Here various tone intervals are described (e.g., unison, major third, octave, and other intervals). Subsequently, different scales such as the pentatonic, hexatonic, and heptatonic scales, follow. Among the heptanonic scales the major and minor scales are in focus. Since Pythagorean times tunings have become very complicated and problematic - even today, especially when instruments are played together. We will try to present them in as much detail as necessary to understand the tonal problems involved. Furthermore, the notion of harmonics and the color of sound (timbre) are briefly characterized. As special topics the horn fifth, the ancient musical instrument guqin, the Picardy third, the problem of the third and the devil’s interval are described.

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Intervals, Scales, Tuning and Harmonics

  • Kinko Tsuji,
  • Stefan C. Müller

摘要

Here various tone intervals are described (e.g., unison, major third, octave, and other intervals). Subsequently, different scales such as the pentatonic, hexatonic, and heptatonic scales, follow. Among the heptanonic scales the major and minor scales are in focus. Since Pythagorean times tunings have become very complicated and problematic - even today, especially when instruments are played together. We will try to present them in as much detail as necessary to understand the tonal problems involved. Furthermore, the notion of harmonics and the color of sound (timbre) are briefly characterized. As special topics the horn fifth, the ancient musical instrument guqin, the Picardy third, the problem of the third and the devil’s interval are described.