PROFESSOR AT HEIDELBERG 217 



harmonic music sounds with harmonic over-tones are preferred, 

 and to produce a good musical effect there must be a certain 

 moderate intensity of the five to six lowest partial tones along 

 with a low intensity of the higher partials, which confirms the 

 significance of the over-tones for melody also. He sums up 

 his results by saying that in music the more or less harmonic 

 effect of the intervals in melody and harmony is connected 

 with the special sensible phenomena of the over-tones, which 

 limit the harmonic intervals the more plainly and exactly in 

 proportion as they are just and simple. 



In treating of the difficult question of scales, for which he 

 had previously developed the essential principles, he proposes 

 the law of the relationship of musical sounds. He defines 

 sounds as related in the first degree when they have two 

 common partial tones, and in the second degree when they 

 are both related in the first degree to the same third tone, 

 so that the strength of the relation depends upon the strength 

 of the common over-tones, and on this ground of the natural 

 relationship of tones to one another he develops the scales, 

 although he admits that they were not exclusively derived from 

 the law of relations of tone in all epochs, so that it was to some 

 extent an arbitrary principle of style. 



Helmholtz's theory of scales, and of harmony and melody, 

 threw light on some of the darkest and most difficult points 

 of general aesthetics, and showed that these considerations 

 were closely allied to the doctrine of sense-perception, i.e. 

 to physiology, while the aesthetic analysis of complete musical 

 works of art, and the comprehension of the reasons of their 

 beauty, seemed to him still to be stopped by apparently insuper- 

 able obstacles. He subsequently affirmed on various occasions, 

 as in his Goethe Lecture at Weimar, that it was a mistake to 

 suppose that any aesthetic investigations could lead to the 

 discovery of rules for the guidance of artists. 



'The real difficulty lies in the complexity of the psychical 

 motives that here come into play. It is indeed at this point 

 that we reach the most interesting part of musical aesthetics . . . 

 since in the last resort we are seeking to explain the marvel of 

 the great works of art, the expressions and impulses of the 

 different psychical temperaments. Attractive, however, as the 

 goal may be, I would sooner leave these inquiries, in which 



