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minute elevations and depressions which constitute the roughness of the surface, a series of irregular vibrations are set up in the materials of the surface, and by them communicated to the air. The more rapid are these vibrations, the shriller does the sound become. The instrument described below, which is called a 'Syren,' gives us the means of following up with accuracy the hint just obtained.

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AB is a thin circular disc of tin or card-board, which, by means of a multiplying wheel, can be set in rapid revolution about a fixed axis through its centre, C. A series of holes (eight in the figure) are punched in the disc at equal distances along a circle having its centre at C. A small tube, ab, is held with one end close to one of the holes. If, while the disc is rotating, we blow steadily and continuously into the tube at a, a certain quantity of air will pass through the disc whenever a hole traverses the

orifice b, of the tube ab. During the intervals of time which elapse between the passage of adjacent holes across b, no air can pass through the disc. Hence, if the disc be revolving uniformly, a series of such discharges will succeed each other at perfectly regular intervals of time. The air on the other side of the disc will necessarily be agitated by the process. Every time that air is driven through one of the holes, an increase of pressure occurs close to it, and accordingly a pulse of condensation is formed there. The elastic force of the air will give rise to a pulse of rarefaction during each interval between successive discharges. Hence the Syren supplies us with a regular series of alternate condensations and rarefactions which when sufficiently rapid will, as we have seen, produce a musical sound.

27. While air is being blown steadily into the tube, let the disc be made to revolve slowly, and then with gradually increasing rapidity. At first nothing will be audible but a series of faint intermittent throbs, due to the impact of the air driven through the tube against the successive portions of the disc which separate its holes. This sound may be exactly reproduced by moving the fore-finger to and fro rapidly before the lips, while blowing through them. It contributes nothing to the proper musical sound of the instrument, and is only audible in its imme

diate neighbourhood. Presently, a deep musical sound begins to be heard, which, as the velocity of rotation increases, constantly rises in pitch. The acuteness of the sound thus obtainable depends solely on the speed to which we can urge the instrument, and is therefore limited only by the drivingpower at our command. The rise of pitch in this experiment is perfectly continuous, that is to say, the sound of the Syren, in passing from a graver to a more acute note, goes through every possible intermediate degree of pitch. It is important that we should familiarize ourselves with this conception of the continuity of the scale of pitch, because in the instrument from which our ideas on this subject are usually obtained-the pianoforte—the pitch alters discontinuously, i.e. by a series of jumps of half a tone each, and we are thus tempted to ignore the intervening degrees of pitch, or even to suppose them non-existent. The more perfect musical instruments, such as the human voice or the violin, are as capable as the Syren of passing through all degrees of pitch from one note to another in the called 'portamento' or 'slurring.'

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It is clear from the nature of the Syren's construction, that the only change which can take place during the rise of pitch is the increased number of impulses communicated to, and therefore of vibrations

set up in, the external air, during any given interval of time. If, when a note of given pitch has been attained by the Syren, we check any further increase of velocity, and cause the disc to rotate uniformly at the rate which it has just reached, no further alteration of pitch will occur, and the note will be steadily held by the instrument, so long as the uniform rotation of its disc is kept up. Hence the number of aerial vibrations executed in a given time determines the pitch of the sound heard.

28. The Syren, besides teaching us this most important fact, gives us the means of determining the number of vibrations corresponding to any given note. If we know the number of rotations which the disc has performed in a given time, we have only to multiply this number by the number of holes on the disc in order to ascertain how many tube-discharges have occurred, and therefore how many corresponding aerial vibrations have been performed, in the period in question. The Syren is provided with a counting-apparatus which registers the number of times its disc rotates per second.

In order, therefore, to obtain the number of vibrations in a second which correspond to an assigned note, we have only to proceed as follows. Let the note be steadily sounded by some instrument of sustained power, e. g. organ or harmonium, and then

cause the Syren sound to mount the scale until its pitch coincides with that of the note under examination. At the instant of coincidence read the figure indicated by the counting-apparatus. This, multiplied by the number of holes in the disc, gives the number of vibrations per second required. It will be convenient, for the sake of shortness, to call the number of vibrations per second, to which any note is due, the vibration-number of the note in question. It is clear, from what has gone before, that any assigned degree of pitch can be permanently registered, when once its vibration-number has been ascertained.

29. The Syren shows that, below a certain rate of vibration, no musical sounds are produced. The position of the absolute limit thus placed to the gravity of such sounds cannot be exactly defined, and probably varies somewhat for different ears. The lowest note on the largest modern organs has 16 for its vibration-number, but it is a moot question whether the musical character of this note can be recognized or not.

In any case we may regard the lower limit of musical sounds as situated in the immediate neighbourhood of this degree of pitch. For some distance above the limit the musical character continues very imperfect, and it is not until we reach 411 vibrations

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