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Interval Dichotomies as an Expression of Contrast

In: The Topos of Music

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  • Guerino Mazzola

    (University of Zurich, Department of Information Technology MultiMedia Laboratory)

Abstract

Summary For contrapuntal composition and theory, consonant and dissonant intervals are a dichotomic concept. We present the mathematical restatement and fundamental properties of the basic concept of an interval dichotomy For the classification of dichotomies, a strong condition on unique symmetries of polarity between the two halves of dichotomies is added. It reveals a distinguished role of the consonance/dissonance dichotomy of classical counterpoint and of the major dichotomy (associated with the major scale). We discuss evidence of the consonance/dissonance dichotomy from theoretical and empirical points of view and open the discourse to an intercultural perspective guided by the classification of dichotomies, as investigated by Jens Hichert [223].

Suggested Citation

  • Guerino Mazzola, 2002. "Interval Dichotomies as an Expression of Contrast," Springer Books, in: The Topos of Music, chapter 0, pages 629-644, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8141-8_30
    DOI: 10.1007/978-3-0348-8141-8_30
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