doornbusch thesis final all

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


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.


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.


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.


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.


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


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.


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.


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”.


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.


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.


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.


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.


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


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


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.


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


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) 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.


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


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.


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


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


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


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:


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.


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).


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 midpoint, 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.


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


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).


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


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


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)


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


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.


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.


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


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.


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)


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


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


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.


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.


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


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


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


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.


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.


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


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.


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


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.


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.


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


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


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(


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


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.


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.


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.


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’


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.


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.


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:


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:


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.


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.


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.


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


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.


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.


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


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).


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


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.


• 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.


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.


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


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.


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.


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!”


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


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.


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


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.


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


(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


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.


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.


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.


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


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.


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


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


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


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


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


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


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


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


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.


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;


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.


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


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.


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


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.


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


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).


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.


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:


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;


• 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.


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


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.


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?


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 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.


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?


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


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 (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


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.


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 mapping 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


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.


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;


• 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


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;


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


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


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.


7 – REFERENCE LIST:

The astute reader will note that I have referenced numerous examples of my own work in

the list below. However, this is not for egotistical or self-promotional reasons, but because

this is an integrating essay which discusses that work. Apel, W. (1969). Harvard Dictionary of Music. Cambridge, Mass., Belknap Press of Harvard University Press. Arfib, D., J. M. Couturier, et al. (2002). "Strategies of Mapping Between Gesture Data and Synthesis Model Parameters Using Perceptual Spaces." Organized Sound 7(2): pp. 127-144. Aron, L. (1996). A Meeting of Minds: Mutuality in Psychoanalysis. Hillsdale, N.J.; London, Analytic Press. Babbage, C. (1832). On the Economy of Machinery and Manufactures. London, Printed by C. Knight. Bailey, D. (1992). On the Edge: Improvisation in Music. London, BBC. Television documentary. Episode One. Barbour, J. B. (2000). The End of Time: The Next Revolution in Physics. Oxford; New York, Oxford University Press. Barrett, R. (2002). "Musica instrumentalis of the Merciless Cosmos: La légende d’Eer." Contemporary Music Review 21(2-3): pp. 69-83. Barrett, R. (2006). "Review Paul Doornbusch: Corrosion: Music for Instruments, Computers and Electronics." Computer Music Journal 30(3): pp. 85-87. Bartolozzi, B. (1982). New sounds for woodwind. London ; New York, Oxford University Press. Bateson, G. (1979). Mind and Nature : A Necessary Unity. New York, Dutton. Berg, P. (1975). ASP - Automated Synthesis Program. Utrecht, Institute of Sonology. Berg, P. (1978a). PILE2 - A Description of the Language. Utrecht, Institute of Sonology. Berg, P. (1978b). A Users Manual for SSP. Utrecht, Institute of Sonology. Berg, P. (1979a). “Background and Foreground” SSP. A Bi-parametric Approach to Sound Synthesis. Utrecht, Institute of Sonology. 05: pp. 9-32. Berg, P. (1979b). "PILE: A Language for Sound Synthesis." Computer Music Journal 3(1): 30-41. Berg, P. (1996). "Abstracting the Future: The Search for Musical Constructs." Computer Music Journal 20(3): pp. 24-27.


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Doornbusch, P. (2002d). Corrosion - Music for Instruments, Computers and Electronics. New York, EMF Media. EMF CD 043. Doornbusch, P. (2004). "Computer Sound Synthesis in 1951: The Music of CSIRAC." Computer Music Journal 28(1): pp. 10-25. Doornbusch, P. (2005a). The Music of CSIRAC : Australia's First Computer Music. Melbourne, Australia, Common Ground Publishing. Doornbusch, P. (2005b). "Pre-composition and Algorithmic Composition: Reflections on Disappearing Lines in the Sand." Context: Journal of Music Research (29/30, printed 2007): pp. 47-58. Doornbusch, P. (2009a). A Chronology of Computer Music and Related Events. The Oxford Handbook of Computer Music. R. T. Dean. Oxford; New York, Oxford University Press: pp. 557-584. Doornbusch, P. (2009b, 27/03/2010). "A Chronology of Computer Music and Related Events 1906 - 2010." Personal website. Retrieved 27 March, 2010, from http://www.doornbusch.net/chronology/index.html. Doornbusch, P. (2009c). Early Hardware and Early Ideas in Computer Music: Their Development and Their Current Forms. The Oxford Handbook of Computer Music. R. T. Dean. Oxford; New York, Oxford University Press: pp. 44-84. Doornbusch, P. and P. Hoffmann (2010). GENDYN and G4 discussions. P. Doornbusch and P. Hoffmann, Personal communication. Electronic mail. Doornbusch, P. and L. Polansky (2010). Mapping and problems. P. Doornbusch and L. Polansky, Personal communication. Electronic mail. Emmerson, S. (2000). Music, Electronic Media, and Culture. Aldershot ; Burlington, USA, Ashgate. Foerster, H. v. (2003). On Constructing a Reality. Understanding Understanding: Essays on Cybernetics and Cognition. New York, Springer: pp. 212-225. Fox, D. (2009). The Time Machine Inside Your Head. New Scientist. Sydney, Reed Business Information. 24 October 2009: pp. 32-37. Gardner, M. (1974). "Mathematical Games: The Arts as Combinatorial Mathematics, or, How to Compose Like Mozart with Dice." Scientific American 231(6): pp. 132-136. Gill, M. M. (1994). Psychoanalysis in Transition: A Personal View. Hillsdale, NJ, Analytic Press. Glasersfeld, E. v. (1995). Radical Constructivism : A Way of Knowing and Learning. London, Falmer Press. Grahame, K., B. Rogers, et al. (1908). The Wind in the Willows. New York, Charles Scribner's Sons. Harley, J. (1994). Algorithms Adapted from Chaos Theory: Compositional Considerations. Proceedings of the International Computer Music Conference 1994. Denmark, International Computer Music Association, San Francisco. 1994: pp. 209-212.


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