va 
[Louvon ] A CENTURY OF PROGRESS IN ACOUSTICS 58 
structed a series of high forks accurately tuned and proceeding accord- 
ing to the intervals of the perfect (major) scale, from €; to the 
enormous pitch of 180,000 v.s., and that without reaching a limit to 
the number of such vibrations. 
As to the audibility of these high forks, it has been remarked by 
Keenig that those between ¢c, and €, are generally audible, whilst c¢,, 
and those above are entirely inaudible. He further remarks that the 
limit of audibility, which thus lies between c, and c,, largely depends, 
as in the case of low sounds, on the intensity, and varies with the 
individual. . 
Intensity With regard to the question of intensity of sound, it is 
only necessary to say that there exists here a great lacuna in our acous- 
tical knowledge, as we do not yet possess a means of measuring the 
physiological intensity of sound. 
Timbre-—To Helmholtz belongs the credit of first elucidating the 
question of timbre by showing that the timbre of a sound depends upon 
the number and intensity of the harmonics which accompany the 
fundamental. The question of timbre is thus intimately connected 
with the study of the phenomena produced by the coexistence of 
two or more sounds. With regard to such phenomena it was stated by 
Helmholtz that when two notes of different pitch are sounded together, 
they give rise to two other sounds, the pitch of which is measured, the 
one by the difference, and the other by the sum of the vibrations of 
the two primary sounds. Further, that these resultant sounds are not 
due to beats. 
These propositions of Helmholtz are controverted by Keenig, 
who, on the contrary, has proved that the sounds actually heard accom- 
panying two primary sounds are always due to beats. Koenig asserts, 
moreover, that the sounds referred to by Helmholtz, even if we could 
prove that they had a real existence, would always be inaudible, and 
therefore without effect on the acoustical phenomena. He further 
establishes the curious fact that even interruptions of a sound give rise 
to another sound. 
As to timbre, Helmholtz’s theory was that it depended solely on 
the number and relative intensities of the harmonics which accompany 
the fundamental, and that itis not affected in any degree by differences 
in the phases of these components. This latter proposition is combated 
by Koenig, who holds that differences of phase as regards harmonics 
exercise a very important influence on the timbre of a sound, so that 
according to him timbre depends on the number, relative intensities 
and differences of phase of the harmonics which accompany the funda- 
mental. Koenig’s experiments on this disputed point were performed 
