Category Structures and Fuzzy Sets (response to Lawrence Zbikowski) (MTO 1.4)

Prior to his examination of the categorical structure of the first main theme in the first movement of Bruckner's Sixth Symphony, Lawrence Zbikowski comments that "The complexity of the phenomenon of typicality may be one reason Zadeh's theory of fuzzy sets has met with only limited s...

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Bibliographic Details
Published in:Music theory online 1995-09, Vol.1 (5)
Main Author: Robison, Brian
Format: Article
Language:English
Subjects:
Bruckner, Anton
Mathematics
Music Theory
Set Theory (Music Theory)
Symphonies
Zibkowski, Lawrence
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Summary:Prior to his examination of the categorical structure of the first main theme in the first movement of Bruckner's Sixth Symphony, Lawrence Zbikowski comments that "The complexity of the phenomenon of typicality may be one reason Zadeh's theory of fuzzy sets has met with only limited success in characterizing the structure of Type 1 categories." The following look at Prof. Zbikowski's analysis highlights (in a non-technical manner) those aspects of it which lend themselves more readily to "fuzzy" rather than "crisp" models, the complexity of their interaction notwithstanding. In particular, I focus on the problems of describing formally those intuitions which enable us to associate different musical phrases in order to group them as members of the same category. [PUBLICATION ABSTRACT]
ISSN:1067-3040
1067-3040
DOI:10.30535/mto.1.5.3