27 January 2012, Seminar on music cognition and computation, Michiel Schuijer

Abstract

In my book Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts, one of my aims was to show that pitch-class set theory was not just tailored to the analysis of revolutionary compositions, and that it neither heralded a new era of computational musicology - although it has been identified with each of these two claims from early on. What struck me was the continuity it exhibited with music theories of the past. And it seemed to enable the same kind of engagement with twentieth-century, "modernist" music as earlier generations had felt for the great masterworks of the eighteenth and nineteenth centuries. This accorded with the way in which pitch-class set theory had developed in later years - gradually loosening its ties with advanced computer technology, and transforming into a vocabulary for educational purposes.

But that is not the whole story. The study of "similarity relations", a branch of pitch-class set theory that rose to prominence in the 1980s and 1990s, was definitely more research-oriented than education-oriented. It hardly even founded application in analysis classes, but it had the lure of being "cutting edge" - at least in the music field - particularly because of its relations with fuzzy logic. However, pitch-class set similarity was an area for specialists only, the density of their texts being too much for many music theorists.

Frankly, looking at this topic through a historical lens yielded me little fruit. Retracing the development of similarity relations in Chapter 5 of my book got me no further than Ernst Krenek and Paul Hindemith, whose chord classifications - unlike those of mere taxonomists like Fritz Klein or Bruno Weigl - were based on a notion of relative musical distance, a notion that similarity relations between pitch-class sets invoke as well. In this paper, I will take my cue from the relation between "similarity" and "distance", and discuss the "roadmaps" that music theorists of the eighteenth and nineteenth centuries conceived to establish the distances between tonal keys.