SKETCH OF RUDOLPH KOENIG. 549 



quality of every musical sound is determined "by the number, 

 orders, and relative intensities of the upper partial tones which 

 accompany the fundamental whenever any ordinary instrument 

 is sounded. Every such compound tone can be graphically rep- 

 resented by its own curve, the form of which may be varied not 

 only by varying the elements just mentioned, but also by varying 

 the phases in which the separate components are joined together. 

 Helmholtz endeavored to test the influence of change of phase in 

 using his apparatus for acoustic analysis, but the results were 

 negative, and his conclusion was, that variation in phase has no 

 physiological effect. Koenig has since attacked this problem, em- 

 ploying wave-sirens of his own invention, by which he has estab- 

 lished quite conclusively the existence of this fourth element of 

 musical quality. . . . The wave-siren may be briefly described as 

 an apparatus in which a blast of air is forced through a narrow 

 cleft against the edge of a moving plate or disk on which a series 

 of determinate wave-forms have been cut. Each sinuosity, as it 

 passes the cleft, interrupts the egress of air, so that a series of 

 compound pulses are propagated whose grouping is determined 

 by the form of the curved edge. The pitch is determined by the 

 speed of rotation and the wave-length cut in the metal, through 

 either the convex surface of a cylinder which rotates on its axis, 

 or the edge of a disk which rotates about its center. A number 

 of such wave-forms, each with its own wind-cleft, may be operated 

 at the same time, with the same speed and with the same pressure 

 of air at each cleft. They may be arranged to either coincide or 

 differ in phase to any required extent. By the use of this new 

 instrument Koenig has found that the complex sound obtained 

 by the composition of a series of harmonics, of even as well as odd 

 orders, quite independently of their relative intensity, has always 

 its maximum of strength and its greatest acuteness of quality for 

 a difference of phase of a fourth of a wave-length ; the minimum 

 of strength, and the softest quality, for a difference of phase of 

 three fourths of a wave-length. It may be said that, if changes 

 in the number and relative intensity of the harmonics produce 

 differences of quality, such as are observed in instruments belong- 

 ing to different families, or such as the human voice shows in the 

 different vowels, the changes due to difference of phase between the 

 same harmonics are yet capable of producing differences of quality 

 at least as sensible as those which are noticeable in instruments of 

 the same kind, or in the same vowels sung by different voices. 



All musicians are able to perceive the general smoothness or 

 roughness of a combination of sounds ; but the analysis of the 

 combination requires exquisite sensitiveness of ear for the detec- 

 tion of variation in both pitch and harmony. In the tuning of 

 the standard forks which are issued from Koenig's laboratory, his 



