Application of Wave Field Synthesis in the composition of electronic music

Abstract

Wave Field Synthesis offers new possibilities for composers of electronic music to add the dimension of space to a composition. Unlike most other spatialisation techniques, Wave Field Synthesis is suitable for concert situations, where the listening area needs to be large. It is shown that an affordable system can be built to apply the technique and that software can be written which makes it possible to make compositions, not being dependent on the actual setup of the system, where it will be played. Composers who have written pieces for the system have shown that with Wave Field Synthesis one can create complex paths through space, which are perceivable from a large listening area.

Full text

Application of Wave Field Synthesis in the composition of
electronic music
M.A.J. Baalman, M.Sc.
Electronic Studio, Technical University, Berlin, Germany
email: baalman@kgw.tu-berlin.de
Abstract
Wave Field Synthesis offers new possibilities for
composers of electronic music to add the dimension
of space to a composition. Unlike most other
spatialisation techniques, Wave Field Synthesis is
suitable for concert situations, where the listening
area needs to be large. It is shown that an affordable
system can be built to apply the technique and that
software can be written which makes it possible to
make compositions, not being dependent on the
actual setup of the system, where it will be played.
Composers who have written pieces for the system
have shown that with Wave Field Synthesis one can
create complex paths through space, which are
perceivable from a large listening area.
1 Introduction
Spatialisation1 has been a topic of interest in the
development of electronic music since the 1950's;
common techniques make use of quadraphonic or
octaphonic setups and are based on providing
localisation cues based on psycho-acoustics or
acoustics (e.g. Chowning 1971). The technique of
ambisonics has become popular since the 1990’s
(e.g. Malham and Matt 1995). There are also various
examples where more loudspeakers are used, mostly
as setups for one specific piece or location and not
as a standardardized setup. A detailed historical
overview of spatialisation techniques can be found
in Malham & Matt (1995).
The limitation of stereo or ambisonic techniques
is that it only works perfectly well for one listener,
who is positioned on the so-called "sweet spot".
Obviously, in common concert environments the
intended effect of movement of the sound will in
these cases not be heard by a majority of the
listeners.
Wave field synthesis is a technique that can
overcome the limitation of only working well for
one "sweet spot" and can provide a good perceptual
1In this paper no comparisons are made to
headphone techniques, as these techniques are
quite different from loudspeaker techniques by
principle and less suitable for concert situations.
localisation in a relatively large listening area. This
makes the techique ideal for concert environments.
Its increasing popularity in audio engineering
shows that it is not unlikely that the technique will
be available in concert halls and becomes affordable
for studios in the near future (see CARROUSO2).
This article describes the first experiences with
the application of wave field synthesis in the
composition of electronic music. A short,
comprehensive explanation of the technique is
given, a description of the system used in the project
at the TU Berlin and the interface software, followed
by a description of the possibilities that were used by
composers. The pieces described were presented on
the Club Transmediale Festival in Berlin, on the 4th
of February 2003.
2 Wave Field Synthesis
The concept of Wave Field Synthesis (WFS) is
based on a principle that was thought of in the 17th
century by the Dutch physicist Huygens (1690)
about the propagation of waves. He stated that when
you have a wavefront, you can synthesize the next
wavefront by imagining on the wavefront an infinite
2 CARROUSO (Creating, assessing and rendering in
real-time of high-quality audio-visual
environments in MPEG-4 context),
http://emt.emt.iis.fhg.de/projects/carrouso/
Figure 1. The Huygens' Principle

