A Study of Event Hierarchies in Tonal and Post-Tonal Music

Abstract

It is paradoxical that although there is general agreemenrt that imlusici pitc1b perception is much more accurate when the listener is givetn a tonal cOl1tt for the stimulus, leading perceptual theories disagree in their definitiois o tonal context itself. Nearly all cognitive theories of so-called pitch istruct Li-., in music assume that relations among acoustical components of sound. or mathematical groups, or geometrical constructs, can serve as adequate bases on which rules of musical composition and comprehension of pitch relationl- ships may be formulated. These theories have an obvious intellectual iippecai but do not describe the temporal structure of pitch relations in actual music, and thus fail to account for significant differences in the compositiona treatment of pitch from one style period, or one culture, to another. I hc perceptual theory of event hierarchies, advanced most notably by Bharucha attempts to describe the perception of pitch relationships in musical timtc and thus is an important exception to the rule that perceptual theories oi musical pitch deal solely in timeless abstractions. The event-hierarchhx theory holds that as musical events (tones, chords) unfold in a specitic composition, they are interpreted hierarchically by the listener; this cxvent hierarchy activates in the listener a tonal hierarchy, a hierarchy of ccivt classes. The two hierarchies are thought to be perceptually co-generativec symbiotic partners in what Deutsch (1984) calls an "elaborate bootstrapping operation". No adequate description yet exists of this bootstrapping opera tion, in which relatively stable and unstable members of a totial hierarchx are said to generate a piece-specific event hierarchy as the event hicrarchx defines the tonal hierarchy. Beyond the critical chicken-egg character of such a theory, there is the likelihood that the theory is far more comuplex than the cognitive act it is supposed to describe. An inspection of represen- tative samples of Western tonal and post-tonal music shows that stvic- dependent differences exist in the time orders of intervals that occtur onlv rarely in the diatonic set. The paper includes the first report of the results of an experiment using temporal organising schemes extracted from actual tonal and post-tonal compositions. These results indicate that aural context conveyed by temporal collocation of rare intervals may be as influenti'il as pitch content is in eliciting a sense of tonal structure in the musical listener. and further that temporal organisation of rare intervals mav provide perceptual cues for metrical organisation in tonal music.