THE PHYSICAL BASIS OF MUSICAL HARMONY. 351 



III. 



I DOW pass to the further part of the researches of Dr. Koenig which 

 relates to the timbre of sounds. Prior to the researches of Dr. Koenig 

 it had been supposed that in the reception by the ear of sounds of com- 

 plex timbre the ear took no account of, and indeed was incapable of 

 perceiving, any differences in phase in the constituent partial tones. 

 For example, in the case of a note and its octave sounded together, it 

 was supposed and believed that the sensation in the ear, when the 

 difference in phase of the two components was equivalent to one- 

 half of the more rapid wave, was the same as when that difference of 

 phase was one-quarter, or three quarters, or zero. I had myself, in 

 the year 1876, when studying some of the i)henomena of binaural audi- 

 tion, shown reasons for holding that the ear does nevertheless take cog- 

 nizance of such differences of phase. Moreover, the j)eculiar rolling or 

 revolving effect to be noticed in slow beats is a proof that the ear per- 

 ceives some difference due to difference of phase. Dr. Kcenig is 

 however the first to put this matter on a distinct basis of observations. 

 That such differences of phase occur in the tones of musical instru- 

 ments is certain ; they arise inevitably in every case where the sounds 

 of subdivision are such that they do not agree rigidly with the theo- 

 retical harmonics. Fig. 5 depicts a graphic record taken by Dr. Kcenig 

 from a vibrating steel wire, in which a note and its octave had been 

 simultaneously excited. The two sounds were scarcely perceptibly 

 different from their true interval, but the higher note was just suffi- 

 ciently sharper than the true harmonic octave to gain about one wave 

 in 180. The graphic trace has in figure 5 been split up into five pieces 



I'is 



to facilitate insertion in the text. It will be seen that as the phase 

 gradually changes the form of the waves undergoes a slow change 

 from wave to wave. Now, it is usually assumed that in the vibrations 

 of symmetrical systems, such as stretched cords and open columns of 

 air, the sounds of subdivision agree with the theoretical harmonics. 

 For example, it is assumed tliat when a stretched string breaks up into 

 ^ nodal vibration of four parts, each of a quarter its length, the 



