On the sensations of tone as a physiological basis for the theory of music / by Hermann L.F. Helmholtz ; translated, thoroughly revised and corrected, rendered conformable to the 4th (and last) German edition of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of musical students, by Alexander J. Ellis.

  • Hermann von Helmholtz
Date:
1895
Catalogue details

Licence: Public Domain Mark

Credit: On the sensations of tone as a physiological basis for the theory of music / by Hermann L.F. Helmholtz ; translated, thoroughly revised and corrected, rendered conformable to the 4th (and last) German edition of 1877, with numerous additional notes and a new additional appendix bringing down information to 1885, and especially adapted to the use of musical students, by Alexander J. Ellis. Source: Wellcome Collection.

    53/604 (page 29)
    EYE AND EAR CONTRASTED. ure advaucing. All these observations assist it in determining whether two Systems of waves are connected or not, and hence in discovering their correspondrag parts. Moreover, on the surface of the water, waves of nneqnal length advance with unequal velocities, so that if tlicy coincide at one moment to such a degree as to be difficult to distiuguish, at the next instant one train pushes on and the other lao-s behind, so that they become again separately visible. In this way, then, the observer is greatly assisted in referring each System to its point of departure, and in keeping it distinctly visible during its further course. For the eye, then, two Systems of waves having different points of departure can never coalesce, foi example, such as arise from two stones thrown into the water at different points. If in auy one place the rings of wave coincide so closely as not to be easily Reparable, they always remain separate during the greater part of their extent. Hence the eye could not be easily brought to confuse a compound with a simple undulatory motion. Yet this is precisely what the ear does under similar circum- U stances when it separates the musical tone which has proceeded from a single source of sound, into a series of simple partial tones. But the ear is much more unfavourably situated in relation to a System of waves of sound, than the eye for a System of waves of water. The ear is affected only by the motion of that mass of air which happens to be in the immediate neigh- bourhood of its tympanum within the aural passage. Since a transverse section of the aural passage is comparatively small in comparison with the length of waves of sound (which for serviceable musical tones varies from 6 inches to 32 feet),* it corresponds to a single point of the mass of air in motion. It is so small that distinctly different degrees of densit}T or velocity could scarcely occur upon it, because the positions of greatest and least density, of greatest positive and nega- tive velocity, are always separated by half the length of a wave. The ear is therefore in nearly the same condition as the eye would be if it looked at one point of the surface of the water, through a long narrow tube, which would permit of H seeing its rising and falling, and were then required to undertake an analysis of the compound waves. It is easily seen that the eye would, in most cases, completely fail in the solution of such a pi'oblem. The ear is not in a condition to discover how the air is moving at distant spots, whether the waves which strike it are spherical or plane, whether they interlock in one or more circles, or in what directiou they are advaucing. The circumstances on which the eye chiefly depends for forming a j udgment, are all absent for the ear. If, then, notwithstanding all these difficulties, the ear is capable of distin- guishing musical tones arising from different sources—and it really shows a marvellous readiness in so doing—it must employ means and possess propertics altogether different from those employed or possessed by the eye. But whatever these means may be—and we shall endeavour to determine them hereafter—-it is clear that the analysis of a composite mass of musical tones must in the first place be closely connected with some determinate properties of the motion of the 5] air, capable of impressing themselves even on such a very minute mass of air as that contained in the aural passage. If the motions of the particles of air.in this passage are the same on two different occasions, the ear will receive the same Sensation, whatever be the origin of those motions, whether they spring from one or sevcral sources. We have alrcady explained that the mass of air which sets the tympanic membrane of the ear in motion, so far as the magnitudes here considered are coucemed, must be looked upon as a single point in the surrouuding atmosphere. Are there, then, any peculiarities in the motion of a single particle of air which would differ for a single musical tone, and for a combination of musical tones? VY e have seen that for each single musical tone there is a corresponding periodical [These are of course rather more than twice the length of the corresponding open flue organ pipes. See Chap. Y. sect. 5, and comparo p. 26d.—Translator.]