Strings, standing waves and harmonics


Introduction: vibrations, strings, pipes, percussion....

Travelling waves in strings

Plucked strings

A bowed string behaves rather differently

Travelling waves and standing waves

Harmonics and modes

Harmonics in music

Complications with harmonic tuning

Some technical information for string players

    How do you work out harmonics if they are not explicitly annotated? Although the touch fourth is the most common harmonic, it has a disadvantage as an example. A touch fourth produces the fourth harmonic, but the two "fourth"s are from quite different context. In no other simple case does a touch nth produce the nth harmonic. For the low harmonics, the rule is obvious: 1/n of the string produces the nth harmonic. This formula starts to fail at very high numbers where the finite thickness of the string is important. Further, it is not a reliable way of producing harmonics above about the 8th.

    String players will know that, if you play five scale notes up a string, you arrive at a position one third of the way along the string, so a "touch fifth" produces the third harmonic. We can write the harmonics in the format:
    scale position touched fraction of string length harmonic number interval above open string
    octave 1/2 2 octave
    fifth 1/3 3 twelfth
    fourth 1/4 4 double octave
    major third 1/5 5 seventeenth
    minor third 1/6 6 nineteenth
    augmented fourth 2/7 7 halfsharp 20th
    minor sixth 3/8 8 triple octave
    major second 1/9 9 twenty third

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