A World in a Grain of Sound

Nov 1, 1999 12:00 PM, By John Duesenberry

A pile of gravel being dumped off a truck may not sound much like a police whistle, a guiro, or a revving motorcycle. But all these sounds have something in common: they are all sound complexes, sounds made up of many smaller sound events. When gravel is dumped, for example, we hear thousands of pebbles sliding along the truck bed and clicking against each other. Multiple rapid air-bursts form the police whistle and motorcycle sounds. When the guiro is scraped, dozens of individual clicks fuse into a single musical gesture. In such sound complexes, the individual sound events are similar but seldom identical, and their exact characteristics and timing are unpredictable. We perceive and remember the character of the whole complex, not the constituent sounds.

Using granular synthesis, we can build sound complexes with properties similar to the examples above, although they may sound quite different. Granular synthesis software generates and assembles a large number of very short sound bursts, or grains, to form larger-scale sound events. These events are often called clouds. Typically, grains are generated at rates of hundreds or thousands per second, so it isn't practical to "compose" each grain. Instead, granular synthesis software offers higher-level controls that shape the evolution of individual grain parameters.

In the 1940s, physicist Dennis Gabor theorized that any sound could be described by a granular representation. Gabor constructed a machine that granulated sound and performed experiments in time compression and expansion. The first musician to study Gabor's work was Iannis Xenakis. In the 1960s, Xenakis created granular sounds using tape manipulation. In 1974, Curtis Roads developed the first computer implementation of granular synthesis. Roads, a composer closely identified with the technique, has done much to make granular synthesis available to musicians. His most recent contribution is the freeware program Cloud Generator for the Mac. Roads has also published numerous landmark articles on the subject.

Since Roads's first work, many others have contributed to the art. Especially notable is composer Barry Truax, who pioneered real-time granular synthesis in the 1980s. To accomplish this, Truax had to microprogram a DSP device and write additional software for a host computer. Today, a variety of granular synthesis software is available to any desktop musician, with little or no programming involved. (See the sidebar "Granular Synthesis Tools.")

Granular synthesis, unlike subtractive or modulation synthesis, doesn't derive from conventional signal processing techniques and has no standard implementation. Curtis Roads's technical vocabulary is the closest thing to an accepted terminology for granular synthesis, and I'll use it in this article.

STRUCTURE OF A GRAIN
Let's start by looking at how a single grain is generated. It's a fairly trivial operation. The classic recipe calls for an oscillator signal with a simple amplitude envelope. An oscillator-based grain of this type is termed synthetic. Any waveform can be used in a synthetic grain, but a sine wave is probably the most common. Another approach, called sound-file granulation, uses audio samples as the source signal. Sample-based grains are called file grains.

For a grain's amplitude envelope, a smooth curve is often desirable because it doesn't produce sharp transients in the grain. The most common grain envelope is the bell-shaped curve of a Gaussian function. Shapes that approximate this curve, such as triangular or simple three-stage envelopes, are also commonly used.

Figure 1 shows a typical sine-wave grain with a Gaussian envelope. Because of the grain's short duration, the ear registers it as a "blip" of ill-defined pitch and timbre. Taken by itself, it's a rather boring sound. However, the objective in granular synthesis is not to produce grains that are interesting individually, but to sequence these neutral-sounding blips into larger events that will interest the listener. In this context, the anonymous character of the grain is actually an asset.

Grain parameters can vary on a grain-by-grain basis. You can vary many aspects of the grain, including the waveform or sample source, and its amplitude, frequency, duration, envelope shape, and pan position. The effect of changing some of these parameters will be obvious. For example, if you synthesize 100 grains over 2 seconds and increase the frequency of each grain by a small amount, you will get some sort of pitch-sliding effect. Other parameters, such as duration and envelope shape, have effects that cannot be fully understood until we consider what happens when we arrange grains in time.

SEQUENCED GRAINS AND AM
Amplitude modulation (AM) is an important component of granular synthesis. If you're not familiar with the basics of AM synthesis, you may want to look over a previous "Square One" article on that topic, which appeared in the March 1999 EM.

The easiest way to understand the relationship between granular synthesis and AM is to consider a stream of evenly spaced sine-wave grains, like that in the top track of Figure 2. This simple example, where the time intervals between grains are equal, is called synchronous granular synthesis (SGS). If the rate of grain generation, or grain density, is lower than about 20 grains per second, the grains will be perceived as a metronomic sequence of sounds. If the grain density is higher, listeners will hear a continuous signal.

SGS is equivalent to amplitude modulation of a carrier signal by a periodic modulator. The carrier, in this example, is a sine wave, and the modulator is the repeated envelopes. To figure out the modulator frequency, take the inverse of the period between one grain and the next. For example, given a period of 11/430 of a second, the fundamental modulator frequency would be 30 Hz. As in conventional AM, sidebands (sums and differences of the carrier and modulator frequencies) appear in the output spectrum.

The shape and duration of the envelopes determine the modulator waveform and therefore its spectrum. In general, envelopes with sharp rise and fall times will generate stronger high-frequency content than smooth envelopes. Thus the choice of envelope can have a considerable effect on the number and strength of the sidebands.

SGS isn't the most typical application of granular synthesis; it's a rather cumbersome way to produce AM effects. (To get ordinary AM, use ordinary signal generators.) However, SGS does let you vary one or more parameters per grain, leading to complexities difficult to produce with AM alone. In the bottom track of Figure 2, the frequency of each grain is random within a 50 Hz to 2 kHz range. We could analyze this as amplitude modulation of a carrier that is also being frequency modulated by a quasi-random step waveform.

SONIC SPRAY GUN
Asynchronous granular synthesis (AGS), in which grains are distributed randomly over some period of time, is a more widely used form of granular synthesis. AGS works like a sonic spray gun, scattering droplets of sound instead of paint. By definition, AGS involves some degree of aperiodicity in the timing of the grains. The effect is often similar to AM with band-limited noise as the modulator signal; there is random sideband energy, which is perceived as noise.