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Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
The importance of parameter mapping in electronic
instrument design
Andy Hunt
Music Technology Group,
Electronics Department
University of York,
Heslington, York
YO10 5DD
email adh2@york.ac.uk
Marcelo M. Wanderley
Faculty of Music,
McGill University
555, Sherbrooke Street West
H3A 1E3 - Montreal - Canada
email mwanderley@acm.org
Matthew Paradis
Music Technology Group,
Music Department
University of York,
Heslington, York
YO10 5DD
email mdjp100@york.ac.uk
Abstract
In this paper we challenge the assumption that an elec-
tronic instrument consists solely of an interface and a
sound generator. We emphasise the importance of the
mapping between input parameters and system parame-
ters, and claim that this can define the very essence of an
instrument.
Keywords
Mapping Strategies, Electronic Musical Instruments,
Human-Computer Interaction
ELECTRONIC INSTRUMENTS AND T H E
MAPPING LAYER
In an acoustic instrument, the playing interface is inher-
ently bound up with the sound source. A violin's string
is both part of the control mechanism and the sound
generator. Since they are inseparable, the connections
between the two are complex, subtle and determined by
physical laws. With electronic and computer instru-
ments, the situation is dramatically different. The inter-
face is usually a completely separate piece of equipment
from the sound source. This means that the relationship
between them has to be defined. The art of connecting
these two, traditionally inseparable, components of a
real-time musical system (an art known as mapping) is
not trivial. Indeed this paper hopes to stress that by
altering the mapping, even keeping the interface and
sound source constant, the entire character of the instru-
ment is changed. Moreover, the psychological and emo-
tional response elicited from the performer is determined
to a great degree by the mapping.
THE IMPORTANCE OF MAPPING
In this section we emphasise the dramatic effect that the
style of mapping can have on 'bringing an interface to
life'. We focus on our own experience in designing digi-
tal musical instruments and comment on several previ-
ous designs. An extensive review of the available litera-
ture on mapping in computer music has been presented
by the authors in [6], [16] and [17].
Informal Observations
The first author has carried out a number of experiments
into mapping. The more formal of these have been pre-
sented in detail in [5] and [3], and are summarised later
in this paper. Let us begin with some rather simple, yet
interesting, observations that originally sparked interest
in this subject. We have retained the first person writ-
ing style to denote that these are informal, personal re-
flections.
The Accidental Theremin
Several years ago I was invited to test out some final
university projects in their prototype form in the lab.
One of them was a recreation of a Theremin with mod-
ern electronic circuitry. What was particularly unusual
about this was that a wiring mistake by the student
meant that the 'volume' antenna only worked when your
hand was moving. In other words the sound was only
heard when there was a rate-of-change of position, rather
than the traditional position-only control. It was unex-
pectedly exciting to play. The volume hand needed to
keep moving back and forth, rather like bowing an in-
visible violin. I noted the effect that this had on myself
and the other impromptu players in the room. Because
of the need to keep moving, it felt as if your own energy
was directly responsible for the sound. When you
stopped, it stopped. The subtleties of the bowing
movement gave a complex texture to the amplitude. We
were 'hooked'. It took rather a long time to prise each
person away from the instrument, as it was so engaging.
I returned in a week's time and noted the irony that the
'mistake' had been corrected, deleted from the student's
notes, and the traditional form of the instrument imple-
mented.
Two Sliders and Two Sound Parameters
The above observation caused me to think about the
psychological effect on the human player of 'engage-
ment' with an instrument.
Figure 1. Simple Mapping for Experiment 1
Osc
Amp
Freq
Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
N
IME02-02
To investigate this further I constructed a simple ex-
periment. The interface for this experiment consisted of
two sliders on a MIDI module, and the sound source
was a single oscillator with amplitude and frequency
controls. In the first run of the experiment the mapping
was simply one-to-one, i.e. one slider directly controlled
the volume, and the other directly controlled the pitch
(cf. Figure 1).
