1890.] on the Physical Foundation of Music. 233 



The seventh disk was constructed by taking 24 waves of perfect 

 sinusoidal form, and superposing upon them a series of small 

 ripples of miscellaneous shapes and irregular sizes, but without 

 essentially departing from the main outline. This disk gives 

 a timbre in which nothing can be separated from the fundamental 

 tone, either with vertical or tilted slit. 



The eighth and last disk consists of another set of 24 perfect 

 waves, from the sides of which irregular ripples have been carved 

 away by hand, with the file, leaving, however, the summits and the 

 deepest parts of the hollows untouched, so that the maxima and 

 minima are isochronous and of equal amplitude. This disk gives 

 also a definite timbre of its own, a little raucous in quality, but still 

 distinctly having a musical unity about it. 



We have every reason, therefore, to conclude that the ear will 

 recognise as possessing true musical quality, as a timbre, a combina- 

 tion in which the constituents of the sound vary in their relative 

 intensity and phase from wave to wave. 



What, then, is a timbre f Dr. Kcenig would be the first to recog 

 nise that these experiments, though of deepest interest, do not afford 

 a final answer to the question. We may not yet be in a position to 

 frame a new definition as to what constitutes a timbre, but we may at 

 least conclude that, whenever that definition can be framed, it will at 

 least include several varieties, including the non-periodic kinds with 

 multiform waves, as well as those that are truly periodic with 

 uniform waves. We must not on that account, however, rush to the 

 conclusion that the theory of von Helmholtz as to the nature of 

 timbre has been overthrown. The corrections introduced into lunar 

 theory by Hansen and Newcomb have not overturned the splendid 

 generalisations of Newton. What we can and must confess is that 

 we now know that the acoustic theory of von Helmholtz is, like the 

 lunar theory of Newton, correct only as a first approximation. It has 

 been the distinctive merit of Dr. Koenig to indicate to us the magni- 

 tude of the correcting terms, and to supply us not only with a rich 

 store of experimental facts but with the means of prosecuting the 

 research synthetically beyond the point to which he himself has 

 attained. 



Fascinating as is the pursuit of such questions, one cannot con- 

 clude these researches without pausing to enquire how much nearer 

 they have brought us to the ultimate explanation of the power which 

 music exercises upon us. And it must be confessed frankly that the 

 discovery of the physical foundations of the science leaves us very 

 much where we were before. For music, though a science, is before 

 all an art, and can be interpreted only by the artist. Science has 

 nothing to say concerning the vast range of musical impressions, 

 which are purely associative in their character. No analysis, how- 

 ever searching, will explain away the thrill that runs through us as 

 we listen to some simple phrase or motif which recalls the stately pre- 

 lude, the inspiring theme, the passionate andante, the gay barcarolle, 



