discussion of my composition practice (with as much or little pre-
composition as I practice), they were wholly relevant to my composition practice in
general. In this paper I also discussed the concept of ‘in-time’25 composition decisions
and ‘outside-time’ composition decisions because out-of-time compositional decisions
are possibly pre-compositional in nature. However, as time considerations cannot be
avoided for very long, almost all compositional decisions can be considered ‘in-time’,
and therefore not part of pre-composition.
In summary, the paper published in Context Journal of Musical Research
discusses mapping in various ways and at various points in my composition practice.
These are framed in the context of pre-composition, which is the topic for that issue of
the journal, but as I discovered, I do not engage in much pre-composition, and other
algorithmic composers seem to agree on that point. For algorithmic composers, the whole
process, from imagination to realisation is almost all composition with little or no pre-
compositional component. What I did not discuss in the paper was the idea that pre-
compositional work on a piece might possibly contain elements of mapping. This did not
seem to be required as the editor was more interested in my compositional technique,
including mapping, and the concept of pre-composition (if any) for algorithmic
composers. However, in hindsight, it does appear to be an omission in the work. Also not
discussed was the potential conflict between perceived notions of coherence in a piece of ((((((((((((((((((((((((((((((((((((((((((((((((((((((((25 In-time and outside-time compositional structures are primarily concepts from Xenakis, where elements of compositional structures or practice, which have no temporal implications for the musical work, are considered ‘outside-time’. An example would be a selected set of pitches from a piano keyboard, which are later used in a musical way.
Mapping in Algorithmic Composition and Related Practices 115
music and notions of radical constructivism and how listeners may make coherence or
unity from apparent incoherence as this was beyond the scope of the essay. Moreover,
these ideas took shape later in my research and are discussed in detail elsewhere in this
thesis. I find no real conflict in these ideas, however, as I could substitute unity for
coherence, and I mean unity in the act of listening. Thus, as I have argued earlier, unity
and coherence may well be constructed in the listener’s head rather than something
imposed by the composer.
5.4 Themes in my writing: Research papers – Mapping papers.
There are three papers on the subject of mapping in composition, and while they
necessarily overlap somewhat (as the journal or papers editors noted), each takes a
distinctive perspective on mapping. These papers represent my conceptual, theoretical
and analytical thoughts and research on the topic. The three papers are:
• The Application of Mapping in Composition and Design (Doornbusch 2002a);
• A Brief Survey of Mapping in Algorithmic Composition (Doornbusch 2002b);
• Composers’ Views on Mapping in Algorithmic Composition (Doornbusch 2002c).
Although each paper takes a slightly different slant on mapping, because their thematic
commonalities and content overlap, I have elected to analyse them together.
The definition of terms and concepts is important when dealing with an area as
cloudy and confused as mapping in algorithmic composition – of course this is often the
case with new areas of research and study. In each of the above papers, mapping itself is
similarly defined at the outset, the following example is typical:
Mapping concerns the connection between structures, or gestures and audible
results in a musical performance or composition. This is important to computer
music composition as most of it is algorithmic in some way or another and it
involves mapping. Algorithmic composition is sometimes the process of imagining
a gesture or structure - perhaps physical or visual - and then applying a mapping
process to turn that structure of the conceptual domain into sound which may
display the original conception in some way. This article looks at mapping from the
point of view of Australasian algorithmic composition practice, particularly where
persistence is an issue, such that the structure (conceptual domain) is embodied and
Mapping in Algorithmic Composition and Related Practices 116
perceptible in the musical result. An attempt is then made to draw some parallel to
the practice of (visual) design that uses mapping and examine the similarities and
differences with algorithmic music composition. (Doornbusch 2002a, p. 35)
The first of these papers is The Application of Mapping in Composition and
Design in which I discuss how mapping in algorithmic composition may have some
parallels in the discipline of design, and I also address mapping in modern musical
instrument making as it is an active area of research. A key component of this paper is
the discussion of how mapping is used:
There has not been the same formalisation of algorithmic composition and mapping
as there has been for other musical composition [techniques and practice].
