Physical model pitch is inversely proportional to delay time, requiring reciprocal computation from note number

In a digital waveguide physical model, pitch is determined by total loop delay time: pitch = sample_rate / total_delay_samples. Since delay time is typically a linear control parameter but pitch is exponentially related to MIDI note number, tuning requires computing the reciprocal of an exponential — i.e., exponentially mapping note number to delay time in the opposite direction. This inverse mapping is non-trivial to implement in hardware modular systems. A further complication is that the feedback filters used for frequency-dependent attenuation introduce additional fixed delay, causing detuning at high frequencies where the filter’s contribution is proportionally larger relative to the short delay line. High-frequency tracking compensation (slight reduction of control value at high pitches) corrects this.

Examples

Nord Modular: NoteVelScaler module set to -6dB/octave implements the required reciprocal of the exponential. High-frequency detuning correction: add note-value-dependent offset to tuning signal.

Assessment

Explain why pitch = sample_rate / delay_samples means that halving the delay doubles the pitch. Describe what artifact appears when you naively use a linear pitch control on a Karplus-Strong patch.