PROFESSOR AT HEIDELBERG 227 



and fits in with the facts of tone-relations in ordinary instru- 

 ments so well, that the problem seems to be solved by it. But 

 I am not prepared to admit that this relation of the octave to the 

 fundamental is the cause of the melodic relation of the tones, which 

 appear in all cases, just as plainly in the tones of rods, plates, 

 and bells, as in those of stringed instruments and the human 

 voice, notwithstanding that in instruments of this kind, accord- 

 ing to your observations, the over-tones may be musically 

 speaking neglected, or, if they were taken into consideration, 

 would necessarily produce quite different melodic relations. . . .' 



Helmholtz replied on June 3 : 



' (i) A weak accompaniment of harmonic over-tones is inevit- 

 ably present, at least in all strong simple tones. They arise from 

 the same law as combination tones, partly accidentally outside 

 the ear, partly in regular series within the ear, as often as the 

 vibrations become so great that the elastic forces are no longer 

 exactly proportional to the displacements. I proved by my 

 work on the mechanism of the auditory apparatus (Pfl. Arch.f. 

 Phys. Vol. I), that the conditions for this are especially favour- 

 able inside the ear, so that there may even be a clashing of 

 tones between the malleus and incus. 



' I did not bring this out strongly enough in the first edition of 

 Sensations of Tone, and have made it plainer in the second 

 edition, the MS. of which has just gone to Vieweg, and will 

 shortly be in the printers' hands. This unmistakably gives the 

 series of harmonic over-tones a new subjective meaning. At 

 the outset I only characterized them as the series which 

 emerges in all exactly periodic vibrations that excite persistent 

 and equal sensations. 



'(2) I believe, however, that a melody can be recognized, when 

 it is given out in weak simple tones, without evoking over-tones 

 of perceptible strength. But on the other hand, I do not believe 

 that music would ever have been discovered if the relation of 

 tones and over-tones had always been lacking, as it is in colour. 

 Pitch of tone and intervals can be remembered and recognized, 

 even where the distinguishing marks, i.e. the over-tones, which 

 give the specific distinction from the adjacent tones, and on 

 which the immediate sensory recognition of their proper value 

 rests, are wanting. Compare this with the case in which we 

 see an object that is usually red as white ... in the latter case we 



Q2 