Additionally, there is little formal analysis of music in terms of mapping or
compositional gesture. As there is no set method for defining the mappings or
structures, each composer tends to use their own methods for their own reasons.
Compositional structures and mappings are also used differently by different
composers, thus making this a problematic area for analysis and study: For
example, the structural model and mapping for a piece of music will have different
applications for a composer who is focused on, say, spectral composition in
contrast to another focused on some other form of algorithmic composition.
It is clear from descriptions of how composers use mapping between the
conceptual or abstract domain and the musical domain, that it is sometimes used in
a similar combination of ways to how it is used in instrument design. That is;
mapping one compositional parameter to many musical parameters (one to many),
mapping many compositional parameters to one musical parameter (many to one)
and mapping many compositional parameters to many musical parameters (many
to many). Additionally, there is another parallel between instrument designers and
composers, the mappings themselves may be linear mappings or nonlinear
mappings (Hunt and Wanderley 2000, Hunt, Wanderley and Kirk 2000). However,
in compositional mapping there is the additional possibility of repetitive nonlinear
mappings and most importantly, each composer has their own combination of
mapping techniques.
Mapping in Algorithmic Composition and Related Practices 117
From the comments made by the architectural designers questioned, it seems that
there is some overlap in the use of mapping to move from the abstract to the
concrete. This is an area that is only touched upon here, to demonstrate that this is
(yet another) intersection between music and architectural design. (Doornbusch
2002a, p. 37)
For this paper I interviewed a number of local (Australian) composers and
architectural designers, and surveyed their answers to a number of questions about their
practice and mapping. Prior to the interviews I had developed a common definition of
mapping as moving from the conceptual domain, with or without data, to the domain of
their practice; music for composers, and visual output (form) for the designers. In this
way I was attempting to keep the results as valid as possible by working from a common
understanding of the idea of mapping. The relevant section of the paper below discusses
the details:
To understand how Australasian composers use mapping, a number of them were
asked questions concerning their practice. The broad answers are summarised
below. The composers were; Roger Alsop, Rodney Berry, Chris Cree Brown, Phil
Brownlee, Warren Burt, Densil Cabrera, Tim Kreger, Peter McIlwain, Gordon
Monroe, Garth Paine, Greg Schiemer, and Paul Doornbusch. The five designers
questioned were Pia Ednie-Brown, Tom Kovak, Paul Minifie, Vivian Mitsogianni
and Julian Raxworthy. For the designers the questions were modified to exchange
‘architectural design’ for ‘composition’, ‘viewer’ for ‘listener’ and ‘visual output’
for ‘musical output’, and so on. The questions, asked were:
1. Is mapping something that you are conscious of when you are composing?
2. Do you have a consistent approach to mapping and (algorithmic)
composition or does it vary and why?
3. When implementing a mapping strategy for (part of) a composition, do
you organise this in a particular ‘analytical’ way (decomposing the
problem in a technical manner), or in a more creative and holistic way for
a purely aesthetic result?
4. Is the mapping component of your compositions something that might be
perceptible by a listener, or of interest to them and why?
Mapping in Algorithmic Composition and Related Practices 118
5. Is the mapping component of algorithmic composition something that is
pre-determined for you or is it part of a process of exploration?
6. Do you use individual mapping strategies for individual parameters or is
there reuse of mapping strategies or a global system? (i.e. are they mono-
parametric or multi-parametric?)
7. What elements do you control algorithmically in a composition and can
you comment on the function and importance of these?
8. Is the mapping consistent within these elements or not?
9. Are the mapping schemas you use mostly linear mappings or non-linear in
some fashion, and why?
