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Analytische Theorie der Iterationsskalen

In: Pythagoras, der Quintenwolf und das Komma

Author

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  • Karlheinz Schüffler

    (Heinrich-Heine-Universität)

Abstract

Zusammenfassung In diesem Kapitel werden zwei neue mathematische Hauptmodelle für Intervall-Iterationen vorgestellt: Das theoretisch elegante Äquivalenz-Klassen-Modell sowie das praxisorientierte Operatormodell der Reoktavierung. Wir betten dank dieser Modelle die Iterationstheorie musikalischer Intervalle in die Mathematik der komplexen Zahlen und ihrer Geometrie („Töne = komplexe Zahlen = Winkel“). Aus dieser Implantierung einer höheren Mathematik in die Konzepte musikalischer Strukturen gelingen sowohl abstrakt-allgemeine als auch moderne Formulierungen einer mathematischen Theorie musikalischer Iterationen. Im abschließenden Satz von Levi-Poincaré werden aus diesem Modell heraus eindrucksvolle Zusammenhänge zur Mathematik dynamischer Systeme gezeigt und genutzt.

Suggested Citation

  • Karlheinz Schüffler, 2017. "Analytische Theorie der Iterationsskalen," Springer Books, in: Pythagoras, der Quintenwolf und das Komma, edition 2, chapter 0, pages 233-272, Springer.
    • Handle: RePEc:spr:sprchp:978-3-658-15186-7_8
    DOI: 10.1007/978-3-658-15186-7_8
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