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Proportionen Und Ihre Musik: Was Brüche Und Tonfolgen Miteinander Zu Tun Haben

Proportionen Und Ihre Musik: Was Brüche Und Tonfolgen Miteinander Zu Tun Haben

          
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About the Book

Klänge können harmonisch sein, Zahlenfolgen auch - ein Zufall?

Dieses Buch behandelt eine musikalische Proportionenlehre, also die antike Lehre der Proportionen als die älteste und wichtigste gemeinsame Verankerung der beiden Kulturwissenschaften Mathematik und Musik.

Die Musiktheorie der Töne, Intervalle, Tetrachorde, Klänge und Skalen ist nämlich das genaue musikalische Abbild der Gesetze der Arithmetik und ihrer Symmetrien in dem Regelwerk des Spiels mit Zahlen, ihren Proportionen und ihren Medietäten. Alleine schon das Wunder der sogenannten Harmonia perfecta maxima 6 - 8 - 9 - 12, deren Proportionen die Quinte sowie die Quarte bestimmen, die Oktave bilden und den ehernen Ganzton in ihrer Mitte haben, prägte das musikalische Gebäude der pythagoräischen Musik über Jahrtausende. Diese elementare Proportionenkette 6: 8: 9: 12 ist zudem vollkommen symmetrisch und aus der arithmetischen wie auch aus der harmonischen Medietät der Oktavzahlen 6 und 12 aufgebaut.

Dieses Buch entwickelt die Proportionenlehre als eine mathematische Wissenschaft und stellt ihr immer die musikalische Motivierung mittels zahlreicher Beispiele gegenüber. Die Leitidee ist die Herleitung einer Symmetrietheorie von der Harmonia perfecta maxima bis hin zur Harmonia perfecta infinita abstracta, einem Prozess unbeschränkter Tongenerierungen durch babylonische Mittelwerte-Iterationen. Dabei wird hieraus simultan sowohl die klassisch-antike Diatonik gewonnen als auch der Weg "vom Monochord zur Orgel" neu beleuchtet.

Das Werk enthält schließlich eine von der Mathematik geleitete Hinführung zu der antiken Tetrachordik wie auch zu den kirchentonalen Skalen und schließt mit einem Exkurs in die Klangwelten der Orgel. Hierbei führt uns die "Fußzahlregel der Orgel" anhand von Beispielen in die Welt der klanglichen Dispositionen dieses Instruments und zeigt die Allgegenwärtigkeit der antiken Proportionenlehre auf.

Dieses Buch eignet sich für alle, die Interesse an Mathematik und Musik haben.


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Product Details
  • ISBN-13: 9783662598047
  • Publisher: Springer
  • Publisher Imprint: Springer Spektrum
  • Height: 244 mm
  • No of Pages: 254
  • Spine Width: 15 mm
  • Weight: 453 gr
  • ISBN-10: 3662598043
  • Publisher Date: 30 Jan 2020
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Sub Title: Was Brüche Und Tonfolgen Miteinander Zu Tun Haben
  • Width: 170 mm


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