Main Group 43: (G)Buzz

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01 Basic Instrument
1 LINEN envelope, automatic inH
1B LINEN envelope, constant inH
2 EXPON envelope
3 EXPSEG envelope
21 Kratio envelope
1 LINEN envelope

Overview

BUZZ and GBUZZ are pulse generators and provide yet another means of effectively generating a complex audio signal. Using the closed form of a sum of sinusoids, only two oscillators are able to produce a complex wave of N partials. In the case of BUZZ, it is a set of harmonically related cosine partials of the fundamental frequency ifqc. For their spectral richness, pulse generators are particularly useful as sources in subtractive synthesis designs.

BUZZ is a special case of the more general GBUZZ in which all harmonics are equally strong, and the series starts with the fundamental.

In GBUZZ one can chose an exponential coefficient multiplier 'kratio' to envelope the harmonic spectrum (One cannot use the variable 'kr' for this ratio, as suggested in the Csound manual; 'kr' is a reserved symbol) of the output. Also GBUZZ allows to specify a lowest harmonic 'klh' different from the fundamental frequency.

A pulse train is obtained by extending the number of harmonics up to the Nyquist frequency. This is done by making the number of harmonics frequency dependent:

knh = int (sr/2/ifqc).

In general pulse waveforms have a significant amplitude only during a short interval of time (pulse width). Repeated periodically, the pulse waveform yields rich spectra, depending on period and shape of the pulse. The pulse width gets narrower with increasing number of harmonics in the spectrum.

Suggested Reading

Dodge, C, and T.A. Jerse 1985.
"Introduction to Discrete Summation Formulae."
Computer Music: Synthesis, Composition and Performance.
Schirmer Books. pp. 149-153, 156-157.

Moorer, J.A. 1976.
"The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulae."
Journal of the Audio Engineering Society 24:717-727.

Moorer, J.A. 1985.
"Signal Processing Aspects of Computer Music: A Survey."
chapter: "Discrete Summation Formulae."
in J. Strawn, ed. 1985.
Digital Audio Signal Processing: An Anthology.
A-R Editions, pp. 180-193.

Winham, Godfrey, and Kenneth Steiglitz 1970.
"Input Generators for Digital Sound Synthesis."
Journal of the Acoustical Society of America 47(2):665-666.

43_01_1

additional parameters: none

This instrument simply shows the effect of varying fundamental frequency on the tone quality, when the number of harmonics is automatically calculated by 

            inH = int (sr/2/ifqc)
The tone is played in six consecutive octaves. It turns out to be rather buzzy for low frequencies, which explains the name of this unit generator. The timbre becomes brighter in the high frequency area.

[flowchart]

Orchestra and Score

WAV and mp3

43_01_1B

additional parameters: none

This time the number of harmonics is constant at 10 per note. The timbre of the tones is more steady, compared to 43_01_1. As the number of harmonics is not put in relation to the sampling rate, the last note contains objectionable, ugly foldover components.

[flowchart]

Orchestra and Score

WAV and mp3

43_01_2

additional parameters:

Same as 43_01_1, this time with an EXPON envelope.

[flowchart]

Orchestra and Score

WAV and mp3

43_01_3

additional parameters:

One hears the BUZZ with an EXPSEG envelope. The instrument plays the same sequence as the two instruments before.

[flowchart]

Orchestra and Score

WAV and mp3

43_21_1

additional parameters: none

The run gives the effect on GBUZZ of varying kratio during performance (values around unity). For this, LINSEG creates a kratio envelope varying with the duration of the note.

A long note of 10 seconds is followed by three shorter notes. This is a very interesting way to control changes in tone colour.

[flowchart]

Orchestra and Score

WAV and mp3

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jpff@cs.bath.ac.uk
Last modified: Sun Aug 2 17:08:01 BST 2009