Main Group 50: Subtractive Synthesis

Overview

RESON

Suggested Reading

Moore, F.R. 1990.
"Digital Filters."
Elements of Computer Music.
Prentice-Hall, pp. 111-148.

Moore, F.R. 1990.
"Time-varying Digital Filters."
Elements of Computer Music.
Prentice-Hall, pp. 264-270.

Slawson, Wayne 1981.
"The Color of Sound: A Theoretical Study in Musical Timbre."
Music Theory Spectrum 3:123-141.

Slawson, Wayne 1982.
"The Musical Control of Sound Colour."
Canadian University Music Review 3:67-79.

Slawson, Wayne 1985.
Sound Color.
Berkeley: University of California Press, 266 pp.

Smith, J.O. 1985.
"An Introduction To Digital Filter Theory."
in J. Strawn, ed. 1985.
Digital Audio Signal Processing: An Anthology.
A-R Editions. pp. 69-136.

Smith, J.O. 1985.
"Fundamentals of Digital Filter Theory."
Reprinted in C.Roads, ed. 1989.
The Music Machine. MIT Press, pp. 509-520.

50_01_1

This simple design shows the basic idea of subtractive synthesis, where a rich source is filtered to produce sounds.

The white noise form RAND's output is here filtered with a narrow bandwidth (5% of the center frequency) RESON. This results in evenly pitched noises for the whole range of audio frequencies. (Dodge 1985: p.170)

Orchestra and Score

WAV and mp3

50_09_1

The instrument gives continuous control over the bandwidth of a noise with a simple, but ingenious use of an LFO oscillator. A sinus is taken from its lowest point at 270 degrees. By addition of 1 and dividing by 2, the sinus takes on an all positive and normalized bell shape. Applying the peak bandwidth value completes the bandwidth controlling contour. The contour will run at irate times a note, as irate is duration dependent. The four notes played by this instrument show four different settings that lead to very different tone qualities. Sounds can be described as "rustling", "thumping", "scurrying", "ringing","blowing", etc. (Dodge 1985: p. 171)

Orchestra and Score

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50_11_1

This design carries the idea of 50_09_1 a little further: center frequency and bandwidth are both subject to continuous changes. The instrument produces glissandoing noise bands.

The amplitude target of EXPON is set to the ratio of the highest to the lowest center frequency. Then, multiplying the output of EXPON with the center frequency lets icfq vary from the minimum to the maximum frequency during the duration of the tone.

The right oscillator (playing a line function from 0 to 1) is fed a peak deviation in percentages. A minimum percentage is added before this control signal is scaled by the value of kcfq, thus making bandwidth dependent on center frequency.

Three notes are played: 1 1/2 octaves up in 4 sec
2 1/2 octaves up in 4 sec
7 octaves down in 6 sec

The minimum bandwidth is in all case 5% of the center frequency (thus starting with a pitched noise) and finishes at a maximum of 50% (35%) of the center frequency (coloured noise). (Dodge 1985: p. 172)

Orchestra and Score

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50_51_1

Here the spectrum is varied, in proportion to the amplitude of the tone, a situation commonly encountered in "natural" music instruments. The technique is frequently used by musicians and referred to as harmonic enveloping.

Care has to be taken to choose the correct scaling factor mediating between amplitudes and bandwidths. In this case the bandwidth is 10% of the amplitude value of the tones. Some different amplitudes values are presented in the score, ranging from 4000 to 160000.

Note also: If RESON is used as a low pass filter (icfq=0), the actual cutoff frequency of the filter will be .707 times the value of kbw. (Dodge 1985: p. 174)

Orchestra and Score

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50_71_1

This subtractive instrument is based on a buzzy source, containing harmonics in equal strength up to the Nyquist. After being filtered by two RESON filters (scaling mode 0: no scaling of the signal) at respective center frequencies of 1000 Hz and 3000 Hz, the input of RESON 1 is balanced with the output of RESON 2.

The first section plays a scale in C major, the second section plays a dominant seventh chord in C major.

Orchestra and Score

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