Woodwind synthesis requires a nonlinear reed model to provide gain and generate harmonics

Woodwind synthesis differs from string synthesis because the excitation is active (player blows continuously) rather than passive (single pluck). The clarinet reed acts as a nonlinearity: as pressure differential across the reed builds, reflected energy increases; further pressure closes the reed and reflected energy drops to zero. This nonlinear pressure-vs-flow relationship provides amplification (gain > 1 in the feedback loop) and generates harmonics — explaining the clarinet’s characteristic square-wave tone rich in odd harmonics. On a Nord Modular, the nonlinearity is approximated with a WaveWrapper module (cubic approximation). Increasing the gain of the nonlinearity can drive the system into different regimes, including chaotic ones where frequency components are inharmonic and noisy. Unlike strings, the pitch of a woodwind is controlled by the loop delay (bore length), not by initial excitation.

Examples

Nord Modular clarinet: bore delay line → WaveWrapper (cubic nonlinearity) → Shaper (rounding) → back to bore delay. Breath pressure = gain of nonlinearity.

Assessment

Explain why the nonlinear reed generates odd harmonics in a clarinet. What would happen if you increased the gain of the nonlinearity beyond a certain threshold?