Shorter grain duration produces wider spectral bandwidth

By the time-frequency uncertainty principle (Gabor’s uncertainty relation), a signal cannot be perfectly localized in both time and frequency: the shorter its duration, the greater its bandwidth. For a granular-synthesis grain, the spectral bandwidth B produced by amplitude-modulation sidebands is inversely proportional to grain duration D, regardless of the waveform inside the grain. A ~1 ms grain has a bandwidth of roughly 1000 Hz — a broadband, click-like burst that smears pitch; a ~100 ms grain has a bandwidth of about 10 Hz — a nearly pure, clearly pitched tone. Grain durations of roughly 10–50 ms are a practical compromise. The tradeoff shapes the timbral palette: short grains yield dense, pitch-ambiguous clouds and percussive transients, while longer grains yield pitched, less dense streams. To gain pitch clarity, lengthen the grain; to gain percussive/broadband character, shorten it.

Examples

1 ms grain at 1000 Hz: bandwidth ~1000 Hz (sounds like a click). 20 ms grain: ~50 Hz (recognizable pitch). 100 ms grain: ~10 Hz (nearly pure tone). A 2 ms grain of a sine sounds like a broadband burst; a 50 ms grain of the same sine sounds clearly pitched.

Assessment

A granular synth uses 5 ms grains tuned to 440 Hz; explain why the perceived sound lacks clear pitch and state the grain-duration change that improves it. If a cloud sounds too buzzy and lacks pitch clarity, should grain duration increase or decrease? Justify using the duration–bandwidth relationship.