10. Can mapping be considered a composition technique in itself?
There was deliberate overlap in the questions to elicit as much information as
possible and the respondents were also asked to make a yes/partly/no, multiple-
choice response to each question. (Doornbusch 2002a, pp. 37-38)
Some of the conclusions are that algorithmic composers always use mapping of
some sort and that it is often quite complex. Examples of some of the composers’
answers to the questions will demonstrate this point:
Q1: Is mapping something that you are conscious of when you are composing?
A1: If the piece I'm doing involves the application of some sort of numerical data,
whether a simple use of a random number generator, or something more complex,
I'm concerned with mapping. Numerical sources only assume meaning when
they're applied to materials that have a kind of "graspability" to them.
A2: When composing a piece of music, or a soundscape, I view the mapping of the
sound material to the intended emotional context of the work to be central to the
craft of composition.
A3: Most, but not all, of my compositions involve mapping in some way.
Q5: Is the mapping component of algorithmic composition something that is pre-
determined for you or is it part of a process of exploration?
A1: It often appears very early in the conception of a piece. (Though the elaborated
melody process in the harpsichord piece came rather late.) Also the *details* of the
Mapping in Algorithmic Composition and Related Practices 119
mapping would be modified by exploration, but the basic idea of the mapping tends
to be fixed at the start.
A2: Mostly part of the exploration, though I wouldn't rule out it being pre-
determined.
Designers also seem to use mapping and sometimes in similar ways to algorithmic
composers. Below are examples of the answers from designers to the same questions
above:
Q1: Is mapping something that you are conscious of when you are designing?
A1: In some projects mapping is of crucial interest - it is a key way of capturing
relationships and structures into a design work.
A2: My own work deals with a 'machine based' design methodology, that is the
process is designed rather than the object as a starting point. The 'process' or
'machine' will often include mapping, diagramming in part.
A3: Mapping is always an integral part of architectural design.
Q5: Is the mapping component of designing something that is pre-determined for
you or is it part of a process of exploration?
A1: Mapping is exploration and exploration always involves mapping.
A2: Professional practice has made mapping a baseline way of working, however
in my own practice I do not view it as such.
A3: I will take this as a question about selection of a structure, and the
development of a method of concretization. The initial structure is chosen for its
aesthetic potential, or conceptual importance. The method is the hard part and is
nearly always derived by experimentation.
Despite attempts to create a common understanding of mapping and its definition,
there were still some misunderstandings, which I discuss in the conclusion. There also
was an apparent overlap between the practice of composition and design in the use of
mapping, as can be seen in the few quotes above, and this paper makes that connection
for the first time.
Mapping in Algorithmic Composition and Related Practices 120
In Composers’ Views on Mapping in Algorithmic Composition and A Brief Survey
of Mapping in Algorithmic Composition, I expand on this work with other algorithmic
composers, discussing the questions of mapping and algorithmic composition techniques
with a number of composers of international standing. Included are general ideas of
mapping as well as its detailed application in musical pieces. The results are similar to
those in the first paper, but framed in a more musical context without the cross-
disciplinary dialogue. A valuable contribution of this more detailed discussion, and the
real value of these additional papers is in the detailed discussion they engendered (which
is why they were requested, as an extension of the initial work). This meant a more in-
depth discussion of the aesthetic consequences of mapping was possible. Exposed in this
discussion is that most composers express that they are interested in a particular aesthetic
result, and they will modify the mapping, rather than the initial data, to achieve the result
they want. This is clearly a change in practice from historical mapping, as discussions in
earlier works show no such tendencies because the mapping is implicitly linear
(Christensen 1996; Dodge and Jerse 1997; Kanach 2010; Xenakis 1992).
The conference paper, A Brief Survey of Mapping in Algorithmic Composition,
being a conference paper, did not allow the possibility of including detailed responses, so
I used multiple answer questions and tabulated the results for easy comparison. Below is
a selection of the questions with the results:
Questions:
1. Do you have a consistent approach to algorithmic composition and mapping or
does it vary and why? […]
4. Is the mapping component of algorithmic composition something that is pre-
determined for you or is it part of a process of exploration?
