of Consonances of the Form h : 1. 431 



41. When beginning the regular course of experiments 

 according to the general outline of Konig's work, I was 

 careful, in the first instance, to examine the various masses of 

 sound presented, with resonators arranged as above indicated. 

 In examining, for instance, the intervals made by the note C 

 with the various notes of the octave above it (up to c), I first 

 fixed the resonator at some one pitch, and then ran the mo- 

 vable note up through the octave. Then, as this did not seem 

 a good process for analysis, I set the mistuned octave beating, 

 or any other combination it was desired to examine, and ran 

 the pitch of the resonator up and down with water to see if 

 any thing could be detected. And here I came across an ob- 

 servation that puzzled me for some time. 



42. Suppose the mistuned octave C : c was sounding, and 

 I examined the lower note with the resonator: sometimes it 

 appeared loud and steady, at other times as if beating power- 

 fully. On removing the resonator-attachment from the ear, 

 the lower note was always heard to beat powerfully. The 

 explanation was simple. When the nipples of the resonator- 

 attachment fitted tightly into the ears, nothing reached the 

 ear but the uniform vibrations of the resonator sounding C. 

 But if there was the slightest looseness between the nipple 

 and the passage of either ear, the second note (c) of the com- 

 bination got in, and gave rise to the subjective difference- 

 tone (first beat-note of Konig), by interference of which with 

 the C I explain the beats on that note. These beats are there- 

 fore subjective. 



43. A considerable number of combinations, including ex- 

 amples of the principal forms of beat, rattle, or roll, were 

 examined in this way; and when the precautions above indi- 

 cated were attended to, the results were in all cases to nega- 

 tive the objective existence of all forms of beats, and beat-notes 

 or difference-tones, except the beats which arise from the 

 interference of approximate unisons, which beats arise from 

 both notes acting on the resonator simultaneously. This of 

 course includes the beats produced by objective harmonics. 



Course of General Experiments. 



44. The following is the detailed examination of the com- 

 binations of the note C, made in a continuous and connected 

 manner. The results have a general correspondence with 

 those of Konig. The numerous rattles and rolls of beats men- 

 tioned were not further analyzed for the most part: the ana- 

 lysis of these is very difficult; and, as has been already stated, 

 a separate investigation is required in every such case. Some 

 attention was devoted to beats of the mistuned fifth, both in 



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