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Looking at these amazing products and wandering what exactly is physcial modeling and why is it so important to these products?
AAS's Co-Founder Marc-Pierre Verge answers all the need to know questions about Physical Modeling;
MARC PIERRE VERGE: Physical modeling is a synthesis method based on the laws of physics. The idea is to simulate how an object or musical instrument vibrates and produces sound. From the simulated motion of the object, one can deduce the sound it produces. This is different from sampling which is based on recordings. Sampling is not concerned with how a sound was produced but just the signal itself. When well done, physical modeling can sound incredibly natural. This is because the model, a kind of black box, outputs the sound produced by the instrument whatever the input signal. The entire range of sounds and tone of the instrument can therefore be obtained with a single model. In a musical context, the input signal, for example the pick and finger force signals on a guitar string, changes all the time depending on the playing of the guitarist. A physical model sounds real and alive because it naturally follows the playing of the musician in a continuous way. In comparison sampling is like a photo of the sound produced by an instrument in certain conditions at a certain time. To get the entire range of sounds of an instrument, one needs to record the instrument in all playing conditions which necessarily results in layers and huge sample files. We are usually interested in reproducing real musical instruments but an interesting aspect of physical modeling is that it can be very creative in terms of tone. Indeed, instead of adjusting the model parameters to those corresponding to a real instrument (ex. geometry, material, etc…), there is no reason why one could not use any other values. It then becomes possible to create completely new instruments and even vary their properties in real time!
Vibration of objects are described by mathematical equations based on the laws of physics. For exemple, the vibration of a string or that of the air column in a tube, is described by a so-called wave equation. With physical modeling, we start with the equations corresponding to the type of instrument we wish to reproduce. An instrument is usually a complex system and the difficulty consists in modeling all the different components and their interaction. For example, a piano requires a model for the hammer action, its interaction with the string, motion of the string, exchange of energy between the string and soundboard at the bridge and finally radiation of sound by the soundboard which constitutes the output of the model and the actual signal we hear. Mathematical equations are only symbols on paper and in order to translate them into software one needs to use numerical techniques to discretize them and be able to implement the model under the form of an algorithm. This algorithm is implemented using a programming language (the C language for example) which is embedded in a more general computer program comprising an interface, management of input and outputs, presets etc… The program received performance data, from a MIDI keyboard for exemple, and sends that to the modeling algorithm which is solved in real-time. The sound output is therefore always different and dependent on the playing of the performer.
Maths is involved at all levels of the process. First at a more abstract level when establishing the basic equations that will be used. Then when developing and implementing the discrete time algorithm which will be implemented and at the output level where DSP (digital signal processing) techniques are used to further shape the sound.
Physical modeling and musical acoustics are in fact very old fields. Physicists and mathematicians, starting with Pythagoras in the 6th century BC, have always used musical instrument to try to understand wave motion. The basic equations of acoustics that we use today were discovered in the 17th and 18th century by the likes of Mersenne, Newton, Rayleigh, Helmholtz, Fourier and many others. Musical instruments, in particular string instruments and organ pipes, provided them with perfect systems for observing and understanding wave motion and acoustic phenomena. From a sound synthesis point of view, physical modeling really became possible at the end of the nineties. Before that, the interest was mostly scientific because computers were not powerful enough to solve complex models. Calculating a few second of sounds literally took hours. Around 2000, it became possible to run fairly elaborate models in real-time without too much noticeable latency.
Musical instruments, despite their apparent simplicity, are very complex systems from an acoustic point of view. Furthermore, many different phenomena are usually involved in shaping the perceived sounds. How close we can get to the real thing depends on the quality of the models which varies from instrument to instrument. For most instruments, I would say that it is now possible to get synthetic sounds that are so close to the real thing that most people could not recognize them from recordings of a real instruments. Musical acoustics is still, however, a very active field of research as some particular aspects of sound production associated with specific playing techniques and instrument making are not perfectly understood. In terms of musical products the main problem, except for keyboard instrument, is still how to play and control these models. Indeed many things happen, for exemple when a saxophone or violin is played, that are difficult to reproduce with a MIDI keyboard. In other words, getting a realistic sound is very much dependent on getting the right control signals. This implies either working with dedicated controllers or integrating the playing technique itself in the synthesis engine. Our Strum GS-2 guitar synthesizer is a good exemple of this where we integrated chord recognition, chord voicing, as well as strumming and picking technique in the engine.
I think we will see more and more physical modeling based instruments appear on different platforms, for exemple portable or modular devices, as computing power is less and less of an issue. Physical modeling is very attractive for this kind of devices as it does not rely on huge sample banks. As it becomes easier to port algorithm on portable devices, it also becomes easier to embed the synthesis engine with special controllers and I think we will see more and more of this. Outside the music world, we will more and more modeling in video games and virtual reality system. The ideas behind modeling can be used to generate different kind of sounds from our environment. Modeling can then be used to automatically generate the sound associated with a virtual environment. This is very attractive because relying on sampling to create sounds for an evolving environment is very difficult.