Sound synthesis by physical modelling with Modalys

Gerhard Eckel, Francisco Iovino, René Caussé
IRCAM
Paris, France

Abstract: In the context of more general considerations concerning the use of sound synthesis in contemporary music composition, the latest version of the physical modelling synthesis system Modalys (previously called Mosaïc) is presented. In Modalys synthesis is based on the modal representation of vibrating objects. Modalys has been extended to allow modifications of the modal representation before and during the synthesis process. This extension is discussed in the light of the musical motivations of using sound synthesis in general and physical modelling in particular. The general trend towards a convergence of signal and physical models is discussed, and future extensions of Modalys following this tendency are presented.

1. Introduction

In order to describe the current features of Modalys and to discuss its future development we first have to introduce the context for which this sound synthesis system was conceived: the domain of music composition including the constitution of sound into its realm.

1.1 Sound technology

The way composers may think and imagine sound changed radically with the development of sound technology in our century. Sound transducers (microphones and loudspeakers) allow to detach the sound phenomenon from its mechanical and acoustical production mechanism (instrument) by the means of analogue representation of sound as electric current. Sound transmission and storage techniques (radio and tape recorder) use this and other analogue representations to delocalize sound in time and space. Analogue sound generation and processing devices (analogue studio) permit the direct production and manipulation of the analogue sound representation. This enables composers to create what could be called abstract sound - sound whose structure is not bound to the constraints of mechanical and acoustical systems (except for the loudspeakers and room acoustics).

The digital representation of sound signals used in today's computer systems increases once more the flexibility with which sound may be manipulated. Digital sound production and treatment does not any longer depend on the ephemeral nature of the electric current which represents sound "in time". In computers, sound is represented "out of time" (as a sequence of samples) and is converted to the analogue representation only when needed (sound input and output). Since digital sound processing is not constrained by the causal nature of the analogue studio it allows to conceive synthesis and transformation techniques that are impossible to realize or control with analogue technology. Moreover, digital sound representation is not restricted to mere sequences of samples: More abstract mathematical models representing sound allow for a direct manipulation of particular sound features.

Generally speaking, modern sound technology made sound at the same time more immaterial (its production is not any longer bound to instruments and instrumentalists) and more object-like (it can be manipulated with tools acting on its representations).

1.2 Sound synthesis

By sound synthesis we understand here all mathematical techniques used to create and transform sound. Each technique is based on a certain model capable of representing and generating a class of sounds. We can distinguish two types of models: On the one hand, there are models that describe the sound phenomenon (the sound signal) and they are sometimes called signal models [1] (e.g. additive synthesis). On the other hand, models are in use that describe the production mechanism of sound, which is usually a physical process and therefore these models are generally referred to as physical models (e.g. modal synthesis). For the composer the main difference between the two types lies in the way the models are parametrized: Physical models use physical parameters (e.g. geometric information, masses, forces, gestures) whereas the parameters of signal models are usually more closely related to sound perception (e.g. frequency and amplitude trajectories). The kind of model used and the types of its parameters are of great relevance with respect to any creative use of sound synthesis: They define the space exploitable by the imagination of the composer.

1.3 Musical motivations

There are various motivations for using sound synthesis in contemporary composition. Among them we find the desire to extend the repertoire of sounds that can be produced with reasonable effort by traditional instruments. Already long before sound could be generated synthetically composers where longing for this possibility. With the increasing availability of sound synthesis tools during the second half of our century this desire could be satisfied. But at the same time yet another potential of sound synthesis became apparent: the possibility to consider the design of sound as an integral part of composition, or as González-Arroyo puts it: "We want to make music with sound, and not sounds to make music with" [2]. Such approach implies a total assimilation of the idiosyncrasies of sound synthesis in the domain of musical imagination and composition. Sound synthesis is not any longer only a means to extend the instrumental sound repertoire but a specific way of conceiving music.

The choice of the synthesis models (usually several at a time) used in a concrete compositional situation is thus of fundamental musical importance. Given that the same sound can usually be synthesized by several models, this choice is not only dependent on the models ability to represent a particular real or imaginary sound but also on the perspectives or the potential of musical development [3] a certain model offers in a concrete compositional situation. Since each model describes a whole family of related sounds (structured sound material), it is the kind of these relations which is of major interest for the composer. This implies that synthesis tools should allow for easy definition of new models and seamless combination of existing ones. With respect to the second requirement Modalys offers interesting possibilities.

