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inch in diameter, containing the same number of holes as in the table, and coinciding with them, is supported by a vertical axis, d, having one bearing below the top of the chamber A, and the other in the box E. The disc c is so placed as just to turn freely without touching the table, and the holes through it are bored in a sloping direction, as shown in Fig. 23, while those in the fixed table slope the contrary way, so as to deliver the wind in the directions shown by the arrows, and thus turn the disc after the manner of a smokejack.

Fig. 23.

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The vertical axis d is furnished at its upper mity, where it enters the box E, with a perpetual screw, which gives motion to a wheel furnished with 100 teeth, and its axle bears one of the hands of the dial shown in front of the box. A single cog on this axle also acts on another wheel of 40 teeth, turning the other index, which accordingly moves over one of the 40 divisions of its dial for every complete revolution of the former index, which revolution corresponds to 100 revolutions of the disc c. Now it is obvious, that during each turn of this disc, the currents of air through it are cut off and reopened 25 times. The circle of holes, both in the disc and in the fixed table, being equidistant, they are all opened and all closed simultaneously, like the apertures of a revolving ventilator; and the hands and dials afford an exact register of the number of these openings and shuttings up to 25 x 100 × 40 = 100,000. The wheels are fixed to the front plate only of the box E, and this plate can be shifted through a small space sidewise, so as to throw the wheels out of gear in a moment.

When this instrument is placed in connection with a dou

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ble bellows, the stream of air enters the chamber, where it undergoes a slight condensation: it escapes rapidly through the holes in the table, forming a series of oblique jets which set the disc in motion with a rapidity depending on the strength of these currents, and as the air is strongly propelled when the apertures of the table and of the disc coincide, and is suddenly arrested between each coincidence, it follows that each of these alternations agitates the surrounding atmosphere, so that each revolution of the disc produces 25 waves of sound. These waves originate simultaneously from each of the 25 holes; for if either the fixed or the moving plate had only one hole (the other having 25), it is evident that the blast would flow and be arrested the same number of times, and would therefore produce the same note, but with less intensity. The use of having 25 holes in each plate is simply to strengthen the note without changing its pitch, on the same principle that the three strings given to each note of a grand piano-forte, without making the pitch of the notes differ from that of a single-stringed harpsichord, improves the power and quality. By regulating the force of the blast, and consequently the speed of rotation of the disc, sounds may be produced from the gravest to the most acute. Let us suppose that by means of this instrument we wish to ascertain the number of vibrations necessary to the production of a note yielded by an organ pipe. For this purpose the pipe is screwed into the upper table of the bellows which supplies air to the syren. The action of the bellows will cause this pipe to sound, and its pitch, as will be explained presently, will not be altered whether the blast be moderate or strong. In the syren, however, the disc will rotate slowly or rapidly in proportion to the strength of the blast, and the resulting note is acute

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in proportion to the rapidity of rotation. It will be easy to regulate the blast so as to make the syren yield a note strictly unisonant with that of the organ pipe; and we know that notes in unison of the same pitch are due to the same number of waves or vibrations per second. Now as the dial plates of the syren indicate the number of waves generated during the time the wheels are kept in gear, it is obvious that this number, divided by the number of seconds during which they were so kept, will give the number of vibrations per second for the note under consideration. A pendulum beating seconds must therefore be at hand.

A moderate degree of practice in the use of this instrument will enable the observer to determine the absolute number of vibrations per second necessary to the production of any given note without a greater error than one vibration in five seconds. Such observation may be prolonged during several minutes, and thus any small error arising from irregularities in the mechanism will scarcely appear in the result.

The syren may be set in action by the flow of air or gas from a gasometer, or by means of a stream of water. When plunged entirely in water, it will yield the same tones as in air, a circumstance which suggested to the inventor the name of this instrument.

Variations in the number, the form, and the size of the apertures of the rotating disc produce corresponding variations in the quality of the resulting notes; the pitch or rapidity of vibration may remain the same, but the quality or timbre may be very different. This is occasioned by some ill-understood connection between the molecular constitution of bodies and the sounds they emit, whereby we are able to call things by their right names from the sounds they emit. It is a most obscure and difficult subject, and the variations in timbre in the

MUSICAL INTERVALS.

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syren do not serve to enlighten it. If the spaces between the apertures in the rotating disc be very small, the tones approach in character to those of the human voice; if the spaces be large, the tones resemble those of a trumpet. A number of experiments with the syren seem to show that the extreme limits of the human voice in males vary from 384 to 1266 vibrations per second, and in females from 1152 to 3240. The highest note in music is about the 14th c* (five octaves above the middle c of the piano-forte), and this is due to 8192 vibrations per second; but much higher tones can still be heard. Savart has produced tones due to 48,000 vibrations per second.

66. Let us now inquire further into the relation between musical pitch and the rapidity of vibration. It has been already stated (62) that, whenever two notes differ by an octave, the upper is due to two vibrations for every one of the lower notes; and, as 8192 vibrations per second produce the note called c, it follows that the next c below this contains 4096, the next 2048, the next 1024, then 512, 256, 128, 64, 32, and 16 vibrations per second, the last number being generally considered the lowest note in music, and is also c, being nine octaves below that first mentioned.

67. It would thus appear that in any series of notes taken at equal intervals, or in arithmetical progression (according to the musical notation), the vibrations really increase or diminish in geometrical progression ; for that which the musician calls equal intervals or differences of pitch, actually indicates equal ratios between the times of the vibrations. But, although this is true not only of the intervals called octaves, but also of those called thirds, fourths, fifths, &c. (if

* So called from its number of vibrations per second, being the 14th power of 2, or 214 8192. All other powers of 2 also give the note c.

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perfect), yet it is not true of those called single tones; for, if we interpolate six geometrical means between any note and its octave, these will not be the six intermediate notes used in music. The reason for this is as follows:

We have said (61) that, to constitute a musical note, the waves or pulses of air must recur in a regular manner. They need not be all equal in intensity or at equal intervals, but their whole cycle of changes (if any) must occupy a very short fraction of a second, and recur in exactly equal periods. Now, when two notes are heard together, they cannot form a compound sound, fulfilling this condition, unless their times of vibration bear a simple numerical ratio to each other, so as to have a short common multiple which forms the cycle of changes above mentioned, and must not be longer thanth of a second. Accordingly all the intervals called harmonic arise from some very simple ratio between the vibrations, as, for instance, the octave already mentioned; the fifth, when 2 vibrations of one note exactly correspond to 3 of the other; the third, when 4 vibrations correspond to 5; the fourth, when they are as 3 is to 4, &c. But two vibrations which are incommensurable, or have no common multiple (or a very long one), produce by their combination such a total irregularity, however regular they may each be separately, that the compound loses all musical character, and becomes a mere noise.

Hence we see it is the object of the musician to fix on such notes as may afford, among themselves, the greatest number of simple commensurable ratios. This object would be entirely defeated by a geometrical progression (that is, by dividing each octave into equal intervals), for no geometrical means that can be inserted between any number and its double will be

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