Titlebook: Classification of Musical Objects for Analysis and Composition; Linshujie Zheng,Guerino Mazzola Book 2023 The Editor(s) (if applicable) an

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Harmony through Third ChainsWe discuss the application of third chain classification to Riemannian harmony for general chords.

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Counterpoint WorldsThe classification of strong dichotomies yields a basis for the rules of counterpoint. We discuss some “exotic” counterpoint worlds (five besides the Fux world) that are generated by this classification.

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Strong Interval DichotomiesClassical Fuxian counterpoint is based upon a dichotomy of the set of 12 intervals within the set of pitch classes, specifying six consonances versus six dissonances. We characterize this dichotomy by its unique autocomplementarity symmetry that exchanges consonances and dissonances, and we calculate all possible dichotomies with this property.

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Microtonal Contrapuntal TheoriesWe shortly present the extension of counterpoint worlds to microtonal environments, an extension that would be very problematic, if at all possible, without the theory exposed above.

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Classification of Musical Objects for Analysis and Composition

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