What is a wavetable

A wavetable is a list of tiny waves. A synthesizer plays one of them over and over to make a note, and slides between them to make the note move.

One cycle makes a note

Any steady note is a wave that repeats. One repeat is a cycle. If you store a single cycle as a short list of numbers and play it in a loop, you hear a steady pitch. The speed of the loop sets the pitch: loop it 110 times a second and you hear 110 Hz. The shape of the cycle sets the tone. A smooth rounded shape sounds mellow. A shape with sharp corners sounds bright.

A table of cycles

A wavetable is an ordered set of single cycles, called frames. A common size is 2048 samples per frame, and 64 or 256 frames per table. The synthesizer has a position control. At position zero it plays the first frame, at the other end it plays the last, and in between it blends neighbouring frames. Move the position while holding a note and the tone changes, because the shape of the wave changes.

The arithmetic is simple. At a sample rate of 44.1 kHz, a note at 110 Hz needs 44,100 divided by 110, about 400 samples for each cycle. The synthesizer reads the 2048 sample frame at the right speed to fit that, which is why the frame length does not set the pitch. It only sets how finely the shape is stored.

Where tables come from

Drawn by hand, wave by wave.
Built by adding harmonics, with a chosen strength for each.
Cut from recordings, taking a cycle every so often from a sound.
Calculated from mathematics. The Cymatic Wavetable Pack reads paths through the mode shapes of a drum and a plate.

Why high notes can alias

A digital system can only represent frequencies below half its sample rate. At 44.1 kHz that limit, called the Nyquist frequency, is 22,050 Hz. A frame of 2048 samples can hold just over a thousand harmonics of its cycle. Play it at 55 Hz and the top harmonics are still below the limit, since 22,050 divided by 55 is 400, and the table is fine. Play the same table at 2,000 Hz and only about eleven harmonics fit. Harmonics above the limit do not disappear. They fold back down as new frequencies that were never in the table. That folding is aliasing, and it sounds harsh and metallic.

Synthesizers deal with this in different ways: they remove the upper harmonics as the pitch rises, they oversample, or they let you filter the result. Check what yours does, and listen at high notes before you trust a table.

Wavetable and single cycle are not the same word

A single cycle waveform is one wave. A wavetable is many of them in a row. Many synthesizers treat a single cycle file as a table of one frame. If a file refuses to move when you change the position, that may be all it is.

Next step

To put one into a synthesizer, read How to load a wavetable into a synth.

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