in number and similar in position to those of the disc above them. Instead, however, of the holes in the two rings being pierced vertically both are inclined obliquely, the lower row The object in one direction, the upper in an opposite sense. of this is to furnish motive power to the rotating disc from the horizontal element of the wind-pressure. It would have been better to omit this device, and rotate the disc by external force, as will be presently described. The upper end of the spindle carrying the disc is furnished with an endless screw, which works into a small registering train of wheels. These can be thrown in and out of gear at will; so that the rotations in any given number of seconds can be approximately indicated on dials outside. The indication is only approximate, since the added friction of the train, however small, tends to slacken the speed of the disc, and lower the pitch of the note when it is applied. A very superior form of the siren has been introduced by Helmholtz, founded on the polyphonic siren of Dove, in which several notes can be sounded together. Helmholtz's instrument consists of two superposed sirens with their respective discs adapted to the same axis or spindle. The two wind-chests are fixed, one below the lower, and the other above the corresponding upper disc. The upper wind-chest with its attached orifices can be rotated on its axis by means of a toothed wheel and handle, whereas the lower receptacle is firmly fixed. On each of the two discs are four rows of holes, which can be blown separately or in combination. The lower sets consist of 8, 10, 12, 18 holes, the upper of 9, 12, 15, 16. In order to damp the upper partial tones by means of a resonance chamber, cylindrical boxes in two sections are attached to the wind-chest by means of screws. G VERSITY OF MICHICAN LIBRARIES The siren, although theoretically a perfect instrument, fails somewhat in practice, chiefly in consequence of the difficulty experienced in keeping its note steady. The character of the note itself is harsh and screaming, so that beats with softer sources of sound are all but inaudible. As it is usually made moreover, there is no way of preventing a steady acceleration of the rotation, or the corresponding rise in pitch. The blast of wind being made to accomplish two purposes, as a driving power as well as a source of sound, cannot be materially altered without at once reducing the impelling force and the tone. Mr. Ellis notes that "as each revolution of the disc reckons as twelve vibrations, an error of one revolution in a second, which is easily made, vitiates the results by twelve vibrations or 4 of a semitone at the pitch of C, which is a large amount. Practically a siren cannot be depended on within ten vibrations." Helmholtz, in whose hands the siren was made to give very fair results, employed an electro-magnetic driving machine to actuate it. It is connected with the discs by a thin driving-band. The siren does not then require to be blown. Instead of blowing, he places on the disc a small turbine constructed of stiff paper, which drives the air through the openings whenever they coincide with those in the chest. "This arrangement," he states, "gave me extremely constant tones on the siren, rivalling those on the best constructed organ-pipes." Error of Siren.-Another source of error in the indications of the siren does not hitherto seem to have been noticed. This is due to the amount of compression to which the air is subjected. For properly driving the disc at high speeds very considerable force is necessary, on account of its inertia and friction. The wind in the chest should support a column of water from 12 to 24 inches in height, a pressure equivalent to from lb. to one pound per square inch. In passing through the perforations of the siren it is therefore altering materially in volume, and still more perceptibly in heat. Both these elements exercise a powerful influence on the tone emitted by wind instruments of all kinds, as will be shown in greater detail in a later chapter, and cannot be neglected in this instance with impunity. Its Real Value.—The real practical use of the siren is for demonstrating the formation of the scale, and the vibration ratios which distinguish the principal concords and dissonances. These remain perfect and undisturbed in spite of variations in the absolute note upon which they are founded. (3) Determination by the Monochord.-One of the earliest successful attempts at accurate determination of pitch was made by Perronet Thompson. For this end he revised and perfected the ancient instrument of Euclid and Pythagoras, the monochord. According to his construction it was five feet long, ten inches broad, and six deep; the wire was of steel the twentieth of an inch in diameter, containing 145 feet to the pound avoirdupois, breaking with a weight of 300 lbs. The load required to produce tenor C of the pianoforte was from 240 to 250 lbs. The sound was brought out by the application of a well-rosined bow, and had the strength of a violoncello. The method of using the above apparatus for the enharmonic tuning of an organ, will be described in a later chapter. Here it will be sufficient to note the direct physical method of measurement with such an instrument. A string is tuned to a given note, and its vibrations are determined by knowing the stretching weight, the weight of the wire as stretched, and the vibrating length of the string. The following is the formula usually adopted, as given by Mr. Ellis in his excellent communication to the Society of Arts. Let V second. W = Number of grains in the stretching weight. Number of inches in vibrating string. Hence SL = Weight of vibrating string; which, cut off, weighed and measured, gives L, SL, and S. P being the length of the seconds pendulum Greenwich, and the constant 3.14159. 1 39.14 at The string is brought into sensible unison with the given note by shortening or lengthening the wire, and cut to the correct length. It is carefully measured for L, and weighed for SL. The weight with its attachments is weighed for W. In this way Dr. Smith, in the year 1755, in the month of September, tuned a wire to give a note two octaves below the D pipe of the organ in Trinity College, Cambridge; arriving Journal of Society of Arts, May 25, 1877, "On the Measurement and Settlement of Musical Pitch," by Alexander J. Ellis, F.R.S., &c. |