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Exploring Musical Spaces - A Synthesis of Mathematical Approaches (Hardcover)
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Exploring Musical Spaces - A Synthesis of Mathematical Approaches (Hardcover)
Series: Oxford Studies in Music Theory
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Exploring Musical Spaces is a comprehensive synthesis of
mathematical techniques in music theory, written with the aim of
making these techniques accessible to music scholars without
extensive prior training in mathematics. The book adopts a visual
orientation, introducing from the outset a number of simple
geometric models-the first examples of the musical spaces of the
book's title-depicting relationships among musical entities of
various kinds such as notes, chords, scales, or rhythmic values.
These spaces take many forms and become a unifying thread in
initiating readers into several areas of active recent scholarship,
including transformation theory, neo-Riemannian theory, geometric
music theory, diatonic theory, and scale theory. Concepts and
techniques from mathematical set theory, graph theory, group
theory, geometry, and topology are introduced as needed to address
musical questions. Musical examples ranging from Bach to the late
twentieth century keep the underlying musical motivations close at
hand. The book includes hundreds of figures to aid in visualizing
the structure of the spaces, as well as exercises offering readers
hands-on practice with a diverse assortment of concepts and
techniques.
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