62 Scientific Proceedings, Royal Dublin Society. 



identically the same tones as the key of A b on the other, their 

 artistic effects will he wholly different. Nor does this variety of 

 effect depend on tempering, for it is present on pianos carefully 

 tuned on- the system of equal temperament, where all the semi- 

 tones are alike, and it continues to be equally perceived by the ear 

 on pianos tuned with all the little deviations from this system of 

 temperament which are common in practice. We are thus driven 

 to attribute it to some inherent difference of effect of the black 

 notes and the white notes on the piano. Helmholtz suggested this 

 as the direction in which the explanation must be sought, and by 

 making that suggestion he furnished the key to the solution, which, 

 however, he does not himself pursue farther. 



Each note of the piano is a complex tone. In addition to the 

 fundamental tone, it contains its octave, its twelfth, and its double 

 octave, but these harmonics are present in proportions which differ 

 somewhat according to the strength with which the note is struck. 

 Hence the quality of the note is subject to a slight variation ac- 

 cording as it is struck firmly or gently. In the first case the tone 

 is of a richer quality ; in the second case it is softer, i. e. it contains 

 a less proportion of the higher harmonics. Now upon the pianos 

 upon which I have experimented there was a very slight, but still 

 perceptible, difference in intensity with its accompanying difference 

 in quality, when the regulated impact of a mechanical apparatus 

 was alternately delivered upon a white and on an adjoining black 

 note. This difference appears to me to be somewhat greater when 

 the two notes are struck successively by the same finger with what 

 is judged to be the same force, and as nearly as possible in the 

 same way. And the difference becomes conspicuous when the 

 black note is struck from the more horizontal and extended posi- 

 tion which the fingers that reach the black notes necessarily assume 

 in the ordinary course of playing. The black notes will then give 

 out a tone which is sensibly gentler, less rich, and softer, when the 

 performer seems to himself to he exerting the same force on them and 

 on the white notes. So far the effect is to be attributed chiefly to 

 the positions of the fingers, and in small degree to the different 

 sizes and proportions of the levers in the piano which terminate in 

 the black and white notes respectively. Helmholtz suggests that 

 the narrowness of the black notes may have some influence, but I 

 have not been able to refer any part of the observed effect to this 



