Pitch -class multisets
Item
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Title
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Pitch -class multisets
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Identifier
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d_2009_2013:bb10ecfbed08:10225
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identifier
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10423
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Creator
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Robinson, Thomas,
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Contributor
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Joseph N. Straus | Jonathan Pieslak
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Date
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2009
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Language
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English
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Publisher
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City University of New York.
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Subject
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Music | Multiplicity | Multisets | Pitch-Class Doubling | Set Theory
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Abstract
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The pitch-class multiset (pcmset) is a collection in which pitch classes may appear as elements more than once and in which any single appearance of a pc represents one and only one instance of that pitch class. For example, pitch classes 1, 2, and 4 comprise the pcmset {lcub}1,2,4,4{rcub}; pc4 occurs twice. This represents some musical situation with two instances of pc4 and only one instance each of pcs 2 and 3. The pcmset has appeared sporadically in the theoretical literature, yet there has been no systematic examination into the ramifications of the distinction between a pitch class and the number of its representatives. This study considers existing music theory in light of pcmsets and considers their use in analysis.;First, from an ontological perspective, this study carefully defines the pcmset as distinct from the pitch set and the pitch-class set. Once the relationship between the canonical set classes and multiset classes is established, what follows is an expansive, combinatorial survey of thousands of mset classes.;Second, this study revisits the standard tools and concepts of pc-set theory. The interval-class vector, the Z-relation, and complementation all are modified only minimally to accommodate pcmsets and mset classes. What is more, this accommodation gives new insight into the nature of these principles.;Throughout, this study uses pcmsets in music analysis by identifying parent class and pcmsets in Webern's Opus 5, by looking at their Fourier balance in a Bach chorale, and by tracking transformations of pitch-class multiplicity in the music of Arvo Part.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Music
