# Distortion synthesis

Distortion synthesis

Distortion synthesis is a group of sound synthesis techniques which modify existing sounds to produce more complex sounds (or timbres), usually by using non-linear circuits or mathematics.[1]

While some synthesis methods achieve sonic complexity by using many oscillators, distortion methods create a frequency spectrum which has many more components than oscillators.

Jean-Claude Risset was one notable pioneer in the adoption of distortion methods.

Some distortion techniques are: FM synthesis,[2] waveshaping synthesis,[3][4] and discrete summation formulas.[5]

## FM synthesis

Frequency modulation synthesis distorts the carrier frequency of an oscillator by modulating it with another signal. The distortion can be controlled by means of an index.[6]

The method known as phase distortion synthesis is similar to FM.

## Waveshaping synthesis

Waveshaping synthesis changes an original waveform by responding to its amplitude in a non-linear fashion.[7][8] It can generate a bandwidth-limited spectrum, and can be continuously controlled with an index.

The clipping caused by overdriving an audio amplifier is a simple example of this method.

(This method should not be confused with wavetable synthesis, which creates sound from lists of numbers, most often representing one period or cycle per wave. However, wavetable synthesis is identical to the special case of waveshaping synthesis where the original waveform is a sawtooth wave.)

## Discrete summation formulas

DSF synthesis refers to algorithmic synthesis methods which use mathematical formulas to sum, or add together, many numbers to achieve a desired wave shape.[9] This powerful method allows, for example,synthesizing a 3-formant voice in a manner similar to FM voice synthesis.[10] DSF allows the synthesis of harmonic and inharmonic, band-limited or unlimited spectra, and can be controlled by an index. As Roads points out, by reducing digital synthesis of complex spectra to a few parameters, DSF can be much more economical.[11]

## References

1. ^ Nb. Some authors refer to these techniques as 'modulation synthesis'; e.g. Chapter 6 of Roads, Curtis (1996). The computer music tutorial. MIT Press.
2. ^ Dodge 1997, pp.115-138
3. ^ Roads, Curtis (June, 1979). "A Tutorial on Non-Linear Distortion or Waveshaping Synthesis". Computer Music Journal (MIT Press) 3 (2): 29–34. JSTOR 3680281.
4. ^ Dodge 1997, pp.139-157
5. ^ Dodge 1997, pp.158-168
6. ^ J. Chowning (1973). "The Synthesis of Complex Audio Spectra by Means of Frequency Modulation". Journal of the Audio Engineering Society 21 (7).
7. ^ Arfib, D. 1979. "Digital synthesis of complex spectra by means of multiplication of non-linear distorted sine waves." Journal of the Audio Engineering Society 27: 10.
8. ^ Marc Le Brun. "Digital Waveshaping Synthesis" in Journal of the Audio Engineering Society, 27(4), 1979, p250-266.
9. ^ Moorer, J. A. (November 1976). "The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulae". Journal of the Audio Engineering Society, 27(4), pp.717-727.
10. ^ T Stilson; J Smith (1996). "Alias-free digital synthesis of classic analog waveforms". Proc. Int. Comp. Music Conf. (ICMC’96 Hong Kong): 332–335.
11. ^ C. Roads 1996, p.260-61.
• Dodge, Charles; Thomas A. Jerse (1997). "5. Synthesis Using Distortion Techniques". Computer Music. New York: Schirmer Books. pp. 115–168. ISBN 0-02-864682-7.
• Chowning, John; Bristow, David (1986). FM Theory & Applications - By Musicians For Musicians. Tokyo: Yamaha. ISBN 4-636-17482-8.