Wavetable synthesis stores one cycle of a waveform and replays it at a variable rate to set pitch

A wavetable is an array in memory holding one (or more) periods of a waveform. To play a note, an algorithm walks through the table at a rate set by the desired frequency and the sample rate — the index increment (phase step). The same precomputed table read at any speed yields any pitch without recomputing the waveform, so the technique is computationally cheap: calculate the waveform once, store it, look up values on demand. Any shape — sine, sawtooth, or arbitrary — can be stored and played this way. Because the read index rarely lands on a stored sample, interpolation (at least linear, preferably cubic) is needed for pitch accuracy. For shapes whose harmonics exceed the Nyquist limit at high pitches, band-limited tables are required: separate tables per octave range, each holding only harmonics that fit below Nyquist, to avoid aliasing. Multiple tables can be mixed to create time-varying timbres. A common misconception is that wavetable synthesis is confined to modular or polyphonic synths — in fact the algorithm underlies virtually all digital software and hardware oscillators.

Examples

A 64-sample sine table at increment 0.64 produces 440 Hz at 44100 Hz; at increment 1.28 it produces 880 Hz. The PPG Wave (1981) used wavetable scanning; modern synths (Vital, Serum, most VSTs) and SuperCollider’s Osc/VOsc UGens are wavetable-based.

Assessment

Given a table length L=64 at 44100 Hz, calculate the index increment for 440 Hz, then state what changes if L doubles to 128. Explain why a digital wavetable oscillator needs a different band-limited table for different frequency ranges, and what artefact occurs if a sharp-edged table is played at high pitches without band-limiting.