Skip to main content

A Survey of Nonstandard Oscillators

Welcome to the first post on my blog that qualifies as a bona fide listicle. Be sure to hit the "YAS" react button.

Every so often -- especially at DAFx -- a new paper pops up that innovates in the space of what I call nonstandard oscillators. These nonstandard oscillators offer interesting timbres beyond standard methods. I define them with the following arbitrary rules:

  1. It must be time-domain.

  2. It must synthesize periodic or quasiperiodic waveforms. (No chaotic oscillators here, sorry.)

  3. It must be derived parametrically using mathematical rules. This excludes wavetable synths, which rely on externally derived lookup tables.

  4. Standard methods such as classic analog waveforms, additive, and vanilla FM/PM are excluded.

Don't get me wrong: subtractive, additive, and FM/PM are powerful synthesis methods that have well earned their popularity. But for musicians that hunger for something more, I've collected a little list of nonstandard oscillator algorithms that I think fit these criteria. Without further ado, here's the list.

Oscillator sync

Oscillator hard sync consists of an oscillator and an impulse train that resets the phase of said oscillator. The impulse train determines the fundamental frequency, while the oscillator's intrinsic frequency creates a screaming formant at that frequency.

There are other variants such as soft sync and reverse sync. Soft sync resets the oscillator only if the phase is below a certain threshold. Reverse sync multiplies the oscillator's frequency by -1, when a trigger is received.

Wavefolding

A waveform, usually a sine wave, is waveshaped with a continuous but nonmonotonic nonlinear transfer function. Timbre is evolved by changing how hard the nonlinearity is driven.

Discrete summation formulas (DSF)

This is an old algorithm for generating evenly spaced sine waves [Moorer1975]. It can generate bandlimited and therefore alias-free waveforms. DSF has used as the underlying algorithm to synthesize bandlimited impulse trains in Csound and SuperCollider.

Outside of antialiasing uses, DSF doesn't seem to receive much love. I believe this is because the partial amplitudes are monotonic, giving DSF a rather bland sound.

Phase distortion (PD)

Introduced in the Casio CZ series, phase distortion synthesis allows transformation of a sine wave by altering the phase ramp with a nonlinearity [Casio].

Fake resonance

Also made famous by the Casio CZ series, fake resonance is produced with windowed oscillator sync. Fake lowpass, bandpass, and highpass waveforms are possible with saw or pulse [Gillet2015], although the highpass configuration produces discontinuities therefore strong aliasing (unless an aliasing suppression method such as PolyBLEP is used).

Breakpoint synthesis (Gendy)

Attributed to Iannis Xenakis, breakpoint synthesis uses a piecewise linear function whose breakpoints (critical points) are randomly jostled around at every pitch period [Serra1993]. The result is a wonderful and unique warbly timbre.

IXA synthesis

See my last blog post. IXA is a variant of PM synthesis, but with a distorted phase on the carrier oscillator so a sine wave is produced when the index is zero.

Scanned synthesis

Scanned synthesis is wavetable synthesis where the wavetable is taken from a physical model that evolves slowly (not the audio-rate physical models of instruments) [Verplank2000]. The wavetable can also come from a physical interface or even video. In a way, scanned synthesis is sonification of any evolving entity as a wavetable. For an impressive application of two-dimensional scanned synthesis in a multitouch context, see Robert Tubb's Wablet [Tubb2011].

VOSIM

Smooth pulses of varying lengths and amplitudes, formed by the function sin(x)^2, are concatenated to produce formants [Kaegi1972]. This makes VOSIM useful as a rudimentary vowel synthesizer.

Vector phase shaping (VPS)

This is a take on phase distortion that adds a second dimension of timbral control [Kleimola2011]. It too can generate formants.

Polygonal waveform synthesis

Polygonal waveform synthesis sonifies a regular polygon (especially a star polygon) by sweeping circularly and interpreting the X and/or Y coordinates as a waveform [Hohnerlein2016].

Vocal FM synthesis

This patented method modifies FM synthesis to be used as a formant synthesizer [Chafe]. Technically, FM can already be used to synthesize formants, by using both sine waves for the carrier and modulator and setting the modulator frequency to be a large multiple of the carrier frequency, but Chafe's research fixes issues when the fundamental or formant is modulated over time.

Acknowledgements

This post was inspired by a discussion with dietcv from the SuperCollider forums.

References

Moorer1975

Moorer, James A. 1975. "The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulae."

Casio

--. Date unknown. Casio CZ-1 Operation Manual.

Gillet2015

Gillet, Emilie. Source code to Mutable Instruments Braids.

Serra1993

Serra, Marie-Hélène. 1993. "Stochastic Composition and Stochastic Timbre: GENDY3 by Iannis Xenakis." Perspectives of New Music, Vol. 13, No. 1 (Winter, 1993), pp. 236-357.

Verplank2000

Verplank, Bill; Matthews, Max; and Shaw, Robert. Circa 2000. "Scanned Synthesis."

Tubb2011

Tubb, Robert. 2011. "The Wablet: An Investigation into Scanned Synthesis and Multi-Touch." Queen Mary University of London MSc project report.

Kaegi1972

Kaegi, Werner and Tempelaars, Stan. 1978. "VOSIM -- A New Sound Synthesis System." Journal of the Audio Engineering Society, Vol. 26, No. 6.

Kleimola2011

Kleimola, Jari et al. 2011. "Vector Phaseshaping Synthesis." Proc. 14th Int. Conf. on Digital Audio Effects (DAFx-11).

Hohnerlein2016

Hohnerlein, Christoph; Rest, Maximilian; and Smith, Julius O. 2016. "Continuous Order Polygon Waveform Synthesis." Proc. Int. Computer Music Conf.

Chafe

Chafe, Chris. Date unknown. "Glitch Free FM Vocal Synthesis."