2. Modalys
2.1 History

Modalys is the successor of Mosaïc, IRCAM's modal synthesis system designed by Jean-Marie Adrien [4] [5] and implemented by Joseph Morrison in 1991 [6]. A detailed introduction to the features of the first version of this modular sound synthesis system based on modal representation can be found in [7]. Research and development work on the system was picked up again at IRCAM in 1994 by the Instrument Acoustics research team headed by René Caussé and the Interfaces and Sound Representations development team directed by Gerhard Eckel. A new version of the program (now called Modalys to avoid name conflict with the widespread Internet World-Wide-Web navigator Mosaic) has been ported to various computer platforms and is now available for DECStation, DECAlpha, NeXT, SGI, Macintosh and PowerMacintosh computers through IRCAM's user group service.

2.2 Synthesis model

Modalys' synthesis model is based on four types of elements (objects, accesses, connections, and controllers) which can be assembled by the composer in order to build and play a particular virtual instrument. Modalys objects describe vibrating structures defined by their geometrical characteristics (e.g. strings, plates, or membranes) and the physical parameters of the (homogeneous) material they are made from. Based on this description, Modalys calculates the (intermediate) modal representation used in the synthesis process (frequency, damping factor, and mode shape for each mode of vibration). Instead of synthesizing the modal representation, modal data stemming from modal analysis or other modal synthesis systems can also be imported. Modalys objects (representing all linear aspects of the synthesis model) can be put into relation by Modalys connections (representing all non-linear aspects) which describe the mode of interaction between objects (e.g. strike, pluck, or bow). Modalys accesses are used to specify the (variable) locations on objects at which they interact with other ones. Modalys controllers are used to specify the trajectories of all time-varying synthesis parameters (e.g. coordinates of accesses, connection parameters, forces, and controller inputs).

2.3 Extensions

The modular nature of Modalys' synthesis model guarantees a large amount of freedom when constructing instruments. This feature, which is due to the uniform representation of all vibrating objects as modal matrices, distinguishes Modalys from many other physical modelling synthesis techniques. But the major advantage of modal synthesis (besides efficiency of calculation) is that the frequencies and the damping coefficients of the modes of vibration are represented explicitly in the model [5]. This is essential for musical applications of sound synthesis where a direct manipulation of the spectral structure of a sound is desirable. Any compositional approach aiming at an articulation of timbre and harmony by means of sound synthesis may serve as an example. There the control over the frequencies and amplitudes of spectral components is often constrained by both the timbral and harmonic organization. Since in the first version of Modalys (Mosaïc) direct access of the modal data was not supported very efficiently the new version includes a set of control modules for static and dynamic modal data manipulation. This allows composers to adapt the modal data according to their needs. Since arbitrary modification of the modal representation may render the model incoherent with respect to any physical reality, direct manipulation of modal data loses its value at the point where the original interest of using a physical model is lost. When exactly this point is reached depends entirely on the concrete musical application and thus should not be defined by the synthesis system (it is rather decided by the composer's ear).

2.4 Why using physical models?

The extensions described above seem contradictory to the very interest of using physical models in sound synthesis: the introduction of the constraints of causality [8]. But why is the maintenance of causality in a synthesis model of any interest if one of the motivations of using synthesis in musical composition is to liberate sound creation from the constraints of physical systems (musical instruments)? Certainly, a composer would never use sound synthesis (physical models) to simulate or replace traditional instruments when they can be used in the first place. Thus is left the interest in sounds ranging between the concrete sounds produceable by musical instruments or other vibrating systems (including physical models) and abstract sounds easily generated by signal models. This interest in (perceptual) ambiguity is shared by many composers and appears as the most plausible motivation of using synthesis when excluding the extreme case of searching for sounds completely unrelated to our listening experience.

