A b is to G # as D b is to ? Analogy as the Core of Music Cognition

Music cognition research in the past several decades has invoked many disparate paradigms in an attempt to explain the cognitive basis of musical syntax and semantics. Rather than focusing on any particular established model of music cognition, this paper serves to highlight the centrality of analogy in music cognition. It presents a collection of specific examples of musical analogy-making on different hierarchical levels, pointing the way towards future work in music cognition driven by recognition of the centrality of analogy. A New Answer for Bernstein In 1976 Leonard Bernstein gave a series of lectures at Harvard entitled The Unanswered Question, in which he discussed possible relationships between Chomskian linguistics and music. In the second of the six lectures he asserts that “there are similar functions, cognate processes operating in both music and language which are discoverable by linguistic method. ” He then proceeds to construct a “quasi-scientific analogy between verbal and musical terms. ” For instance, he likens musical notes to phonemes, motives to morphemes, musical phrases to words, etc. but then declares these to be bad analogies. His next attempt describes motives as nouns and chord types such as major or minor as adjectives in a musical grammar. Likewise, rhythm becomes the analogue of verbs. Bernstein settles on a thesis equating transformational grammar with musical transformations and proceeds to discuss musical syntax and semantics. Although Bernstein’s lectures may not have been successful in discovering a universal, innate musical grammar, some aspects of the lectures do make a great deal of intuitive sense. Indeed, Lerdahl and Jackendoff were inspired by Bernstein’s musico-linguistics to create their Generative Theory of Tonal Music (GTTM), a formalized generative grammar approach to musical syntax. Bernstein’s original motivation, however, seemed closer to an interest in universal cognitive mechanisms for music appreciation than the generative approach of GTTM. A second major school of thought on music cognition derives from Meyer’s (1956) work on emotion and meaning in music. This paradigm is focused on how listening to music generates future expectations (or implications) for the listener. The Implication-Realization (I-R) model (Narmour 1990) describes how listeners expect melodies to continue with respect to the tension and release resulting from the building-up and later satisfaction of melodic implications. A third category of music cognition models derives from Schenker’s (1935/1979) work in music theory. Larson’s theory of musical forces (2004) combines Schenkerian analysis with a metaphor of melody as directed motion through a musical space involving analogues of physical gravity, magnetism, and inertia. More difficult to categorize is Margulis’ computer model (2005) of melodic expectation which combines ideas from GTTM, I-R, and musical forces to predict expectations and various types of affective response evoked by music as it evolves in time. Indeed, a synthesis of each of these approaches to music cognition is reasonable since each serves to explain certain interesting features of the cognitive experience of listening to music. However, the diversity of methods points towards the possibility of finding a unifying principle behind these approaches. Both Larson’s use of a metaphor linking music and physics and Bernstein’s analogy between music and transformational grammar are particularly provocative. They both involve a particular explicit analogy between concepts. Hofstadter (2001) argues that the core cognitive mechanism, not just for linguistics or music, but for thought in general, is analogy itself. I propose, then, a particular subcase of Hofstadter’s thesis to provide an alternative answer for Bernstein: analogy is the core of music cognition. Phoneme is to Note as Word is to. Bernstein began his comparison of music and language by starting with the smallest unit of an individual note and moving upwards through levels of increasing complexity such as groups of notes, entire phrases, sections, and finally an entire piece. In the following section I also ascend through levels of complexity, from small-scale details to large-scale musical forms, but with a different goal in mind: showing how analogy is a fundamental component of music cognition at each hierarchical level. In most cases I will show examples of how two musical items are heard as “the same thing” even when there are real difference between the two items – the listener creates a musical analogy between the two chunks of music in order to hear them as “the same”. Figure 1: The beginning of Chopin’s “Raindrop” Prelude. Figure 2: The key change to C# Minor between measures 28 and 29. Ascending through the Levels Our source of examples in this section is Chopin’s “Raindrop” Prelude, Op. 28 No. 15. The note seems to be the smallest unit of music and logical starting point for an ascent through levels of increasing hierarchy. However, in analogy with physics, this atomic note is not really the smallest unit after all. Instead I begin by breaking the atom into constituent parts – the parameters that make up a note such as timbre, pitch, and rhythm – before ascending to higher levels of musical organization.