of Consonances of the Form h : 1. 427 



Some of these are probably due to the imagination; others 

 probably exist in small intensity. And I am satisfied that 

 there still exists a large field of work in the farther prosecu- 

 tion of this subject. But of the main result I have no doubt 

 whatever; and that is: — 



24. The beats of mistimed consonances of the form h : 1, 

 where h is nearly some whole number, consist mainly of vari- 

 ations of intensity of the lower note when the beats of the 

 harmonics are eliminated. 



25. I was prepared for this result in the case of the octave 

 by my preliminary experiments (Phil. Mag. viii. p. 293), 

 but did not proceed further till I had verified it and got my 

 ear to perceive it readily under the new conditions, which 

 required two or three days. I then got Mr. Parratt to come 

 and listen. He was much disturbed by the trifling noises 

 from the engine, belts, &c; and I blew the bellows myself for 

 a time. Eventually he came to the same conclusion, but 

 with an amount of hesitation and difficulty which showed me 

 what an important element practice is in these observations. 



26. I then started these observations with the mistuned 

 twelfth, proceeding in the same way. I seemed to have the 

 same difficulty as before in seizing the phenomenon; and when 

 I eventually decided that these beats were also on the lower note, 

 it was not in pursuance of any preconceived conclusion; for 

 1 had no idea at that time of the explanation I now give, and 

 certainly none of the presence of the second difference-tone, 

 or its identity with one of Konig's beat-notes. 



27. Having got so far, I found the remaining verifica- 

 tion, of the beats of the mistuned double octave, somewhat 

 easier. These are also on the lower note when they are 

 heard. I have never heard the beats of a mistuned conso- 

 nance with any wider interval, with the notes I employ, as clear 

 and unmistakable phenomena. Such beats may be discern- 

 ible by more acute ears, or with notes of a more powerful 

 quality, as they were discerned by Konig. But in such cases 

 it will be incumbent on the observer to purge the beats from 

 the suspicion of containing the beats of harmonics, as I have 

 done. 



28. Mr. Parratt subsequently convinced himself, as before, 

 that the beats of the twelfth and double octave were all heard 

 on the lower notes. I endeavoured, as far as possible, to make 

 his observations independent by avoiding communicating my 

 conclusions to him beforehand. 



29. The elimination of the beats of the harmonics depends 

 on the following considerations. The notes employed were 

 examined, with and without resonators, as to the presence of 

 harmonics. These, so far as they are objective, are readily 



