Presentation to L'Academie Internationale de Musique Electroacoustique

Bourges, France, June 1999


I. Introduction

It is often argued that time is the most basic element of sound and aural experience, because what all sounds have in common is that they occur "in time" and have some finite duration. Prior to Einstein, Western science developed a concept of time as a uniform continuum, visualized as a line, that could be quantized into a grid of convenient units, whether they be milliseconds or years. Electroacoustic music, which is grounded in that science, implicitly adopted these concepts of time. Analog practice measured time in tape speeds of various cm/sec, and in the digital domain, scores are frequently expressed in seconds and time is ultimately quantized at the sampling rate.

Moreover, digital technology gave composers accurate access to the micro-level time domain which remains the "final frontier" to be explored in electroacoustic music. The traditional Fourier model of analysis, however, regarded the time domain as the inverse of the frequency domain with various "transforms" to pass from one to the other and back. To do so, the theory had to postulate an infinite time window in order to define a perfectly singular frequency. Likewise, the concept of the instantaneous impulse resulted in the necessity to imagine an infinite bandwidth. The digital domain merely band-limited the frequency domain to half the sampling rate and quantized time at the sample level to the microsecond domain. No frequency above the Nyquist frequency can be generated and no event less than around 20 microseconds can be specified.

II. The time scales of electroacoustic music

Other ways of understanding time are conceivable, and in some cases are even made possible by electroacoustic techniques. For instance, sound events do not have to be thought of as occurring "in" time; instead, sound can be understood as "creating" time, whether in the physical sense of measured time or the perceptual and cognitive experience of time. At the micro level, the rate of change of position of a vibrating object creates changes in sound pressure, and the rate of change of phase of that sound pressure creates frequency. The fact that time and frequency are created by the same process is most succinctly expressed by the Gabor quantum or grain which is an "event" in frequency-time space. Mathematically, a Gaussian envelope describes the grain equally well in both the time and frequency domains. When the grain is "squeezed" in one domain, it expands in the other: short grains have broader bandwidths, and longer grains have narrower ones, namely a specific frequency. So-called time-frequency synthesis techniques (e.g. granular, FOF, Vosim) recognize this interdependence of domains such that spectral design is performed in the time domain, and vice versa.

The "arrow of time" is not defined at the micro level; that is, at the quantum level of the grain, a symmetrical grain is also symmetrical in time - it sounds the same forwards and backwards. It is at the next higher level that the envelope and the succession of events establish the directionality of time and the sense of rhythm. However, even at this most familiar level of musical time, it was probably only during the Industrial Revolution - the machine age, with the appearance of the Maelzel metronome, for instance - that musical time became associated with clock time in terms of beats per minute. Prior to that, rhythm was a way of experiencing time with reference to the body in particular and motion in general - "form cut into time" as Ezra Pound put it. Natural rhythms, whether human or those of nature, are never as regimented as those of the machine age, variation and fluidity being more the norm than exactitude of repetition. The delicate balance between the predictability of repetition and the expressiveness of variation forms the basis for the rhythmic experience of time at this level.

From a psychoacoustic point of view, the auditory system can be understood as needing to balance the perception of temporal variation with frequency or spectral variation. Again, it is a matter of the linkage between the time and frequency domains. If we were able to track the time behaviour of sound precisely - the waveform level being the most ridiculous example - we could not perceive anything in the frequency domain. And likewise, more precise spectral analysis than that of the critical bandwidth would have to occur at the expense of tracking temporal variations. Speech perception probably defines the normal balance between temporal and spectral tracking on the part of the auditory system where phonemes occur at a speed of around five per second. This aspect of perception is sometimes termed "demodulation" because it is not primarily the sound "carrier" that is most important, but rather the changes that have been "encoded" into it in both the time and frequency domains.

