This chapter is devoted to traditional European music which is analyzed on the basis of phase plots. One can clearly recognize in the phase plots the difference between monophony, polyphony, canons and concertos. Ornaments are usually written in musical scores with tiny letters or symbols and are sometimes misinterpreted by beginners. By contrast, phase plots of ornaments show substantial effects along the main line of melodies. Rhythms can also be presented clearly by this kind of plots, as underlined by examples of triplets and multiplets. The divergence and convergence in Bach’s music, the small joke of Mozart’s 180 \(^\circ \) rotation of sheet music, symmetric scales of Messiaen and a (quite ambitious) discussion on the Fibonacci series in Bartók’s works are described.

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Physical and Mathematical Aspects in European Music

  • Kinko Tsuji,
  • Stefan C. Müller

摘要

This chapter is devoted to traditional European music which is analyzed on the basis of phase plots. One can clearly recognize in the phase plots the difference between monophony, polyphony, canons and concertos. Ornaments are usually written in musical scores with tiny letters or symbols and are sometimes misinterpreted by beginners. By contrast, phase plots of ornaments show substantial effects along the main line of melodies. Rhythms can also be presented clearly by this kind of plots, as underlined by examples of triplets and multiplets. The divergence and convergence in Bach’s music, the small joke of Mozart’s 180 \(^\circ \) rotation of sheet music, symmetric scales of Messiaen and a (quite ambitious) discussion on the Fibonacci series in Bartók’s works are described.