I let several test subjects freely play with the instrument,
and talked to them afterwards. In the second experimen-
tal run, the interface was re-configured to emulate the
abovementioned 'accidental Theremin'. One slider
needed to be moved in order to make sound; the rate of
change of movement controlled the oscillator's ampli-
tude. But I decided to complicate matters (on purpose!)
to study the effect that this had on the users. The pitch,
which was mainly controlled by the first slider, operated
'upside-down' to most people's expectations (i.e. push-
ing the slider up lowered the pitch). In addition the
second slider (being moved for amplitude control) was
used to mildly offset the pitch - i.e. it was cross-coupled
to the first slider (cf. Figure 2).
Figure 2. Complex Mapping for Experiment 2
A remarkable consistency of reaction was noted over the
six volunteers who tried both configurations. With Ex-
periment 1, they all commented within seconds that
they had discovered how the instrument worked (almost
like giving it a mental 'tick'; "yes, this is volume, and
this is pitch"). They half-heartedly tried to play some-
thing for a maximum of two minutes, before declaring
that they had 'finished'. Problem solved.
With Experiment 2, again there was a noted consistency
of response. At first there were grumbles. "What on
earth is this doing?" "Hey - this is affecting the pitch"
(implied cries of "unfair", "foul play"). But they all
struggled with it - interestingly for several more minutes
than the total time they spent on Experiment 1. After a
while, their bodies started to move, as they developed
ways of offsetting one slider against the other, while
wobbling the first to shape the volume. Nearly all the
subjects noted that somehow this was rewarding; it was
"like an instrument". Yet in both cases the interface
(two sliders) and the sound source (a single oscillator)
were identical. Only the mapping was altered, and this
had a psychological effect on the players.
Mapping Experiments
Several formal investigations have been carried out by
the authors in order to explore the essence and the effect
of this mysterious mapping layer.
Complex mapping for arbitrary interfaces
The first author carried out an investigation into the
psychology and practicality of various interfaces for real-
time musical performance [3]. The main part of this
study took the form of major series of experiments to
determine the effect that interface configuration had on
the quality and accuracy of a human player’s perform-
ance. The full thesis is available for download online
[15], and the details of the theory, experiments and re-
sults have been published [5]. They are summarised
here, in order to give an overview of their implications
for mapping strategies.
Three interfaces were used, and these are now described.
The first interface (cf. Figure 3) represented a typical
computer music editing interface with on-screen sliders
connected one-to-one to each sound parameter.
Figure 3. The ‘mouse’ interface
The second (cf. Figure 4) involved physical sliders (on a
MIDI module) again connected in a one-to-one manner
to the synthesis unit.
Figure 4. The ‘sliders’ interface
The third interface (cf. Figure 5) consisted of a series of
multi-parametric cross-mappings, and—like the acciden-
tal Theremin mentioned above—required constant
movement from the user to produce sound.
Osc
Amp
Freq
Rate of
change
Invert
Scale
+
Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
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Figure 5. The ‘multi-parametric’ interface
Users attempted to copy (using each interface) a series of
sounds produced by the computer. The accuracy of re-
production was recorded for each user, over several at-
tempts, spread out over a number of weeks. Results
were gathered numerically, and plotted on a series of
graphs to compare the effect - over time - of each inter-
face. These quantitative results can be summarised for
the multiparametric interface as follows:
• The test scores in general were much higher than
those for the other two interfaces, for all but the
simplest tests.
• There was a good improvement over time across all
test complexities.
• The scores got better for more complex tests!
This last result may seem rather counter-intuitive at first
sight; that people performed better on the harder tasks.
However, this brings into question the definition of a
‘hard task’. If an interface allows the simultaneous con-
trol of many parameters, maybe it really is easier to per-
form the more complex tasks, and harder to accurately
isolate individual parameters.
A range of qualitative results was also gathered by inter-
viewing the test subjects to establish their subjective
experience of using each interface. They all concluded
that the 'mouse' interface was the most limited - as they
could see how impossible it would be to operate more
than one parameter simultaneously. Surprisingly per-
haps, they were nearly all extremely frustrated and an-
gered by the 4 physical sliders. Comments abounded
such as "I should be able to do this, technically, but I
can't get my mind to split down the sound into these 4
finger controls". Some users actually got quite angry
with the interface and with themselves. The multi-
parametric interface, on the other hand, was warmly re-
ceived - but not at the very beginning. At first it
seemed counter-intuitive to most users, but they rapidly
warmed to the fact that they could use complex gestural
motions to control several simultaneous parameters
without having to 'de-code' them into individual
streams. Many users remarked how "like an instrument"
it was, or "how expressive" they felt they could be with
it.
