We began our study of sound-curves by examining the curve produced by a tuning-fork. A tuning-fork was chosen, because it emits a perfectly pure tone. But, as every musician knows, its sound is not only perfectly pure, but is also perfectly uninteresting to a musical ear—just because it is so pure.

The artistic eye does not find pleasure in the simple figures of the geometer—the straight line, the triangle or the circle—but rather in a subtle blend of these in which the separate ingredients can hardly be distinguished. In the same way, the painter finds but little interest in the pure colours of his paint-box; his real interest lies in creating subtle, rich or delicate blends of these. It is the same in music; our ears do not find pleasure in the simple tones we have so far been studying but in intricate blends of these. The various musical instruments provide us with readymade blends, which we can combine still further at our discretion.

In the present chapter we shall consider the sounds which are emitted by stretched strings—such as, for instance, are employed in the piano, violin, harp, zither and guitar—and we shall find how to interpret these as blends of the pure tones we have already had under consideration.

Experiments with the Monochord

Our source of sound will no longer be a tuning-fork but an instrument which was known to the ancient Greek mathematicians, Pythagoras in particular, and is still to be found in every acoustical laboratory—the monochord.

The last two chapters have been concerned with the vibrations of tuning-forks and of strings. The vibrations of tuningforks proved to be mainly of theoretical interest, helping us to understand vibrations and sound-curves in general. On the other hand, the discussion of the vibrations of strings established direct contact with practical musical problems, the sounds produced by the violin, piano, harp, etc. In the present chapter we shall consider a further class of musical instruments in which the vibrating structure is a column of air—organ-pipes, flutes, whistles, oboes, fifes, etc.

The Spring of Air

For our first experiment we need only very simple apparatus—an ordinary bicycle or motor-tyre pump with a reasonably close-fitting piston. Let us cork up the tube at the outlet end, and stand the pump vertically, with the piston near the top, as in fig. 39.

The piston does not immediately fall to the bottom, because the pressure of the air in the tube holds it up. We can push it down by pressing hard on the handle, but the moment we take the pressure off, it bounces up again, just as though the air inside the tube formed a spring. Indeed we have discovered what Robert Boyle called “the spring of air”.

We shall understand the mechanism of this “spring of air” if we bear in mind that a gas consists of an immense number of molecules which dart about to-and-fro at very high speeds, each moving in a straight path until it either collides with another molecule or runs into some solid object.