prominence of the overtones which are blended with the fundamental. He first constructed a large number of resonators, like that shown in Fig. 364, each of which would respond to a note of some particular pitch. By holding these resonators in succession to his ear while a musical note was sounding, he picked out the constituents of the note; that is, he found out just what overtones were present and what were their relative intensities. Then he FIG. 364. Helmput these constituents together and repro

holtz's resonator

duced the original tone. This was done by sounding simultaneously, with appropriate loudness, two or more of a whole series of tuning forks which had the vibration ratios 1, 2, 3, 4, 5, 6, 7. In this way he succeeded not only in imitating the qualities of different musical instruments but even in reproducing the various vowel sounds.

408. Sympathetic vibrations. Let two mounted tuning forks of the same pitch be placed with the open ends of their resonators facing each other. Let one be set into vigorous vibration with a soft mallet and then quickly quenched by grasping the prongs with the hand. The other fork will be found to be sounding loudly enough to be heard over a large room. Next let a penny be waxed to one prong of the second fork and the experiment repeated. When the sound of the first fork is quenched, no sound whatever will be found to be coming from the second fork.

The experiment illustrates the phenomenon of sympathetic vibrations, and shows what conditions are essential to its appearance. If two bodies capable of emitting musical notes have exactly the same natural period of vibration, the pulses communicated to the air when one alone is. sounding beat upon the second at intervals which correspond exactly to its own natural period. Each pulse, therefore, adds its effect to that of the preceding pulses; and though the effect due to a single pulse is very slight, a great number of such pulses produce a

Sound waves corresponding to spoken words, from a photograph by Professor D. C. Miller. The words were spoken
by a barytone voice (Professor Miller's) having a normal pitch of from 150 to 180, varying with the inflection. The
sound waves cause vibrations in a diaphragm. These vibrations are transferred to a very small mirror, which reflects
a beam of light to a moving photographic film

This record was taken by the American Sound Ranging Service and illustrates the method developed during the World
War for locating enemy guns by determining the center of the sound wave caused by the explosion of the gun. Sound
detectors at from three to seven different positions a mile or so apart were electrically connected to a central station
where each registered the instant of arrival of the sound wave at its position. From the differences in these times of
arrival obtained from the records at the central station (six such records are shown in the figure) the position of a gun
ten miles away could be located with an error of not more than fifty feet. Hundreds of enemy guns were located and
put out of action by this method. The curves show a terrific uproar of guns at 58 minutes 59 seconds after 10 o'clock, but at
1 minute 0 seconds after the armistice hour, 11 o'clock, there is almost complete silence of artillery

large resultant effect. In the same way a large number of very feeble pulls may set a heavy pendulum into vibrations of considerable amplitude if the pulls come at intervals exactly equal to the natural period of the pendulum. On the other hand, if the two sounding bodies have even a slight difference of period, the effect of the first pulses is neutralized by the effect of succeeding pulses as soon as the two bodies, on account of their difference in period, get to swinging in opposite directions.

Let notes of different pitches be sung into a piano when the dampers are lifted. The wire which has the pitch of the note sounded will in every case respond. Sing a little off the key and the response will cease.

409. Sympathetic vibrations produced by overtones. It is not essential, in order that a body may be set into sympathetic vibrations, that it have the same pitch as the sounding body, provided its pitch corresponds exactly with the pitch of one of the overtones of that body.

Thus, if the damper is lifted from the C string of a piano and the octave below, C1, is sounded loudly, C will be heard to sound after C1 has been quenched by the damper. In this case it is the first overtone of C1 which is in exact tune with C, and which therefore sets it into sympathetic vibration. Again, if the damper is lifted from the G string while C1 is sounded, this note will be found to be set into vibration by the second overtone of C1. A still more interesting case is obtained by removing the damper from E while C1 is sounded. When C is quenched, the note which is heard is not E, but an octave above E; that is, E'. This is because there is no overtone of C1 which corresponds to the vibration of E; but the fourth overtone of C1, which has five times the vibration number of C1, corresponds exactly to the vibration number of E', the first overtone of E. Hence E is set into vibration not as a whole but in halves.

410. Physical significance of harmony and of discord. Let two pieces of glass tubing about an inch in diameter and a foot and a half long be supported vertically, as shown in Fig. 365. Let two gas jets (made by drawing down pieces of one-fourth inch glass tubing until, with full gas pressure, the flame is about an inch long) be thrust inside these tubes to a height of about three or four inches from the bottom. Let

S

the gas be turned down until the tubes begin to sing. Without attempting to discuss the part which the flame plays in the production of the sound, we wish simply to call attention to the fact that the two tones are either quite in unison or so near it that only a few beats are produced per second. Now let the length of one of the tubes be slightly increased by slipping the paper cylinder S up over its end. The number of beats will be rapidly increased until they will become indistinguishable as separate beats and will merge into a jarring, grating discord.

FIG. 365. Illustrating the production

of discords

The experiment teaches that discord is simply a phenomenon of beats. If the vibration numbers do not differ by more than five or six, that is, if there are not more than five or six beats per second, the effect is not particularly unpleasant. From this point on, however, as the difference in the vibration numbers, and therefore in the number of beats per second, increases, the unpleasantness increases, and becomes worst at a difference of about thirty. Thus, the notes B and C, which differ by about thirty-two beats per second, produce about the worst possible discord. When the vibration numbers differ by as much as seventy, which is about the difference between C and E, the effect is again pleasing, or harmonious. Moreover, in order that two notes may harmonize well, it is necessary not only that the notes themselves shall not produce an unpleasant number of beats, but also that such beats shall not arise from their overtones. Thus, C and B are very discordant, although they differ by a large number of vibrations per second. The discord in this case arises between B and C', the first overtone of C.

Again, there are certain classes of instruments, of which bells are a striking example, which produce insufferable discords when even such notes as do, sol, do', are sounded simultaneously