54 ROYAL SOCIETY OF CANADA 
with his large wave-siren. Even this wider definition of timbre is, 
however, according to Keenig’s most recent view and experiments, 
insufficient, as not being applicable to certain classes of timbres—for 
example, those produced by most musical instruments, especially 
stringed instruments. In these cases the fundamental is accompanied 
not only by harmonics, but also by other sounds which are not harmonic, 
the superposition of which produces series of waves which change their 
form successively. These wave forms have been investigated by Koenig 
in a paper “Sur les timbres à ondes de formes variables,” in which he 
determines the conditions under which such timbres may be con- 
sidered musical, and concludes that in these cases the fundamental 
is accompanied by harmonics which continually change their 
relative intensities and their phase-differences. 
In conclusion, I may state that, according to Keenig, the fact that 
differences of phase amongst harmonics produce differences of timbre 
is explained for the first time by his recent discovery that the intensity 
of a sound can be increased by the addition of another sound when the © 
maxima of intensity in the vibrations in the two cases correspond more 
or less exactly, and that several sounds produced together may reinforce 
a sound of lower pitch than any of them. For example, with the 
same six primary sounds, by changing their phases only, he produces 
not only timbres differing in intensity and in richness, but timbres 
in which, at one time, the octave (2) and at another time the fifth 
above (3) is heard. The difference between these two timbres is, — 
indeed, so great that when heard in succession, there appears to be — 
an interval of a fifth between them, although their fundamentals are 
exactly the same. These experiments may be said to be the last on — 
this difficult subject in the years of the century which has just — 
closed. 

