Leonardo

Computer Music Produced with the Aid of a Digital-to-Analog ConverterAuthor(s): Frank BrownSource: Leonardo, Vol. 11, No. 1 (Winter, 1978), pp. 39-40Published by: The MIT PressStable URL: http://www.jstor.org/stable/1573501 .

Accessed: 18/06/2014 20:55

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The MIT Press and Leonardo are collaborating with JSTOR to digitize, preserve and extend access toLeonardo.

http://www.jstor.org

This content downloaded from 91.229.248.184 on Wed, 18 Jun 2014 20:55:05 PMAll use subject to JSTOR Terms and Conditions

Leonardo, Vol. 11, pp. 39-40. Pergamon Press 1978. Printed in Great Britain

COMPUTER MUSIC PRODUCED WITH THE AID OF A DIGITAL-TO-ANALOG CONVERTER

Frank Brown*

1. Automatic music composition The use of a digital computer in conjunction with a digital-to-analog converter (DAC) for composing music is an exciting possibility. With the aid of appropriate computer programs, a computer can compose musical scores that, after suitable conversion, can be heard as sounds.

The Group BBK (composed of Pierre Barbaud, Frank Brown and Genevieve Klein) is concerned with producing musical works by procedures in which human involve- ment is minimal. Barbaud has described his technique for automatic music composition in his books [1,2] and in numerous articles. The computer programs that he has written can produce either musical scores of a traditional type in a harmonic or contrapuntal style intended for musicological studies or psychological experiments, or musical scores that I consider to be leading examples of computer music. He has prepared numerous computer programs for computer music under the general title TERRA IGNOTA (Fig. 1). As the title suggests, the programs involved musical sounds that cannot be produced by traditional musical instruments.

2. Writing traditional scores Among the computer programs written by the group,

the one called 'SCRIPTU' is the most suitable for coding a traditional musical score (Fig. 1). It is the only program by the Group written in Cobol language, a computer language that emphasizes organization. A wide variety of means of transcription is provided and a score can be produced on magnetic disk by the computer.

An example of two measures of a piece of music is shown in Fig. 2. It is represented in SCRIPTU language (French version) as follows:

CHORDS T04 D02;M12;S02;D03

SCORE 102 R04 BO1, T08 101 D04, S04, 105 T32 D04. 102 R04 BO1, 101 P02 T02 F#4, S04, F#4, T04 S04, LA4.

END

The notes are represented by the tones DO, MI, SO, F # and LA. Two Instruments, I, are designated by numbers 01 and 02. R stands for 'repeat'; 04 following R means 'repeat four times'. T indicates relative time duration; here there are durations of 02, 04, 08 and 32. Similarly, P02 represents a relative time duration of silence equal to 02. B represents a chord, and 01 signifies the first chord (the first line listed under 'chords'). A

*Physicist, 15 Rue de la Lancette, 75012 Paris, France. (Based on text in French) (Received 23 July 1976)

comma entered between two notes indicates that they are sounded successively; a semicolon indicates that they are sounded simultaneously. A period punctuation mark indicates the end of the measure. The designation T32 D04 states that the tone D04 has a relative duration of time 32, which means it sounds during the two measures.

The following is another example:

CHORDS

EXP SCORE

I01 DOO,R85 B01. END

DIGITAL- TO -

ANALOG > X JJ CONVERTER

Fig. 1. Diagram showing the several steps in producing computer music with the aid of a digital-to-analog converter (DAC).

I 7 . n

r~ - FJ-

Fig. 2. Two measures of a musical score.

39

r) I

This content downloaded from 91.229.248.184 on Wed, 18 Jun 2014 20:55:05 PMAll use subject to JSTOR Terms and Conditions

Frank Brown

Here, in the absence of other statements, the parameter EXP raises the preceding tone by a halftone. thus one can produce all the tones on the piano beginning with the tone (DOO = 32 Hz,... D03 = 256 Hz by halftones; 85 measures are to be produced. If a semicolon followed B01, then the 85 tones would be sounded simultaneously.

The scores are recorded on a magnetic disk in the computer (Fig. 1). They are 'numerical musical scores' in which notes are specified by five parameters: frequency, amplitude, duration, starting time and instrument (designated by number).

the signals are converted into numbers representing voltages that in turn are converted into a varying electrical current for activating a loudspeaker. (The DAC was made by the Centre National d'Etudes des Telecommunications, at Issy-les-Moulineaux, France.)

w -a

CL.

