SYNTHESIS EXTENSION

Physical Modelling — Simulating the Instrument, Not the Sound

Sampling starts with a recording. Conventional synthesis constructs a sound from oscillators and processing. Physical modelling instead builds a simplified model of the thing that vibrates — a string, tube, membrane or resonant body — and then excites that model.

The change of question: instead of asking “what waveform sounds like a string?”, we ask “what simple system behaves enough like a string that, when we excite it, a string-like sound emerges?”

1. Pluck a modelled string

This demonstration uses the classic Karplus–Strong idea. Press PLUCK: a very short burst of noise excites a feedback delay. Each trip around the loop loses a little energy and high-frequency content, rather like vibration gradually dying away in a real string.

Play the keyboard to change the modeled string length. Loop gain controls how much energy is returned around the feedback loop; values close to 1 sustain longer, while lower values lose energy quickly. Damping and brightness shape how that energy decays.

2. A snare is a different physical system

A snare drum is not a single vibrating string, so we model it differently: a short burst of noise excites several damped resonances, while a brighter noisy component represents the snare wires.

NOISE / IMPACT → RESONANT MODES + SNARE-WIRE NOISE → DECAY → OUTPUT
Same philosophy, different model: we do not need to imitate a snare recording directly. We create a simplified system with an impact, resonances, loss and noise, and the characteristic behaviour emerges from their interaction.

3. What is actually happening?

EXCITATION → DELAY / STRING LENGTH → FILTER / ENERGY LOSS → OUTPUT
　　　　　　　　↑　　　　　　　　　　　　　　↓
　　　　　　　　└──────── FEEDBACK ────────┘

Excitation: a pluck injects a short burst of energy. We use noise because a real pluck initially contains a broad mixture of frequencies.

Delay: the excitation circulates through a short memory buffer. The delay length determines how long one trip takes, so it strongly determines the perceived pitch.

Feedback: instead of playing the burst once, the output is returned to the beginning of the delay. The energy therefore keeps circulating — our simplified equivalent of a vibrating string continuing to move after the finger has left it.

Loss / filtering: a real string does not retain energy forever, and high frequencies tend to disappear differently from low frequencies. Each pass through our loop is therefore slightly attenuated and smoothed.

shorter delay → faster repetition → higher pitch    |    longer delay → lower pitch

4. Why doesn't it just sound like repeating noise?

The first burst is noise, but after repeated trips around the feedback loop the delayed samples begin reinforcing a repeating pattern. The loop settles into an organised vibration whose repetition rate is determined by the delay length.

The pitched sound is an emergent result of the model. We did not begin with a sawtooth or sine oscillator and try to disguise it as a string. We created a small resonating system and excited it.

5. Compare the three approaches

Sampling
“Record a real plucked string and play the recording.”
Conventional synthesis
“Construct a string-like timbre using oscillators, envelopes and filters.”
Physical modelling
“Construct a simplified vibrating string and pluck the model.”

6. Physical models can describe more than strings

Strings
Waveguides/delays can represent travelling vibration and reflections.
Wind instruments
Model excitation plus a resonating bore or air column.
Drums / membranes
Model interacting resonant modes across a surface.
Bells / metal
Use multiple resonances with characteristic relationships and decay rates.
Instrument bodies
Add resonant structures that colour energy transferred from the primary vibrator.
Models do not have to reproduce every atom of the real object. They simplify the physics to capture behaviour that matters perceptually and musically.

7. This is also a preview of DSP

Our “string” sounds complicated, but look at the ingredients:

NOISE + BUFFER/DELAY + ADD/MIX + MULTIPLY/GAIN + FILTER + FEEDBACK

Those are exactly the kinds of small operations we are about to study. Later, the same ingredients will reappear in delays, comb filters, flangers, chorus and reverberation.

That is why physical modelling is a useful final synthesis extension: it sounds like a new synthesis method, but underneath it is another clever arrangement of simple DSP operations.