Krumhansl, C. L., Louhivuori, J., Toiviainen, P., Järvinen, T., & Eerola, T. (1999). Melodic Expectation in Finnish Spiritual Folk Hymns: Convergence of Statistical, Behavioral, and Computational Approaches. Music Perception, 17, 151-196.
Abstract

This article is a study of Finnish spiritual folk hymns, combining three different approaches to understanding melodic expectancy. The first is a behavioral experiment in which listeners made judgments about melodic continuations. Two groups of listeners participated. One had extensive experience with the style and was familiar with the particular hymns. The other consisted of musicians who were unfamiliar with the hymns. The second approach was a statistical style analysis of a representative corpus of 18 hymns. The analysis determined the relative frequencies of tone onsets and two- and three-tone transitions. The third approach simulated melodic expectancy with neural network models of the self-organizing map (SOM) type (Kohonen, 1997). One model was trained on the corpus of 18 hymns, while another was trained with only the materials used in the experiment. Comparing the results showed strong convergence between the three approaches. The correspondences found between the behavioral judgments and the statistical style analysis supports the idea that listeners are sensitive to the distributions of tones and tone combinations in music. The non-experts' responses more strongly reflected the general distribution of tones than the experts, whereas the experts' responses more strongly reflected the specific tone transitions. Correspondences between the behavioral judgments and the SOMs were also strong and showed effects of expertise. The non-experts' responses were modeled better with the SOM that had been trained on the 18 hymn corpus, whereas the experts' responses were modeled better with the SOM that had been trained on the experimental materials, thus simulating the process of recognizing the particular hymns. Finally, all three approaches gave support to the implication-realization model (Narmour, 1990) of musical expectancy. Moreover, the relative weighting of the principles was similar for behavioral, statistical, and computational measures.

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