Physical modeling emulates actual physical processes with digital means - oscillators, resonators and acoustic impedances are modeled with buffers and filters, respectively LTI systems. Although first realized when computers had sufficient power, the foudations are much older. Hiller et al. (1971) were the first to transport the 1774 wave equation by d'Alambert to the digital domain for synthesizing sounds of plucked strings.
Although physical modeling algorithms sound great, offer good means for control and enable the design of interesting instruments, their had less impact on the evolution of music and digital instruments. Hardware synths for physical modeling from the 1990s, like the Korg Prophecy or the Yamaha VL1 did not become a success, in the first place. There are many possible reasons for the lack of success. Cheaper and larger memory made sampling instruments more powerful and virtual analog synthesizers sounded more attractive, followed by the second wave of analog synths.
Yamaha VL1 (1994)
- Pianoteq Pro 6
- Organteq Alpha
- Strum GS 2
- AAS Chromophone 2
Since simple physical models are easily implemented on small embedded systems, various modules exist on the market:
Physical Models in Experimental Music
Eikasia (1999) by Hans Tutschku was realized using the IRAM software Modalys: