Wavetable synthesis


Wavetable synthesis is a sound synthesis technique used to create periodic waveforms. Often used in the production of musical tones or notes, it was developed by Wolfgang Palm of Palm Products GmbH in the late 1970s and published in 1979, and has since been used as the primary synthesis method in synthesizers built by PPG and Waldorf Music and as an auxiliary synthesis method by Ensoniq and Access. It is currently used in hardware synthesizers from Waldorf Music and in software-based synthesizers for PCs and tablets, including apps offered by PPG and Waldorf, among others.
It was also independently developed in a similar time frame by Michael McNabb, who used it in his 1978 composition Dreamsong.

Principle

Wavetable synthesis is fundamentally based on periodic reproduction of an arbitrary, single-cycle waveform. In wavetable synthesis, some method is employed to vary or modulate the selected waveform in the wavetable. The position in the wavetable selects the single cycle waveform. Digital interpolation between adjacent waveforms allows for dynamic and smooth changes of the timbre of the tone produced. Sweeping the wavetable in either direction can be controlled in a number of ways, for example, by use of an LFO, envelope, pressure or velocity.
Many wavetables used in PPG and Ensoniq synthesizers can simulate the methods used by analog synthesizers, such as Pulse Width Modulation by utilising a number of square waves of different duty cycles. In this way, when the wavetable is swept, the duty cycle of the pulse wave will appear to change over time.
As the early Ensoniq wavetable synthesizers had non resonant filters, some wavetables contained highly resonant waveforms to overcome this limitation of the filters.

Confusion with sample-based synthesis (S&S) and Digital Wave Synthesis

In 1992, with the introduction of the Creative Labs Sound Blaster 16 the term "wavetable" started to be applied as a marketing term to their sound card. However, these sound cards did not employ any form of wavetable synthesis, but rather PCM samples and FM synthesis.
S&S and Digital Wave Synthesis was the main method of sound synthesis utilised by digital synthesizers starting in the mid 80's with synthesizers such as Sequential Circuits Prophet VS, Korg DW6000/8000, Roland D50 and Korg M1 through to current synthesizers.

User wavetables

The creation of new wavetables was previously a difficult process unless supported by specialized editing facilities and real-time playback of edited wavetables on the synthesizer. Such editors often required the use of extra hardware devices like the PPG Waveterm or were only present in expensive models like the Waldorf WAVE. More commonly, pre-computed wavetables could be added via memory cards or sent to the synthesizer via MIDI. Today, wavetables can be created more easily by software and auditioned directly on a computer. Since all waveforms used in wavetable synthesis are periodic, the time-domain and frequency-domain representation are exact equivalents of each other and both can be used simultaneously to define waveforms and wavetables.

Practical use

During playback, the sound produced can be harmonically changed by moving to another point in the wavetable, usually under the control of an envelope generator or low frequency oscillator but frequently by any number of modulators. Doing this modifies the harmonic content of the output wave in real time, producing sounds that can imitate acoustic instruments or be totally abstract, which is where this method of sound creation excels. The technique is especially useful for evolving synth pads, where the sound changes slowly over time.
It is often necessary to 'audition' each position in a wavetable and to scan through it, forwards and backwards, in order to make good use of it, though selecting random wavetables, start positions, end positions and directions of scan can also produce satisfyingly musical results. It is worth noting that most wavetable synthesizers also employ other synthesis methods to further shape the output waveform, such as subtractive synthesis, phase modulation, frequency modulation and AM modulation.

Table-lookup synthesis

Table-lookup synthesis is a class of sound synthesis methods using the waveform tables by table-lookup, called "table-lookup oscillator" technique.
The length of waveforms or samples may be varied by each sound synthesis method, from a single-cycle up to several minutes.

Terminologies

The term "waveform table" is often abbreviated to "wavetable", and its derive term "wavetable oscillator" seems to be almost same as "table-lookup oscillator" mentioned above, although the word "wave" may possibly imply a nuance of single-cycle waveform.
However, a derive term "wavetable synthesis" seems slightly confusing. In a natural usage of words, its original meaning is basically same as "table-lookup synthesis", and possibly several actions on waveform may be expected, as seen on a paper about Karplus–Strong string synthesis.
Then in the late-1970s, Michael McNabb and Wolfgang Palm independently develop the multiple-wavetable extension on the table-lookup synthesis which was typically used on PPG Wave and known with wavetable sweeping, and it was later referred as "multiple wavetable synthesis" by.
Simultaneously since late-1970s, also the sample-based synthesis using relatively long samples instead of single-cycle waveforms, have become influential by the introductions of the Fairlight CMI and E-mu Emulator.

Background

On the above four terminologies for the classes of sound synthesis methods, i.e.,
  1. Wavetable synthesis — original, generic meaning.
  2. Multiple wavetable synthesis — developed by McNabb and Palm, typically used on PPG Waves.
  3. Wavetable-modification algorithm — including digital waveguide synthesis.
  4. Sample-based synthesis
if these had been appropriately used to distinguish each other, any confusions could be avoided, but it seems failed historically.
At latest in the 1990s, several influential sample-based synthesis products were marketed under the trade names similar to "wavetable synthesis", and these confusions have further affected on the several industry standards.
As a rebound of these, at the latest since the mid-2000s, a new confusion seem to begin flourish. Merely a subclass of generic wavetable synthesis, i.e. McNabb and Palm's multiple wavetable synthesis, tends to be erroneously referred as if it was a generic class of whole wavetable synthesis family, exclusively.
As a background of these confusions, the difficulties of maintaining the consistencies between concepts and terminologies during the rapid developments of technology, may be significant.
And it is a reason why this slightly classical terminology "Table-lookup synthesis" is explained on here.