measuring pitch it is never necessary to consider more than two places of decimals, and even the last place is used only to prevent an accumulation of error. = III. French Normal Pitch, C 514 to 527.-About forty years ago there was a French pitch in use almost coincident with that theoretically established in Paris in 1859; one fork from a good maker measured by Scheibler in 1834 actually gave A 434.9 or practically C 517. The pitch, however, must have risen rapidly to about A 452, and the object of the French Commission was to regain this older pitch. This modern version of the older fork in the Paris Opera and Conservatoire was preceded in England by the almost identical but flatter pitch of Sir George Smart, and Broadwood's vocal pitch, and also by the very slightly sharper pitch of Scheibler in Germany, which being chosen by him as the mean pitch of Vienna grand pianofortes, represents the Vienna pitch of the time. From having been accepted by a congress of German physicists, who met at Stuttgart in 1834, it is commonly known as the Stuttgart pitch. Altogether, this group, which is comprised within about a quarter of a tone, represents that most in vogue now on the Continent, and consequently has the greatest claims on our attention, although its highest forks are of a semitone below our present high pitch. IV. Medium Pitch, C 520 to 536.-The interval of about of a tone between the French normal and high pitch is not well marked. We have indeed within this group a fork from Leipzig, purporting to be the Dresden low pitch; one from Vienna, measured by Scheibler, but differing materially from the other Vienna forks; one from the Liceo Musicale at Bologna, in 1869; the medium pitch empirically adopted by Messrs. Broadwood and in the organ of St. Paul's. There were also several foreign forks in this group. The theoretical fork of the Society of Arts which begins it, was never really made, and Griesbach's A, like Hullah's C, were accidental errors. It would seem that the whole of this group is not generally satisfying; it is both too sharp and too flat, and can only be regarded as a neutral medium pitch. V. Modern High Pitch, C above 536.-The highest group contains the moderately high pitch which the French Commission found so excessive, and the still sharper English concert and military pitch of the present day, with the high pitch of Brussels, strongly advocated in a report of a committee to the Belgian Minister in 1863.1 We find that there The pitches given should be corrected by subtracting 4 for the error which Mr. Ellis attributes to the French Normal. = = = C 529-2 C 534.6 for C 537.5 for the was a tuning-fork in Paris in 1826 giving A 445 = for the French Opera, another giving A 449.5 the Italian Opera, and another A 452 Opera Comique. The two first belong to the preceding group. Many operas were composed to the last pitch which was afterwards raised to A 455 C 541. The report mentions that when the French Commission was appointed the Opera pitch was A 453 C 5387, and that Lissajous wished to lower it to A 449.5 C 534-6, but that a contrary opinion prevailed. The Committee say that to this high pitch belong the tuning-fork of the Brussels Conservatoire, one in use at Ghent, an old fork of the Paris Opera Comique in 1820, the tuning-fork of the Philharmonic Society of London, that of the Berlin Opera in 1861, and lastly that of the Choral Society of Cologne. = = We have thus, according to Mr. Ellis's observations, a rise for C from 467 to 546, or 80 vibrations 2.6 semitones in 130 years, or, if the early observations be rejected as possibly erroneous, from the undoubtedly authentic fork of Handel, which gives 5074 to the vibration number of 546.5, at which the band of the Belgian Guides were playing in 1859. The writer can state from his own careful observations made at the Handel Festival of 1877, during the performance of the Israel in Egypt, on an extremely hot day in June, the thermometer being nearly 80° under the dome of the orchestra, that the pitch of A rose to 460, which is equivalent to a C of 547, and is higher than any previously recorded. Causes of the Rise in Standard Pitch.-It will be seen that the tendency of the standard pitch has always been to rise, except when authoritatively and suddenly lowered, as in France, and more recently, though with little success, in England. It is also obvious that the rise occurs chiefly in orchestral performances. Much of this is due to temperature. All wind instruments rise with the warm breath of the player, especially the clarinet, which varies almost a semitone. Some part is also due to the fact that stringed instruments tune to perfect fifths, which can be shown to be incommensurable, from their larger interval, with the octave. Considerable weight must be given to the fact that the ear is physiologically liable to select the sharper of two notes for. imitation; but the chief cause is an instinctive but vulgar inclination in the players themselves to give their own instrument an undue prominence at the expense of the others by slight sharpening. Alteration of Pitch from Motion of Source.