Science and music / [by Sir James Jeans].

  • Jeans, James, 1877-1946.
Date:
1947
Catalogue details

Licence: In copyright

Credit: Science and music / [by Sir James Jeans]. Source: Wellcome Collection.

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    Even if the hammer were perfectly hard, the seventh har¬ monic could be eliminated entirely by allowing the hammer to strike the string at a point a seventh of its length from one end, this being a node for the vibration in question. This would, however, leave the ninth and eleventh har¬ monics fairly strong, their positional factors being o-6o and 0*30 respectively. Or the ninth harmonic could be elimi¬ nated by striking the wire at a point one-ninth along its length, but then the seventh and eleventh harmonics would each sound with a positional factor 0-41., In practice, the string is usually struck at about a seventh of its distance from the end, although with a felted hammer this does not entirely eliminate the seventh harmonic; sometimes a compromise is attempted between the elimination of the seventh and ninth harmonics. But no compromise can be found which will of itself reduce both these harmonics to negligible proportions. The mainstay of the manufacturer must always be the felting on the hammer, and if this wears thin or hardens too much from prolonged use, the un¬ wanted upper harmonics will again ring out, giving the piano a metallic or “tinny” tone. The same effect may be produced if the piano-keys are struck with undue force, so that the felt on the hammers is much compressed during its impact on the strings—indeed if we strike with absolutely immense force, every hammer, no matter how well felted, behaves like a perfectly hard hammer and produces a mere jangle of metallic tone. The following table, calculated by Helmholtz, shews the energies of the different harmonics for a string which is struck with varying degrees of force at a point a seventh of the length of the string from one end, the force being