4 - The beguiling harmonic theory

Summary

Helmholtz Resonators

Whatever theories and ideas about the nature of music had been put forward before, the work of Hermann Helmholtz was a major landmark. He demonstrated how to analyse steady-pitched sound into its components, the harmonics, and based on that, put forward what may be called a general theory of tonal music in his great book On the Sensations of Tone (1870). As we shall see in this chapter, it had and indeed still has a profound effect on ideas about music, both valuable and in important respects misleading. Like many other terms used by musicians, the word harmonic has at least three different meanings, but we shall use it only for a component of a sound, and qualify the word if it is used in one of its other meanings.

A column of air in a narrow tube, such as in a panpipe, flute or whistle, resonates. It produces a pitched note which can be seen to be related in some way to the length of the tube. A volume of air still has a resonance when it is enclosed in a container of any other shape; if one blows across the mouth of a bottle, the contained air resonates and a pitched note is produced. A large pitcher is used in this way to provide a single repeated bass note in the simple folk music of some parts of southern Europe. The pitch of the note depends on the size and shape of the volume of contained air, and it was used in the early pot flutes, exciting the air resonance with a whistle mouthpiece. If finger holes are made in the container, the pitch rises each time a hole is uncovered. This must have been discovered in primitive experiments, for it is a very easy way of getting several pitches from an artefact, but why was it never developed into a serious musical instrument? The ocarina, which works on this principle, has remained as either a crude whistle, a bird decoy or a toy. The puzzle is that, unlike tubes, the effect of opening holes in the container does not have any simple logic. If there are half a dozen similar-sized finger holes, the pitch rises by about the same amount whichever one is opened. Open two holes and the pitch rises again, but the pitches are not readily related.