IT- SOUND 1 : 2, 1 : 3, 1 : 4, 1 : 5, &c. The lowest sound I** -n-i-ivi -.1 is -enerally the most intense, and is Sited the fundamental." This is the sound which i- indicated in musical notation, and which drsi-nates the pitch of the composite sound. But really when we produce one of
- mds indicated by musical notation, we
generally at the same time evolve a long series of sounds Waring to each other the vibration relations of 1, 2, 3, 4, 5, 6, &c. This series of sounds is called the harmonic series, and is sometimes designated as the series of overtones of the fundamental sound. But the members of this series do not always all coexist ; thus the sounds of the clarinet only contain the odd numbers of the series, viz., 1, 3, 5, 7, &c. It is evident from the above facts that an in- definite number of different composite sotfnds can be formed by combining simple sounds and giving to them various relative intensities ; and that each of these composite sounds will be characterized by its own peculiar timbre. This great discovery, that all simple sounds have one and the same timbre, and that the characteristic timbre of any other sound is due alone to the number and relative intensities of the harmonics or overtones forming the sound, was made by Ilelmholtz ; he not only succeed- ed first in proving this by the experimental analysis of various composite sounds, but also by reproducing these composite sounds with their characteristic timbres by simultaneously sounding their simple sonorous components with their proper relative intensities. This ex- planation of timbre, as Helmholtz has shown, has a dynamic basis, and is the direct conse- quence of the celebrated theorem of Fourier, which may thus be rendered in the language of dynamics: Every periodic vibratory motion can always, and always in one manner, be re- arded as the sum of a certain number of pen- ulum vibrations. There are various methods of analyzing a composite sound. They are generally founded on the fact that if we have two bodies which give exactly the same num- ber of vibrations in a second, and vibrate one of them, the other, although somewhat distant from the first, will be thrown into vibration by the action of the aerial pulses which have em- anated from the first body. This must neces- sarily follow, for the pulses which the second body receives from the air synchronize with the number of vibrations in a second which this body alone can give. This phenomenon may be called " co-vibration." Helmholtz in his in- vestigations generally used as co- vibrating bod- ies masses of air contained in hollow spheres if various sizes. These spheres are called reso- nators, and one of them, as made by Konig of Paris, is shown in fig. 8. These spherical mass- es of air are so graduated in volume that a series of resonators is formed, and each re- sonator will resound only to the number of vibrations in a second which is stamped on it. Tin- manner of using these resonators is as fol- lows: The compound sound falls upon the open mouth of the resonator, while the nipple- shaped tube opposite the mouth is placed in one ear, and the other ear is closely stopped with beeswax. If the sound, to which the FIG. 8. mass of air contained in this resonator enters into co- vibration, exists in the composite sound, then the ear will perceive this sound with some intensity, to the exclusion of the other component sounds. Thus by placing to the ear each resonator of the series and noting those which resound, we can readily ascertain the simple sounds, whose union forms the com- posite sound which we have analyzed. The writer has often replaced the resonators ap- plied to the ear by tuning forks mounted on resonant boxes. If the mouth of one of these boxes, like fig. 9, be placed near a sound- ing reed pipe, and if the note of the fork on the resonant box exists in the composite sound of the reed, then this fork will be set in vibration and will continue to vibrate after the reed has ceased to sound ; for the mass of air in the box acts like a resonator, and is set in vibration by the pulses of that harmonic of the reed which is in unison with it. But, as the fork is also in unison with the mass of air in the resonant "box, it follows that it also is set in motion by the latter, so that, after the composite sound ceases, we find that the fork sings out alone, and thus shows that it has selected from a chorns of harmonics that one FIG. 9. which is in unison with its own tone. It has thus been easy, by using one fork after another of the harmonic series of the reed, to show the composition of its sound to a
