12. Physical Modeling#
So far in this book, we have modeled the acoustics of musical instruments indirectly, by synthesizing the properties that emerge from them, like harmonics. In this chapter, we model those acoustics directly, by simulating the physics of an instrument. If the simulation is faithful, the same properties should emerge from it on their own. This approach is called physical modeling synthesis.
Imitating real instruments with additive or FM synthesis is notoriously difficult. Recall the trumpet from Chapter 6, whose harmonics shift in balance continuously over the course of a single note. Additive and FM synthesis must imitate such behaviors explicitly, but in a physical model, they arise naturally from the simulated physics. Here are a few examples of how realistic physical models can sound:
Plucked strings, synthesized on a NeXT computer (1989)
An electric guitar with a bass pickup, from Stanford’s Sondius project
An oboe and a bassoon, synthesized on the Yamaha VL1 (1994)
Three physical models, from Julius O. Smith III’s collection of sound examples.
Physical models have numerous use cases (we only focus on the first in this chapter):
Synthesis of realistic instruments, or of imaginary instruments that would be impossible to build, like a string a kilometer long.
Analysis of recorded sound, by estimating the physical parameters of a model that best reproduce a recording.
Instrument design, by prototyping an instrument in simulation before building it.
Unlike additive synthesis which refers to a single technique, physical modeling synthesis is a family of techniques that share common building blocks. In this chapter, we explore these techniques through a case study: building a model of a plucked string, which formed the basis of early research on physical models. But to simulate the physics of an instrument, we must first understand that physics.
This chapter is only a cursory overview of a field that has been researched for decades. Readers who want to go further should consult Julius Smith’s Physical Audio Signal Processing [SI10], a thorough treatment that is freely available online.