# 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.

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 a modulation 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, changing a sine wave into a square-like wave. (Note that direct digital implementations suffer from aliasing of the clipped signal's infinite number of harmonics, however.)

## 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]

## Notable users

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

## 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. doi:10.2307/3680281. 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. CiteSeerX 10.1.1.60.4437.
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.