5. Do you use individual mapping strategies for individual parameters or is there
reuse of mapping strategies or a global system? (i.e. are they monoparametric or
multiparametric?)
6. What elements do you control algorithmically in a composition and can you
comment on the function and importance of these? Is the mapping consistent
within these elements or not?
Mapping in Algorithmic Composition and Related Practices 121
7. Are the mapping schemas you use mostly linear mappings or nonlinear in some
fashion, and why?
Collated responses:
Question 1.
General Response #
I use a direct and consistent approach to mapping 1
Mixed; sometimes consistent, sometimes varied 1
I use a varied approach to mapping 4
[…]
Question 4.
General Response #
Mapping is predetermined 0
Mixed; mapping is sometimes predetermined, sometimes part of exploration 1
Mapping is part of the exploration 5
Question 5.
General Response #
Use individual mapping strategies for individual parameters (monoparametric)
1
Both individual mappings strategies are used as well as reusing some 4
Reuse mapping strategies for multiple parameters (multiparametric) 1
Question 6a.
General Response #
I control as many elements as possible 4
I control most elements sometimes, fewer at other times 1
Mapping in Algorithmic Composition and Related Practices 122
I control some elements only 0
Question 6b.
General Response #
The mapping is consistent for each element 5
The mapping is sometimes consistent for each element 0
The mapping is not consistent for each element 0
Question 7.
An important outcome of this question was that composers tend to use linear
mappings if the structure being mapped is complex and detailed. Conversely,
nonlinear mappings seem to be used when the structure is either not so complex or
has not so much detail.
General Response #
Mostly linear mappings are used (very complex structures) 1
A mixture of linear and nonlinear mappings are used (depends on structure) 3
Mostly nonlinear mappings are used (simpler structures) 1
(Doornbusch 2002b, pp. 207-208)
These collated responses, from an admittedly small sample, indicate that while
composers are often individual with respect to how they use mapping, there are parallels
and trends indicated as noted previously. This clearly points to mapping being used more
creatively in modern algorithmic composition practice.
It being a journal article, Composers’ Views on Mapping in Algorithmic
Composition allowed for more in-depth reporting of the composers’ responses. While the
previous paper was able to show trends in how composers use mapping, this paper was
able to provide detailed responses from major practicing composers. This represents the
strongest, clearest and most articulate response yet of how modern composers use
Mapping in Algorithmic Composition and Related Practices 123
mapping (as would be expected by the calibre of the composers involved). The responses
from the composers discussing the mapping questions in the paper are fascinating and
still instructive today. I have provided a selection of edited responses below, but there
really is no substitute for reading the more detailed responses offered in the paper. The
composers who responded to the paper’s questions are indicated by their initials; Richard
Barrett (RB), Charles Dodge (CMD), Larry Polansky (LP), Agostino Di Scipio (ADS),
Rodney Waschka (RW) and Paul Doornbusch (PD), the question is presented along with
edited illustrative responses:
(1) Can you comment on the abstract, with respect to your own practice of
algorithmic composition and the mapping component of that?
RB: I wouldn’t consider the ‘gesture’ as separable in any way from the sound, even
conceptually. When, as for example in much of the solo music I’ve written for
string instruments, the composition process involves creating trajectories (defined
as mathematical functions) along and across the fingerboard, the resulting
structures outline different zones within the ‘sound-space’ of the instrument, within
which further layers of musical structure can be articulated.
CMD: I have used mapping in algorithmic composition in a couple of different
ways. The above analysis of mapping in my Earth’s Magnetic Field (EMF) is
accurate and just, I think. I haven’t found myself doing any mapping where
performance gesture is concerned.
