Some Musical Groups Selected Applications of Group Theory in Music

The groups mentioned in the title are not groups such as Metallica or the Chicago Symphony Orchestra, but groups in the algebraic sense. There are many ways in which elements of musical structure may be described by group-theoretic constructions; these constructions and related topics form the subje...

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Bibliographic Details
Published inDiffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47) p. 209
Main Author Julian Hook
Format Book Chapter
LanguageEnglish
Published Princeton University Press 08.09.2014
Subjects
Acoustical properties
Acoustics
Arts
Equivalence relation
Formal logic
Keyboard instruments
Logic
Logical topics
Major chords
Mathematical logic
Mathematical relations
Mathematical set theory
Minor chords
Music
Music analysis
Music ensembles
Music theory
Musical chords
Musical instruments
Musical intervals
Musical performance
Musical pitch
Musical structure
Neo Riemannian theory
Performing arts
Philosophy
Physical sciences
Physics
Sound pitch
String instruments
Tonal theory
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ISBN9780691125459
0691125457

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Summary:The groups mentioned in the title are not groups such as Metallica or the Chicago Symphony Orchestra, but groups in the algebraic sense. There are many ways in which elements of musical structure may be described by group-theoretic constructions; these constructions and related topics form the subject of this chapter. One important large class of musical groups may be calledinterval groups, formalizing and generalizing the notion of the musical interval between two notes. Ageneralized interval system, orGIS[15], consists of: a setS, called thespaceof the GIS; a groupG, called theinterval groupof
ISBN:9780691125459
0691125457