That the source of a sustained sound is an elastic body in a state of vibration is a fact of which, in most cases, we are easily made aware by the evidence of sight and touch; as a bell, a violoncello string, a pianoforte wire, or a tuning-fork. On p. [656] is described a simple method by which a tuning-fork may be made to write down its own vibrations, and the more exact plan of recording them on the surface of blackened paper on a revolving and advancing cylinder has also been referred to. By the intervention of appropriate apparatus, a similar record may be obtained from all sounding bodies. From observations of this kind, and others in which totally different methods are used for counting the number of vibrations per vibrations made in a given time, it is known that the pitch of the sound or note depends on the rapidity of the vibrations—the pitch rises with the number of them per second, and the relationship between the notes of a musical scale depends entirely on these numbers. Thus, when the vibrations for the eight notes of an octave are counted, the numbers always have this proportion, beginning from the lowest note-–24, 27, 30, 32, 36, 40, 45, 48. Thus of the two notes—
as produced on musical instruments tuned to the concert pitch of the present day, the lower corresponds with 264 complete vibrations per second, the higher with 528. It will be observed, too, that all the harmonies are determined by some simple ratio in the rates of vibration: the interval of the fourth is 3, 4; that of the fifth is 2, 3, etc. Another easily discoverable fact is that the loudness of the sound depends upon the amplitude of the vibrations. This is sufficiently obvious by a few experiments with a tuning fork; and by close examination of such tracings as have been mentioned, we shall soon become aware of another circumstance—namely, that the vibrations not simple, but that the larger or general movement has one or more sets of small vibrations within it. In Fig. [319a], A is the curve that would be traced by the tuning-fork in a state of simple vibration; B and C are tracing such as are given by a fork in two of its modes of vibration. The fork gives out its proper or fundamental note in both cases; but the ear recognizes a difference in the quality of the sound due to the smaller and more numerous vibrations. Differences of the same kind are recognized in the notes produced by different musical instruments; but these are usually more complicated, and their forms are characteristic of the particular quality of the tone, which is thus shown to be due to the superposing of several related systems of vibration upon the fundamental one. Thus three out of the four qualities of sound recognized by the ear have had their physical causes assigned. As for the fourth—namely, the distinction we perceive among the different vowels sung on the same note—it has a physical origin identical with the last. For since parts of the vocal organs assume different positions in enunciating the different vowels, they constitute for the time being so many varied musical instruments, and the graphical traces of the sounds (for they can be obtained) show a corresponding modification. Here, in Fig. [319b], for example, are represented the tracings of the vibrations given to the air in various vowel sounds. It is also through the vibrations conveyed by the air to the little membrane called the drum of the ear that the sensations of sound are received, and of the nature of these vibrations a few words must be said presently. In considering the different qualities of sound, we have so far confined ourselves to sustained musical notes, as, for instance, the vowel sounds in singing. This has been done to show the relations of rapidity of vibration to pitch and for simplicity of illustration of the superposition of vibrations, etc. Two other remarks must be added—viz., that the vibrations of musical tones are isochronous—that is, whether the note be loud or soft, the same time is taken up in each vibration corresponding with the same fundamental note. Other vocal sounds than sustained vowel notes are found to be due to still more complicated combinations of vibrations of shorter duration, and noises, as distinguished from musical sound, are formed also by the superposition of a greater or less number of systems of vibrations, the rapidities of which are wanting in harmonic relations such as we have pointed out belong to the musical scale. Even in noises, however, there is often one or more predominant systems of vibrations which a musical ear can detect. If the reader will hold a pencil or penholder at one end and tap with it on the edge of the table, passing in quick succession to parts progressively nearer where the pencil is held, he will hardly fail to recognize a rising pitch in the little noises.
Fig. 319a.—Traces of Vibrations of a Tuning-Fork.
Fig. 319b.—Phonautographic Tracings of Different Vowel Sounds.
Fig. 319c.—Diagram.
