Statistical Models of Melodic Structure: Gestalt, Minimalism, and Information Content

Statistical Models of Melodic Structure

Research in music perception frequently borrows from psychological theories developed in other domains. This may be just a convenient way to simplify methodology or it could point to overlapping cognitive building blocks across fields. As one example, the Gestalt principles of proximity and similarity — first developed to account for visual experiences — have been reconfigured into models of melodic group perception (Lerdahl and Jackendoff, 1983) and of the mental processes behind melodic expectation (Narmour, 1990).

Two compositions by Philip Glass, the monodic, isochronous, monotimbral minimalist works Gradus and Two Pages, create an interesting test bed because they allow experimental tightness while retaining genuine musical validity. The questions such music raises about how listeners perceive group and formal boundaries were explored using a statistical model of melodic prediction proposed by Pearce and Wiggins (2006). Their model works with a symbolic musical surface — essentially notation-like bits of pitch and rhythm — and codes its knowledge of sequential patterns alone, learning from an entire corpus and simultaneously picking up the structure of the piece being interpreted during prediction.

The analysis revealed clear bursts or dips in what is called information content exactly at movement boundaries within each composition—that is significant shifts determined by prior statistical expectations (or the lack thereof). Furthermore, these quantitatively derived shifts matched almost exactly with one expert’s structural judgment published by a musicologist. The view thus suggests a model, not simply a restatement of psychological outcomes as qualitative Gestalt accounts might provide: listeners devote neural fast resources into detecting statistical pockets of ordination that later, in ways yet to observe, project into form recognition.

Studying information content shifts within the works predicted with success points back tó earlier experiments done allowing human segmentation of tonal sequences attunes to rule out completely an other hypothesis that verbal stimulus plus negative environmental returns yields that focus. Right under the minimum materials of such narrow musical events lies huge functional power to point how perception responds similarly inside careful shifts in mathematical probability, as be codified tracking conditional expectancy step-by-step across two decades of this specific minimalist repertoire.