Musical Style, Psychoaesthetics, and Prospects for Entropy as an Analytic Tool

Information theory as formulated by Shannon (1948) has been intermittently pursued as a potential tool for musical analysis; however, significant problems have prevented it from coalescing into a fruitful theoretical approach. Papers examining music from the perspective of information theory are widely distributed among journals from different fields (Nettelheim 1997) and do not show a steady, cumulative trajectory in time. Rather, a cluster of papers in the late 1950s and 1960s (Pinkerton 1956; Meyer 1957; Youngblood 1958; Krahenbuehl and Coons 1959; Cohen 1962; Hiller and Fuller 1967), another in the 1980s (Knopoff and Hutchinson 1981, 1983; Snyder 1990), and a few contemporary studies (Huron 2006; Temperley 2007) represent the primary efforts.

Three challenges have hindered the development of information-theory applications in music: first, obscurities in the framing of the musical questions that information theory might answer; second, practical obstacles to tabulating the musical entities needed for information-theoretic analysis; and third, uncertainties regarding the type of musical entity that should serve as the unit of analysis.

For music, information has been understood to refer “to the freedom of choice which a composer has in working with his materials or to the degree of uncertainty which a listener feels in responding to the results of a composer’s tonal choices” (Youngblood 1958, p. 25). This conceptual framework has led to studies that appropriate information theory as a compositional tool (Pinkerton 1956), as an identifier of musical style (Youngblood 1958; Knopoff and Hutchinson 1981, 1983), and as a mechanism for the analytical comparison of sections within a piece (Hiller and Fuller 1967). It is relatively straightforward to think about entropy as a measure of the freedom with which musical elements are strung together in a specific style, but it is less clear how to conceptualize entropy’s relationship with listener perceptions. What sorts of statistics do listeners track, and for what sorts of items? What are the behavioral, cognitive, or affective consequences of perceiving high or low entropy in a piece, style, or section?

In addition to the difficulty of establishing a conceptual framework for relating entropy to music, the practical obstacle of extracting and tabulating the musical items whose entropy is of interest has stymied progress in the musical application of information theory. Early researchers, such as Youngblood, recorded frequencies by hand—a painstaking process that necessitated a small sample from various styles (melodies from eight songs by Schubert, six by Mendelssohn, and six by Schumann, in the case of his study). Yet Knopoff and Hutchinson (1983) showed that to disambiguate noise from statistically significant characterizations requires pools of at least 7,900 characters. Hand tabulating samples of this size seems a quixotic enterprise, and this practical barriermay partially account for the decline of interest in information theory as a music-analytic tool.

Large corpuses of musical data exist in three commonly available forms: graphic (musical scores), aural (sound recordings), and symbolic (e.g., MIDI). Despite some effort (e.g., Poliner et al. 2007), no reliable technology yet exists to automatically extract pitches, rhythms, and other musical quanta from printed scores or sound recordings. Some excellent tools exist for the manipulation of MIDI data (e.g., Eerola and Toiviainen 2004), but they are not yet sophisticated enough to extract the units desirable for information-theoretical analysis. Only one form of symbolic data (scores in the **kern format) is associated with a set of tools, the Humdrum Toolkit (Huron 1993), that allows for the extraction and manipulation of the kinds of data likely to be useful in a perception-based account of entropy. Although the amount of music encoded in the **kern format (4,290,411 notes in 20,318 files) is substantially smaller than the corpus of music available in the MIDI format, it is still large enough to permit information-theoretic analysis (by the standards of Knopoff and Hutchinson 1983); moreover, unlike MIDI, the **kern representation preserves many elements present in actual scores: key signatures, staves, and stem directions, for example. Although Huron has used Humdrum to perform many fascinating statistical analyses (e.g., Huron 2006), no published...