The lower string is vibrating in thirds, having divided itself into four portions. If it were damped in the middle, it would divide itself into two portions, and sound octaves.
The subject is a most interesting one, but our space is nearly exhausted, and we must pass to another branch of it.
In all brass instruments furnished with a mouthpiece, and not with a reed, the notes are obtained by vibrations of the enclosed air, caused by the movement of the lips. They are all set to some definite tonic, sometimes C natural, but mostly to a flat tone, such as B flat or E flat.
Taking the ordinary military trumpet or bugle as an example, we have (when we have learned how to play it), first, the tonic. By alteration of the lips we get the octave above the tonic. Then comes the fifth; then the third, which is, in fact, another octave; and then a few other notes, the truth of which depends on the ear of the player.
Now, all these notes are obtained by means of the lips, which set the column of air vibrating, and divide it into harmonics. The apparently complicated bugle-calls of the army are nearly all formed from four notes only, i.e. (taking C as the tonic) C G C E G.
The Trombone, which is shown on the right hand of the illustration, has the advantage of being lengthened at will, and thus giving the performer a fresh tonic, and consequently another series of harmonics. Valved and keyed instruments have a similar advantage, the one acting by lengthening, and the other by shortening, the column of air. The former is infinitely the better plan, as it sets more harmonics vibrating, and consequently gives a greater richness of tone.
A familiar example of this is to be found in the Ophicleide and Euphonium. The former is eight feet in total length, and alters its tonic by eleven keys, which shorten the column of air. The latter is of the same length, but, by the employment of valves, can be made sixteen feet in length. Consequently the euphonium has practically killed the ophicleide, just as the ophicleide killed the serpent. The cornet-à-pistons, the brass contra-basso, the flugel horn, the tenor sax-horn, &c., are all constructed on the same principle.
On the left hand of the illustration is shown the wonderful apparatus by means of which the Swan produces its far-resounding cry. The windpipe, or “trachea,” as it is technically named, passes down the neck, protected by the bones, until it reaches the chest. There it leaves them, enters the cavity of the chest, and contorts itself in such a manner as to obtain greater length, just as is the case with the trombone and valved instruments.