When using signal models, the problem of controlling the synthesis process consists mainly in creating a system of constraints (a control model) that forces the synthesis parameters to evolve in a way that gives rise to a certain identity of the sound phenomenon such that the latter can be used in a musical discourse (i.e. is recognizable in a certain context, can be ordered in scales, etc.). With physical models such system of constraints (causality, spatial representation) is included in the synthesis model. This is why it is so easy to produce so-called realistic sounds with physical models and abstract sounds with signal models. Realistic means in this context that our perception is easily able to link a given sound phenomenon to its production mechanism (source) and abstract means that it is hard for our perception to imagine a source for a given sound. This does not imply that there are no natural abstract sounds - also natural sounds can become abstract to our perception, but they are usually very hard to produce and control (e.g. multiphonics). Physical models can be used in this case to allow for a better control (given that they are refined enough to produce the sounds in question). But the more important aspect of physical models for musical composition is that the set of constraints introduced by causal systems is an especially interesting one because our perception is specialized to recognize sounds produced under these constraints. And even if we are interested to produce abstract sounds only, these constraints (which will always be present in our perception as reference) can teach us how to avoid realistic sounds. Thus if we are interested in articulating abstract and realistic sound material we should search for possibilities to modify the systems of constraints of physical models. This is what the discussed extension of Modalys is all about: The modal data calculated by Modalys respecting the physical description of vibrating objects can be modified arbitrarily. In its current form this new feature is not yet very powerful and we consider it rather experimental but the experiences composers will make with it are vital to guide any future development in this direction.

2.5 Future directions

The general goal in the development of synthesis systems can be seen in a convergence between signal models and physical models [1]. Modalys' synthesis model offers several interesting possibilities to approach this goal. The clear distinction between linear and non-linear components of the model allows to combine modal synthesis easily with signal models. Already the first version of Modalys allowed to produce control signals with additive or frequency modulation models. In the future we plan to integrate Modalys more closely with other synthesis models, aiming at a homogeneous synthesis platform comprising all models of interest.

Concerning more directly the physical modelling aspects, it is planned to make available a data base of analysed modal data usable with Modalys and to allow access to the data base of IRCAM's resonance models [9]. These data sets stemming from analysis of percussive instruments are compatible with the modal representation with the exception that they do not contain spatial information. It is planned to introduce into Modalys an object type that simulates "out-of-space vibrations of a single point" [5]. Such an object could directly use the resonance model description and thus make the resonance models available in Modalys. Again, from a physical modelling point of view such an extension seems contradictory since the essential difference between modal synthesis and other synthesis techniques "is that the spatial properties of the causal devices are included in the modelling" [5]. But from an integrative viewpoint this extension seems only logical.

Further extensions are planned on the level of different interaction modes such as the introduction of more general non-linear devices usable to compose complex interactions in a modular manner from basic elements. This will also compensate for the currently rather poor repertoire of interaction types available in Modalys.

References

1. Depalle, Ph., Rodet, X., "De la voix aux instruments", Cahiers de l'IRCAM, No. 2, pp. 121-139 (1993).

2. Eckel, G., González-Arroyo, R., "Musically Salient Control Abstractions for Sound Synthesis," Proceedings of the 1994 International Computer Music Conference, pp. 256-259 (1994).

3. Cohen-Levinas, D., "Entretien avec Marco Stroppa", Cahiers de l'IRCAM, No. 3, pp. 99-117 (1993).

4. Adrien, J.M., "Etude de Structures Complexes Vibrantes, Applications à la Synthèse par Modèles Physiques", Ph.D. thesis, Université de Paris VI, Paris, 1988.

5. Adrien, J.M., "The Missing Link: Modal Synthesis", in: G. De Poli, A. Picalli, and C. Roads, eds. Representations of Musical Signals. MIT Press, Cambridge, Massachusetts, 1991.

6. Morrison, J., Adrien, J.M., "Control Mechanisms in the MOSAIC Synthesis Program", Proceedings of the 1991 International Computer Music Conference, pp. 19-22 (1991).

7. Morrison, J., Adrien, J.M., "MOSAIC: A Framework for Modal Synthesis", Computer Music Journal, Vol. 17, No. 1, pp. 45-56 (1993).

8. Cadoz, C., "Timbre et causalité", in: J.B. Barrière, ed. Le timbre, métaphore pour la composition, Christian Bourgois Éditeur / IRCAM, Paris, 1991.

9. Potard, Y., Baisnée, P.F., Barrière, J.-B., "Méthodologie de synthèse du timbre: l'example des modèles de résonance", in: J.B. Barrière, ed. Le timbre, métaphore pour la composition, Christian Bourgois Éditeur / IRCAM, Paris, 1991.