Pitch Dispersal and the Perception of Tonal Strength in Schoenberg’s Oeuvre

Abstract

The idea that listeners’ tonal/atonal sense represents a special case of multiple causation was examined, and the following hypothesis was tested: pitch dispersal (i.e., distance in pitch between successive tones) is a secondary determiner of tonality and atonality, the former being strengthened by low levels of pitch dispersal and the latter by high levels of pitch dispersal. A correlational study was conducted in which eight trained listeners judged the degree to which 78 melodies extracted from A. Schoenberg’s oeuvre convey a tonic. In line with the present hypothesis, results suggest that listeners’ judgments were influenced not only by consonance or pitch class distributions (i.e., by underlying “scales”), as expected from previous research, but also by pitch dispersal. Interestingly, it was also found that Schoenberg’ melodies became not only less diatonic over time, but also more dispersed, which suggests that the joint manipulation of pitch class distributions and pitch dispersal might have been a strategy on Schoenberg’s part to weaken the sense of tonality. Some of the key musicological, theoretical, and psychological implications of these findings are discussed.

“Bold and Ragged”: A Cross-Cultural Case for the Aesthetics of Melodic Angularity

“…Perhaps the most predictable result among European composer data was that Schönberg’s interval size is the largest of all the individual pieces considered. This is consistent with Anta’s claim that pitch dispersal is a “secondary determiner” of atonality (2017). However, tonal music may also be dispersed.…”

Dimensions of Atonality: A Response and Extension of von Hippel and Huron (2020)

“…Krumhansl, Sandell, and Sergeant's methodology immediately lends itself to an empirical method of answering this question, comparing row segments to Krumhansl and Kessler's (1982) tonal hierarchy. More recent research has continued to show that correlation with tonal key profiles is a good predictor of listener judgments of tonality (Anta, 2017). Von Hippel and Huron's results are musicologically interesting: in certain broad respects, they confirm what we might expect (Berg encourages tonal hearing, Webern discourages it), but they also provide additional nuance to those judgments.…”

Interpreting the tonal hierarchy through corpus analysis.

“…This correlation became the basis for Krumhansl and Schmuckler’s key finding algorithm (Krumhansl, 1990; Krumhansl & Schmuckler, 1986), which matches frequency distributions to probe-tone profiles. Today, both perceptual and corpus-based experiments continue to draw on this framework and the associated idea of statistical learning of the tonal hierarchy via frequency counts, with theories of tonal hierarchy and frequency distributions becoming so intertwined that researchers use the term “key profile” interchangeably to refer either to profiles of probe-tone ratings (Anta, 2017; Arthur, 2018) or profiles of frequency counts (Anta, 2015; Quinn & White, 2017).…”