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Brown, Andrew R. and Jenkins, Greg (2004) The Interactive Dynamic Stochastic Synthesizer.
In Norris, Michael, Eds. Proceedings Australasian Computer Music Conference, pages pp. 18-22,
Wellington, New Zealand.
Accessed from http://eprints.qut.edu.au
Copyright 2004 the authors.
Brown & Jenkins, Copyright © 2004
Page 1
Proceedings ACMC 2004
ISSN: 1448-7780
http://acma.asn.au
The Interactive Dynamic Stochastic Synthesizer1
Andrew R. Brown †* & Greg Jenkins †
† Queensland University of Technology (QUT)
* The Australasian CRC for Interaction Design (ACID)
a.brown@qut.edu.au
g.jenkins@qut.edu.au
1 Brown, A. R. & Jenkins, G. 2004. “The Interactive Dynamic Stochastic Synthesizer” Proceedings of
the Australasian Computer Music Conference 2004. Wellington, NZ: ACMA, pp. 18-22
Abstract
Throughout musical history new sounds and
instruments have opened new opportunities for music
making. In this paper we outline a new interactive
digital instrument that implements the dynamic
stochastic synthesis algorithm devised by Iannis
Xenakis. We discuss the history and operation of this
synthesis process, previous implementations of it, and
how our implementation is the first we know of
designed specifically for live performance. Finally,
the behaviour tendencies of the synthesis system and
how these impact upon interactivity are discussed.
1 Introduction
The role of chance and random occurrence as a
musical technique has played a significant part in
Western compositional developments in the 20th
century. Among the leaders of this development, that
include John Cage, Gottfried Michael Koenig,
Karlheinz Stockhausen, Lejaren Hiller & Leonard
Issacson, and Luciano Berio, Charles Dodge and
Brian Eno, is Iannis Xenakis.
Xenakis’s interest in stochastic systems was
informed by modern scientific theories including
probability theory derived from quantum mechanics,
and kinetic theories of gases. His conception of
stochastic processes was as indeterminate functions
with entropic tendencies or, more simply, processes
that “evolve in different directions” and move
between states of “order to disorder, or vice versa”
[6:16].
Uniquely, Xenakis applied probability not only to
the organisation of musical objects and structures but
also directly to the generation of sound waves, with a
process he called Dynamic Stochastic Synthesis
(DSS). This synthesis process applies constrained
random processes to the moment by moment
fluctuations in air pressure that are fundamental to
sound creation.
In this paper we outline an implementation of the
dynamic stochastic synthesis algorithm that is
intended for real-time performance, discuss some of
the historical contexts that inform the design and
discuss issues of interaction design that have arisen
during its use in performance.
2 Dynamic Stochastic Synthesis
For most of his life Iannis Xenakis was concerned
with the use of probabilities for creating music. He
conceived of DSS as a way to apply stochastic
functions to the generation of audio waveforms. His
early compositional uses of stochastic processes were
primarily in determining aspects of works at the level
of note attribute selection and the organisation of
musical form. It was not until later in his life, that he
applied these processes directly to the dynamic
stochastic synthesis process although he had
previously worked with stochastic functions as
elements of synthesis parameter control in processes
including granular and FM synthesis. Xenakis termed
the organisation of music at this sample-by-sample
level, microstructure [7].
Dynamic Stochastic Synthesis involves multiple
levels of probabilistic functions that determine the
positions of break points in an envelope which in turn
describes one cycle of an audio waveform, as shown
in figure 1. The number of points in the waveform is
predetermined by the user or programmer.
Figure 1. A breakpoint waveform description
Brown & Jenkins, Copyright © 2004
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Proceedings ACMC 2004
The amplitude and time position of each break
point are varied at each repetition by a random walk
function. A random walk is a constrained stochastic
function where each subsequent event is selected at
random within a limited range above or below the
previous value. The pitch (cycle duration) and
dynamic (peak amplitude) are thus constantly varying
from cycle to cycle. Each amplitude-time point varies
independently and they all change concurrently.
Slight variations produce a more stable ‘phasing pitch
glide’ sound and larger variations result in a more
‘noisy’ timbre. The amplitude and pitch range can be
compressed by setting maximum values for each,
what Xenakis calls “elastic barriers.”
Sample values for the waveform are calculated by
interpolating between the stochastically generated
amplitude-time points. The resolution of the
interpolation is traditionally quite course, adding to
the ‘low tech’ character of the DSS sounds (Xenakis,
I. 1991; [2]).
Part of the appeal of this process to Xenakis was
its computational efficiency and the fact that it did not
rely on a harmonic or Fourier conception of the sound
world. He comments that “the challenge is to create
music, starting, in so far as it is possible, from a
minimum number of premises but which would be
‘interesting’ from a contemporary aesthetic
sensitivity, without borrowing or getting trapped in
known paths” (Xenakis 1991:295).
