Abstract:

The evolution of musical expression is intertwined with the development of musical instruments. This has never been more evident than in the 20th century. Beginning with the gigantic Telharmonium synthesizer unveiled in 1906, research has ushered forth a steady stream of electronic instruments that have irrevocably molded the musical landscape.

The most precise and flexible electronic music instrument ever conceived is the digital computer. Like the pipe organ invented centuries earlier, the computer's power derives from its ability to emulate, or in scientific terms, to model phenomena. Unlike the pipe organ, the computer's models are expressed in symbolic code. Thus it does not matter whether the phenomena being modeled exist outside the circuitry of the machine, or whether they are pure fantasy. This makes the computer an ideal testbed for the representation of musical architecture.

Music theory has long recognized a hierarchy of structure in music compositions. A central task of music composition has always been the management of the interaction amongst structures on different time scales. Starting from the topmost layer or form and proceeding downward, one can dissect layers of structure, arriving at the bottom layer of individual notes.

This hierarchy, however, is incomplete. Beneath the level of the note lies another multi-layered stratum, the micro-sonic hierarchy. Like the quantum world of the quarks, leptons, gluons, and bosons, the micro-sonic hierarchy remained invisible for centuries. Modern tools let us view and manipulate the micro-sonic layers.

Here we distinguish six time scales, starting from the longest, corresponding to different levels of perception.

1. Macro - The overall musical architecture or form, measured in minutes or hours.
2. Meso - Groupings of objects into hierarchies of phrase structures of various sizes, measured in minutes or seconds.
3. Sound object - A basic unit of musical structure, generalizing the traditional concept of note to include complex and mutating sound events on a time scale ranging from a fraction of a second to several seconds.
4. Micro - Sound events on a time scale that begins at the object level and extends down to the thresholds of auditory perception (measured in thousandths of a second or milliseconds).
5. Sample - The "atomic" level of digital audio systems: individual binary samples or numerical amplitude values, one following another at a fixed time interval. The period between samples is measured in millionths of a second (microseconds).
6. Sub-sample - Fluctuations on an infinitesimal time scale, too brief to be properly recorded or perceived, measured in billionths of a second (nanoseconds) and ranging down to the infinitesimal durations.

This presentation examines this temporal hierarchy, paying particular attention to the micro-time scale. We explore new methods of sound synthesis and processing that operate on the micro-time level, and study the aesthetic implications of these techniques. The presentation will be accompanied by diagrams and sound examples.