XXV 



qualities of tone which are best adapted for musical purposes." In 

 connection with this subject special mathematical and experimental 

 researches were instituted on the various modes of producing musical 

 sounds. The theory of oscillations in open tubes was discussed 

 from the point of view of the velocity potential, the mode of treat- 

 ment being at that date (1859) of a very advanced type. Another 

 interesting investigation threw a flood of light on the behaviour of 

 violin strings. A bright point on the string was observed through a 

 microscope the object glass of which was attached to the prong of a 

 tuning fork and vibrated parallel to the string. A study of the 

 curves produced by the luminous point led to the discovery that 

 the motion which produces the fundamental vibration consists of a 

 displacement at uniform speed in one direction, and a return move- 

 ment, at another constant velocity, to the original point of 

 departure. 



From problems such as these Helmholtz passed to the study of 

 vowel sounds. In his view the mouth when adjusted to produce a 

 particular vowel resounds to a particular note, and the quality of 

 the sound is determined by the tendency to reinforce that note. He 

 constructed the well-known apparatus for the synthesis of vowel 

 sounds, and arrived at the important generalisation that the quality 

 •of a sound depends only on the intensities of the harmonics and not 

 upon their relative phases. 



But, as in the case of optics, Helmholtz was not content without 

 following up the external physical phenomena to the point where 

 they affect the nerves. He published several papers on the 

 anatomy of the ear, and developed a theory as to the mechanism by 

 which the appreciation of musical pitch is developed in that organ. 

 In the first edition of his work (published in 1863) it was to the 

 fibres of Corti that he looked for the origin of this sense, but as it was 

 afterwards proved that they are absent in birds and amphibia, 

 Helmholtz concluded that it is probably " the breadth of the 

 memhrana basilaris of the cochlea which determines the tuning." 



The second part of the * Tonempfindungen ' was devoted to the 

 theory of consonance. Helmholtz explained the dissonance of com- 

 pound tones as caused by beats between the fundamentals or some of 

 the more important partials. In the case of simple tones the neces- 

 sary means of discrimination was found in beats due to the presence 

 of combination tones. Of these Helmholtz discovered the summa- 

 tion tone, and though holding that under favourable condi- 

 tions, which depend upon the mode of production of the notes, the 

 combination tones are objective, he developed a theory of their 

 formation in the ear depending on the asymmetry of the vibrations 

 of the drum-skin. Somewhat lengthy controversies have arisen on 

 several of these points into which this is not the place to enter, but 



