of recognising the note in question would be proportionately increased. Such an instrument has been invented by Helmholtz. It consists of a hollow ball of brass with two apertures at opposite ends of a diameter, as shown in Fig. 25.

The larger aperture allows the vibrations of the external air to be communicated to that within the ball; the smaller aperture terminates in a nipple of convenient form for insertion in the ear of the observer. The air contained in the ball resounds very powerfully to a single note of definite pitch, whence the instrument has been named by its inventor a resonator. The best way of using it is, first to stop one ear closely, and then to insert the nipple of the instrument into the other. As often as the resonator's own note is sounded in the external air, the instrument will sing it into the ear of the observer with extraordinary emphasis, and thus at once enable him to single out that note from among a crowd of others differing from it in pitch. A series of such resonators, tuned to particular previously selected notes, constitutes an invaluable apparatus for analysing a composite sound into the simple tones of which it is made up.

CHAPTER IV.

ON QUALITY.

43. THE laws of resonance enable us to establish a remarkable, and by most persons utterly unsuspected fact, viz. that the notes of nearly every regular musical instrument with which we are familiar, are not, as they are ordinarily taken to be, single tones of one determinate pitch, but composite sounds containing an assemblage of such tones. These are always members of a regular series, forming with each other fixed intervals which may be thus stated: if we number the separate single tones of which any given sound is made up, 1, 2, 3, &c., beginning with the lowest, we have

(1) The deepest, or 'fundamental,' tone, whose

pitch is ordinarily regarded as that of the whole sound.

(2) A tone one Octave above (1).

(3) A tone a Fifth above (2), i.e. a Twelfth above (1).

(4) A tone a Fourth above (3), i.e. two Octaves above (1).

(5) A tone a Major Third above (4), i.e. two

Octaves and a Major Third above (1).

(6) A tone a Minor Third above (5), i.e. two Octaves and a Fifth above (1).

These are the most important members of the series. Their vibration-numbers are connected by a simple law, which is easily deduced from the above relations. If the fundamental tone makes 100 vibrations per second, (2) will make twice as many, i.e. 200; (3), being a Fifth above (2), will have for

its vibration-number

3

× 200, or 300. For (4),

2

which is a Fourth above (3), we get similarly

6

× 500, or 600.

5

Thus the numbers come out 100,

200, 300 and so on; or generally, whatever be the vibration-number of (1), those of (2), (3), (4), &c., are respectively twice, three times, four times, &c. as large. If C in the bass clef be selected as the fundamental tone, the series, complete up to the tenth tone, is shown in musical notation as follows:

The asterisk denotes that the pitch of the 7th tone is not precisely that of the note by which it is here represented, but slightly flatter.

The reader must not suppose that, because the tones into which a note of a musical instrument may usually be decomposed are members of a fixed series, all those which we have written down are necessarily present in every such note. No more is meant to be asserted than that those which are present, be they few or many, must occupy positions determined by the law connecting each tone with its fundamental. The sound may contain, say, (1), (3) and (5) only, or (1), (4) and (8) only, and so on, the rest being entirely absent, but in no case can a tone intermediate in pitch between any two consecutive members of the series make its appearance.

44. Experimental evidence shall now be produced in support of the extremely important proposition just enunciated.

We will begin with the sounds of the pianoforte.

Let the note

be first silently pressed down,

and then

be vigorously struck, and, after three or four seconds, allowed to rise again. The lower note is at once extinguished, but we now hear its Octave sounding with considerable force from the wires of If we permit the damper

to fall back on these, by releasing the key hitherto held down, the whole sound is immediately cut off. Next, retaining the same fundamental note,

let

be quietly freed from its damper,

and the experiment repeated as before. We shall then hear this note sounding on after the extinction

Similar results may be obtained with

of

the three next tones,

but they drop

off very rapidly in intensity. The tones above

are so weak as to be practically inaudible.

The series of tones produced in this succession of cases can only be due to resonance. But, as has been already shown, the vibrations of any instrument are excited by resonance only when vibrations of the same period are already present in the surrounding air. Accordingly, the only sound directly originated in each variation of our experiment, viz. that of the must have contained all the tones suc

note

,