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This article describes an approximate set theory modeling intuitions shared by musicians such as Cowell, Schoenberg, Messiaen, and Persichetti. The author considers five approximation strategies, showing that in each case the result resembles an exact seven-tone set theory. Since most seven-tone...
One of the most prominent characteristics of Johannes Brahms's approach to sonata form is the return to the tonic at the start of the second section (or “rotation”) for a restatement of the exposition's primary theme. Well-known examples include the finales of the First and Third Symphonies, the...
Abstract compositional spaces have long been used to illustrate structural relationships within and between musical works. However, despite robust scholarship employing spaces to depict the possibilities available to composers, space-based analytical methods have rarely been used to study the...
A hybridization of two recent innovations in music theory—a focus on the progression of two triads as a unitary analytical object, and a component-wise formation of a set of equivalence classes—brings together under one conceptual and labeling system eight different approaches to the...
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