84 The Upper Partial Tones of a Pianoforte String. [Jan. 15, 



harmonics should be audible, simply because the 8th partial would 

 thus be damped. But as they were heard in my experiments, it was 

 objected that they were created by the system of stopping with a 

 piece of felt at the exact node, which was the plan that I adopted. I 

 therefore endeavoured to find an independent mode of determining 

 what partials were present without having recourse to " resonators/' 

 against which others have raised similar objections, for if the 8th 

 partial did not exist, there could be no 8th harmonic. 



No doubt existed respecting the presence of the first four partials, 

 and the chief interest centred about those 'near to the 8th. On 

 referring to the table in my last paper, it will be seen that, when the 

 piano was tuned in the equal temperament, e", b"\>, e'" were sharper 

 than the 5th, 7th, and 10th partials would be, and /'" much flatter 

 than the 11th partial, and that g", c'", d" were very nearly of the 

 same pitch as the 6th, 8th, and 9th partials. This led me to flatten or 

 sharpen the strings of those notes on the piano to a small extent, 

 leaving the original note untouched, and taking care to damp the 

 unison strings of all the notes with the tuner's " wedges," so that 

 only one string of each note sounded. The following were the results 

 of sounding the original note simultaneously with the others in 

 succession : — 



The " beats " of untouched e" with the bass c of 1352 vibrations 

 were very rapid, but by flattening the e" slightly, the beats became 

 slow and very distinct. This unmistakably proved the existence of a 

 simple tone nearly of the pitch of this flattened e", in the compound 

 tone of c. That is, the beats established the existence of the 5th 

 partial. 



Similarly, on very slightly flattening g", the beats were quite 

 distinct, hence the existence of the 6th partial was established. 



The &"b had to be rather more flattened, but then the beats came 

 out clearly, establishing the 7th partial. And on producing the 7th 

 harmonic by touching the strings at a node, the beats were recognised 

 as precisely the same. 



The c" was flattened very slightly indeed, and while c was struck 

 loudly, this flattened c"' was struck lightly. The beats were much 

 fainter, but quite distinct and well heard by all present. The result 

 was that the existence of the 8th partial on the c string, struck at 

 one-eighth of its length by a pianoforte hammer, was fully established. 

 The reason of its existence may be the elastic nature of the hammer, 

 which necessarily affected the string on each side of the node. But 

 the important point is that, although the c string, struck at one of 

 the nodes of the 8th partial, was untouched at any other of its nodes 

 (as it was touched in three of those nodes successively in the experi- 

 ments of my last paper), the 8th partial clearly existed. The beats 

 also came out with the 8th harmonic when produced. 



