Computer Analysis of Musical Allusions

In this article I describe a computer program called Sorcerer. Sorcerer provides analytical verification of the presence of musical allusions for what I call referential analysis, a semiotic approach roughly situated between hermeneutic (interpretive) analysis (e.g., Agawu 1991, 1996; Gjerdingen 1988; Nattiez 1990) and Rétian (motivic) analysis (Réti 1962). Sorcerer associates patterns found in a target work—music under study—with several potential source works—music assumed to either influence or be influenced by the target work. Sorcerer then presents these patterns as possible references or allusions. The program lists its findings without regard for whether the composer of the target work consciously or subconsciously referenced the source work, only that the found allusions exist. I further describe the possible relevance and importance of this type of analysis as a complementary approach to more standard harmonic, melodic, and formal types of analysis, as a method for performers to better interpret the music they play, and as one possible approach to the deeper understanding of meaning in music.

Background

Allusions have occurred throughout music history, though very few systematic studies of them have taken place. With the exception of Deryck Cooke's landmark book The Language of Music (1959), for example, few articles or books are devoted exclusively to allusions. Certain musical forms like organum, motets, cantatas, and other cantus firmus–based styles often depend on allusions. Furthermore, certain composers' styles, like those of Ives and Berio, use allusions extensively, deliberately, and obviously. Many late Romantic Russian composers use allusions as a benchmark of their nationalism, considering them not only honorable but also requisite to their stylistic heritage.

Burkholder (1994) has devised a detailed methodology for what he calls a "typology of musical borrowing." He carefully denotes categories of borrowed material, including the relationship of a work to the work from which it borrows, the elements of a work alluded to by another work, how borrowed material in one work relates to the original work, how borrowed material is altered in its new environs, and the function of the borrowed material within its new context. Among the latter approaches, Burkholder describes how borrowed material might lend a certain character; pay homage to, comment on, or critique its source; or have extra-musical significance. Burkholder's overview provides a very useful template to follow, although it lacks detail. Burkholder and others have also produced an extraordinary Internet bibliography of books and articles relating to borrowed materials in music.

I have opted for a somewhat simpler approach than Burkholder, classifying allusions into five basic categories—from nearly exact quotation to the use of more common musical conventions. My taxonomy for referential analysis includes Quotations (as in citations, excerpts, or renditions); Paraphrases (as in variations, caricatures, or transcriptions); Likenesses (as in approximations, translations, or similarities); Frameworks (as in outlines, vestiges, or redactions); and Commonalities (as in conventions, genera, or simplicities). Note that I do not use negative words such as cliché here. I wish to avoid the stigma of what some feel as a weakness in art and which I feel can be a strength. Note as well that the boundaries of these categories are imprecise and may, at times, overlap.

Clearly, potential for listener recognition proceeds from strong to weak through these categories and the potential for stylistic integration proceeds inversely. A more detailed and exampled description of these categories follows.

Quotations

Quotations often involve exact note and/or rhythm duplication. The plainchant Dies Irae represents a good example of quotation when heard in such works as Symphony Fantastique (1830) by Hector Berlioz (in the Witches' Sabbath), Liszt's Dance of Death and the Inferno from his Dante Symphony (1857), Saint-Saëns's Danse Macabre (1874), the Trepak in Mussorgsky's Songs and Dances of Death (1877), and Rachmaninoff's Isle of the Dead (1907) and Rhapsody on a Theme of Paganini (1934) (Keppler 1956).

Figure 1.

(a) Beethoven's Sonata Op. 13 ("Pathétique"), mvt. 2, mm. 1–3; (b) Mozart's Sonata K. 457, mvt. 2, m. 24.

Beethoven quotes a Mozart fragment in the second movement of his Path...