loudness is elicited. But as the clockwork lifts and drops its weight at regular periods, before the first vibration is extinguished, two conditions may occur; either the hammer may meet the bell in the same phase as its own, in which case an extremely loud toll results, or it may fall on it in the opposite phase, when great part of the momentum is employed in cancelling the interfering vibrations already set up and a very feeble sound is given out. These differences of intensity in the successive strokes can be plainly heard at 11 o'clock or midnight when the air is still.

CHAPTER IV.

PITCH. ITS MEASUREMENT, LIMITS, VARIATION, STANDARDS, AND TONOMETRY.

IT has been already stated that all sound consists of three elements, namely, intensity, pitch, and quality. The first of these depends entirely on the amplitude of the vibrations; the last has been shown by Helmholtz to be connected with certain secondary and affiliated oscillations termed harmonics, from which few musical tones are entirely free. This will be adverted to in a subsequent chapter. The remaining constituent, namely, pitch, has been the subject of much important research. It depends entirely on the number of vibrations in a given time.

Limits of Audible Sound.-Savart showed that the faculty of perceiving sounds depends rather on their intensity than on their acuteness, and by increasing the diameter of his toothed wheel, carried it up to 24,000 vibrations per second.

For deep sounds he substituted for the toothed wheel a bar about two feet long, revolving on an axis between two thin wooden plates about 0.08 of an inch distant from it. A grave, continuous, very deafening sound was thus produced, with 7 to 8 vibrations in a second. These results are disputed by Despretz and Helmholtz, the former placing the limit at 16, the latter at 30 vibrations, the definite musical character according to the latter observer being only obtained at 40 vibrations per second. These discordant results are no doubt due to the different capacities of different observers for the perception of sound, indeed the extreme upper limit of audible sound appears to vary materially with the individual. M. Despretz had a diatonic octave of small forks from 8,000 to 16,000 vibrations in the second, tuned by M. Marloye, who declared that with practice he could tune still higher scales.

He did tune an octave fork to that last named, which would give 32,000 vibrations. He states that in the process of tuning he went twelve times over the whole octave. On the two first attempts he heard nothing. At the third attempt he was able to distinguish the intervals in the following order: Fourth, Fifth, Minor Sixth, Minor Third, Major Sixth, Major Third, Minor Seventh, Major Seventh, and at last with great difficulty, the Major Second. Upon this he makes the suggestive remark that if there be a natural scale for the ear, these observations would point to its being minor rather than major.

Appunn has made thirty-one tuning-forks, in true major scales from 2,048 vibrations up to 40,960, which most ears can distinguish, although they often produce a very painful sensation.

Captain Douglas Galton has shown a method of producing even higher tones, by means of small whistles. Many of these notes appear to be more audible to the smaller mammalia, especially to cats, than they are to the human ear.

Preyer has made experiments of considerable precision by means of which he fixes the minimum limit for the average ear between 16 and 24 single vibrations per second, the maximum at 41,000; many persons of fair hearing powers being however deaf to sound of 16,000 or even fewer vibrations.

It appears, from experiments made by the writer, that the musical character of low tones depends materially upon the presence or absence of a sufficient consonant body for their reinforcement and co-ordination. Sixteen-foot C can be obtained on the double bass, with distinct musical character, by special treatment of the resonant body of the instrument. The size of the room, moreover, must be considerable for the large waves thus originated to spread without damping and interference. The 32-foot octave of pedals in the organ at the Albert Hall is perfectly musical in effect. Probably the experiments of Helmholtz, which were made with feeble sources of sound such as metal strings, were deficient in the requisites just named. The lowest and grandest note to be heard occurs when a train passes into a short tunnel. The successive explosions of issuing steam, varying in rapidity from 8 to 20 in a second, can, if the speed be gradually increasing, be clearly heard to coalesce into a profound humming note of steadily rising pitch due to the consonance of the gigantic resonator furnished by the bore of the tunnel itself.

The determination of the number of vibrations in a given period corresponding to a particular musical note may be made by the various methods of TONOMETRY, as this branch of acoustics has been termed. These may be given, in tabular form, as follows:

I., Mechanical methods.

II. Optical methods.

III. Photographic methods.

{Prof. Blake's experiments.

(1. Meyer's electrical tonometer.

IV. Electrical methods. (2. Lord Rayleigh's pendulum

V. Computative methods.

experiment.

1. Chladni's rod tonometer.
2. Scheibler's Tonmesser with
tuning-forks.

3. Appunn's tonometer with free
reeds.

I. Mechanical Methods.-The simplest mechanical method in the above list of contrivances is founded on the fact that slight successive noises caused by collision, which individually present no musical character whatever, gradually coalesce into a definite tone if their intervals be regular and if their succession be sufficiently rapid. A common watchman's rattle, and even a stick passed rapidly across the bars of a grating, may be used as a popular illustration of the fact; Dr. Haughton has furnished an excellent example, named in the introductary remarks.

"The granite pavement of London is four inches in width, and cabs driving over this at eight miles an hour, cause a succession of noises at the rate of thirty-five in the second,

which corresponds to a well-known musical note, that has been recognised by many competent observers; and yet nothing can be imagined more purely a noise, or less musical,

than the jolt of the rim of a cab-wheel against a projecting stone; yet if a regularly repeated succession of jolts take place, the result is a soft, deep, musical sound, that will well