The preliminary meeting of the Society of Arts was held on the 3rd of June, 1859. A large number of musical gentlemen and one lady, Madame Qoldschmidt (Jenny Lind), attended, together with a few scientific men. It was agreed that the pitch had gradually risen, was still rising, that it ought to be checked, and that the settlement of a definite standard, once for all, was very desirable. Madame Gold schmidt stated that within the abort space of twelve years the pitch had risen sufficiently to make the change painful to the singers of soprano music. A committee was appointed to examine and report on the question : the deliberations lasted twelve months. It is worthy of remark that Sir John Herschel addressed a letter to the committee, in which he expressed his astonishment that the French commission should have fixed upon the number 870 for their A fork, or 522 for c; and he expressed his conviction that sooner or later the mathemati cally simple and easily calculated 512 must be adopted. His proposal was to re-form the pitch effectually, and once for all, by the adoption of that number. The instrument-makers, he remarks, would be some what puzzled by ails change, but that the embarrassment would not be increased by making the full required alteration at once. The committee, however, reported in favour of a number between the two extremes—namely, 528, nr the pitch established by the Stuttgard musicians in 1834. The instrumental performers stated to the com mittee that they could lower the Opera pitch of 546 down to 528, but if they had to lower it to 512 some of them would have to purchase new instruments. On the other hand, the vocalists who would have preferred 512 were content to accept 528 as a compromise in the right direction. Besides this, 528 was recommended as a good number for the fundamental note of the octave, since it admits of the other notes of the scale being expressed in whole numbers without fractions. At the presentation of the report a strong attempt was made to obtain a vote in favour of 512, but without success; so that for some time to come this number will probably only reign in Professor ullah's singing-classes.
The scientific process by which the number of vibrations per second is determined, consists in the use of one of three or four methods. The first is by means of the monochord, a string of known length and diameter, stretched by a known weight usually in a horizontal position. The length of the string is the vibrating portion between two well-defined edges or bridges, and the weight is guided over a very small pulley. Fischer was, we believe, the first to point out a source of error in this arrangement, namely, that in the horizontal position the string is prevented by friction from experiencing the full effect of the weight, and the calculation will give the number of vibrations in excess of the true value. The string must therefore be in a vertical position. The formula convenient for calculation results from the mathematical theory of the vibrations of a stretched cord :— - - - - . - - in which 9'8257 is g being the accelerative force of the gravity of the earth at its surface, expressed in inchea.
Mr. Woolhouse Essay on Musical Intervals') took a piece of the stoutest plain string of the pianoforte, weighing very nearly 2 grains to the inch : 272 inches weighed just 9drams or 540 grains. A length of inches, stretched in a vertical position by a weight of 28 lbs. avoir„ sounded the common pitch-note A : hence, according to the preceding formula, c= 98726 inches; inches; a/c x inches; and "We therefore conclude that 718 the pitch-note • vibrates about 424 times in one second. This may differ one or two vibrations from the troth, on account of the unavoidable small defects of the materials used in the experiment." According to this determination the notes of the octave have the following values :—c 254, n 286, E 318, r 339,a 382, 424, n 477, and c 509 vibrations per second respectively.
The second mode of determining the pitch of a given note is by means of the BYBEE, and the method of doing so is briefly, but perhaps sufficiently, described under that head. For the method of BEATS. we may refer to that head, and likewise to the articles ACOUSTICS. and TEMPERAMENT and TustNo. But the most rapid and striking method of determining the number of vibrations in a given note is that recently introduced by M. Liersajnux [Nonat POINTS AND LINES?. By means of an eleetro-magnetic machine a disc one metro in moves with tenet uniformity, and makes one revolution in one second. This disc is covered with a thin layer of copperplate printer's ink, and the fork is furnished with a small ivory point. On vibrating the fork and bringing the point up to the rotating disc, it will engrave a number of tooth-like waves, which have only to be counted in order to deter mine the number of vibrations per second of the fork.
The law which regulates the vibrations of a tongue of metal fixed at one extremity, and free to vibrate at the other, is that the number of vibrations of similar tongues, but of different lengths, are in the inverse ratio of the squares of those lengths. Thus if one tongue be twice as long as the other, the ahorter will perform four times as many vibra tions in a given time as the longer. The method of tuning a fork by a standard is to sound the fork with that standard, and if it agrees with it, the two notes will sound in unison as ono; if it do not agree, a system of beats will be heard more or hum rapid according to the divergence. The tuner then adopts one of two methods : by means of a flat file he rubs off a portion from the ends of the prongs, thus reducing them in length, and making them vibrato quicker; or he introduces a rat's tail file and removes a portion from between the prongs, thus increasing their effective length and causing them to vibrate slower.
It is undoubtedly true, that the pitch even of the tuning-fork is liable to slight variations from change of temperature. While writing this article wo have performed the following experiment : two forks were sounded together and found to be strictly in unison; one of them was plunged into hot water for a few seconds, then wiped dry, and again sounded with the other fork, when a very painful beat was evident.