Logic-Programming Models of Music: A Semiotic Evaluation

Abstract

LOGIC-PROGRAMMING MODELS OF MUSIC: A SEMIOTIC EVALUATION JOHN ROEDER HIS ARTICLE IS BASED ON A TALK given at a Symposium on Music and Science organized by John Rahn at the University of Washington in February 1991. The topics it interconnects—the nature of musical and scientific theories, signification, and logic programming—were in the air. Brown and Dempster (1989) had recently judged Boretz (1969 and 1970) and Rahn (1979) to be lacking as “scientific” theories. Whereas the latter scholars’ responses to this critique (Boretz 1989; Rahn 1989) focused on broad misunderstandings of their work, this paper answers some specific technical concerns that were raised about the adequacy of Rahn’s set-theoretical logic of level analysis (c.f. also Boretz [2001]). In that sense it may be taken as a modest tribute to one of his many intellectual achievements. More generally, though, it foregrounds issues of music representation that are newly relevant in our era of “big data.” For this version, I have taken the opportunity not only to revise the text but also to update and make accessible the logic-programming models described here, so that readers can verify my claims and explore them further. Source-code files and sample queries can be accessed on the PNM website and run in the free, user-friendly, web-based Prolog T 376 Perspectives of New Music interpreter SWISH (swish.swi-prolog.org). To preserve the paper’s historical context, I have not augmented the inline author-date references, but I have inserted a few endnotes that link it to more recent developments in the philosophy of science, Rahn’s thinking, computational musicology, and music theory more widely. * * * In Italo Calvino’s fable “A Sign in Space,” a metaphysical narrator named Qfzfq relates an experiment it initiated, before the advent of other sentient beings, for determining the duration of the galactic year. The procedure consisted of placing a sign at a certain point in space then measuring how long it took the sun to orbit completely around the galaxy and back to the same point. The meaning of this sign resided not in its form but in its purpose, to distinguish that point from the other points in space. Unfortunately, before Qfzfq could observe the sign again, other beings arose and took measure of their existence by placing new signs and erasing old ones until “the universe was scrawled over on all sides.” This proliferation established “a continuity . . . with no precise boundaries . . . [so that] there was no longer any way to establish a point of reference.” Although the story ends amusingly with the narrator’s purposes frustrated, its moral is nonetheless telling: “independent of signs, space didn’t exist and perhaps had never existed” (Calvino 2014, 41–42). Semiotics, the study of signs, helps explain how we attribute structure and meaning to the physical universe. Umberto Eco’s theory of signification posits that it involves a “code” that correlates an element of a purely formal syntactic system with one or more elements of a semantic system. The correlation establishes a “sign-function” that is “transitory,” specific to particular communicative context, so that in other contexts the same syntactic element may signify a different semantic entity (Eco 1976, 48–49). For instance, many scientific theories use structured mathematical symbols to denote physical quantities and to express laws that govern them (Marcus 1979). One theme of Calvino’s tale, accordingly, is that we, as semiotic beings, comprehend the universe only through the sign-functions we create, and that those codes can lead to imprecision and multiple meanings. Moreover, codes are constrained both by our sensory limitations and by our culture(s). As an example, Eco (1979, 76–81) cites differences in the way that civilizations analyze the continuum of light wavelengths into colors: the band that Western Europeans (“we”) call blue would be regarded by Russians as including two distinct colors, and by Logic-Programming Models of Music: A Semiotic Evaluation 377 classical Greeks as only part of a larger category that includes what we would call green. This has a profound implication for the scientific enterprise: how we formulate scientific laws depends strongly on how we represent physical quantities and their structures...