246 



NATURE 



[May 8, 1913 



PIANOFORTE TOUCH. 

 \,A THEN the editor of Poptdar Mechanics 

 * * submitted a list of modern inventions to 

 a referendum to select the " seven principal 

 wonders of the modern world," the piano-player 

 and player-piano were conspicuous by their absence 

 from the long collection, although they possess 

 quite as many features of scientific interest as 

 many of the inventions actually submitted. 

 These mechanisms have, moreover, failed, for 

 some not very obvious reason, to form the subject 

 of discussion in scientific and technical journals 

 where frequent mention is made of such pro- 

 prietary inventions as motor cars, gramophones, 

 kinematographs and the like. Yet a number of 

 subjects for scientific discussion may be 

 suggested in connection with piano-players. 

 The psychologist, for example, will notice that 

 after a very little experience the performer does 

 not consciously move his regulator to play faster 

 or slower ; but he unconsciously plays the notes 

 at the exact instants that he thinks of them quite 

 as much as if he were striking the keys with his 

 fingers. 



The attempt to compare pneumatic playing 

 with finger playing in the matter of "touch" lands 

 us in a very difficult problem of dynamical 

 acoustics which has not received so much atten- 

 tion as it deserves from physicists. We are told 

 that the piano-player cannot reproduce the clear 

 sinking pianissimo of the finger pianist, that there 

 is a certain element wanting which only the human 

 fingers can supply. What is this element? A 

 piano-player can be played as softly or as loud 

 as is desired, it allows full use of the pedals, and 

 a slight jerk of the time lever enables the performer 

 to " linger on a note " as well as an ordinary 

 pianist. But still, we are told, the "touch" is 

 not the same, and if a few notes are played from 

 the music roll and then played with fingers, a 

 certain difference in the quality of the tone often 

 appears noticeable. 



Now the quality of a note, apart from its actual 

 loudness, depends on the relative intensity of the 

 fundamental tone and its several harmonics, and 

 we are thus led to inquire into the question how 

 far the harmonics of a pianoforte note are capable 

 of being intensified or reduced independently of 

 the fundamental tone. 



It is obvious that great differences in quality 

 are produced by the use of the loud pedal, and 

 the old-fashioned soft pedal which shifted the 

 hammer off one of the strings and caused a softer 

 part of the hammer to strike the others had an 

 equal effect ; moreover, the singing qualities and 

 delicate harmonics are quite destroyed by shutting 

 up a piano and covering it with ornaments. But 

 even when other conditions are kept constant, 

 differences are noticeable according to whether 

 the same note is struck with a sharp blow or a 

 heavy pressure, and we are thus led to the im- 

 portant question : Are the intensities of the funda- 

 mental tone and its harmonics functions of one 

 variable only, or are they functions of two or 

 more variables? 



NO. 2271, VOL. 91] 



Now upon this point 1 rind that a great dis- 

 agreement of opinion exists. Man)' piano-makers 

 in this country hold to the single-variable hypo- 

 thesis on the ground that when the hammer is 

 striking the strings it is disconnected from the 

 keys; if this were not the case the note would 

 be "blocked." On this hypothesis the striking 

 velocity of the hammer constitutes the single 

 independent variable. The single-variable theory 

 is not inconsistent with the possibility that the 

 character of a note may vary according to its 

 loudness ; this only requires that the intensities 

 of the various components shall be different func- 

 tions of the same variable instead of being 

 multiples of the same function. 



Other people will tell us that if it were possible 

 to produce differences in the quality of. a piano- 

 forte note, they would be too small to be 

 appreciable. 



In Germanv, on the other hand, I am informed 

 that great importance is attached by teachers of 

 the pianoforte to differences in the manner of 

 applying pressure to the keys. During the small 

 interval of time that the key is being depressed, 

 this pressure is an arbitrary function of the time, 

 or, if preferred, of the displacement, the form of 

 the function depending on the action of the fingers 

 and in particular on their elasticity, and the 

 German method distinctly assumes the existence 

 of a relationship between the form of this function 

 and the quality of the note sounded. 



Neither Helmholtz's nor Kaufmann's theories 

 afford an explanation of the " two-variable " hypo- 

 thesis. I believe other papers have been published 

 dealing with this question, both experimentally 

 and theoretically, and I hope the present article 

 will be the means of eliciting information on the 

 subject. It is evident that such investigations 

 have not become widely known among physicists. 

 From the point of view of applied mathematics, 

 the difficulty of the problem consists in finding 

 fundamental assumptions which lead to the desired 

 conclusions, and are at the same time con- 

 sistent with the structural conditions as they exist 

 in the pianoforte. Two possible explanations 

 suggest themselves : — 



1. Although the hammer is at a slight distance 

 from the wires in its position of equilibrium, it 

 may still be acted on by some impressed force 

 while touching the string, owing to the elasticity 

 of the connections. 



2. The stem of the hammer is flexible and 

 capable of independent vibration, so that the cir- 

 cumstances of the impact may depend on the 

 bending set up in projecting the hammer. 



I am now investigating the equations of motion 

 based on these two alternative assumptions, but 

 the problem is a very difficult one, and it seems 

 desirable to obtain further experimental evidence 

 before any final conclusions can be reached. 



For some time past I have obtained results with 

 a piano-player which exhibit conspicuous dis- 

 crepancies from what one would expect on the 

 single-variable theory, and a good deal of care 

 has been exercised in ascertaining that these effects 



