Percy Buck 'The Scope of Music'
"A musical sound has three characteristics: pitch, intensity, and quality. We have discussed pitch and intensity, and I now want to tell you how your ear distinguish between two sounds of different quality.
It may surprise you to know that, just as nearly everything we have ever tasted is a combination of certain elements which a chemist could analyse, so almost every sound you have ever heard, even when you thought it was a single note, is a combination of other sounds. If you would like to train your ears I beg you, when you get home, go to the piano and strike the C which is two leger lines below the bass stave. Strike it hard several times, holding it down the last time, and listen attentively until it is almost inaudible. Alter a very few trials—possibly the first time—you will notice there is another note sounding strongly, the G in the top space of the bass stave. After a few more trials you will plainly hear the E on the bottom line of the treble stave. You will then have discovered a fact known for ages to men of science, viz. that a note is almost invariably a combination of sounds. These various sounds which combine to form a note are called the ‘Partial Tones’ of that note, which is itself called the ‘Fundamental Partial’.
It is just possible to get a sound that has no partials - called a ‘Simple’ Sound - just as it is possible to get a simple primary colour; but you have probably seldom heard one. The nearest approach to it is the sound of a tuning-fork struck very gently, or the soft cooing of a dove. And the fact I want you to grasp is that ‘quality’ in a sound is due to the number and relative strength of the partial-tones which constitute it. They need not all be present-in fact, as the series extends upwards to the extreme limit of hearing we may safely say they are never all present. But if you get a flute, a trumpet, a violin, and a singer all to produce the same note at the same intensity, then the only difference between the four sounds is a difference of quality, which is entirely due to the fact that each of the four sounds, though their 'fundamental partial’ is the same, contains different ‘upper partials’.
I do not think, unless you are definitely a musical student, it is at all important for you to know more about the mysteries underlying ‘quality’. But I should like to point out one fact about the ‘harmonic chord' (as it is called) in EX. 6, lest you should think this matter of partial-tones to be mere theorizing. If you study the numbers at the side you will see that 1, 2, 4 and 8 are all an octave apart; and if you continued the series you would find that 16, 32, and 64. were all of them the note C. Similarly 3, 6, 12, 24. etc., are all G; 5, 10, 20, etc. always E. These facts have a practical result. For we can tell two things in consequence of them, viz. the vibration-numbers of the notes, and the length of pipe or string necessary to produce them. For instance, if we know that the bottom C of Ex. 6 has 60 vibrations per second and is produced by a pipe of 8 feet, then the vibration-number of the G which is the third partial is 60x3, and its pipe-length is 8/3 feet; similarly the vibration-number of the E which is the 5th partial is 60x5, and its pipe—length is 8/5 feet. If you pursue the subject of partial-tones a little farther—which you can do by studying any elementary text-book on sound—you will be initiated into some fascinating and bewildering mysteries in connexion with the ordinary major scale that you know so well. And you will learn some surprising things, such as why an expert piano-tuner is a man who is paid for putting your piano definitely out of tune. But perhaps you would rather pay in peace and leave such puzzles alone. I have just scratched the surface of the field of acoustics for you, in the hope of convincing you that it is interesting, and that by being interested in the material of which music is made, you will find your appreciation of the music itself a little more intelligent in quality, and certainly no less in quantity, than heretofore."
Percy Buck 'The Scope of Music' OUP