“Granular synthesis is an innovative approach to the representation and generation of musical sounds” (DePoli 139). The conception of a granular method of sonic analysis may have been first proposed by Isaac Beekman in his article Quantifying Music (Cohen). This late Nineteenth Century document discusses the organization of music into “corpuscles of sound”. Unfortunately, granular synthesis theory was not investigated further for quite some time. British physicist Dennis Gabor stimulated new interest in granular synthesis around 1946 (Gabor). Gabor believed that any sound could be synthesized with the correct combination of numerous simple sonic grains. “The grain is a particularly apt and flexible representation for musical sound because it combines time-domain information (starting time, duration, envelope shape, waveform shape) with frequency domain information (the frequency of the waveform within the grain)” (Roads 144). Before magnetic tape recorders became readily accessible, the only way to attempt granular composition was through extremely sophisticated manipulation of a large number of acoustic instruments (as in many of the early compositions of Iannis Xenakis). The tape recorder made more sophisticated granular works possible. However, the laborious process of cutting and splicing hundreds of segments of tape for each second of music was both intimidating and time-consuming. Serious experimentation with granular synthesis was severely impaired. It was not until digital synthesis that advanced composition with grains became feasible.

Basics of Granular Synthesis

The grain is a unit of sonic energy possessing any waveform, and with a typical duration of a few milliseconds, near the threshold of human hearing. It is the continuous control of these small sonic events (which are discerned as one large sonic mass) that gives granular synthesis it’s power and flexibility. While methods of grain organization vary tremendously, the creation of grains is usually relatively simple. A basic grain generating device would consist of an envelope generator with a gaussian curve driving a sine oscillator (figure 1). The narrow bell-shaped curve of the gaussian fill is generated by the equation: The signal from the oscillator enters an amplifier that determines spatial position of each grain. Quadraphonic amplification is very popular for granular synthesis because of the great spatial positioning capabilities. The typical duration of a grain is somewhere between 5 and 100 milliseconds. If the duration of the grain is less than 2 milliseconds it will be perceived as a click. The most musically important aspect of an individual grain is its waveform. The variability of waveforms from grain to grain plays a significant role in the flexibility of granular synthesis. Fixed-waveforms (such as a sine wave or saw wave), dynamic-waveforms (such as those generated by FM synthesis), and even waveforms extracted from sampled sounds may be used within each grain. A vast amount of processing power is required to perform granular synthesis. A simple granular “cloud” may consist of a only a handful of particles, but a sophisticated “cloud” may be comprised of a thousand or more. Real-time granular synthesis requires an endless supply of grain generating devices. Several currently available microcomputers are capable of implementing real-time granular synthesis, but the cost of these machines is still quite prohibitive. Therefore, most granular synthesis occurs while the composer waits, sometimes for quite a while. This time factor prevents many electronic and computer composers from working with granular synthesis.

Methods of Grain Organization

Screens

One of the first composers to develop a method for composition with grains was Iannis Xenakis. His method is based on the organization of the grains by means of screen sequences (figure 2), which specify the frequency and amplitude parameters of the grains (FG) at discrete points in time (Dt) with density (DD) (DePoli 139). Every possible sound may therefore be cut up into a precise quantity of elements DF DG Dt DD in four dimensions. The scale of density of grains is logarithmic with its base between 2 and 3, and does not exist on the screens. When viewing screens as a two dimensional representation, it is important not to lose sight of the fact that the cloud of grains of sound exist in the thickness of time Dt and that the grains of sound are only artificially flattened on the plane (FG) (Xenakis 51). Xenakis placed grains on the individual screens using a variety of sophisticated Markovian Stochastic methods which he changed with each composition. The first compositions to use this method were Analogique A, for string orchestra, and Analogique B, for sinusoidal sounds, both composed in 1958-59. More recently, a variation on Xenakis’ screen abstraction has been implemented into the UPIC workstation discussed below.

Pitch-Synchronous Granular Synthesis

Pitch-synchronous granular synthesis (PSGS) is an infrequently performed analysis-synthesis technique designed for the generation of pitched sounds with one or more formant regions in their spectra (Roads 191). It makes use of a complex system of parallel minimum-phase finite impulse response generators to resynthesize grains based on spectrum analysis.

Quasi-Synchronous Granular Synthesis

Quasi-synchronous granular synthesis (QSGS) creates sophisticated sounds by generating one or more “streams” of grains (figure 3). When a single stream of grains is synthesized using QSGS, the interval between the grains is essentially equal. The overall envelope of the stream forms a periodic function. Thus, the generated signal can be analyzed as a case of amplitude modulation (AM) (Roads 151). This adds a series of sidebands to the final spectrum. By combining several QSGS streams in parallel it becomes possible to model the human voice. Barry Truax discovered that the use of QSGS streams at irregular intervals has a thickening effect on the sound texture. This is the result of a smearing of the formant structures that occurs when the onset time of each grain is indeterminate.

Asynchronous Granular Synthesis

Asynchronous granular synthesis (AGS) was an early digital implementation of granular representations of sound (figure 4). In 1978, Curtis Roads used the MUSIC 5 music programming language to develop a high-level organization of grains based on the concept of tendency masks (“Clouds”) in the time-frequency plane (DePoli 140). The sophisticated software permitted greater accuracy and control of grains. When performing AGS, the granular structure of each “Cloud” is determined probabilistically in terms of the following parameters:

1. Start time and duration of the cloud
2. Grain duration (Variable for the duration of the cloud)
3. Density of grains per second (Also variable)
4. Frequency band of the cloud (Usually high and low limits)
5. Amplitude envelope of the cloud
6. Waveforms within the grains
7. Spatial dispersion of the cloud

Obviously, AGS abandons the use of specific algorithms and streams to determine grain placement with regard to pitch, amplitude, density and duration. The dynamic nature of parameter specification in AGS results in extremely organic and complex timbres.

