Compositional Strategies for Point-Source Spatialization

by Christopher Burns (Department of Music, University of Wisconsin-Milwaukee)

Introduction: compositional motivations

My personal, compositional interest in electroacoustic music for multichannel loudspeaker systems stems from a desire for music which emphasizes polyphony, layering, and multiplicity. Spatial articulation can be a very clear and direct way of emphasizing the independence of different musical gestures or textures; conversely, it can be a technique for relating disparate materials. In composing Strain, Questions and Fissures, and Hero and Leander, my use of point-source spatialization has been guided by my interest in polyphony and simultaneity; at the same time, the possibilities for spatial treatment of these materials have influenced my thinking about layering and multiplicity in other works, both electroacoustic and instrumental.

The polychoral approach: Strain and Questions and Fissures

One of the simplest techniques for spatially differentiating musical materials in a multi-loudspeaker setup is to establish and maintain fixed assignments between musical materials and loudspeakers. Strain for four-channel tape (1999) pursues this approach rigorously, treating the four loudspeakers as a quartet of monaural voices. Two loudspeakers introduce the music, a third enters the dialogue after about forty seconds, and the fourth is revealed only at the very end of the first section of the work. In this work, the musical materials are typically similar from loudspeaker to loudspeaker, and differentiated from one another by specific details of pitch, rhythm, timbre, and gesture. The relationship between voices (and therefore loudspeakers) is essentially contrapuntal.

In Questions and Fissures, a work for soprano saxophone and stereo CD (1999), materials are still rigorously associated with loudspeakers; however, the two voices are much more strongly contrasted with one another, emphasizing a multiplicity of experience rather than the chamber-music æsthetic of Strain (John Cage’s Williams Mix is an important precedent for this approach). Questions and Fissures emphasizes the independence of its two electronic layers; each monaural musical argument expresses contrasting phrase and sectional durations, and emphasizes different textural and timbral aspects of their shared synthesis technique (an idiosyncratic method using frequency-modulated speech recordings, resonant filter banks, and waveshaping). However, the presence of the soprano saxophone adds another layer of contrast; most listeners group the loudspeakers together as the “electronic” aspect of the work in comparison with the fundamentally “acoustic” saxophone.

Of the set of pieces under consideration, Questions and Fissures is perhaps the work which goes farthest towards embodying the loudspeakers as meaningful and physical presences in the music; the drastic amplitude modulations and spitting, noisy textures occasionally go so far as to make the movement of the speaker cones a visible phenomenon. This “activation” of the loudspeakers is an interesting side-effect of the fixed mapping between monaural materials and spatial locations, and is enhanced by the absence of artificial reverberation in the works under discussion. As with instrumental music, these works acquire the reverberant qualities of the space in which they are performed, subject to the diffusion patterns of the loudspeakers used.

The sculptural approach: additive- and convolution-based materials in Hero and Leander

Where the polychoral approach begins from individually produced monaural soundfiles, the sculptural strategy starts with multichannel conceptions of material or texture. In Hero and Leander for eight-channel tape (2003), the sculpturally-treated materials are eight-channel soundfiles, with all the channels derived from a common synthetic or signal-processed source. These soundfiles present a unified texture; however, the eight channels are subtly individuated from one another. In the case of additive synthesis textures, different partials are assigned to different channels; with convolution textures, the analyzed spectra are rotated by different offsets prior to resynthesis via the Inverse Fourier Transform.

These subtle distinctions are revealed when amplitude envelopes are applied individually to each channel of the soundfile, carving away from the amplitude of the composite sound to reveal particular facets of the overall texture. As with the polychoral approach, the distinctive features of any particular channel are rigorously associated with a fixed loudspeaker, creating a perceptible connection between sound quality and spatial location.

Hero and Leander presents a sculptural treatment of four different sound materials, each of which occurs eight times; each occurrence has a ten-stage amplitude envelope (including starting and termination in silence) for each of eight channels. 2,048 amplitude values are thus required for the sculpture envelopes (the time bases of the envelopes are generally held consistent across the eight channels, so the amount of data required for these values is much smaller). While these amplitude envelopes could potentially be established through careful listening, intuition, and labor, I was inclined to generate the amplitude values via a more algorithmic approach.

In calculating the moment-to-moment amplitudes, I began from a premise I think of as “Sol Lewitt serialism” — enumerating permutations of the eight channels and eight intuitively defined amplitudes, but allowing different permutation strategies to interfere with one another, and thus constrain the total number of possible results. Simple strategies like continuous crescendo, continuous decrescendo, transition towards identical envelopes, and transition towards independent envelopes govern the selection of specific serial permutations and their temporal sequence in the overall work.

The specific amplitudes chosen, and the quartic interpolations between those envelopes, form a certain kind of signature for the piece — the finished work sounds the way it does in part because of the particular (and repetitive) qualities of the amplitude envelopes. More generally, the tendency towards algorithm in the composition (a tendency which pervades the temporal structure and disposition of material as well as the spatialization) gives the music a unusual quality. The violent gestures of the feedback network are constrained by their algorithmically-specified durations, creating a tension between activity and stasis.

The sonification approach: waveguide-based materials in Hero and Leander

Another musical layer of Hero and Leander begins from a different spatialization premise: the sonification of a feedback network (Burns 2003). The network is a waveguide-like structure, with eight pairs of delay lines arranged in a circular structure, and with each pair connected to adjacent pairs around the ring by a junction. Any soundfile can be injected into the network as an initial excitation which then recirculates, experiencing recursive resonant filtering.

