Doctor of Philosophy
All melodies have shape: a pattern of ascents, descents, and plateaus that occur as music moves through time. This shape—or contour—is one of a melody’s defining characteristics. Music theorists such as Michael Friedmann (1985), Robert Morris (1987), Elizabeth Marvin (1987), and Ian Quinn (1997) have developed models for analyzing contour, but only a few compare contours with different numbers of notes (cardinalities), and fewer still compare entire families of contours. Since these models do not account for familial relations between different-sized contours, they apply only to a limited musical repertoire, and therefore it seems unlikely that they reflect how listeners perceive melodic shape.
This dissertation introduces a new method for evaluating familial similarities between related contours, even if the contours have different cardinalities. My Familial Contour Membership model extends theories of contour transformation by using fuzzy set theory and probability. I measure a contour’s degree of familial membership by examining the contour’s transformational pathway and calculating the probability that each move in the pathway is shared by other family members. Through the potential of differing alignments along these pathways, I allow for the possibility that pathways may be omitted or inserted within a contour that exhibits familial resemblance, despite its different cardinality.
Integrating variable cardinality into contour similarity relations more adequately accounts for familial relationships between contours, opening up new possibilities for analytical application to a wide variety of repertoires. I examine familial relationships between variants of medieval plainchant, and demonstrate how the sensitivity to familial variation illuminated by fuzzy theoretical models can contribute to our understanding of musical ontology. I explain how melodic shape contributes to motivic development and narrative creation in Brahms’s “Regenlied” Op. 59, No. 3, and the related Violin Sonata No. 1, Op. 78. Finally, I explore how melodic shape is perceived within the repetitive context of melodic phasing in Steve Reich’s The Desert Music. Throughout each study, I show that a more flexible attitude toward cardinality can open contour theory to more nuanced judgments of similarity and familial membership, and can provide new and valuable insights into one of music’s most fundamental elements.
Wallentinsen, Kristen, "Fuzzy Family Ties: Familial Similarity Between Melodic Contours of Different Cardinalities" (2017). Electronic Thesis and Dissertation Repository. 5037.