#### Using mathematics to create sounds

Generating sounds through mathematical models to describe the physical characteristics of the material of certain instrument and its behavior. This would be the basic definition of physical modeling synthesis. Unlike other forms of audio synthesis, like wavetable, spectral and nonlinear synthesis that interpret sound in the time and frequency domain, physical modeling is a leap forward. This is because it is functioning by modeling directly the sound mechanism instead of the sound.

This approach invokes the laws of acoustics that is resulting in 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 alike. Its using 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 the way how musical instruments produce so 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 key change occurred when computers become strong enough and able to faithfully reproduce the complexity of musical instruments in real time. Back in the 1990‚s, Yamaha introduced 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 totally 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 one closest to recreate the richness, liveness and complexity of the natural sounds. It possesses other advantages as well. Since it is possible to control large number of parameters, for example geometry and material of resonator body of the cello, it allows us to play this cello with the characteristics of the soundboard of the piano. Therefore, it is possible to create something completely new, let us say hybrid instruments.

#### Electric instruments application

Certainly, physical modeling is not strictly limited to acoustic instruments. The same approach is applicable to electric instruments such as synthesizers. Physical modeling is able to faithfully convey the behavior of electrical circuits. It filters and tube amps of the vintage synthesizer for example. As with the previously mentioned acoustic instruments, the richness and vibrancy is 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 occupies the computer memory. There is no need for storing gigabytes upon gigabytes of the sound banks like in the case of sampling synthesis.

##### Additional Resource & Source Texts

http://www.jstor.org/stable/3681331?seq=1#page_scan_tab_contents