-It is clear that the pitch of a sound is liable to modification when the source and recipient are in relative motion. This fact was first stated by Doppler, and has been experimentally verified by Buijs Ballot and Scott Russell, who examined the alterations of pitch of musical instruments carried on locomotives. It is clear that an observer approaching a fixed source will meet the waves with a frequency exceeding that proper to the sound by the number of wave-lengths passed over in a second of time. If v be the velocity of the observer and a that of sound, the frequency is altered in the ratio a±v: a according as the motion is towards or from the source. Since the alteration of pitch is constant, a musical performance would still be heard in tune, though when a and v are nearly equal the fall in pitch would be so great as to destroy all musical character. If we could suppose v to be greater than a, sounds produced after the motion had begun would never reach the observer, but sounds previously excited would be gradually overtaken and heard in the reverse of the natural order. If v = 2a the observer would hear a musical piece in correct time and tune, but backwards.1 Similar results occur when the source is in motion and the observer fixed. With a relative motion of 40 miles per hour the alteration of pitch amounts to about a semitone. This can easily be substantiated by watching the whistle of a locomotive passing through a station. A laboratory instrument for demonstrating this phenomenon has been invented by Mach, consisting of a tube six feet long turning on an axis at its centre; at one end is a whistle or reed blown by wind forced through the axis; when this is made to rotate rapidly, the pitch is found to fluctuate by an observer standing at the side, according as the rotating arm is approaching or moving away from him. Koenig uses two C tuning-forks, giving four beats with one another. If the graver of them be made to approach the ear while the other remains at rest, one beat is lost for each two feet of approach; if however the more acute be moved, one beat is gained by the movement... Rayleigh op. cit. II. 140. CHAPTER V. NATURE OF MUSICAL TONE. QUALITY. HARMONICS. Nature of Musical Sounds. Quality. It has been accepted as an axiom that the sensation of musical tone is due to a rapid periodic motion of the sonorous body; that of noise, to non-periodic motions; and it has been shown that musical tones are distinguished: 1, By their force or loudness. 2, By their pitch or relative height. 3, By their quality. Quality. It is to the third of these constituents that attention is now to be directed. The quality of a tone, which was formerly denoted by the anglicised French term Timbre, is that peculiarity which distinguishes the violin from the flute or the clarinet, and these from the human voice, when uttering sounds of the same pitch or frequency. Until. the researches of Helmholtz this last characteristic had remained unexplained. He showed in a conclusive manner that the observed differences depended on no abstruse or recondite property, but simply on the co-existence with the principal of other secondary and affiliated vibrations, which accompany and modify the sensation by alterations which they produce upon the form of the sound-wave itself. Helmholtz aptly illustrates the possibility of difference even in periodic motions such as are so slowly performed as to be capable of being followed by the unassisted eye. For instance, the motion of a pendulum or an ordinary vibrating spring is one which is rapid in the middle of its path, and slow at either extremity : that of a hammer moved by machinery is marked by being slowly raised and falling suddenly. A ball thrown up vertically and caught on its descent by a blow which sends it up again to the same height, occupies the same time in rising as in falling, but at the lowest point its motion is suddenly A', interrupted; whereas above it passes through gradually diminishing speed of ascent into a gradually increasing speed of descent. None of these forms of motion are similar to one another, nor would they, if translated into sound, produce the same effect. The pendulum may be graphically represented by the double curve of sines before named, passing equally on either side of a straight middle line; the hammer by a series of long inclined planes terminated by a short downward curve; the ball by a series of arches abruptly reflected from one side of a base line. It is upon this difference in the form of the vibration that quality of tone depends. Ohm was the first to declare that there is only one form of vibration which will contain none of these secondary waves, and will therefore consist solely of the prime tone. This is the form peculiar to the pendulum and to tuning-forks, and hence they are called simple or pendular vibrations. Partials. The affiliated or secondary waves, when occurring in the same period as the primary, are termed harmonics, overtones, or most accurately, upper partial tones. The character given to a particular note by their presence, by an over-literal translation of a German word, has been termed "clang-tint,” it was formerly designated as timbre, but is best represented by the familiar English word quality. When several resonant bodies simultaneously excite different systems of waves Fig. 51.-Curve representing a sound-wave. of sound, the changes of density of the air, and the displacement, and velocities of the particles of air within the ear are each equal to the algebraical sum of the corresponding changes of density, displacements, and velocities, which each system of waves would have separately produced if it had acted independently.1 The multiplicity of vibrational forms which can be thus produced by the composition of simple pendular vibrations is I Helmholtz, Sensations of Tone, p. 43 et seq. |