Physical Modelling Synthesis

Using Mathematics to Create Sounds

Physical modeling synthesis is generating sounds through mathematical models to describe the physical characteristics of the material of a particular instrument and its behavior. It is a leap forward unlike other forms of audio synthesis, like wavetable, spectral, and nonlinear synthesis, that interpret sound in the time and frequency domain. This is because it functions by modeling the sound mechanism directly instead of the sound. This approach invokes the laws of acoustics that result in the physical description of the main vibrating structures in the musical instrument with the help of partial differential equations. Today, physical modeling is incorporated into many commercial hardware and software instruments. It uses appropriate models for excitation (e.g., plucked, struck, and bowed strings) and boundary conditions. Additionally, it is also capable of providing a sound basis for creating artificial instruments like bowed flutes.  

History of Physical Modelling Synthesis

This idea is not so new. Scientific giants such as Newton, Helmholtz, and Rayleigh planted the seeds. Among their other scientific works, they were devoted to understanding how musical instruments produce incredible sound. With the emergence of computers, scientists have tried to implement these mathematical models. They were using algorithms and programmed them to create sound. We can say that the critical change occurred when computers became strong enough to reproduce musical instruments' complexity faithfully in real-time. In the 1990s, Yamaha introduced the first synthesizer that offered physical modeling algorithms.

Later on, a company by the name of ASS has released a VST instrument called Tassman. This VST instrument is dedicated to physical modeling. Side by side with sampling synthesis, which is still the best choice for capturing the original sounds of live instruments, physical modeling is the closest to recreating the natural sounds' richness, liveness, and complexity. It possesses other advantages as well. Since it is possible to control many parameters, for example, the geometry and material of the resonator body of the cello, it allows us to play this cello with the characteristics of the piano's soundboard. Therefore, creating something completely new, such as hybrid instruments, is possible.  

Electric Instruments Application

Indeed, physical modeling is not strictly limited to acoustic instruments. The same approach applies to electric instruments such as synthesizers. Physical modeling can faithfully convey the behavior of electrical circuits. For example, it filters and tube amps of the vintage synthesizer, as with the previously mentioned acoustic instruments, and the richness and vibrancy are faithfully transferred without exception. One of the disadvantages of physical synthesis is the need for a certain CPU power. This form of audio synthesis does not contain pre-recorded samples. Therefore, sounds are generated on the fly. On the other hand, this method generally doesn't occupy the computer memory. There is no need to store gigabytes upon gigabytes of the sound banks, like in the case of sampling synthesis.