Recent work on "musical forces" asserts that experienced listeners of tonal music not only talk about music in terms used to describe physical motion, but actually experience musical motion as if it were shaped by quantifiable analogues of physical gravity, magnetism, and inertia. This article presents a theory of melodic expectation based on that assertion, describes two computer models of aspects of that theory, and finds strong support for that theory in comparisons of the behavior of those models with the behavior of participants in several experiments. The following summary statement of the theory is explained and illustrated in the article: Experienced listeners of tonal music expect completions in which the musical forces of gravity, magnetism, and inertia control operations on alphabets in hierarchies of embellishment whose stepwise displacements of auralized traces create simple closed shapes. A "single-level" computer program models the operation of these musical forces on a single level of musical structure. Given a melodic beginning in a certain key, the model not only produces almost the same responses as experimental participants, but it also rates them in a similar way; the computer model gives higher ratings to responses that participants sing more often. In fact, the completions generated by this model match note-for-note the entire completions sung by participants in several psychological studies as often as the completions of any one of those participants matches those of the other participants. A "multilevel" computer program models the operation of these musical forces on multiple hierarchical levels. When the multilevel model is given a melodic beginning and a hierarchical description of its embellishment structure (i.e., a Schenkerian analysis of it), the model produces responses that reflect the operation of musical forces on all the levels of that hierarchical structure. Statistical analyses of the results of a number of experiments test hypotheses arising from the computer models' algorithm (S. Larson, 1993a) for the interaction of musical forces as well as from F. Lerdahl's similar (1996) algorithm. Further statistical analysis contrasts the explanatory power of the theory of musical forces with that of E. Narmour's (1990, 1992) implication-realization model. The striking agreement between computer-generated responses and experimental results suggests that the theory captures some important aspects of melodic expectation. Furthermore, the fact that these data can be modeled well by the interaction of constantly acting but contextually determined musical forces gives support to the idea that we experience musical motions metaphorically in terms of our experience of physical motions.
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