Xenakis had been explicitly exploring stochastic
systems in his works as early as 1957 with
Achorripsis and, not long after, with the ST
(Stochastic) series of compositions. He had been
using random walks in his instrumental compositions
since the 1970s, the most paradigmatic of which was
Erikthon (1977) where both note level and larger
structures were heavily determined by random walks
[1] [3]. The extension to use stochastic functions to
control audio signal generation was an insightful one,
even if it appears as a natural extension of his work in
hindsight.
The use of non-linear processes at the level of
microstructure and the constant updating of the
waveform, means that DSS has an ‘organic’ quality
because it is in a constant state of evolution. The
dynamic qualities of continual development and the
emergent nature of the sound’s pitch, loudness and
timbre result in a system that can produce a wide
variety of outcomes, but is not always easy to control.
In the early 1990s when Xenakis was able to realise a
complete DSS implementation, almost 20 years after
the initial conceptions, the system was a non real-time
computer assisted compositional tool. This paper
outlines some of our attempts to enhance the
performability of DSS.
3 Previous DSS Implementations
The original implementation of dynamic
stochastic synthesis was in the Gendyn program,
written by Xenakis in BASIC with the assistance of
Marie-Hélèn Serra [4]. The program generated
completed works including Gendy3 (1991) and S.709
(1992) by employing stochastic processes at both the
macro and micro structural levels.
The Gendyn program introduces complexities into
DSS beyond those described in the previous section.
At the level of microstructure these include the
cascading of two random walks for each of amplitude
and time rather than one, and the use of “mirrors” for
maximum boundaries that reflect values above the
maximum back into the desired range, rather than
“brick wall” limiters that result in significant areas of
peak values.
At the level of macrostructure, the Gendyn
program controls the form of the piece enabling it to
produce a complete work, not just a continuous sound
stream. The program allows for multiple voices, 16 in
the case of Xenakis’ implementation. Short periods of
activity or silence in each voice are stochastically
determined which produces a kind of chaotic
rhythmic counterpoint. Xenakis refers these short
periods as ‘fields.’ A probabilistic choice about the
number and start location of these fields determines
the texture and duration of the piece overall.
A faithful re-implementation of the Gendyn
program was undertaken by Peter Hoffman in the mid
1990s. This version, which Hoffman called The New
GENDYN Program [2], was written in C++ and
Visual Basic and was efficient enough to run in real-
time. Hoffman’s intention was to gain a full
understanding of the Gendyn program and his
implementation even reproduced some of the
programming ‘errors’ in the original implementation
that had important sonic results. Our implementation,
described later in this paper, while building on
Hoffman’s work has a different purpose. It intends to
make the opportunities of DSS available to the
computer music performer, and to add some
extensions that broaden the sonic potential even
further.
The Stochos program [1] employs many functions
used by Xenakis including elements of dynamic
stochastic synthesis. The application, implemented in
Max/MSP, is a computer-assisted composition tool
that enables the user to apply its functions to a
composition’s macro and micro structure and to work
in real-time or render audio files if the processing
load exceeds real-time performance limits. As well as
enabling DSS as one of the synthesis process in
Stochos, Bokesoy and Pape apply the DSS concepts
of stochastic line segment envelope curves, and
mirrors as reflective limiters of stochastic data, as
general tools throughout their program. While
Stochos has a broader range of stochastic sonic
functions than Gendyn or New GENDYN, they each
explore the features of sonic space opened up by
dynamic stochastic synthesis.
Brown & Jenkins, Copyright © 2004
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Proceedings ACMC 2004
4 Sonic Behaviour
In a stable state where the random walk variations
of both amplitude and time are reduced to zero, the
DSS process acts as a stable oscillator at a fixed pitch.
The precise sonic spectrum depends on the wave
shape but the tendency is for a bright ‘buzzy’ tone,
not unlike a sawtooth wave. Given enough points in
the wave envelope and a lot of luck in freezing the
points, a simple tone close to a sine wave is
theoretically possible.
The addition of a small amount of amplitude
variation creates a warmer chorusing or phasing
effect. Allowing slight variations to the time positions
of the points results in a wandering pitch glissando, at
times not unlike the sound of a Blow Fly. Larger
random walk steps in amplitude and time positions
cause the sound to become frantic, a result
reminiscent of asynchronous granular synthesis with
random pitch shifting or of waveshaping. This is not
surprising given that Hoffman describes DSS as “a
non-linear stochastic distortion of the shape of the
waveform over time” [2:32]. Further increasing of the
random walk step size causes the timbre to approach
Brownian noise or, with tightly constrained time
mirror boundaries, white noise.