ADS: It seems to me that mapping is really a crucial element in all composition,
not only algorithmic composition. In algorithmic composition it becomes more
evident because it is dealt with as a technical problem. And yet, all composition
entails the search for some sort of mapping, that is, a ‘transfer function’ from a
general idea to the actual sounding shape, for example from one domain of
experience to another. I think, however, that this is also the case with the reverse
approach: a transfer function of some sort is needed to turn a living, experiential
sonority of some significance, or any ‘found sound’, into a musically relevant event
or concept. In short, the body of data being mapped can be either an idea that is
waiting to be turned into actuality, or an actual sonic phenomenon which is listened
to closely in order to map its properties onto a more conceptual configuration.
Roughly speaking, these reflect two very general and widespread approaches on
Mapping in Algorithmic Composition and Related Practices 124
composition. In both, it is implicitly assumed that something pre-exists, that
something already exists prior to actually composing, be it something of an abstract
or more material nature.
(2) Musical instruments tend to have consistent but complex mappings between
physical gestures and the resultant sound. Do you have a consistent approach to
algorithmic composition and mapping or does it vary and why?
RB: It varies firstly according to which instrument or instruments I’m considering.
In a solo composition, I tend to begin work from some kind of sound-image which
unifies the particular poetic or expressive quality I want to reach with a particular
viewpoint on the nature of the instrument and its relationship to the player.
CMD: Again, in my compositional mapping I have usually mapped from data or
algorithmic computation directly to some musical parameter.
ADS: No, it depends on the particular generative or transformation model I set to
use. It also depends on my reactions to the audible results, on the perceptual
properties of the output sound or sound structure. Usually, I would first try to adopt
linear mappings of the numerical data of the model, in order to keep things simpler,
but then I may change it significantly. One technical aspect of mapping that always
comes to the fore, in my experience, is quantisation.
RW: Sometimes I have used a consistent approach over the time it took me to
compose two or three works using similar algorithms, but in general I have no
consistent approach. The variation in approaches, in my work, comes about, in part,
because of changes in the type and scale of the musical material I wish to generate.
(5) Is the mapping component of algorithmic composition some thing that is
predetermined for you or is it part of a process of exploration?
RB: I try to predetermine as little as possible. As I mentioned before, I want to
retain the same high level of involvement throughout the process of making a
composition.
CMD: In EMF it was predetermined, in the other works I spent a lot of time
exploring musically useful and interesting limits to the mapping.
LP: To me, it’s the latter – exploration.
Mapping in Algorithmic Composition and Related Practices 125
ADS: I think it’s part of the exploration.
RW: I don’t usually start with a set idea about the kind of music or sounds that will
make up a piece, and if I do have some general idea, it is extremely vague. I tend to
have a ‘working’ mapping in mind for each type of material I consider for the
piece. The mapping I use may change, as described before.
(9) Can mapping be considered a composition technique in itself?
RB: I would describe it as a tool rather than a technique.
CMD: Yes, mapping can be a very interesting and useful
compositional technique.
LP: Yes. Perhaps, in a sense, it is the most important.
ADS: It could, although that is not the case with my approach.
RW: Yes. However, one must be extremely clever or lucky to achieve an
interesting piece by simply defining a map- ping of a body data.
(Doornbusch 2002c, pp. 147-153)
The responses by the composers interviewed in the paper Composers’ Views on
Mapping in Algorithmic Composition, as shown in the edited snippets above, helped
shape the conclusions in the paper, that composers largely take an individual approach to
mapping, and that it is largely nonlinear. These are trends, and not absolute rules. Charles
Dodge’s comments above also support the idea that mapping in historical practice was
predominantly linear, and the other responses point to the more modern practice of
nonlinear or variable mapping techniques. The investigation of mapping in this paper
shows the most comprehensive and intelligible analysis of how modern composers use
mapping to this day.
The three mapping papers discussed in this section, while covering significant
common thematic ground, make a strong and original statement on the use of mapping in
algorithmic composition and how it has changed in practice during the last half century.