Focusing on the Effect of Mapping Strategies
In the above experiment several factors may have af-
fected the results. For instance, the multiparametric
interface used cross-coupled parameters in addition to
the user's energy. It also decreased reliance on visual
feedback, and provided two-handed input, all of which
may have contributed in varying degrees to the inter-
face’s effectiveness. An additional experiment was sub-
sequently carried out by the third author to focus en-
tirely on the user's reaction to a change in mapping
strategy.
These tests utilised three contrasting mapping strategies,
with a fixed user interface and synthesis algorithm. The
mappings were;
a) simple one-to-one connections between input and
output,
b) one-to-one requiring the user's energy as an input.
This was implemented by requiring the user to con-
stantly move one of the sliders in a ‘bowing’-like action
c) many-to-many connections from input to output, but
also requiring the user’s energy as in b).
These mappings were used to control the parameters of a
stereo FM synthesis algorithm, including amplitude,
frequency, panning, modulation ratio and modulation
index. The input device used was a MIDI fader box.
Users were asked to play with each interface until they
felt they had a good sense of how to ‘drive it’ to per-
form musical gestures. No time limit was given to this
process; the users were encouraged to explore the possi-
bilities of each set-up. Data was collected on the users’
(subjective) views on the comparative expressivity and
learnability of each mapping and the accuracy of musical
control that could be achieved.
Whilst experimenting with the first mapping test (one-
to-one) many users noted that the simple division of
parameters was not very stimulating. Users tended to
learn the parameter associations very quickly but then
struggle to achieve any improvement in their perform-
ance or expressive output.
The second test generated a range of comments, which
suggested that the process of injecting energy into a
system presented a much more natural and engaging
instrument. However, due to the proximity of sliders
on the interface they found it difficult to control other
sliders whilst providing the required 'bowing' action.
However, this problem lessened over time as the user
practised.
The third and final user test (many-to-many mappings)
provided some interesting results. Most of the test sub-
jects noted that the appeal of this instrument was that it
was not instantly mastered but required effort to achieve
satisfactory results. The instrument presented a chal-
lenge to the user, as one would expect from a traditional
expressive instrument.
These tests highlighted the differences between a gen-
eral-purpose interface, (such as the mouse) which has
simple mappings but allows the user to begin working
instantly, and an interface with more complex mappings
which must be practised and explored in order to achieve
truly expressive output.
Learning from Acoustic Instruments
In [12] the second author and collaborators discussed the
fact that by altering the mapping layer in a digital musi-
Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
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cal instrument and keeping the interface (an off-the-shelf
MIDI controller) and sound source unchanged, the essen-
tial quality of the instrument is changed regarding its
control and expressive capabilities.
Previous studies, notably by Buxton [2], presented evi-
dence that input devices with similar characteristics (e.g.
number of degrees of freedom) could lead to very differ-
ent application situations depending on the way these
characteristics were arranged in the device. In that study,
however, the devices were not exactly the same me-
chanically (one had two separate controllers and the
other one two-dimensional controller), so the situation
is not the same as when using the same input device
with different mapping strategies, even if the results are
similar.
In [12], a Yamaha WX7 wind controller was used as the
input device, and sound was generated using additive
synthesis models of clarinet sounds in IRCAM’s FTS
environment (later in jMax).
The idea behind the project was simple: many wind
instrument performers complained that MIDI wind con-
trollers tend to lack expressive potential when compared
to acoustic instruments such as the clarinet or saxo-
phone. A common path to solving this problem in-
volves improving the design of the controller by adding
extra sensors. However, it was decided to challenge this
assumption and to solely work on the mapping layer
between the controller variables and the synthesis inputs
(for a complete description see [12]).
