In the present book, we are dealing with subjects which lie partly within the province of science and partly within that of art, and the boundary between the two provinces is not always perfectly clear. If the question is debated as to whether the music of John Sebastian Bach is superior to that of his son Philipp Emanuel, science can bring nothing to the discussion. The question is purely one for artists, and it is quite conceivable, although perhaps rather improbable, that they may not be able to agree as to the answer. On the other hand, if the question is whether the music of either Bach is superior to that produced by a chorus of cats singing on the roof, there will be little doubt as to the answer. The artists will all agree, and science is able to explain to a large extent why they agree.

To say the same thing in another way, the aim of music is to weave the elementary sounds we have been discussing into combinations and sequences which give pleasure to the brain through the ear. As between two pieces of music both of which give pleasure in a high degree, only the artist can decide which gives more, but the scientist can explain why some give no pleasure at all. He cannot explain why we find Bach specially pleasurable, but he can explain why we find the cat music specially painful.

The Coming of Music

The lantern of science, throwing its light down the long corridors of time, enables us to trace out the gradual evolution of terrestrial life. Far away in the dim distances of the remote past we see it emerging from lowly beginnings—possibly single-cell organisms on the sea shore—and gradually increasing in complexity until it culminates in the higher mammals of to-day, and in man, the most complicated form of life which has so far emerged from the workshop of nature. And as living beings become more complex, they acquire an ever more intricate battery of sense-organs which help them to find their way about the world, to escape danger, to capture their food and avoid being themselves captured as food.

One of these is of special interest to musicians, for out of it has developed our present organ of hearing. Sunk into the skin of a fish, and running the whole length of its body, from head to tail on either side, there is a line of pits or depressions. Under these lies an organ known as the “lateral-line” organ. This is believed to register differences of pressure in the water, which will acquaint the fish with the currents and eddies in which he is swimming, and may also warn him of the proximity of other fish, especially of large fish of hostile intentions.

We have now considered the generation of sound and its transmission through the air to the ear; we must finally consider its reception by the ear, and transmission to the brain.

When the air is being traversed by sound-waves, we have seen that the pressure at every point changes rhythmically, being now above and now below the average steady pressure of the atmosphere—just as, when ripples pass over the surface of a pond, the height of water in the pond changes rhythmically at every point, being now above and now below the average steady height when the water is at rest. The same is of course true of the small layer of air which lies in contact with the ear-drum, and it is changes of pressure in this layer which cause the sensation of hearing. The greater the changes of pressure, the more intense the sound, for we have seen that the energy of a sound-wave is proportional to the square of the range through which the pressure varies.

The pressure changes with which we are most familiar are those shewn on our barometers—half an inch of mercury, for instance. The pressure changes which enter into the propagation of sound are far smaller; indeed they are so much smaller that a new unit is needed for measuring them—the “bar”. For exact scientific purposes, this is defined as a pressure of a dyne per square centimetre, but for our present purpose it is enough to know that a bar is very approximately a millionth part of the whole pressure of the atmosphere.

Much has been added to our scientific knowledge of musical sound, since Helmholtz published his great work Tonempfindungen in 1862. The new knowledge has been often and well described, but mostly by scientists writing for scientists in the technical language of science.

In the present book I have tried to describe the main outlines of such parts of science, both old and new, as are specially related to the questions and problems of music, assuming no previous knowledge either of science or of mathematics on the part of the reader. My aim has been to convey precise information in a simple non-technical way, and I hope the subject-matter I have selected may interest the amateur, as well as the serious student, of music.

I need hardly say that I am indebted to many friends and books. A considerable fraction of my book is merely Helmholtz modernised and rewritten in simple language. Another considerable fraction is drawn from the wealth of material provided in the notes added to Helmholtz's book by his English translator, A. J. Ellis. On the less technical side, I have borrowed largely from Dayton C. Miller's book The Science of Musical Sounds (The Macmillan Company, 1934), and am especially indebted to the author for permission to reproduce eleven excellent photographs of sound-curves.

We have now considered the way in which musical sounds are produced by various instruments, and the way in which the quality of those sounds depends on the proportion of the various harmonics of which they are the blend. We have further considered the combining of single sounds into chords, and the choice of a musical scale which shall give as much pleasure as possible—or, perhaps, more accurately, as little pain as possible—to the sensitive ear. But our problem does not end with the production of musical tone; it ends only with the perception of this tone by the brain. After a musical tone has been produced in the orchestra, it has to go through two further stages—transmission from the instrument to the ear-drum of the listener, and transmission from his ear-drum to his brain. We consider these two stages in this and the following chapter.

The Transmission of Sound-Waves

Imagine that we are listening to an orchestra out in interstellar space. As we have seen that some material medium is necessary to transmit the sound from the instruments to our ear-drums, let us give free rein to our fancy, and imagine interstellar space filled with ordinary air.

Sound leaves each instrument in the form of waves which spread in all directions. If there is nothing to absorb their energy, they travel on for ever, but their intensity naturally diminishes as they spread out.