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Physical modeling synthesis approximates acoustic instrument physics using mathematical models of wave propagation

Concept L3Craft B · Sound design & synthesis E · Modular, Eurorack, grooveboxes & dawless

Physical modeling synthesis (PMS) aims to model the physical processes that give rise to sound in real acoustic instruments using simple mathematical approximations. The approach works best for instruments whose sound-generation can be described as excitation of a transmission line or waveguide — primarily stringed instruments and woodwinds. The governing equations (wave equations) are relatively simple and computationally tractable. PMS is fundamentally different from subtractive or FM synthesis: rather than shaping a generic waveform, it simulates the physical resonance of the instrument’s body. Key parameters are the relative amounts of wave energy transmitted, reflected, lost (as heat), and stored at each waveguide section, plus frequency-dependent propagation delay. A common misconception is that PMS requires a complete, accurate physical simulation — in practice, simplified lumped models produce convincing results.

Examples

Karplus-Strong is the simplest physical model: a single delay line with a lowpass filter in feedback produces convincing plucked strings. More complete waveguide models add multiple sections.

Assessment

Explain why physical modeling works better for strings and woodwinds than for percussion. Identify two parameters in a waveguide model that determine pitch and two that determine timbre/decay.

Prerequisites — understand these first

Don't confuse with

Karplus-Strong physical modeling feeds an excitation signal into a tuned feedback delay to synthesize plucked or bowed strings

Sources

“Physical modelingsynthesis is the investigation of sound synthesis from principles of acoustics. The models are often involved to build, sometimes hard to control, and specifically de- veloped for each given sound source”

corpus · nick-collins-introduction-to-computer-music-free-author-edit · chunk 65

“Physical modeling refers to a synthesis technique that aims to model, using simple mathematical approximations, the physical processes that give rise to the sound in a real acoustic instrument.”

corpus · physical-modeling-karplus-strong-waveguides-strings-and-wood · chunk 1

“Physical modeling (PhM) synthesis starts from mathematical models of the physical acoustics of instrumental sound production.”

corpus · the-computer-music-tutorial-curtis-roads-archive-org-copy · chunk 56

Taught in modules

Physical modeling: Karplus-Strong, waveguides, and instrument models

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