Sound has been represented to us in a number of different ways by acoustical theorists. Helmholtz postulated that when our ears are presented with a complex audio signal our brain analyses it as a superimposition of sine waves with harmonically related fundamental frequencies. This theory however does not properly allow for the fact that sound changes in time. Gabor (1947) formulated a theory in which he claimed that sound was perceived as a series of short, discrete bursts of energy, each slightly changed in character from the last. He suggested that within a very short time window (10 - 21 microseconds) the ear is capable of registering one event at a specific frequency. This theory has since been mathematically verified by Bastiaans (1980). In fact it is this property of sound that makes it possible for the now familiar digital audio formats to store and reproduce sound as a series of discrete samples.

Granular synthesis of sound is the generation of thousands of short sonic grains which are combined linearly to form large scale audio events. The characteristics of the grains are definable, and these combine to give the characteristics of the overall sound. However the parameters used in defining the grains do not map directly to the parameters of the large scale event. It is the interaction of the various grain parameters which define the micro structure of an event. The macro structure of an event is generated by the change in the characteristics of the grains.

To more fully understand the unique properties inherent in granular synthesis it is necessary to examine the perception of sound.

When a musical note is heard it is common to associate it with a specific pitch, a characteristic timbre, and a definite duration. Frequencies can be perceived from around 20,000 cycles per second (Hz) down to around 20 Hz. Rhythms can be perceived from a few beats per minute up to about 16 beats per second. Above this frequency we begin to discern a pitch. It is in this area, 15-25 Hz, that rhythm and pitch become blurred.

Here there is potential for the examination of the effects of frequency on our perception of sound. The transformation from rhythm to pitch highlights the properties of the transformations present in the perception of discrete sound events as a continuous series of grains.

If heard as a large scale sound event the listener would first hear an increasing amplitude, this being the attack part of the grain. The listener would then hear a steady state, the sustain part of the grain. This would then be followed by a decrease in amplitude through the release part of the envelope.

If this same grain was heard as a part of the microstructure of a large scale event the listener would perceive the grain envelope not as a changing amplitude but as a waveform, the timbral characteristics of which are determined by the Attack, Sustain, and Release times. The frequency will be a function of the total duration and delay between grains.

Barry Truax (1988) has identified a threshold which occurs with a grain duration of 50 msec. When the grain length is much less than 50 msec the ear percieves a continuous texture, whereas grains with durations longer than 50 msec are heard as discrete events.

This is a phenomenon explored within the sound generation of rainforestbeech, a large part of which is heard as a continuous texture. However, after the climax a pulsing rhythm can be heard in the background. This pulsing is the result of the use of a delay time of up to 60 msec between grains.

The textures used in rainforestbeech are sparse when compared with those of Truax.
Truax has used examples of duration and delay times in the order of 15 and 5 msec respectively. This gives a relationship of 3 : 1 for duration : delay times. rainforestbeech typically has a relationship of 1 : 3.

Curtis Roads (1985) has suggested an upper bound of 20 msec for grain duration, and has found grains of 10 msec useful. Some experiments have suggested that the ability of the ear to detect discrete events and discern their order extends down to 1-2 msec.

Granular synthesis is dependent on the generation of thousands of events per minute, and so it is impractical to define a set of characteristics for each grain. A practical application of granular synthesis involves the use of a micro-computer to generate a stream of grains to which time varying characteristics can be applied.

This is exactly what has been done using the fof module in Csound. The fof module is convenient in that it already generates a stream of grains, and although it is tailored for a specific function it can be modified quite simply to conform closely to the functions of a grain generator of a more useful nature.

Sounds developed for Couture Cosmetique (Terre Thaemlitz) emphasize residual noises produced by techniques such as Granular Synthesis, Pitch/Time convolution and heterodyn filter analysis. The CD is an excellent reference for those wishing to hear the amazing sounds these techniques are capable of producing.

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