Another point became clear in this process: even if the
WX7 was a faithful model of a saxophone providing the
same types of control variables (breath, lip pressure and
fingering), these variables worked totally independently
in the MIDI controller, whereas they are cross-coupled
in acoustic single-reed instruments. This natural cross-
coupling is the result of the physical behaviour of the
reed, and since the equivalent “reed” in the controller
was a plastic piece that did not vibrate, and moreover
was not coupled to an air column, variables were simply
independent.
Based on these decisions and facts, the authors proposed
different mappings between the WX7 variables and the
synthesis parameters. The first was basically a one-to-
one relationship, where variables were independent. The
second was a model where the “virtual airflow” through
the reed (loudness) was a function of both the breath and
lip pressure (embouchure), such as in an acoustic in-
strument. The third was a model that took into account
both the “virtual airflow” and the relationship between
spectrum content to breath and embouchure; a model
that would match even more closely the real behaviour
of the acoustic instrument.
Using these three different models, the system was per-
formed by different musicians and non-musicians. Re-
sults indicated that wind instrument performers tended
to stick with complex cross-coupled mappings similar
to the single reed behaviour (the third mapping strategy
used), whereas beginners initially preferred simpler
mappings (easier to play and produce stable sounds).
breath
breath
breath
lip pressure
lip pressure
lip pressure
fingering
fingering
fingering
dynamics (Y)
dynamics (Y)
dynamics (Y)
loudness
vibrato (X, relative)
vibrato (X, relative)
vibrato (X, relative)
fundamental frequency
(X, absolute)
fundamental frequency
fundamental frequency
(X, absolute)
(X, absolute)
loudness
loudness
WX7
Figure 6. Several mappings used in the clarinet
simulation presented in [12].
The two most important consequences of this work
were:
- By just changing the mapping layer between the con-
troller and the synthesis algorithm, it was indeed possi-
ble to completely change the instrumental behaviour and
thus the instrument’s feel to the performer. Depending
on the performer’s previous experience and expectations,
different mappings were preferred.
- By deconstructing the way that the reed actually
works, it was noted that the choice of mapping could be
important as a pedagogical variable. Indeed, in stark
contrast with acoustic instruments where the dependen-
cies between parameters are unchangeable, cross-
coupling between variables can easily be created or de-
stroyed in digital musical instruments. This means that
performers could focus on specific aspects of the instru-
ment by explicitly defining its behaviour. Possible op-
tions could include:
• complex (cross-coupled) control of loudness with
one-to-one control of timbre,
• one-to-one loudness and complex timbre controls,
or,
• complex loudness and timbre controls, such as in
the real instrument.
Even if these results supported the essential role of
mapping (and the importance of devising mapping
strategies other than one-to-one during the design of
digital musical instruments), they could not be easily
extrapolated to more general situations. In fact, in the
above specific case, there did exist a model of complex
mapping to be followed, since the controller was a
model of the acoustic instrument. So what about map-
pings in general digital musical instruments using alter-
nate controllers, those not based on traditional acoustic
instruments?
Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
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MODELS AND GUIDELINES FOR
MAPPING
Since there will not always be ready models for inspira-
tion when designing mapping strategies for new digital
musical instruments, the task then becomes one of pro-
posing guidelines for mapping and also, if possible,
devising models that can facilitate the implementation
of mapping strategies other than simple one-to-one rela-
tionships.
In trying to answer this question of how to extend a
specific mapping solution to a more general case, a
model of mapping for digital musical instruments was
proposed in [13]. It was based on the separation of the
mapping layer into two independent layers, coupled by
an intermediate set of user-defined (or “abstract”) pa-
rameters. This model was presented in the framework of
a set of extensions to jMax later known as ESCHER
(actually, a set of objects developed by Norbert Schnell
to perform interpolation using additive models).
This idea is based on previous works, such as those of
Mulder et al. [9], Métois [8], and Wessel [18]. A similar
direction was presented by Mulder and Fels in [10] and
later by Garnett and Goudeseune [7]. Basically, all these
works have used higher levels of abstraction as control
structures instead of raw synthesis variables such as am-
plitudes, frequencies and phases of sinusoidal sound
partials. The main point made in [13] was to explicitly
think about two separate mapping layers and the strate-
gies to implement these, and not on the choice of inter-
mediate parameters themselves, whether perceptive,
geometrical or “abstract” [14].