number of small sources, whose waves will together
form the next wavefront (figure 1).
Based on this principle, Berkhout (1988)
introduced the wave field synthesis principle in
acoustics.
By using a discrete, linear array of loudspeakers
(figure 2), one can synthesize correct wavefronts in
the horizontal plane (Berkhout, De Vries and Vogel
1993). For a complete mathematical treatment is
referred to Berkhout (1988, 1993) and various other
papers and theses from the TU Delft3.
An interesting feature is that it is also possible to
synthesize a sound source in front of the speakers
(Jansen 1997), which is not possible with other
techniques.
Comparisons between measured wave fields and
wave fields reconstructed with WFS have shown
that the differences between the two are small
(Bourdillat 2001); most faults in the WFS
reproduction were due to reflections in the
reproduction room. Perceptual experiments and
practical experience have shown that with WFS one
can achieve a large listening area, where the sound
source is perceived correctly at the specified location
(Vogel 1993, Verheijen 1998). Malham’s (2001)
comments that WFS cannot achieve a perfect sound
image on all locations are true, but perceptually not
so relevant that it makes the technique not worth
considering for application in spatialisation of
electronic music.
2.1 Synthesizing moving sound sources
Jansen (1997) derived mathematical formulae for
synthesising moving sound sources. He took into
account the Doppler effect and showed that for its
application one would need to have continuously
time-varying delays. He also showed that for slowly
3Sound Control Group, TU Delft,
http://www.soundcontrol.tudelft.nl
moving sources the Doppler effect is negligible and
one can resort to updating locations and calculating
filters for each location and changing those in time.
This approach was chosen in this project.
Additionally, in order to avoid clicks in playback, an
option was built in to fade between two locations to
make the movement sound smoother.
3 System setup at the TU Berlin
The prototype system in Berlin was created with
the specific aim to make a system for the use in
electronic music (Weske 2001). The system consists
of a LINUX PC, driving 24 loudspeakers with an
RME Hammerfall Soundcard.
The loudspeaker signals are calculated in real
time with the program BruteFIR by Torger4. This
program is capable of making convolutions with
long filters in realtime. The filter coefficients can be
calculated with the interface software described in
this paper.
The current system is capable of playing
maximal 9 sound sources with different locations in
realtime, even when the sources are moving. This is
the maximum amount of sources; the exact amount
of sources that can be used in a piece depend on the
maximum distance range5 of each source and the
amount of reflections added. Both of these aspects
influence the total filter length and the filter length
determines the amount of calculation power needed.
In table 1 an overview is given of the capability of
the system in Berlin (running on a Dual Pentium
III). The filter lengths are indicated in samples. The
distances are based on the assumption that the
sample frequency is 44.1 kHz. The numbers
indicated in the table are the real time index
calculated by BruteFIR and are a measure for the
processor load; to have BruteFIR run stable while
sources are moving, it is best not to let the real time
index go above 0.80. It can be seen that the
maximum filter length and thus the distance range,
within which a source can move, can become quite
large. On the other hand, the larger the filter length,
the larger the I/O delay6 will be and the time step
after which one can change filter coefficients
(important for the movement of sources). In some
cases, using several partitions of a smaller filter
length can diminish the I/O delay.
4Torger, A., BruteFIR,
http://www.ludd.luth.se/~torger/brutefir.html
5 During calculation, the smallest delay, considering
all path points and all speakers, is subtracted
from all delays, so that only delay differences
between speakers remain. Thus the filter lengths
are based on the largest distance between points
on a path.
6 The I/O-delay is twice as large as the filter length.
Figure 2. The Wave Field Synthesis Principle

4 Interface software
In order to work with the system, interface
software was needed to calculate the necessary filter
coefficients. The aim was to create an interface that
allows composers to define the movements of their
sounds, independent of the system on which it
eventually will be played. That is, the composer
should be bothered as less as possible with the actual
calculations for each loudspeaker, but instead be
able to focus on defining paths through space for his
sounds.
The current version of the program allows the
composer to do so. The composer defines the
locations and paths through space and gives the time
parameters for these. The program will then
calculate the necessary filters, based on the hardware
setup of the system. As such, compositions can be
saved and loaded on different systems, with different
hardware setups, and the composition in space that
the composer intended will be played back. The
sound input needs to be presented at the inputs of the
sound card and can come from any source (also a
live source).
Figure 3. Screenshot of source and path definition. Graphical
results of this input is shown in figure 4.
Table 1. Overview of processor load (realtime index) and amount of sources per filterlength measured with
BruteFIR v0.99f on a Dual Pentium III, 1004 MHz.
Sources
Filt. Len. Dist. (m) time
123456789
256 1.97 6 ms 0.17 0.23 0.30 0.38 0.49 0.58 0.67 0.77 0.82
512 3.95 12 ms 0.18 0.25 0.33 0.40 0.53 0.61 0.71 0.80 0.87
1024 7.89 23 ms 0.20 0.27 0.35 0.42 0.55 0.63 0.72 0.80 0.88
2048 15.8 46 ms 0.22 0.29 0.37 0.43 0.56 0.64 0.73 0.83 0.91
4096 31.6 93 ms 0.24 0.31 0.38 0.45 0.59 0.70 0.81 0.94 -
8192 63.2 0.19 s 0.27 0.36 0.45 0.55 0.72 0.85 0.96 - -
16384 126 0.37 s 0.34 0.45 0.58 0.68 0.90 - - - -
32768 253 0.74 s 0.46 0.63 0.86 - - - - - -
65536 505 1.49 s 0.65 0.84 - - - - - - -
131072 1011 2.97 s 0.73 0.91 - - - - - - -