Digital time-stretching techniques are all based on techniques of "windowing" the sound into short grain-like segments which allow the composer to change the time scale of the sound without varying its frequency content. By changing the time scale of a particular sound we inevitably change our perception of it. Slowing down speech, for instance, draws attention to the patterns of inflection as melodies, and the phonemes as timbres. Extreme amounts of stretching where we hear a nearly steady-state sound, changing almost imperceptibly slowly, makes a speech sound more like an environmental one and draws the ear's attention to the spectral domain. Ironically, it is this granular technique which was proposed by Gabor as an alternative to the Fourier model which makes the timeless Fourier analysis of the frequency domain a perceptual reality! Given an arbitrarily long time to perceive a sound, we can abandon our wholistic perceptual strategies and employ our most analytical ones to listen "inside" the sound to its spectral evolution.

Finally, at the level of musical time beyond rhythm, we find musical structure and form where repetition and variation take on a different, but perhaps analogous role. It is here that electroacoustic music seems to offer the widest range of possibilities. By having an expanded repertoire of timbral and textural resources, electroacoustic music can shape its structures in a seemingly infinite variety of ways. I like to think of each piece as creating its own form based on the interactions of its different component layers, in other words, form as an emergent property, rather than a predetermined shape. If that is true, each piece will also create its own unique sense of time, one that seldom seems to correspond to clock time. For instance, when introducing new pieces to my students, I find that when they are caught up in the temporal experience of the piece, they always underestimate its length and "lose track" of time, whereas when they are unengaged by it, they overestimate its length because of their lack of involvement. One only has to think of the different experiences of time in pieces such as Trevor Wishart's Redbird, Léo Küpper's Litanea, Justice Olsson's Up! and my work Riverrun, to realize how varied that experience can be.

Zooming out beyond the experience of time shaped by a piece of music we come to the level of our own memory, and then the memory of the culture, the life cycles of the biosphere and ultimately the unfolding of the universe. Maybe on a personal level we are only what we remember, and our culture is only what it remembers, and we can wonder if the universe "remembers", i.e. will show any trace of influence of what has happened in our small role within it. In terms of electroacoustic music, and its 50 years of modern history, each year that we live, we increase the percentage of its history that we have experienced and helped shape. It increasingly becomes, as Gertrude Stein put it, "the history of us all".

But we also know that both cultural memory and personal memory will inevitably discard items from this history in favour of those which, to use the Darwinian term, have best adapted to their environment. How many thousands of works have we heard and how many do we remember? And how many will survive, both physically and culturally? We also find that, as we get older, time appears to pass more quickly, each year being a smaller percentage of our entire life. When this experience is combined with the rapid pace of technological change that has shaped and is affecting our field, it seems as if we are experiencing an historical acceleration where more is happening but less seems meaningful. The only permanence seems to be transience, and this "postmodern" sensibility seems founded on insecurity.

III. Conclusion

Technology seems capable of rationalizing nearly everything, including time. I am reminded of the tribe whose "unit" of time was how long it took to boil water, a concept that seems more practical and intuitive than our current scientific definition of the second which I recall is a rather large number of vibrations of some isotope of cesium! Of course this standardization of time has proved useful in such diverse tasks as bringing people together at some specified place without any communication between them being required, or for determining the amount of money we should receive for the performance of one of our works - a convenient way of ignoring all issues of artistic value in favour of their only common property, duration.

However, what all of our work really has in common is the organization of sound, and what sound creates is the experience of time. And for time to be experienced requires consciousness. As Tolstoy wrote in his journal in 1910: "Consciousness is motionless. And it is only because of its motionlessness that we are able to see the motion of that which we call time. If times passes, it is necessary that there should be something which remains static. And it is consciousness of self which is static."


B. Truax, "Musical Creativity and Complexity at the Threshold of the 21st Century," Interface, 21(1), 1992, 29-42.

B. Truax, "Discovering Inner Complexity: Time-Shifting and Transposition with a Real-time Granulation Technique," Computer Music Journal, 18(2), 1994, 38-48 (sound sheet examples in 18(1)).