The intrinsic advantage of this model is its flexibility.
Indeed, for the same set of intermediate parameters and
synthesis variables, the second mapping layer is inde-
pendent of the choice of controller being used. The
same would be true in the other sense: for the same con-
troller and the same set of parameters, multiple synthesis
techniques could be used by just adapting the second
mapping layer, the first being held constant. Specifi-
cally in this case, the choice of synthesis algorithm is
transparent for the user
The original two-layered model has recently been ex-
panded to include three mapping layers in two inde-
pendent performance works by Hunt and Myatt [11], and
by Arfib and collaborators [1]. These works support the
idea that, by using multi-layered mappings, one can
obtain a level of flexibility in the design of instruments
and that moreover, these models can indeed accommo-
date the control of different media, such as sound and
video, in a coherent way.
One-to-one Mappings – Multiple Layers
We have noted that there is a tendency for designers to
make one-to-one mappings when constructing an inter-
face. We can use this tendency to improve the mapping
process if we utilise the many layered models outlined
above. The following scenario may illustrate this:
Imagine a system whose interface inputs included ‘but-
ton 1’,’button 2’ ‘slider 1’, slider 2’, ‘mouse x’ and
‘mouse y’. Let us suppose that the synthesis system
was a Frequency Modulation module with inputs such
as ‘carrier frequency, ‘carrier amplitude’, ‘modulation
frequency’ etc. Now consider the two possibilities be-
low:
Case 1: let us consider a designer working to connect
the above inputs to the above outputs. We are quite
likely to see arbitrary connections such as “mouse x
controls carrier frequency”, and “slider 1 controls modu-
lation frequency”. These give us the oft-encountered
one-to-one mappings.
Case 2: let us imagine that a mapping layer has already
been devised to abstract the inputs to parameters such as
‘energy’, ‘distance between sliders’, ‘wobble’ etc. Also
let us imagine that there is a mapping layer before the
FM synthesis unit, providing higher-level control inputs
such as ‘brightness’, ‘pitch’, ‘sharpness’ etc. Now we
can picture the designer making a relationship such as
“energy controls brightness”. On the surface this may
appear to be yet another one-to-one mapping. Indeed it
is – at the conceptual level. However, when you con-
sider how ‘energy’ is calculated from the given inputs,
and how ‘brightness’ has to be converted into the FM
synthesis primitives, you will notice how many of the
lower-level parameters have been cross-coupled.
Thus the many-level mapping models are a way of sim-
plifying the design process, and of helping the designer
to focus on the final effect of the mapping, as well as
providing a convenient method of substituting input
device or synthesis method.
FUTURE DISCUSSION OF MAPPING
From the evidence presented above in both informal and
controlled experiments, there is definitely a need to
come up with better-designed mappings than simple
(engineering style) one-to-one relationships. General
models of mappings have been proposed and expanded
to incorporate multimedia control, but also to fit several
levels of performance, from beginners to highly skilled
players.
One attempt to foster the discussion in this direction has
been initiated in the context of the ICMA/EMF Work-
ing Group on Interactive Systems and Instrument De-
sign in Music [4]. A further effort is currently being
carried out in the form of a special issue on “Mapping
Strategies for Real-time Computer Music” guest-edited
by the second author [17] to appear as volume 7, num-
ber 2 of the journal Organised Sound later this year.
We therefore welcome comments and criticism on issues
related to mapping so as to push the discussion on this
essential—although often ignored—topic.
CONCLUSIONS
The mapping ‘layer’ has never needed to be addressed
directly before, as it has been inherently present in
acoustic instruments courtesy of natural physical phe-
nomena. Now that we have the ability to design in-
struments with separable controllers and sound sources,
we need to explicitly design the connection between the
two. This is turning out to be a non-trivial task.
We are in the early stages of understanding the com-
plexities of how the mapping layer affects the perception
Proceedings of the 2002 Conference on New Instruments for Musical Expression (NIME-02), Dublin, Ireland, May 24-26, 2002
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(and the playability) of an electronic instrument by its
performer. What we know is that it is a very important
layer, and one that must not be overlooked by the de-
signers of new instruments.
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