While the shape of the waveform has a significant
effect on the timbre of the sound, the characteristic
behaviour of DSS derives from this non-linear change
over time. Hoffman suggests that “it is this change
that makes up the specific quality of GENDYN sound
by continually transforming its spectrum” [2:36]. He
goes on to explain that DSS is a dynamic system
where the dynamic behaviour of the system is fractal
in nature (like all random walks) and, further, that the
cascading of random walks means that the sound is
governed by ‘strange’ attractors. When using the
system for performance the challenge is to balance
the interest generated by instability with a degree of
control that enables musical expressiveness. The
performer of DSS systems will have better control
given an understanding of dynamic system tendencies
and the importance of the relationship between the
successive random walk states in creating different
attractor diffusion patterns.
Another variable in DSS is the choice of
stochastic distribution. For example, random
functions usually generate a linear distribution, but
Gaussian, Cauchy, Logistic and Poisson functions
were favourites of Xenakis who explored the different
tendencies of each in some depth. The general sound
of the DSS system is similar regardless of the
distribution function, but the behaviour of the system
over time can be significantly affected by changes in
stochastic distribution functions and their parameters.
The role of the mirrors in DSS is to constrain the
boundary limits of the sonic space. In the case of
amplitude change the mirrors act as dynamic
compressors and also as peak level limiters. The
reflective nature of the mirror boundaries also means
that at more constrained amplitude ranges they have a
timbral effect in producing jumps in the waveform’s
fundamental pitch within the overtone series because
the reflections cause “transient inner symmetries” in
the waveform [2:37]. The time mirrors act to
constrain the pitch range, with more restricted
boundaries forcing the pitch range into higher and
narrower frequency regions. When generating broad
spectrum signals (noisy sounds) the time mirrors can
act like a high pass filter.
Because the waveform is made up from line
segments between points, the resolution of the
rendering of those into sample values can effect the
sound. Lower sample bit depths result in a ‘course’
sound, because of associated changes in quantisation
noise. This will also effect dynamic range, of course.
Changes in sample rate can act as a crude low pass
filter by changing the upper frequency limit.
Hoffman’s analysis of the sonic behaviour of
Xenakis’s original algorithm and code were incisive
and although his implementation could be altered in
real time, the system was focussed more on reflective
composition and analysis than real time performance.
The aim of our implementation of DSS is to make
these behavioural characteristics available to the
performing computer musician in a way that he/she
can best exploit these tendencies.
5 An interactive implementation
In order to explore dynamic stochastic synthesis
in live performance a real-time system was required.
In this section we outline the considerations and
design of an Interactive Dynamic Stochastic
Synthesizer (IDSS) program.
The need for a new implementation was several
fold. Xenakis’ original Gendyn software was not real-
time, nor was it available. Hoffman’s New GENDYN
operates in real-time but is not focused on
performance control and was designed for the
Windows 95/98 platform. The Stochos system is
possibly more complex than required or even suitable
for performance and in any case was not published
until after our implementation was written. Finally,
the benefits of fully understanding DSS through
implementing it in software are significant in their
own right, and an informative aspect of this
creative/research project.
The IDDS is a real-time application developed in
Java and uses the audio system from the jMusic
library [5] which includes the DSS algorithm which
was added to jMusic as a consequence of this project.
The IDSS program features a graphical user
interface (GUI), one channel strip of which is shown
in figure 2. The top area of the interface has start and
stop buttons, below which are sliders for each of the
random walks (1 & 2) that specify the step size
(Step1 and 2) and mirror positions (Max1 and 2) for
amplitude (A) and time (T).
Brown & Jenkins, Copyright © 2004
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Proceedings ACMC 2004
There is a visual display of the animated
waveform and the secondary mirrors are also
displayed here. Sliders to the left of and below the
display box control the secondary mirrors for
amplitude and time respectively. In the bottom left
corner of the wave display area are triangular buttons
that move secondary time and amplitude mirrors
concurrently.
Figure 2. The graphical interface of one IDSS voice.
Below the wave display area are radio buttons for
choosing the stochastic distribution type. Linear and
Gaussian distributions are available. Below these are
sliders to control sample bit depth, panning and
volume gain for this voice.
To assist in the performability of the application,
selected sliders have associated automated controller
buttons. These buttons toggle fades (slow and fast, up
and down) and the central button starts fader
oscillation up and down repeatedly. The maximum
and minimum values between which automation
occurs are specified by numbers above and below the
button array. These max and min values can be
adjusted by clicking dragging on the number display.
