1890.] on the Physical Foundation of Music. 233 



timbre of the presence of upper partial tones or sounds of subdivision 

 that do not agree with any of the true harmonics ? A mistuned 

 harmonic — if the term is permissible — may be looked upon as a 

 harmonic which is undergoing continual change of phase. The 

 mistuned octave which yielded the graphic curve of Fig. 5 is a case 

 in point. The wavelets are continually changing their form. It is 

 certain that in a very large number of musical sounds, instrumental 

 and vocal, such is the case. 



It was whilst experimenting with his large compound wave-siren 

 that Dr. Koenig was struck by the circumstance that under no con- 

 ditions, and by no combination of pure harmonics in any proportion 

 of intensity or phase could he reproduce any really strident timbres 

 of sound, like those of harmonium reeds, trumpets, and the like ; nor 

 could he produce satisfactory vowel qualities of tone. Still less 

 can these be produced satisfactorily by von Helmholtz's apparatus 

 with electro-magnetic tuning-forks, in which there is no mode of vary- 

 ing the phases of the components. The question was therefore ripe 

 for investigation, whether, for the production of that which the ear can 

 recognise as a timbre, a definite unitary quality of tone, it was 

 necessary to suppose that all the successive wavelets should be of 

 similar form. Or, if the forms of the successive wavelets are con- 

 tinually changing, is it possible for the ear still to grasp the result 

 as a unitary sensation ? 



If the ear could always separate impure harmonic or absolutely 

 anharmonic partials from their fundamental tone, or if it always 

 heard pure harmonics as an indistinguishable part of the unity of the 

 timbre of a fundamental, then we might draw a hard and fast line 

 between mere mixtures of sound and timbres, even as the chemist dis- 

 tinguishes between mere mixtures and true chemical compounds. 

 But this is not so : sometimes the ear cannot unravel from the in- 

 tegral sensation the inharmonious partial ; on the other hand, it can 

 often distinguish the presence of truly harmonious ones. Naturally, 

 something will depend on the training of the ear ; as is the case with 

 the conductor of an orchestra, who will pick out single tones from a 

 mixture of sounds which to less perfectly trained ears may blend 

 into a unitary sensation. 



Dr. Koenig accordingly determined to make at least an attempt to 

 determine synthetically how far the ear can so act, by building up 

 specific combinations of perturbed harmonics or anharmonic partials, 

 giving rise to waves that are multiform, as distinguished from the 

 uniform waves of a true periodic motion. The wave-siren presented 

 a means of carrying this attempt to a result. On the table before 

 me lie a number of wave-disks constructed with this aim. These I 

 will now set into rotation by aid of a silent-running water-motor, and 

 will blow against them by means of a wind-chest, which supplies air 

 to the slit at a sufiiciently great and steady pressure. But I ought to 

 warn you that these experiments are intended for the laboratory 

 rather than for the lecture theatre, and only those who sit in the 



