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Medietäten

In: Proportionen und ihre Musik

Author

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  • Karlheinz Schüffler

    (Heinrich-Heine-Universität Düsseldorf, Mathematik)

Abstract

Zusammenfassung In diesem Kapitel 3 (Medietäten) werden zunächst die babylonischen – sodann die wichtigsten anderen historischen Mittelwerte – vorgestellt, und sie werden in erster Linie mittels der Proportionenketten-Darstellungen beschrieben. Es werden dann Formalismen zwischen den Mittelwerte-Magnituden und den zugehörigen Teilungsparametern entwickelt, welche insbesondere in der Hyperbel des Archytas zu bemerkenswerten Zusammenhängen zwischen Medietäten-Proportionen und der Geometrie führen. In erster Linie gewinnt man hieraus die Symmetrien babylonischer Proportionenketten, woraus die „Harmonia perfecta maxima“ entstanden ist. Im Zentrum dieses Kapitels steht nun die Generalisierung der Harmonia perfecta von dem historischen Kanon 6 – 8 – 9 – 12 bis hin zur Harmonia perfecta abstracta (diatonica) als ein universelles musikalisches Symmetrieprinzip der Diatonik und ihren abstrakten Verallgemeinerungen. Die Sonderrolle des geometrischen Mittelwertes wird dabei in diesem Zusammenhang an herausgehobener Stelle beleuchtet.

Suggested Citation

  • Karlheinz Schüffler, 2019. "Medietäten," Springer Books, in: Proportionen und ihre Musik, chapter 0, pages 77-140, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-59805-4_3
    DOI: 10.1007/978-3-662-59805-4_3
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