The automated faders are particularly useful in the
control of multiple DSS voices as they offer the
performer dynamic control over multiple parameters
simultaneously when using the ubiquitous point and
click controller (mouse/track pad). Computer
keyboard shortcut commands for several functions
also improve interaction in this regard. This level of
multiple parameter control has been an important
consideration of IDSS from its inception, in an effort
to avoid the ‘serial change’ restriction often
encountered in ‘laptop’ performances.
6. Interaction Considerations
During performance each IDSS voice produces
alternate active and silent sound fields of variable
duration, therefore the main task of playing the
software is to vary parameters to stimulate and
maintain an interesting polyphonic blend. Random
walk step sizes and mirrors can be set so that a voice
is quite stable or varies widely of its own accord.
Each extreme has it’s own challenges for
performance. More stable settings involve less risk of
drift into inappropriate regions of sonic space, but
require more tweaking to maintain interest. Unstable
settings can almost create a piece by themselves, not
unlike the way Xenakis used his Gendyn program,
however, control over the outcome is transferred to
the algorithm to a large extent and performance
consistency can vary widely. Composers using other
DSS implementations have the luxury of throwing
away unsuccessful outcomes. For example, Xenakis’
first DSS piece, Gendy3, was named after it’s full file
name GENDY301, so we can assume that it took
Xenakis more than three hundred attempts to arrive at
a satisfactory outcome. The intent of our IDSS
application is not a “sound -producing automaton
creating complete composition ‘out of nothing’,
purely through the structure-generating power of
probabilities” [2:31]. but to enable a partnership
between the processing algorithms and the live
performer. Within this partnership, the processing
algorithms determine the detail of the sonic
microstructure while the performer is chiefly
responsible for the macrostructure.
Brown & Jenkins, Copyright © 2004
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Proceedings ACMC 2004
The live performance risk with generative music
systems can be acute at times, and stochastic
processes are often quite an imprecise tool. To help
alleviate this risk the IDSS program can save and
recall settings allowing the performer to act like DJ in
scheduling and tweaking prepared sections of work.
Unlike a pre-sequenced stream of MIDI information,
or banks of sampled loops the generative nature of the
real-time system maintains a degree of uncertainty
even in this scenario. A skilled performer needs to
not only understand every available parameter’s
operation and interrelation but also the degree of
unpredictability likely to result from different
relationships between settings.
Like other computer and electronic music
performances the juggling of many sound sources is a
critical skill. The software has been designed to
operate with only the standard mouse and keyboard
controllers. The automated controllers in the IDSS
program assist the execution of several parallel tasks
despite the often awkward one-mouse controller
situation. The IDSS program supports assignable
MIDI controllers, a feature that greatly enhances real
time control and expressive capabilities by enabling
the use of physical hardware controllers (knobs
and/or slider boxes). With only two hands, such
devices rarely permit simultaneous control of more
than a few parameters so a combination of qwerty
keyboard, mouse and MIDI control hardware is
normally employed.
7. Conclusion
The application of a synthesis process in an
interactive software environment requires a clear
understanding of the operation, behaviour and
potential of the process in order to adequately reveal
the useful attributes to the musician and hide
irrelevant details. We have outlined our approach to
this task in relation to dynamic stochastic synthesis
and its implementation in the Interactive Dynamic
Stochastic Synthesizer. The design and development
was informed by an understanding of the historical
context, a familiarity with the technical aspects of the
process, experimentation with DSS leading to
analysis of tendencies in the synthesis process and
methods of harnessing them for efficient use in live
performance. However, as with all such efforts, our
work is ongoing and further performances and
exploration will suggest enhancements. Some already
planned include stochastic macrostructure controls,
meta controller assignment mapped to multiple
parameters and an increased choice of probability
distributions and interpolation functions.
References
[1] Bokesoy, S. and G. Pape (2003). "Stochos: Software for
Real-Time Synthesis of Stochastic Music."
Computer Music Journal 27(3): 33-43.
[2] Hoffman, P. (2000). "The New GENDYN Program."
The Computer Music Journal 24(2): 31-38.
[3] Matossian, N. (1986). Xenakis. London, Kahn &
Averill.
[4] Serra, M.-H. (1992). "Stochastic Composition and
Stochastic Timbre: Gendy3 by Iannis Xenakis."
Perspectives of New Music 31(1): 236-257.
[5] Sorensen, A. and A. R. Brown (2000). Introducing
jMusic. The Australasian Computer Music
Conference, Brisbane, ACMA.
[6] Xenakis, I. (1971). Formalized Music: Thought and
Mathematics in Composition. Bloomington,
Indianna University press.
[7] Xenakis, I. (1991). Formalized Music. New York,
Pendragon Press.