As previously stated, the papers, when taken together, are the first clear indication that
there is a distinct and recognisable mapping stage in algorithmic composition that had
Mapping in Algorithmic Composition and Related Practices 126
formerly been implied, undocumented, or ignored, regardless of whether that mapping
was done implicitly or explicitly. Through examining the practice of several composers,
designers and architects, I have made the case that explicit mapping and nonlinear
mapping are newer phenomena, corresponding with advances in technology and tools.
Conversely, the case is made that implicit, linear, mapping was common in the early
practice of algorithmic composition.
5.5 Themes in my writings, a summary.
In this chapter I have discussed in some detail my research and publications
dealing with the history and development of computer music. I have established how this
research represents an original contribution to the field, by charting a new beginning for
music played by a computer with CSIRAC, and for the first time tracked how hardware
advances enabled and afforded artistic developments. Concepts of mapping have shaped
this research by exposing relationships where these were not previously recognised, and
allowed important events from the past to be mapped to the present.
The research, and the resulting book, book chapters, journal and conference
papers delineated in this chapter, discuss in detail a range of significant innovations in
computer music and developments in hardware, software and in compositional practices.
I have drawn on my own compositional practices and novel conceptualising of mapping
to explore and elucidate the practice of others. In these works, new knowledge has been
generated about the practice of mapping in algorithmic composition, revealing that many
composers and indeed designers engage in explicit and nonlinear mapping as part of their
practice.
In this chapter, I have identified, discussed and demonstrated how my published
research represents a significant and unique contribution to the discipline of algorithmic
composition and the broader field of computer music. In the concluding chapter that
follows I draw together all of the elements canvassed in this thesis, setting out the
thematic connections between them and their combined significance and contribution to
the body of knowledge in the field.
Mapping in Algorithmic Composition and Related Practices 127
6 – CONCLUSIONS:
Somewhere underneath, very deeply, there’s a common place in our spirit where
the beauty of mathematics and the beauty of music meet. But they don’t meet on
the level of algorithms or making music by calculation. It’s much lower, much
deeper–or much higher, you could say.
– Györgi Ligeti (Borgo 2005, p. 85)
This dissertation brings together and presents a series of original compositions,
artistic work, rigorous research and a range of publications including a book, book
chapters and published papers, which are united through their thematic presentation via
mapping. In this thesis I have argued that the pieces of music are inseparable from the
mapping used in their creation, from the micro to the macro level, so much so that for at
least some parts of the music, the music and structure is the mapping rather than the
music being a product of the underlying data. In addition, the themes in the texts, from
examining the practice of mapping itself to uncovering new connections in the history of
electronic and computer music, have involved mapping and making connections in
various ways. In these analyses it has been shown that new and unique knowledge has
been created for the field in areas that had not been previously investigated or
documented.
6.1 Significant contributions.
The most significant contributions of this dissertation to the body of knowledge
and practice have been drawn from: a thorough analysis of mapping in my own musical
works and the works of other composers; research efforts, exploring both historical and
contemporary developments in computer music; and documenting the current use of
mapping as a creative impetus in the composition process. In summary, I believe the
most significant contributions of this work are:
• An historical overview of algorithmic composition and mapping as used in
compositional practice, showing how mapping has been used by a previous
generation of algorithmic composers;
Mapping in Algorithmic Composition and Related Practices 128
• An in-depth analysis, examination and discussion of mapping in my musical
works, investigating how stochastic and nonlinear mapping has been used
creatively as part of the composition process, including a brief analysis of each
piece and how the practice relates to historical mapping practice.
• A philosophical rationale for algorithmic composition, relating it to historical
musical practice and showing how it is an appropriate musical aesthetic response
to the modern world, and our understanding of and place in that world.
• The insights provided via my written work, revealing new understandings of the
history and context of computer and electronic music, with new relationships
discovered via the mapping of hardware advances to artistic developments.
• A new appreciation of how mapping is used in the modern practice of algorithmic
composition, showing how the use of nonlinear, creative and exploratory
mapping differs from its use in historical algorithmic composition practice, and
how it relates to design and other artistic practice.
