356 



DR. KfENIG S RESEARCHES ON 



as resultant of a decreasing series of partial tones (Fig. G, a). Jf the 

 slit be inclined in the same direction as the forward movement of the 

 waves, the quality ])roduced is the same as if all the ]);utial tones coin- 

 cided at their origin, or with fJ = 0; while if inclined in the opposite 



Fig. 8. 



direction the quality is that corresponding to <y = A. It is easy to ex- 

 amine whether the change of phase produces any effect on the sound. 

 Before you is rotating a simj^le wave disk, and air is being blown across 

 its edge through a slit. Dr. Kienig will now tilt the slit alternately 

 backward and forward. On tilting the slit forward to give 6 = 0, you 

 hear a purer and more perfect sound j and on tilting it back, giving 

 (J = J, a sound that is more nasal and forcible. 



All the preceding experiments agree then in showing that differences 

 of phase do produce a distinct effect upon the quality of compound tones; 

 what then must we say as to the effect on the timbre of the presence of 

 upper partial tones or sounds of subdivision that do not agree with any 

 of the true harmonics ? A mis-tuned harmonic — if the term is permissi- 

 ble — may be looked upon as a harmonic which is undergoing continual 

 change of phase. The mistuned octave which yielded the graphic curve 

 in Fig. 5, is a case in point. The wavelets are contiinuilly 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 exi)erimenting with his large compound wave siren that 

 Dr. Kienig was struck by the circumstajice that under no conditions, 

 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 aj)])aratus with electro-magnetic 

 tuning forks, in which there is no control over the phases of the com- 

 ponents. The question was therefore rii)e for investigation whether 

 for the production of that which the ear can recognize 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 



