Main Group 10: Random Number Generation

Overview

The unit generators RAND, RANDI and RANDH use a pseudo-random formula (Dodge 1985: p.89-90). Therefore, random number sequences are reproducible by using the same (optional) seed value.

RAND produces uniformly distributed values over the range +iamp to -iamp. The r.m.s. value will be iamp/root 2. RAND and RANDI produce band-limited noise.

Suggested Reading

Jones, K.J. 1980.
"Computer Assisted Application of Stochastic Structuring Techniques in Musical Composition and Control of Digital Sound Synthesis Systems."
Ph.D.thesis, The City University, London.

Jones, Kevin 1981.
"Compositional Applications of Stochastic Processes."
Computer Music Journal 5(2).
Reprinted in C.Roads, ed. 1989.
The Music Machine. MIT Press, pp. 351-379.

Knuth, Donald 1969.
The Art of Computer Programming (Vol. 2) Seminumerical Algorithms.
Reading, Massachusetts: Addison-Wesley, pp. 1-160.

Lakacs, L. 1966.
Stochastic Processes.
London: Methuen.

Lorrain, Denis 1980.
"A Panoply of Stochastic 'Canons'."
Computer Music Journal 4(1):53-81.
Reprinted in C.Roads, ed. 1989.
The Music Machine. MIT Press, pp. 351-379.

Roads, C. 1978.
"Automated Granular Synthesis of Sound."
Computer Music Journal 2(2):62-63.

Siegel, L., K. Steiglitz and M. Zuckerman. October, 1975.
"The Design of Markov Chains for Waveform Generation."
Proceedings of the Institute of Electrical and Electronics Engineering (EASCON).

Xenakis, Iannis 1971.
Formalized Music.
Bloomington, Indiana: Indiana University Press.
Revised Edition 1992. Pendragon Press.

10_01_1

This instrument generates 4 seconds of white noise.

Orchestra and Score

WAV and mp3

10_02_1

RANDI produces band-limited noise. Here a sequence of 10 notes is played. The bandwidth of the signals is decreasing from 10000 to 25 Hz. The envelope gives .4 sec of rise and decay over the duration of the notes.

The soundfile 10_02_1.SF serves as input for the PLUCK unit generator in main group 15.

Orchestra and Score

WAV and mp3

10_02_2

This instrument uses RANDI to produce a band-limited noise with control of center frequency ifqr. Actually RANDI is ring modulating a sinus oscillator, thereby translating the noise band to both sides of the center frequency. A good sensation of pitch is reached by setting the bandwidth to 20% of the center frequency.

Suggestions:
Add a parameter that specifies the pitched-ness (that is: the bandwidth) in % of the center frequency.

Noise glissandos are obtained by adding an LFO onto the frequency slot of the oscillator. J. Tenney has made use of this type of instrument in his 'Noise Study'. (Dodge 1985: p. 93)

Orchestra and Score

WAV and mp3

10_03_1

Here the RANDH version of the most basic noise instrument: band-limited noise depending on ifr.

RANDH produces new random numbers at the rate specified by ifqr, and holds the chosen value till a new one is picked. RANDI would interpolate with a straight line of values between two successively chosen numbers.

The difference between RANDI and RANDH is clearly audible. Compare with 10_02_1...

Orchestra and Score

WAV and mp3