The program can also calculate room reflections,
when a room is defined by the user through the
position of four walls of a rectangular room, an
absorption factor and the order of calculation. The
calculations are done with the mirror image source
model (see also Berkhout 1988).
Though with WFS one can in principle also
create virtual sources in front of the loudspeaker
array, this was not yet implemented in the current
version. It will however be implemented in a future
version.
4.1 Sound source definition
The user can define various sources, each with
their own characteristics. A source in this context is
the virtual source from which sound emanates in
space, whose spatial parameters can be given by the
user.
For each source, the user can set the type of
source (a point source having a specific location or a
plane wave having only a direction), whether it is
moving or stationary, its location or angle, the sound
input channel at which the sound will be supplied
and in the case of a point source, whether reflections
have to be calculated or not. If reflections have to be
calculated, room characteristics can be defined
(these can be different for each source). In the case
of a moving source, one can define a path through
space and choose to let the movement loop along the
path. In figure 3 a screenshot of the source and path
definition dialog is given.
After supplying all information and storing it, the
user can get two overviews: a general overview in a
list, with some of the most important parameters for
each source, and a graphical overview showing the
paths of the sources through space (figure 4); one
can indicate of which sources the path is shown. It is
also possible to play a movie to get an impression of
the movement in realtime.
For the movement of the sounds, one can set the
number of breakpoints along the path and a fade
order. A breakpoint is an intermediary point on a
path; movement is created by switching from one
breakpoint to another. By using a fade between
succesive breakpoints, the movement can become
smoother and possible clicks in playback can
become softer. The user can choose to let the
amount of breakpoints on each segment be
calculated automatically. In that case, the program
uses a total of 40 breakpoints per source and divides
these over the segments of the path, depending on
the length of the segment and of the path and on the
time interval.
Figure 4. Screenshot of the graphical overview of the source path. The
numbers at the points between segments indicate the departure (dark) and
arrival (light) times. The dots in between the path and the reference point
are indicating the loudspeaker array.

In practice, one needs to experiment with the
optimal settings for the amount of breakpoints and
the fade order in order to bring clicks to an
acceptable level. Whether clicks are audible also
depends on the type of sound that is moving. Sounds
with a narrow frequency band, tend to create more
clicks when moving than broadband signals.
In some instances one cannot get rid of the clicks
altogether as BruteFIR has a minimum time after
which it can update filter coefficients. The exact
time depends on the filter length or block size. In the
program the minimum time step was set to 200 ms.
between breakpoints and to 50 ms. for a fade step.
5 Experiences with composers
For the Club Transmediale festival seven pieces
for the system were prepared by seven composers:
Frieder Butzmann, Boris Hegenbart, Marc Lingk,
Robert Lippok, Markus Schneider, Ilka Theurich
and Marije Baalman. All composers had different
backgrounds; all had previously composed
electronic music. I will elaborate about three works
that were created.
Marc Lingk, a composer residing in Berlin,
wrote a piece called Ping-Pong Ballet. The sounds
for this piece were all made from ping-pong ball
sounds, which were processed by various
algorithms, alienating the sound from its original.
Using these sounds as a basis, the inspiration for the
movements was relatively easy as the ping-pong ball
game provides a good basis for the distribution in
space of the sounds. In this way he created various
loops of movement for the various sounds as
depicted in figure 5. Paths 1 & 2 are the paths of the
ball bouncing on the table, 3 & 4 of the ball being hit
with the bat, 5 & 6 of multiple balls bouncing on the
table, 7 & 8 of balls dropping to the floor. Choosing
mostly prime numbers for the loop times, the
positions were constantly changing in relative
distance to each other. The movement was relatively
fast (loop times were between 5 and 19 seconds). In
the beginning, the piece gives the impression of a
ping-pong ball game, but as it progresses the sounds
become more and more dense, creating a clear and
vivid spatial sound image.
The author, Marije Baalman, made a piece where
the movements were based on a painting created
before in a rather improvisational way. The different
colours in the painting were mapped to different
sounds and they also had different movement
characteristics. One source was moving
perpendicular to the array, another parallel to the
array. Yet another was zigzagging to and from the
array, one source was jumping from one location to
another. The other two sources had other types of
paths that are less easily stereotyped. The exact
movement in time was made dependent on the
sounds. Silences on the sound input were used to let
the virtual source jump to another position for the
next sound to start its path.
As the movements were relatively slow and the
sound was not very dense, the movements and
different positions of the sound could be heard quite
clearly.
These two examples show that with WFS it is
possible to create more complex paths through space
than is possible with most other spatialisation
techniques.
Ilka Theurich, a student of sound sculpture in
Hannover, was interested most by the possibilities of
including virtual rooms and reflections into the
composition.
One sound was placed in a rather small room
with fully reflecting walls. This resulted in a sound
that was virtually at several locations (due to the
mirror image source model). As the sound from the
actual source location was the first sound to reach
the listeners’ ear, the sound would however still be
located there by the listener.
Other sounds were placed in a larger room, while
others were moving without being placed in a room.
One of the sources was created as a plane wave,
which allowed the listener to get different
perspectives on the composition by moving through
the listener area. The plane wave sound only had a
direction and as such was always in front of one,
with a specific angle, whereas the other sounds had
clearly defined locations. While the listener moved,
the plane wave sound would “walk along”, while the
point source sounds stay fixed in their position. In
this way the listener could determine his own
version of the composition by chosing his own
location.
Figure 5. “Ping-Pong Ballet” movement
overview. The large numbers indicate the path
numbers; the small numbers are the time
indications. The row in the front is the
loudspeaker array.