<I 'ime

3. Program AUDITU Program AUDITU serves for converting information

provided by the score on the magnetic disk into sound produced by an electronic DAC [3,4]. It employs very rapid recursive mathematical generators:

Yi+l= 2a (cos 0) Yt - a2Y,_1

Y,= A sin 4

Y= A sin (~ + 0)

Here X is the phase and 0 equals 6.28 f/F, where fis the frequency of sound to be produced and Fis the number of values specified in a waveform over an interval of one second. It can be verified that Y, = Aan sin (d + nO). The behavior of amplitude Yn depends on the value given to a (Fig. 3).

It is important that the passage from one value to the next be done in few operations (one multiplication and one subtraction if a equals 1.) The parameters need four memory spaces. These parameters are: 2a cos 0, -a2, Yt and Y,_-; these involve amplitude, phase, pitch and decay.

4. Spectral variations From the spectral standpoint, electronic sound is

stationary sound. It has been known for a long time that the quality of a sound is linked more to its temporal spectral variation (that is, the seperate development of each harmonic) and contrast in intensity than to an average of the spectral and intensity variations (that is, the approximate proportion that the harmonics share among themselves).

The program AUDITU employs functions of the form:

F = Aa" sin (ot + d) -(1 - X) - k

_1 - cos p t _

which is calculated recurrently. Such functions are rich in harmonics and, depending on the values of ~, k, co, p and x, spectra of great variety, both harmonic and nonharmonic, may be obtained.

5. Sound conversion The magnetic tape upon which the computer has

imposed a series of coded numerical signals is fed into a DAC [5,6,7] where by means of the AUDITU program

Yn, Yn

-a L (a less than I) (a equal to I) (a greater than 1)

Time, t I

Fig. 3. Variations of amplitude with time.

Magnetic 0 0 o 0 o 0 o 0 tape 0 0 0 0 0 0 0

0,

Fig. 4. Input or analog-digitl conversion. Fig. 4. Infirmation inputJ/br analog-digital conversion.

If, for example, one desires a sound of given pitch and intensity and a certain wave (Fig. 4), the successive values of the amplitude are registered on the magnetic tape. The precision obtained depends on the number of values read in a one-second interval. Often 30,000 values must be registered for faithful sound production. The large number of values needed results in tedious calculations. A sinusoidal wave could be programmed in an elementary fashion, however, using:

Y = A sin (owxt)

for successive values of time t, but this method would be very costly.

The programs have been written to simplify, in the extreme, the production of the computer music, otherwise the enormous amount of effort required would make the work of the Group impracticable. The Group has used an IBM/168 digital computer to perform the calculations for the complex score for six voices using 26000 values per sec.

The program AUDITU has been used to produce more than 20 hours of music, of which a very large portion was produced by TERRA IGNOTA programs for automatic compositions, and the remainder were done with the SCRIPTU program.

The first concert of the Group that was composed and produced entirely automatically was given on 28 February 1975 during an inaugural musical program at the Palais Guimet, Paris, for the Association pour la Collaboration des Interpretes et des Compositeurs.

References 1. P. Barbaud, Initiation a la composition musicale automa-

tique (Paris: Dunod, 1966). 2. P. Barbaud, La musique, discipline scientifique (Paris:

Dunod, 1968). 3. F. Brown, Le code SCRIPTU: Manuel d'utilisation (Le

Mans, France: Facult& des Sciences, 1976). 4. F. Brown, G. Klein and R. Lehmann, Le programme

AUDITU, Revue d'acoustique, p. 206 (No. 38, Oct. 1976). 5. F. Brown and R. Lehmann, Synthese rapide de sons

musicaux, Revue d'acoustique, p.211 (No. 38, Oct. 1976). 6. H. Howe, Electronic Music Synthesis (New York: Norton,

1975). 7. M. Mathews, Technology of Computer Music (Cambridge.

Mass.: MIT Press, 1969).

40

This content downloaded from 91.229.248.184 on Wed, 18 Jun 2014 20:55:05 PMAll use subject to JSTOR Terms and Conditions