i 9 4 HERMANN VON HELMHOLTZ 



tions of Tone, in consequence of the radical discoveries he 

 was making. In 1860 he writes to Bonders : ' I have decided 

 to put my acoustic work together in a book. It will be 

 a small volume, as popular in style as possible, so as to make 

 it available to lovers of music. I think I shall be able to 

 expound the physico-physiological basis of the theory of 

 harmony.' 



Helmholtz sought comfort and distraction in hard mental 

 work : his home, despite the devoted and tender ministration 

 of his mother-in-law, who looked after the two little children, 

 was empty and desolate. All the external honours that poured 

 in on him his appointment as Corresponding Member of the 

 Academy of Gottingen, the Sommering Prize given him by the 

 Senkenberg Naturforschende Gesellschaft at Frankfurt-a.-M., 

 and so on affected him little, though in former days he would 

 have welcomed them for the pleasure they gave his father and 

 his beloved wife. In the summer of 1860 he betook his sorrow, 

 and the fatigue engendered by the term's work and his cease- 

 less study of the deepest problems of human knowledge, to his 

 friend W. Thomson (Lord Kelvin) in the island of Arran, 

 returning after some weeks, refreshed in body and mind, via 

 Edinburgh and Hamburg, to Heidelberg. 



He now occupied himself almost exclusively with acoustics, 

 and writes to his brother Otto : 



' The physiological basis of consonance and dissonance may 

 be thus simply expressed : consonance is a continuous sensa- 

 tion of tone, dissonance is discontinuous. Two tones that are 

 near each other give coincident beats, i. e. intermittent excita- 

 tion of the nerve. The whole theory of Harmony, and of 

 our modern System of Tone, follows directly from the beats 

 of harmonic over-tones, combinational tones, &c.' 



On Nov. 23 he gave a lecture to the Nat. Hist. Med. Verein 

 on ' Musical Temperament ', in which he dealt with the dis- 

 advantages of tempered intonation for various instruments, and 

 in which the breadth of his historical studies, which in itself 

 makes his later theory of the sensations of tone such a mar- 

 vellous achievement, is obvious. In any given major scale, the 

 major third and the fifth are always tuned so that their vibra- 

 tion numbers are as 4 : 5 and 2:3; the three chords contained 

 in the scale are then pure. On passing into another key, the 



