216 HERMANN VON HELMHOLTZ 



historical studies of the development of music, that the system 

 of scales and modes, and the harmonies built up from them, 

 do not rest merely on unalterable laws of nature, but are at 

 least in part the consequence of aesthetic principles, which 

 have been modified with the progressive development of 

 Humanity, he shows that music, like architecture, has evolved 

 along essentially distinct lines. He distinguishes three principal 

 periods in the art of music the homophonous (univocal) music 

 of Antiquity, with which we may connect the existing music 

 of Oriental and Asiatic peoples ; the polyphonous music of the 

 Middle Ages, multivocal, but as yet having no regard to the 

 independent musical significance of harmony, which persisted 

 from the Tenth to the Seventeenth Century ; and lastly modern 

 or harmonic music, characterized by the independent signi- 

 ficance of harmony as such, which originated in the Sixteenth 

 Century. The demonstration and deduction of this classification 

 for the history of music in all nations is not only one of 

 Helmholtz's greatest titles to fame, but is for all time an 

 admirable instance of the way in which it is possible to 

 connect historical with scientific investigation. 



Even in his earlier works he had shown that the over-tones 

 play a great part in musical composition as regards harmony, 

 but that the law which determines the melody of harmonious 

 combinations of tones is unconscious, since, though the over- 

 tones are perceived by the nerves, they do not come under the 

 heading of conscious representations, although their consonance 

 or dissonance is none the less felt. Harmony and discord 

 are but the means to the higher spiritual beauty of music, 

 while the melody expresses a movement of which the character 

 is plain and obvious to the direct perception of the hearer. 

 Since the degrees of the motion must be exactly measurable 

 to direct sense-perception by their velocity and magnitude, 

 melodious movement is for Helmholtz merely alteration of 

 pitch in time, and since the eye may follow a continuous 

 movement, while the ear fails to do so, inasmuch as it has 

 no capacity for retracing the path correctly and comprehending 

 it as a whole, melodic progression must advance by easily 

 estimated and definite stages. In the music of all peoples the 

 alteration of pitch in melodies takes place by successive steps, 

 and not by a continuous progression : in both melodic and 



