Modeling the Perception of Tonal Structure with Neural Nets

Abstract

What can we say about the perception of music by the silent majority of listeners, those for whom music is written but who neither create music nor can articulate their musical experience? How do they acquire their demonstrably sophisticated intuitions about music patterns typical of their culture? Experiments in the cognitive psychology of music have cast some light on the first question. Recent developments in neural net learning now enable us to explore answers to the second. In this article, we discuss one aspect of the experience of the nonmusician listener-contextual influences on the perception of pitch. We limit our discussion to tonal implications and expectations and to memory for pitch sequences. We do not presume that this description captures the listener's experience in all its intricacy. We first summarize some psychological research and then explore how neural nets can be employed to model the acquistion of these phenomena through passive exposure. Two forms of tonal expectancy will be discussed-schematic and veridical. Schematic expectancies are culture-based expectancies for events that typically follow familiar contexts. Veridical expectancies are instance-based expectations for events that follow in a particular familiar sequence. Schematic and veridical expectancies may conflict, since a specific piece of music may contain atypical events that do not match the more common cultural expectations. This conflict, which was attributed to Wittgenstein by Dowling and Harwood

The costs and benefits of tonal centers for chord processing.

“…4 Schematic expectations for musical events might be influenced not only by the level of tonal stability but also by the typicality of sequential chord progressions (Bharucha & Todd, 1989). Our material focuses on the influence of tonal stability, as progressions created by the last two chords in related and less related sequences (V-I and I-IV, respectively) are both deemed as highly probable root progressions in Western tonal music (Piston, 1978, p. 21).…”

Harmonic and rhythmic influences on musical expectancy

“…rhythmic factors in the mental representation of musical structure. This is particularly true ofmodels that attempt to account for the formation ofmusical expectancies that are extrapolated from an underlying tonal system (Bharucha, 1987a(Bharucha, , 1987b(Bharucha, , 1989Bharucha & Todd, 1989).…”

Varieties of musical experience

“…Unlike Fodor, who embraces a strong nativism (see Fodor, 2000), we postulate representational codes within a causal neural system that can learn some of its connectivity, based on some innate constraints (Bharucha, 1991a(Bharucha, , 1991b(Bharucha, , 1999Bharucha & Mencl, 1996;Bharucha & Todd, 1991;Tillmann, Bharucha, & Bigand, 2000).…”

“…Mapping over time also includes the expectations generated by a musical context: both schematic expectations (expectations for the most probable continuations) and veridical expectations (expectations for the actual next events in familiar sequences, whether they are schematically likely or not; see Bharucha & Todd, 1991). Mapping functions are thus a form of long term memory -either schematic knowledge or memory for specific musical sequences.…”

“…In our modeling work (Bharucha, 1991a(Bharucha, , 1991b(Bharucha, , 1999Bharucha & Mencl, 1996;Bharucha & Todd, 1991;Tillmann et al, 2000), we have shown how cultural learning of chordal expectations might occur through passive perceptual exposure (see also Leman, 1995). Neural net models assume a set of primitive feature detectors that have innate tuning characteristics.…”