Using Connectionist Models to Explore Complex Musical Patterns

Abstract

Music teachers often ask their classes to take musical dictation. The teacher commonly plays a short excerpt, perhaps a phrase from a Bach chorale, and then the students attempt to translate the various pitches and durations into the symbols of standard musical notation. Each resulting symbol can be judged true or false, right or wrong. Music teachers also ask their classes to analyze the musical syntax of phrases from Bach chorales. The resulting answers will likely have varying shades of truth or falsity. Students can have legitimate differences of opinion about how to interpret ambiguous musical events or events that have one meaning in prospect and a second in retrospect. And not only students differ in their assessments of complex musical patterns. Acknowledged experts in eighteenth-century music are known to disagree about how, in a given phrase, the chords, rhythms, contours, melodies, textures, timbres, and counterpoint all interact. Connectionist models offer elegant ways of dealing with multidimensional complexity of the type found in polyphonic, harmonically oriented music. One can, for example, define a musical event as an input pattern of activation that is then transformed by a network of interconnected processing units into an output pattern of activation representing an interpretation of the event. Models that allow for learning often require an explicit teacher prepared to state unambiguously whether, and to what degree, the output pattern is in error (Rumelhart, Hinton, and Williams 1986; Werbos 1988). For relatively low-level musical tasks, like the transcription problem described above, this requirement poses no serious obstacle; but for higher-level tasks, the notion of an explicit teacher becomes problematical. One wonders, for example, if anyone would be comfortable in claiming that one interpretation of a musical phrase is only 69 percent as true as another? An alternative class of connectionist models