Wavetable Synthesis

Wavetable synthesis extends the principle of table-lookup oscillators. The approach became popular in the early 80s because it allowed the creation new, complex sounds. Early hardware instruments relied on a digital waveform generation, paired with analog filters and amplifiers. The novelty were arbitrary waveforms that resulted in timbres that were impossible to achieve with previous technologies. Although the approch was revolutionary, these early wavetable instruments could not compete with other devices of the early 80s (like the DX7).

Notable Instruments¶

PPG Wave:

• PPG Wave
  • 1981 (Palm Products, Germany)
  • 8-voice polyphony
  • analog VCA & VCF
  • $7,000-10,000
• Waldorf Microwave
  • 1989 (Waldorf, Germany)
  • 8-voice polyphony
  • analog VCA & VCF
  • $5,000
• Massive
  • 2006 (Native Instruments, Germany)
  • sofwtare synth with 64 voices
• Serum
  • 2015 (Xfer Records, USA)
• Argon8
  • eight-voice polyphonic
  • 2020 (Modal Electronics, UK)

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Well Known Examples¶

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Synthesis Principle by Example¶

Wavetable synthesis extends the table lookup oscillator principle with a simple feature:

• Interpolation between different waveforms (tables).

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1: Define the Wavetable¶

A wavetable is a collection of waveforms that can be stored in different data formats, such as arrays/matrices or dictionaries. The following example uses a simple wavetable with three waveforms:

• Sine wave
• Square wave
• Sawtooth

Each of the waveforms has the length $N=4096$, resutling in a matrix $\mathrm{WT}_{M,N}$ with $M=3$ different waveforms:

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2: Waveform Interpolation¶

With the matrix representation of the wavetable, the index $m$ can be used to blend between neighboring waveforms, using linear interpolation.

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Example A: LFO¶

The following plots and audio example show a LFO modulation through all three waveforms:

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Example B: Exponential Attack¶

The following plots and audio example show a modulation with an exponential envelope, resulting in an attack transient: