Synthesis instruments must band-limit waveforms to avoid aliasing above Nyquist

Aliasing occurs during digital synthesis whenever a waveform contains frequency components above the Nyquist frequency (half the sampling rate). Unlike analysis of recorded audio, synthesis instruments generate waveforms from scratch and can easily produce harmonics well beyond Nyquist. These aliased components fold back into the audio range as spurious tones at unpredictable frequencies. Synthesis instruments therefore require preventative band-limiting measures: bandlimited oscillators (BLIT, minBLEP), oversampling, or low-pass filtering of the synthesis output. Granular synthesis is particularly susceptible because short grain durations produce broad spectra (AM sidebands) that can easily exceed Nyquist.

Examples

A sawtooth oscillator with 50 harmonics at 440 Hz has components up to 22 kHz - fine at 44.1 kHz. But at 400 Hz fundamental, the 56th harmonic (22.4 kHz) aliases. A bandlimited saw limits harmonics to below Nyquist.

Assessment

Why does digital synthesis require aliasing prevention that digital recording does not? What specific property of short grains makes aliasing a concern in granular synthesis at high frequencies?