The effect of the movement and reflections were
the most clear for recorded sounds (having a rich
spectrum), as opposed to synthetic sine-based tones.
In order to limit the CPU-load, some
compromises had to be made: the total amount of
reflections calculated was reduced.
During the work the idea came up to enable the
room characteristics to change in time, which
possibly can also provide an interesting effect. This
will be implemented in a future version.
6 Concert
The concert took place at the Club Transmediale
Festival on the 4th of February. This is a festival that
includes electronic music both from (underground)
club culture and from more academic approaches.
The hall in which the concert took place
measured about 105 square meters and was
relatively reverberant. The array was positioned on
the stage a little bit above ear height.
The concert was preceded by a short presentation
explaining the wave field synthesis technique and
the software that the composers used to create the
movements of their sounds.
During the concert, the biggest problem was that
the system with its 24 loudspeakers could not create
enough loudness for the amount of people who filled
the hall (ca. 100 listeners). This had as a
disadvantage that the people in the back could not
perceive the music very well and were a bit loud as
they started to talk. During the sound check (without
the sound absorbing people in the hall) the system
was loud enough for the whole hall and the effect
was even clear in the back of the hall.
For the presentation of a prototype system the
concert can be regarded rather as a success. The
listeners who were in the front could perceive very
well the movements of the sounds in the
compositions. Especially when closing the eyes,
some people commented that the music created a
vivid visual image with its movements through
space. Others were quite amazed that they could
really move around the source, that is, position
themselves on a different relative location to the
virtual source. A sound artist, who works a lot with
ambisonics, commented that especially the distance
of various sources can be much better modelled with
WFS than with ambisonics.
The pieces of Lingk, Lippok and Baalman were
received best, as the movements of the sounds in
these pieces were the clearest. This is probably due
to the type of sounds that they used, which all had a
broad frequency spectrum, thus enabling listeners to
locate the sound more clearly.
Some listeners were disappointed, as the system
was not yet a full surround system.
After the concert several other composers
showed an interest in applying the system for their
own work, varying from electronic music concerts,
to sound installations, to a combination of electronic
music with dance.
7 Conclusions
From the experiences of working with
composers to create electronic music with
application of wave field synthesis, we can conclude
that the technique opens up new possibilities for
spatialisation of electronic music. The interface
proved to be easy to use, as the composers did not
need to know the exact mathematical calculation and
could think in familiar terms of positions in meters;
the graphical feedback provided a good overview.
Paths through space could be made more complex
than is possible with other spatialisation systems.
Reactions from the public show that the effect
reached with WFS provides a new experience for
electronic music, as they can choose their own
position relative to the positions of the various
virtual sound sources.
For application in concert environments it
became clear that a larger system is needed, both to
meet the problem with loudness and to create a
surround effect, where the benefits of WFS will
become clearer, especially with regard to modelled
reflections.
It can be expected that more work with
composers will open up new possibilities of the
WFS-technology for the spatialisation of electronic
music. By involving composers in the development
phase of the system, composers can influence the
direction of development of the system and interface
software.
8 Future work
The work at the Electronic Studio in Berlin will
be continued to implement new options in the
interface software. The possibilities for defining the
path in time will be expanded, variable room
dimensions will be included, as well as the
possibility to synthesize sources in front of the array.
Also, in order to increase realistic distance
perception, high frequency decay with distance will
be implemented.
The next step will then be to implement real time
control over the movements, in order to allow
application in live electronic music performances.
Control can then be issued with commonly used
protocols such as MIDI or OSC.
Plans are made to enlarge the prototype system,
so that a surround effect can be created. This will
allow more freedom for movement and enable to get
more realistic room reflections. An interesting

problem to solve will come up then: synchronising
multiple computers to drive the different speaker
arrays with the needed precision.
Future research will include modelling more
complex source characteristics (which could be
more realistically resembling acoustic instruments;
thinkable is frequency dependent, directional
sources) with WFS.
Application of WFS for auralisation in order to
be able to listen to a composition in its performance
environment in the studio is also a topic for future
research.
Next to further development on the technical
side, we plan to work more with composers with the
system, also to see whether combinations of the
WFS-system with other spatialisation techniques
deliver interesting results.
9 Acknowledgements
To Club Transmediale7 for giving the
opportunity to present the work at their festival and
inviting composers to work with the system.
To the Sound Control group at the University of
Technology in Delft for use of their figures.
7http://www.clubtransmediale.de
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