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.

1

Let V: =

second. W =

Ꮪ =

string.

L =

Pitch, or number of double vibrations in one

Number of grains in the stretching weight.

Number of grains in one inch length of stretched

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.

= 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 Álexander J. Ellis, F.R. S., &c.

=

at the result of D=262 or mean tone C 468.7 more than a whole tone below the usual pitch at the present time.

The above method, in spite of its theoretical beauty, is so liable to constructive difficulties that it is of little or no practical value for the determination of pitch.

A somewhat better form of the monochord for this purpose was introduced by Griesbach, and is preserved in the collection at South Kensington. It consists of a thick gutstring stretched over a body like that of a double bass. It was tuned two octaves below the note to be measured. Then a fine point being attached to one part of the string, a long strip of paper was passed over it at uniform velocity, and in passing was pricked by the point at every double vibration of the string. The notes being then counted and multiplied by four, the pitch of the fork was approximately determined. The employment of this method, also open to numerous sources of error, rendered the fork issued by the Society of Arts too sharp by 37 of a semitone.

The monochord, although it produced good results in the hands of Perronet Thompson, for tuning correctly the different notes of the scale, is hardly so satisfactory as a means of determining absolute pitch. Scheibler sums up his long experience with it thus :-"Had it been possible to obtain exact results with a monochord, I could not but have succeeded, during the many years that I devoted to it, in tuning the forks of my scale correctly. My ear, and those of all others, were satisfied with the purity of the notes on instruments tuned by my monochord forks. But my mind would not be satisfied, because my results were not constant. When for example, one monochord showed me that a certain fork was one stroke of the pendulum too sharp, another monochord gave it as too flat. I became convinced that a mathematical monochord could not be constructed. I had also discovered that the string could not be protected from the warmth radiated by the observer's body, even when it was so thoroughly covered that there was only just space enough left for striking it. The string of a monochord, from this cause, does not remain for 30 seconds at the same pitch, but varies constantly by one-tenth to one-half of a double vibration."

In another place he estimates the possible error of the monochord at five double vibrations.

(4) Graphic Methods have the advantage of substituting a purely mechanical operation for a process requiring the assistance of an accurate musical ear. In their simplest form,

they may be typified by attaching a small point or style to the prong of a tuning-fork, and allowing this to trace its movements upon a piece of smoked paper or glass allowed to travel

steadily before it. If the fork be not sounding, the point will describe a straight line. But if it be first set in vibration, the attached point will constantly move backwards