Other Synthesis Methods - Part 2 Physical Modeling

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.

Physical modeling is a sound synthesis technique in which the waveform of the sound to be generated is calculated using a mathematical model that simulates a physical source of sound. Engineers created the model by simplifying the law of physics involved in sound generation. The parameters that can be found in this kind of synthesizer are of two kinds; some change the constants that describe the physical materials and dimensions of the instrument, while others are time-dependent functions that describe the player’s interaction with it. (e.g. how the instrument is played by rubbing or striking or opening and closing tone holes).

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

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.

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.

Bibliography:

AAS - Tech Talk - Physical modeling. (n.d.). Retrieved June 24, 2016, from
https://www.applied-acoustics.com/techtalk/physicalmodeling/

Ness - Physical Modeling Synthesis (n.d.) Retrieved June 24, 2016 from
http://www.ness-music.eu/overview/physical-modeling-synthesis

Gregory Taylor - Physical Modeling Synthesis for Max Users: A Primer Published October 10, 2012, Retrieved June 24, 2016 from
https://cycling74.com/2012/10/09/physical-modeling-synthesis-for-max-users-a-primer/#.V20bE1fmpuU

Hiller, L.; Ruiz, P. (1971). "Synthesizing Musical Sounds by Solving the Wave Equation for Vibrating Objects". Journal of the Audio Engineering Society.

Karplus, K.; Strong, A. (1983). "Digital synthesis of plucked string and drum timbres". Computer Music Journal (Computer Music Journal, Vol. 7, No. 2) 7 (2): 43–55. doi:10.2307/3680062. JSTOR 3680062.

Julius O. Smith III (December 2010). Physical Audio Signal Processing.
Cadoz, C.; Luciani A; Florens JL (1993). "CORDIS-ANIMA : a Modeling and Simulation System for Sound and Image Synthesis: The General Formalism". Computer Music Journal (Computer Music Journal, MIT Press 1993, Vol. 17, No. 1) 17/1 (1).