Schema Theory
as a

Music Theory Online 21.2 (2015)


[7.1] To a surprising degree the methods and approaches seen to date in schema-theoretic studies in music match the basic principles of construction grammar in language. This may be due to both being predicated on domain-general cognitive functions like categorization, chunking, rich memory storage, analogy, and cross-modal association. Humans build up the constructions of such grammars from the experience of sound used communicatively in the contexts of real life. Patterns of sound that recur frequently will be learned preferentially, and the structure of a pattern will be learned jointly with its meaning. Perceived similarities between pattern exemplars may lead to the formation of a mental category, though the constituent exemplars may be recalled in evaluating collocations and typicality. The cues of specific features or contexts associated with a construction can trigger its rapid and automatic recall, facilitating fluent speech or fluent musical improvisation and composition.

[7.2] In many respects the philological “thick description” of usage-based musical constructions is one of the oldest traditions in music theory. Walter Piston, author of a standard harmony text (Piston 1941, with later editions still in print), was himself a beneficiary of artisanal training in Paris with Nadia Boulanger. Boulanger had been a winner of the Paris Conservatory harmony contest of 1903 and the fugue contest of 1904. In her “old school” lessons she directed Piston to complete a fugue (ca. 1924–26) on a subject from one of the partimento fugues of the venerable maestro Fenaroli. Thirty years later, reflectiing on the art of music, Piston emphasized the importance of a community of music makers and listeners who infer meaning and function from an appraisal of usage:

The musical meaning of tones is an inescapable fact. It is, however, not at all certain that the logic we perceive in the behavior of tones is of physical or acoustic origin. . . . The analogy with spoken and written language is close. Successions and combinations of tones, like those of letters and syllables, take on meaning through usage, and that meaning is understood by all those who participate in the usage. (1957, 275)

[7.3] Similarly, William Poland, whose work at Ohio State University in promoting music theory and music psychology began in the late 1940s, saw the study of patterns of music usage in a social context to be a central focus of music theory:

If this is true for those interested in the physiology and psychology of hearing [i.e., that the brain seems to focus on patterns of sound, not individual sounds out of context], how much more important must be the problem of pattern recognition—that is, how do we learn to perceive sounds as musically meaningful—to those who wish to increase our understanding of music, which must surely be the most important task for the music theorist. If I am right about this, then we must necessarily study music as a behavioral phenomenon. (1987, 69)

[7.4] The views of these and other scholars were submerged in the structuralist waves that swept through many disciplines in the 1970s and ‘80s. In comparison with the precise tree-structures and multi-level hierarchies of structuralist music theories, construction grammars create networked tangles of many distinct types of patterns. Yet what may have seemed eclectic, unsystematic, and ad hoc during the floodtide of structuralism may now seem like an eminently reasonable approach in a world where the messy, Darwinian complexity of human cognition is beginning to be appreciated.

[7.5] Harmony has always been the subject most frequently addressed in discussions of musical grammar. How might one judge whether young musicians have internalized the usage and meanings of professional-level harmony? The method employed at the Paris Conservatory was, once a year, to set before advanced students an unfigured bass and a melody, each about 30 to 40 measures long. In six hours, seated at tables with pen, ink, and staff paper, students were to complete a pair of four-voice realizations in open score. Prizes would be awarded to realizations that included all the collocations and collostructions cued by the given bass and given melody (basse donnée and chant donné).

[7.6] In 1827, the year of Beethoven’s death, Luigi Cherubini, the conservatory director, composed an examination for students finishing the class in “harmony and accompaniment” (in the French context “accompaniment” meant thoroughbass, partimenti, and keyboard improvisation). The first test was a “Bass to be realized in four parts by the contestants in separate cubicles” (Basse à remplir à 4 parties par le concurrents en loge), the first part of which is shown in Example 22 (annotations by the authors). Contestants who could recognize, from the experience of their training, that only a handful of medium-size constructions were needed to serve as blueprints for the seventy-seven notes in that excerpt would have had a significant advantage over contestants who could not. And only contestants who could remember the contrapuntal and motivic collostructions taught to them and associated with each pattern would have had a chance at one of the prizes. Cherubini (1827) provided thoroughbass figures as an answer sheet for the examination, and those figures confirm each of the constructions identified in Example 22.

Cherubini Test

[7.7] Piston, Poland, and the other “native speakers” of their generation would have quickly recognized in Cherubini’s bass all of these constructions, and they might have smiled knowingly as they appreciated how obvious the bass would have been for advanced students in the old tradition and how impenetrable it might be for someone outside the tradition.

[7.8] Linguists in the tradition of Chomsky (1965) and Saussure (1916) would likely claim that the students in Paris were being asked to demonstrate an abstract harmonic competence (Saussure: langue) shaped by individual performance (Saussure: parole). While we recognize the attractions of that position and how it resonates with prominent dichotomies in music history (prima prattica vs seconda prattica, or strenger Satz vs freier Satz), we find it at odds with facts of "music acquisition" within the community of music makers at the Conservatory. Pre-teen boys like Debussy and Ravel might participate in the class in "harmony and accompaniment" for six years, learning to play and write literally hundreds of specific constructions with all their attendant surface detail and performative nuance. In the class of Émile Durand, Debussy’s master, one had to learn almost three hundred constructions and needed to be able to realize them at will in response to a partimento bass. From the perspective of a construction grammarian, Durand (1884) was loading his students’ minds with "a rich store of memories," one filled with communicative behaviors and embodied knowledge. Partimenti or formal examinations then served as probes of a student’s storehouse of learned form-function pairings.

[7.9] Musical semiotics, implication-realization theory, research in musical topics, descriptions of Satzmodelle, schema theory, and studies of formal functions could all be thought of as related attempts to move the focus of music theory toward our shared general-purpose cognitive abilities. The ability to recognize and categorize similarity and difference in patterns of sound, for example, is axiomatic for implication-realization theory (Narmour 1990, 1992). This shift, which is simultaneously a move away from assuming that certain traits of the European classical tradition are innate, opens up considerable space for accommodating the diversity of the world’s musics, both geographically and historically. Memory becomes a central actor in the formation and production of constructions, and as described by Vasili Byros (2012b), the resulting products of research are more likely to be mini-theories of individual constructions specific to one culture and/or historical period. “Usage” and “constructions” are broad concepts that can be applied to the particular designs of ragas or sonatas without distorting the unique features of either. For historians of music theory, a construction-oriented framework can lead to a more sympathetic understanding of the ritualized, largely nonverbal training of young professional musicians and thus can help to put the speculative treatises intended for university students or middle-class amateurs in a new, more critical light. For music psychologists, constructions offer descriptions of music syntax more amenable to empirical research and to comparison with statistical analyses of music corpora. For music analysts, an approach that can be directed not only toward the artisanal traditions of the European conservatories but also toward the vernacular and improvisatory traditions of our own time seems clearly worthy of future study. And for music educators, we believe a construction-grammar pedagogy, with small constructions learned and manipulated through improvisation (cf. Bamberger 1995), has equally as much to offer the training of future musicians as it offered generations of young musicians in the past.

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