Some Recent Hardware and Software Developments

The UPIC Workstation

UPIC (Unite Polyagogique Informatique du CEMAMu) is a machine dedicated to the interactive composition of musical scores (Xenakis 329). It was conceptualized by Xenakis and created at the CEMAMu (Centre for Studies in the Mathematics and Automation of Music) in Paris. The UPIC software consists of pages on which a composer draws “arcs” which specify the pitch and duration of a sonic event (figure 5), and a voice editing matrix with which the “arcs” are described. Waveform, envelope, frequency and amplitude tables, modulating arc assignment, and modification of audio channel parameters (dynamic and envelope) may all be manipulated for each “arc” in real-time.

The hardware of the UPIC system consists of a Windows-based computer with a digitizing tablet, and the UPIC Real-Time Synthesis Unit:

64 Oscillators at 44.1 kHz with FM converter board:

• 4 audio output channels
• 2 audio input channels
• AES/EBU interface

Capacity:

• 4 pages of 4000 arcs
• 64 waveforms
• 4 frequency tables
• 128 envelopes
• 4 amplitude tables

The UPIC Workstation is ideal for granular synthesis for several reasons. First, it allows any waveform (including sampled waveforms) to be assigned to each “arc”. Second, it currently permits 64 “arcs” to be layered vertically. This enables the composer to design “clouds” of sound up to 64 grains in density and of infinite duration at any point in a composition. Finally, and perhaps most importantly, the UPIC requires no time to process any of its functions.

Csound

Csound is a music programming language for IBM-compatible, Apple Macintosh, Silicon Graphics, as well as several other computers. It was written by Barry Vercoe at the MIT Media Lab. The programmer is required to give Csound an “Orchestra” file using an infinite number of instruments and instrument parameters, and a “Score” file which may be equally as complex. Csound then creates a soundfile containing the completed work.

A typical Csound granular “Orchestra” specification:

;;; granulate.orc

sr=44100
kr=22050
ksmps=2
nchnls=1

instr 1
next: timout 0,p6,go1 ;;; p6 = grain duration time… I could allow for an envelope on this
reinit go1
timout 0,p5,go2 ;;; p5 = inter-grain time… I could allow for an envelope on this
reinit next

go1:
k1 oscil1i 0,1,p6,3
a1 soundin p7,p4,4 ;;; p7 is which soundin file to use…
a2 = a1 * k1
rireturn
go2:
k2 oscil1i 0,1,p3,4 ;;; envelope output sound.
out a2*k2
endin
;;Copyright 1992 by Charles Baker

A “Score” written for this particular “Orchestra”:

;; sample .sco file
f 3 0 8193 9 1 -.5 90 0 .5 90 ;; grain envelope
f 4 0 8193 9 1 -.5 90 0 .5 90 ;; Note amplitude env.
;;ins st dur amp inter-grain-time grainduration soundinfile#
i 1 0.000 2.750 1 0.000 0.020 1
i 1 2.750 2.612 1 0.010 0.020 1
i 1 5.362 2.482 1 0.020 0.020 1
i 1 7.844 2.35
i 1 0.030 0.020 1
i 1 10.202 2.240 1 0.04 0.020 1
i 1 12.442 2.128 1 0.05 0.020 1
i 1 14.570 2.022 1 0.06 0.020 1
i 1 16.591 1.920 1 0.07 0.020 1
i 1 18.512 1.824 1 0.08 0.020 1
e
;;Copyright 1992 by Charles Baker

Many granular composers currently use Csound. The power of the program to control even the smallest nuance of a soundfile, as well as the ability to import sampled sounds, and the convenience of recycling sophisticated granular “Orchestras” and “Scores”, make it a powerful granular synthesizer.

Cloud Generator

Cloud Generator is a granular synthesis application for the Apple Macintosh (figure 6) . The software was conceived and programmed by Curtis Roads and John Alexander at Les Atelier UPIC in Paris. Cloud Generator creates clouds using Quasi-Synchronous or Asynchronous Granular Synthesis based on the parameters listed in that section on AGS above . Each QSGS stream and AGS “Cloud” must be created individually and is output in AIFF format.

Conclusion

Granular synthesis is a very powerful means for the representation of musical signals. Each of the techniques outlined above provides an opportunity for a composer to expand his or her sonic “palette”. Asynchronous Granular Synthesis is a particularly powerful means for creating sonic events that are both unique and sophisticated. “In musical contexts these types of sounds can act as a foil to the smoother, more sterile sounds emitted by digital oscillators” (Roads 183). When granular synthesis techniques are used in conjunction with sampled waveforms, the possibilities for new sounds are infinite.

References

Cohen, Michael, ed. Isaac Beekman. Dordrecht, The Netherlands: D. Reidel, 1990.

DePoli, Giovanni, ed. Representations of Musical Signals. Cambridge, Massachusetts: The MIT Press, 1991.

Gabor, Dennis. “Theory of Communication.” Journal of the Institute of Electrical Engineers Part III, 93: 429-457.

Roads, Curtis. “Asynchronous Granular Synthesis.” Representations of Musical Signals. Cambridge, Massachusetts: The MIT Press, 1991.

Strange, Allen. Electronic Music: Systems, Techniques and Controls. Dubuque, Iowa: W.C. Brown Company, 1983.

Truax, Barry. “Real-time granular synthesis with a digital signal processor.” Computer Music Journal 12(2): 14-26.

Xenakis, Iannis. Formalized Music. Stuyvesant, NY: Pendragon Press, 1991.