These structures are “waveguide-inspired” (Essl 2003; Burns, Burtner and Serafin 2003) rather than being classical waveguides, and don’t easily encourage a physical modeling interpretation. The two delay rails can change length (delay time) independently of one another; the gain structures change continuously, and don’t necessarily sum to less than unity (nonlinear waveshaping stages are used to assure that amplitudes are bounded); not every pair of delays implements a sign change between upper and lower rail; and the circular (and often lossless) topology has no obvious acoustic analogy. However, these more idiosyncratic structures still feature many of the benefits of physical models: they produce very “articulate” textures, with continuous microfluctuations in timbre. Because of their disregard for some of the traditional tuning techniques for physical models, these networks are more likely to enter marginal and turbulent states, with swooping frequency contours, inharmonic pitch relations, and punctuating noisy explosions.

Most important for this discussion, fixed mappings of the waveguide section outputs to loudspeakers results in a direct sonification of the acoustic energy propagating around the network. Gestures cascade audibly around the network, making it possible to hear the influence of particular network regions on their adjacencies. The connection between virtual acoustic distance (in the form of delay lines) and physical distance (between the loudspeakers) is made explicit, and results in a variety of convincing and interesting spatialization effects (Burtner and Serafin 2002, van Walstijn, Alcorn and Bilbao 2005).

As a final stage of composition, the output from the feedback network is treated using the sculptural strategy outlined above; this serves to concentrate the listener’s attention on selected areas of the network at specific times, to bring the density and quality of the feedback gestures into balance with the other textures, and to integrate the feedback material into the work through common processing techniques. If anything the “sculpting” serves to make the unique spatial character of the network more readily identifiable: the listener can compare the relationships between a few outputs at a time, rather than taking in all eight continuously.

Evaluation and practical considerations

One advantage of the point-source spatialization techniques described above is that they are highly adaptable to different configurations of loudspeakers. Effective performances of Strain have included not only the conventional “square” and “diamond” quadraphonic setups, but also idiosyncratic configurations, such as four loudspeakers arrayed in a line stretching from left to right in front of the audience. The absence of conventional panning techniques greatly de-emphasizes the importance of inter-loudspeaker geometry and distances, which are so crucial to other spatialization techniques. The only multichannel scenario I’ve encountered in which these works don’t adapt well is in open outdoor environments: my injunction against artificial reverberation in these strategies becomes problematic when the performance space provides little or no natural reverberation. An “outdoor mix” incorporating reverberation is probably the most appropriate solution to this issue.

Unfortunately, the adaptability of these works do not extend to stereo mixes. Multichannel works composed with these point-source strategies can be particularly difficult to mix to two channels for CD or radio presentation. Strain works reasonably well with its four discrete channels mapped to hard left, left-of-center, right-of-center, and hard right stereo pannings. However, this strategy doesn’t scale well for translating eight-channel works, and I still haven’t found an effective stereo mix of Hero and Leander. (Of course, one might argue that any music which is truly conceived for a multichannel situation will be difficult to render faithfully in stereo).

As mentioned while discussing Questions and Fissures, an interesting feature that these strategies all share is the tendency to activate and embody the loudspeakers as physical presences in the performance of the work. This effect is the opposite of the more familiar dematerialization of the loudspeakers possible with a well-made stereo recording in a lights-out presentation. Rather than encouraging an immersion in sound, the point-source strategies emphasize the role of the loudspeakers in presenting the music.

As the number of point-sources and/or musical elements in the work increases, forms of algorithmic structuring become increasingly relevant to the compositional process. Just as in other realms of electroacoustic composition, the “data explosion” becomes a very real problem! Algorithms are one technique not only for producing mix data (in the sculptural strategy) or waveguide configurations (in the sonification strategy), but also for generating, differentiating, contrasting, and relating textures and materials.

Finally, these approaches emphasize spatialization as a compositional practice. These strategies require that spatialization be considered not as a post-processing, mixing, or mastering concern, nor as a performance technique for live diffusion, but as something embedded in the initial conceptualization of a project.

References

Burns, Christopher. ‘Emergent behavior from idiosyncratic feedback networks’, in the Proceedings of the International Computer Music Conference. 2003.

Burns, Christopher, Stefania Serafin, and Matthew Burtner. ‘Musical applications of generalised multichannel digital waveguides’, in the Proceedings of the Stockholm Musical Acoustics Conference. 2003.

Burtner, Matthew, and Stefania Serafin. ‘Strictly Bowlroom: the physically modeled singing bowl as a transformative immersive environment’, in the Proceedings of the International Symposium on Musical Acoustics. 2002.

Essl, Georg. ‘The displaced bow and APhISMs: Abstract physically informed synthesis methods for composition and interactive performance’, in the Proceedings of the Florida Electroacoustic Music Festival. 2003.

van Walstijn, Maarten, Michael Alcorn, and Stefan Bilbao. ‘Spatialisation using sounding objects’, in the Proceedings of the International Computer Music Conference. 2005.

Further Reading by the Author

Burns, Christopher and Matthew Burtner. 2004. ‘Recursive Audio Systems: Acoustic Feedback in
Composition’ in Leonardo Electronic Almanac 12/2. February 2004.

Burns, Christopher. ‘Realizing Lucier and Stockhausen: Case studies in the performance practice of electroacoustic music’ in Journal of New Music Research 31/1, pp. 59–68. 2002.