-181]

The Tuning-Fork.

183

lishments in France, and a standard has been deposited in the Conservatory of Music in Paris.

It makes 870 single or 435 double vibrations in a second, and

Fig. 159.

yields the note la of the treble stave; the do or C of the same stave makes thus 261 double vibrations in a second.

The standard tuning-fork adopted by the Society of Arts in London, on the recommendation of a committee of eminent musicians, makes 264 double vibrations in a second, and gives the middle C of the treble stave. The corresponding A or la gives therefore 440 vibrations in a second.

The middle C is the note sounded by the white key immediately on the left of the two black keys which are near the middle of the keyboard of a pianoforte. It is designated in musical notation as

For purposes of comparison it is convenient to call

this note c', and the next lower octave c; the octave lower than this C, and the still lower one C,, and so on. The lowest note of grand pianos is A,,, which gives 27.2 vibrations in a second.

In like manner the higher octaves are distinguished by affixes, thus c'', c''', civ, and so forth. In height the pianoforte reaches to air with 3,520 or c with 4,422 vibrations in a second.

The practical range of musical sounds is comprised within 40 and about 4,000 vibrations in a second ;. or within a range of 7 octaves.

182. Resonance of air. The action of the resonance-box in strengthening sound (fig. 159) may be illustrated by the following experiment (fig. 160). AB is a glass cylinder about 8 inches in height, and I to 1 in diameter. If now an ordinary tuning-fork

Fig. 160.

B

be made to vibrate, its

sound is very faint, and if it is held over the empty cylinder probably no alteration will be experienced. When, however, water is slowly and noiselessly poured into the cylinder, on reaching a certain height the previously faint sound is far louder. Any other tuningfork, which yields a different note, if held over the cylinder, will not have its note strengthened. Reverting now to the original tuning-fork, if, while it is still sounding and its sound is being strengthened by its nearness to the cylinder, we continue

to pour in water, the sound becomes as faint as it was originally. If now the excess of water be again removed until the tone of the fork is once more strengthened, and if, removing the fork, we sound the column again by blowing into it, we find that the column of air emits the same note as the tuning-fork. Hence then the tuning-fork could set a column of air of a particular length in vibration so as to produce the same note; and this adding itself to the original note strengthened it.

The rushing sound heard when certain large shells are held near the ear is caused by the fact that the mass of air in the shell responds to certain sounds and strengthens them.

183. Compound musical tones. Harmonics. Overtones. We have already seen that there is a peculiar quality or timbre

-183]

Compound Musical Tones.

185

as it is called, by which the notes of different instruments are characterised. Thus we readily distinguish between the note C when sounded on a pianoforte and the same note sounded on an organ or a trumpet. This peculiarity of the tone is due to the fact that only in very few cases does an instrument give a pure note, but that in most cases it is accompanied by a series of upper notes or harmonics. To understand what these are we may refer to art. 195, in which it is stated that by successively intensifying the current of air we get in a stopped pipe a succession of notes the numbers of whose vibrations are as the series of odd numbers, I, 3, 5, 7, etc. So, too, if we sound an open pipe in a similar way, we get the series of notes whose numbers of vibrations are represented by the series of numbers, 1, 2, 3, 4, 5, etc. These are called respectively the odd and even harmonics of the primary note.

Now, if we sound a particular note on the piano, a practised ear can discover, by a little attention, that the primary note is accompanied by a series of higher notes, each of which gradually gets fainter. These upper notes may be detected, and the compound nature of the primary sound analysed, even by an unpractised ear, by the use of resonance globes which Helmholtz devised for this purpose. These instruments,

Fig. 161.

one of which is represented in fig. 161, are an application of the principle explained in the foregoing paragraph. They are small hollow a spheres; the projection b, which has a small hole, is placed in the ear while the wider aperture a is directed towards the source of sound. Each of these resonators is constructed or tuned for a particular note; so that if, having sounded the string of a pianoforte, we hold near it a resonator tuned for a particular note, this note if present will be intensified. Thus, if we depress the key c we hear no particular strengthening if a resonator tuned for g be held near the ear; but when the resonators sounded for c', g', c', are used we hear them powerfully respond when held to the ear. Hence the notes c', g', c', are contained in the mass of sound which is produced when the key c is depressed.

Helmholtz's researches show that the different timbre or quality of the sounds yielded by different instruments is due to

the fact that they are accompanied in each case by special harmonics or overtones in varying intensity; his principal results are as follows:

Simple tones-those, that is to say, without any admixture of overtones—are most easily produced when a tuning-fork is held near a resonance-box of suitable length. These notes are soft and are free from all sharpness and roughness.

The notes of the flute are also nearly pure, for their overtones are very feeble. Wide-stopped organ pipes give the fundamental note almost perfectly pure; narrower ones give along with it the fifth of the octave.

Wide open pipes give the octave along with the fundamental note; and narrower ones give a series of overtones.

The overtones present in the sound of stretched strings depend on their substance and on the manner in which they are made to sound. In good pianos the overtones are powerful up to the sixth. In stringed instruments the fundamental note is comparatively stronger than in pianos; the first overtones are feebler, the higher, from the sixth to the tenth, on the contrary, are far more distinct, and produce the penetrating character of the sound of stringed instruments.

Metallic rods and plates produce, along with the fundamental note, a series of very high overtones which are discordant with each other, but are continuous and of equal strength with the primary note. Thus is produced that peculiarity known as a metallic sound.

By the occurrence of the lower harmonics along with the primary note the tone is more sonorous, richer and deeper than the primary note; by the occurrence of the higher overtones, the clang acquires its penetrating character.

-185] Laws of Transverse Vibrations of Strings. 187

CHAPTER III.

TRANSVERSE VIBRATIONS OF STRINGS.

STRINGED INSTRUMENTS.

184. Transverse vibrations of strings.—We have already seen (160) that when an elastic string, stretched at the ends, is removed from its position of equilibrium, it reverts to it as soon as it is let go, making a series of vibrations which produce a sound. The strings used in music are commonly of catgut or metal wire. The vibrations which strings experience may be either transverse or longitudinal, but practically the former are alone important. Transverse vibrations may be produced by drawing a bow across the string, as in the case of the violin ; or by striking the string, as in the case of the pianoforte; or by pulling them transversely and then letting them go suddenly, as in the case of the guitar and the harp.

185. Laws of the transverse vibrations of strings.-The number of transverse vibrations which a string can give in a certain time-that is, the sound it yields-varies with its length, its diameter, its tension, and with its specific gravity, in the following

manner :

The tension being constant, the number of vibrations in a second is inversely as the length; that is, if a string makes 18 vibrations in a second, for instance, it will make 36 if its length is halved, 54 if its length is one-third, and so on. On this property depend the violin, the contrabasso, etc., for in these instruments, by pressing the string with a finger, the length is reduced or increased at pleasure, and the number of vibrations, and therewith the note,

is regulated.

With strings of the same length and tension the number of vibrations in a second is inversely as the diameter of the string; that is, the thinner a string, the greater its number of vibrations, and the higher its pitch. In the violin, the treble string, which is the thinnest, makes double the number of vibrations of that which would be made by a string the diameter of which is twice as great.