Each of these points illustrates and contributes to an understanding of how mapping
has developed and how it has become an integral element in the creative
compositional process. This would not be possible without both a paradigm shift in
the conceptual and actual practice of algorithmic composition, and the technical
(computer hardware and software) means to realise it. This process has been analysed
in detail in this thesis, and represents the first exposition of this kind.
6.2 Limitations of this research and opportunities for further research.
While I have demonstrated in this thesis that mapping is used creatively in
contemporary algorithmic composition practice, and that this is different from how
mapping was used traditionally, there is no single method which is used, but rather
composers employ a range of mapping techniques to move from one domain to another.
As I wrote in the mapping papers, there might be some pedagogical value in creating a
detailed catalogue of mapping techniques (linear, exponential, logarithmic, shape-based,
nonlinear, free, and so on) including musical examples of how these could be used. Such
a catalogue could be particularly useful for beginning composers as a way of
understanding and applying foundational concepts. However, producing such a catalogue
Mapping in Algorithmic Composition and Related Practices 129
runs the risk of becoming music theory, and as composition is an expansive and creative
activity, composers will quickly find ways to go beyond what has been catalogued. As I
highlighted in Composers’ Views on Mapping in Algorithmic Composition:
In this way, mapping in algorithmic composition could be demystified and more
complex, varied and musically appropriate practices could be developed by
building on the work of others. The counter argument to this is that there is
something valuable in the effort of developing sophisticated mappings for oneself.
There is certainly interest in the effort required to play an instrument and how
mapping relates to this (Ryan 1992). (Doornbusch 2002c)
Also mentioned in the above paper is the view that there does not appear to be any
research on the links between cultural associations and mapping, and this may be of
interest to some composers. There may be, for example, mappings which are culturally
invariant, such as pitch or intensity (volume) and height. There is an obvious example of
this in instrumental design in the western world with the original Theremin, where the
volume of the sound output increased with the proximity of the left hand to the left
(horizontal) antenna, which is low. Thus a performer would raise their hand to make the
sound quieter. This was done for practical reasons so that the instrument would not be at
full volume as the player approached, but it caused such cognitive dissonance to the
audience and performers that modern Theremins have swapped this arrangement around.
I have also elected not to investigate other potentially salient matters such as, when
it was that composers shifted from linear to more complex and creative mappings or what
specific roles were played by various software and hardware developments in affording
these shifts for specific composers. However, some of these connections can be inferred
from an analysis of the tables in A Chronology of Computer Music and Related Events.
Moreover, as this thesis is an integrating essay designed to discuss my own practice I
considered such matters to be beyond the scope of my investigations. Suffice to say I
have not seen evidence in the literature of the timing of this shift, but it may well be
concurrent with the trend in creative mapping in instrument making which occurred
during the 1990s with the research, design and development of new musical instruments.
Mapping in musical instruments has been an area of intense research where such
mapping was often nonlinear (Hunt and Wanderley 2002; Hunt, Wanderley et al. 2002;
Mapping in Algorithmic Composition and Related Practices 130
Nort, Wanderley et al. 2004). The developments in this area may have influenced
composers during the same period – I mention such a possibility in the mapping papers
(Doornbusch 2002b) – as there was a similar preference for complex mappings. It would
not be the first time in the history of music that composers and instrument designers (and
the performers) have influenced each other (Apel 1969; Hoeprich 2008).
Another potential, albeit challenging area for research, related to the areas noted
above, would be to investigate how composers make aesthetic mapping decisions in their
practice. This of course raises many points, not the least of which is how composers or
artists make aesthetic decisions in general. This could fruitfully be approached from the
psychoanalytical and radical constructivist approach previously outlined. Modern
research techniques and cross-disciplinary research with medicine, where, for example,
functional magnetic resonance imaging of the brain is proving useful, might also help
clarify some of the mystery around this and the other issues to do with the creation of
form as outlined in the discussion of G4 in section 4.4. Thus, there are numerous
opportunities for research into mapping, not only in relation to musical composition but
more generally, mapping information from one domain to another in other creative
endeavours.
