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Physical modeling has become a fashionable term, but what is it exactly? How does it differ from other synthesis techniques? Let's find out with Marc-Pierre Verge, AAS' co-founder, who answers our questions.

Marc-Pierre, can you tell us what physical modeling is exactly?

In music, physical modeling refers to a sound synthesis technique which is based on models of the sound production mechanisms involved in musical instruments. The idea is to generate sound by reproducing how real musical instruments actually function and produce sound.

This approach may seem straightforward but is in fact very different from other techniques, such as FM, additive, subtractive and sampling, which could all be referred to as 'signal-based' methods because they attempt to reproduce the output signal from an instrument without worrying about how it was produced. A physical model is obtained from the laws of physics which describe how the world around us behaves. As in other fields of physics, a physical model is nothing else than a set of mathematical equations able to reproduce what can be measured experimentally.

In the case of a guitar for example, a physical model would reproduce how the pick moves the string away from its rest position; how the string vibrates once it is released; how the string vibration is transmitted to the soundboard through the bridge; and finally how the soundboard radiates sound which we can hear.

OK, I get the idea, but how does this materialize into a piece of software?

Physical models are sets of mathematical equations that enable one to calculate the output of a specific system (musical instruments in our case) submitted to input signals. Going back to our guitar exemple, a model will enable one to calculate the sound from the guitar (the output signal) given the position of the fingers on the string, the pick position on the string, the force applied by the pick on the string; its stiffness as well the velocity of its motion (the input signals).

Various techniques have been developped to transform mathematical equations and write them under the form of an algorithm which can then be programmed on a computer. The sound synthesis program therefore solves in real-time the set of mathematical equations wich constitute the model. It listens to input signals, usually MIDI signals sent by controllers connected to the computer, and then calculates the sound samples that are then sent to the sound card. The resulting sound usually also depends on the adjustments of physical parameters by the user on the graphical interface of the software.

We hear a lot about physical modeling these days. Is it a new synthesis technique?

In fact not at all, physicists such as Newton, Helmholtz, and Rayleigh have for centuries tried to understand and model how musical instruments function and produce so incredible sounds.

With the development of computers, scientists began to find ways to implement these models as algorithms and program them in order to produce sound. This field of research became very active in the 80's but the situation was then very different from the one we know today. It then took literally hours of number crunching on the most powerful computers of that time to obtain just a few seconds of sound. That's far from real-time! Even listening to the sound samples was not that simple as sound cards were not very common back then.

So the key factor for physical modeling has really been the increase of the power of computers which now enables us to run in real-time sophisticated enough models that can reproduce the complexity of real musical instruments.

If one looks at the music industry, Yamaha was the first company to offer a synthesizer based on physical modeling. In the early nineties, they released the VL1 which implemented physical modeling algorithms on dedicated electronics. Tassman, released by AAS in 2000, was the first software synthesizer entirely based on physical modeling. On top of that, it is a modular environment and is still unrivalled in its scope and quality.

Is it possible to reproduce exactly acoustic instruments?

The answer here is yes and no depending on the instruments. In some cases, the physical models that we have are accurate enough to obtain extremely realistic results. For example, the AAS Lounge Lizard electric piano is so close to the real thing that most people will not be able to distinguish it from a real piano. On the other hand, we have to admit that with other instruments, such as the violin, there is still some work required.

But the real interest of physical modeling is not so much how realistic it can be but how natural and expressive it is. As we explained previously, physical modeling generates sound in response to input signals. Its output is not deterministic and always varies depending on the nature of the control signals and what is being played. In other words, it is dynamic and this is how real life instruments behave!

For example, hit a note on a piano regularly. The note played will always be the same but if you listen carefully , the sound is always different. Why? Because when you hit the note the first time, the hammer hits a note at rest which sets it into vibration. When the hammer hits the string again, it is already vibrating and will now interact differently with the hammer. Hit it once more and the hammer will hit the string when it is in another point in its oscillation and again will produce a different sound. This is what makes acoustic sounds so rich and lively, they are never quite the same. Now this is something physical modeling reproduces naturally which is not the case with other methods such as sampling.

Another department in which physical modeling is very strong is in the reproduction of transients. This is the part of a sound during which the signal varies very rapidly, such as in attacks as opposed to the sustained part of a note where the waveform is very stable. Perceptually, transients are crucial and they give the tonal signature of an instrument. There is a very interesting psycho-acoustic experiment where one removes the attacks from recorded notes played on different instruments. In other words, one then only listens to the sustained phase of the notes. Well, in these conditions, it becomes very difficult to recognize the instrument.

Physical modeling does not make a distinction between transient and sustain phase of sounds, a model just keeps reacting depending on what is being played. This is another reason why physical modeling sounds so natural and rich.

Overall, compared to any other synthesis methods, physical modeling is the only one which can recreate the richness, liveliness and complexity of natural sounds but also the only one that can reproduce the interactive feeling associated with playing a real acoustic instrument.

How would you compare sampling and physical modeling?

They are two very different and complementary approaches. Basically, sampling consists in a play-back of a recording and therefore is very realistic in terms of the reproduction of the tone. A sample, however, is like a photo; it consists of a recording of one instrument or group of instruments played in a certain context in a certain way. It is basically static and will always sound the same over and over again.

A physical model, however, is very dynamic and lively. Its sound is always evolving and dependent on the way it is played and how it is tweaked. Many parameters, linked directly to the physical properties of the instrument (such as the geometry or material) are left to the user. It is therefore possible to adjust these parameters in ways that do not correspond to real instruments. Why not play a cello with a body as large as the soundboard of a piano? Why not play a guitar and change the material of the strings as you are playing? Indeed physical modeling is a very creative field that opens the road to a realm of unheard sounds that are still characterised by the acoustic qualities of real instruments.

To summarize, I would say that sampling is still certainly the best way to go in order to reproduce sounds such as orchestral string sections. On the other hand, physical modeling is unbeatable as an inspiring and creative sound design tool. It is also the most rewarding technique for performers who want to find in a synth the unmistakable feeling of playing a real musical instrument.

Why is physical modeling CPU intensive?

With physical modeling, there are no pre-recorded samples and sound needs to be generated on the fly which requires a certain amount of CPU power. When well programmed and optimised, however, the amount required to get good instruments is reasonable. On the other hand, physical modeling requires virtually no memory. No gigabytes of sound banks to load when installing the program or changing presets.

Does physical modeling only apply to acoustic instruments?

This technology is definitely not limited to acoustic instruments. One can apply exactly the same approach to electronic instruments such as vintage synthesizers. In these cases, the computer solves in real-time models of how electric circuits used in vintage synths, filters, tube amps and effect processors functionned and behaved. The benefits are the same as for acoustic instruments. Indeed the models can reproduce the complex behavior of these electronic components resulting in sound as lively and rich as that of the hardware units. Ultra Analog VA-1 from AAS is a very good exemple of this.