December 27, 1901.] 



SCIENCE. 



995 



TIMBRE. 



To Helmholtz belongs the credit of first 

 elucidating the question of timbre by show- 

 ing that the timbre of a sound depends upon 

 the number and intensity of the harmonica 

 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 con- 

 troverted by Koenig, who, on the contrary 

 has proved that the sounds actually heard 

 accompanying two primary sounds are al- 

 ways due to beats. Koenig asserts, more- 

 over, that the sounds referred to by Helm- 

 holtz, even if we could prove that they had 

 a real existence, would always be inaudible? 

 and therefore without effect on the acoustic- 

 al 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 rel- 

 ative intensities of the harmonics which 

 accompany the fundamental, and that it is 

 not afiected 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 influ- 

 ence on the timbre of a sound, so that ac- 

 cording to him timbre depends on the num- 

 ber, relative intensities and differences of 

 phase of the harmonics which accompany 

 the fundamental. Koenig's experiments on 

 this disputed point were performed with his 

 large wave-siren. Even this wider defini- 



tion of timbre is, however, according to 

 Koenig's most recent view and experiments, 

 insufiicient, as not being applicable to cer- 

 tain 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 a ondes 

 de formes variables,' in which he deter- 

 mines the conditions under which such 

 timbres may be considered musical, and 

 concludes that in these cases the funda- 

 mental isaccompanied by harmonics which 

 continually change their relative intensities 

 and their phase-differences. 



In conclusion I may state that, according 

 to Koenig, 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 inten- 

 sity in the vibrations in the two cases cor- 

 respond more or less exactly, and that 

 several sounds produced together may rein- 

 force 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) are heard. 

 The difference between these two timbres 

 is, indeed, so great that when heard in suc- 

 cession, there appears to be an interval of a 

 fifth between them, although their funda- 

 mentals are exactly the same. These ex- 

 periments may be said to be the last on this 

 difficult subject in the years of the century 

 which has just closed. James Loudon. 



University of Toronto. 