As stated at the end of section 2, it would be worthwhile investigating the
circumstances in which mapping creates the dominant character of a composition or
compositional gesture, as opposed to merely reflecting the character of the initial data,
where that data is dominant in the perceived aural result. It could be that sometimes the
mapping is more important than the initial data, and I offer at least anecdotal evidence to
suggest that this is the case, at least some times. Thus, we might consider that how things
have been mapped may determine, to a lesser or greater extent, the aesthetic character
and quality of the piece. This could be at least partially be determined experimentally by
having several, controlled, data sets, and also a data set of random numbers (noise).
These data sets could be passed through different mappings to produce a sonic result.
Upon listening to the results (as this is surely the only worthwhile test of musical output),
the effects of the mapping will be most evident on the random data, but if other data sets
are substituted and there is little perceptual difference, then it is the mapping itself which
is producing the character and aesthetic quality of the composition rather than the data. I
Mapping in Algorithmic Composition and Related Practices 131
acknowledge that this would require a great deal of effort to undertake properly, and may
not, in the end, be conclusive.
This work as presented does not complete the cycle of practice-led research to
research-led practice as advocated in a recent book on this topic (Smith and Dean 2009),
and this is worthy of further research and consideration. As presented in the above book,
this cycle suggests that the value of practice in informing research (in the present case the
practice is creating compelling and interesting works of music) and the research can be
interpreted as investigating the broad issue of mapping. However, it also suggests the
importance of research informing practice, and ideally the practice of others as well as
ones own. Further research (beyond the scope of this document) could be undertaken
with respect to the items identified above, particularly the issue of mapping providing the
dominant musical character. The papers on mapping note that mapping is useful or
important even if it is not perceived by listeners (as I think it often is in my music), and
this issue could be further explored, as could many other similar questions: Is there a
possibility that mapping may be able to generate some kind of musical expression?
Might nonlinear mapping permit the generation of greater information content (in the
technical sense) in the result than in the data plus a linear mapping? Are there other
possible applications of the insights highlighted here which might be applicable to other
artists? This would require further comparative research by myself, and others or at least
in collaboration with others, and it is a large-scale investigation. While it is beyond the
scope of this essay, it being an essay on published practice and research, the
aforementioned extensions and further research would ‘close the circle’ of practice-led
research to research-led practice.
6.3 Summary.
This thesis has demonstrated that mapping can be an important, even crucial,
element in the practice of algorithmic composition and that the use of mapping has
developed with increasing computational capabilities such that mapping is now used in a
creative, nonlinear and exploratory manner. These developments are evident in my own
musical works, as discussed, and in the works of others. I expect this trend to continue
with further developments in hardware and software and more sophisticated computing
Mapping in Algorithmic Composition and Related Practices 132
power and tools. This thesis has further shown that the practice of mapping, making or
uncovering connections and representation, is a useful technique for exploring the history
of electronic music from technical, artistic and aesthetic viewpoints.
The key themes and ideas established throughout this thesis, which have been
outlined above, clearly establish that there is a genuine musical and compositional
significance of mapping in electronic and computer music, particularly with respect to
the practice of algorithmic composition. This thesis has drawn together the various
themes of my published works, showing how the conceptual territory explored in my
musical and text publications relate and combine to create a significant, original and
unique contribution to the body of knowledge in the field of electronic and computer
music, and algorithmic composition, in terms of both its theory and practice. The
combination of this thesis and my published works provides others in the field with a
layered, multimodal and nuanced appreciation of the musical and compositional
significances of mapping in electronic and computer music.
Mapping in Algorithmic Composition and Related Practices 133
7 – REFERENCE LIST:
The astute reader will note that I have referenced numerous examples of my own work in
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