Sounding of two Notes. 425 



Another peculiarity of the beats of harmonic intervals is 

 that the two primary notes appear alternately. If at the same 

 time with the powerful C we sound c only a small fraction of 

 a vibration out of tune, so that very slow beats are formed, we 

 hear the fundamental note and the octave alternately so clearly 

 that, when c is very powerful, we should sometimes be inclined 

 to count each vibration double ; if, on the other hand, c is 

 weak, we only hear the fundamental note becoming alternately 

 stronger and weaker. I have succeeded in making precisely 

 the same observations with the very slow beats of the twelfth 

 and the double octave, C : g and : d ; but when the vibra- 

 tions are at all quick the periodical appearance of the higher 

 notes is no longer perceptible. 



These phenomena also are more easily explained by means 

 of beats of these intervals than by the supposition of resultant 

 intermediate notes which cannot be heard. In the beat of 

 the octave and the twelfth the fundamental note alone appears 

 at a, and at b the higher note is distinguishable. 



B. Intervals ivith the fundamental note c ( = 256 v. s.). 



If we form the different intervals from the unison to the 

 third octave with e ( = 256 v. s.) for the fundamental note, the 

 beats of the different periods being twice as numerous, can no 

 longer be observed with such wide intervals as were possible 

 with the fundamental note C. 



The first single audible beats change to a simple roll at the 

 second, and to a confused rattle at the third, which, after the 

 fourth, becomes feeble. Between the fifth and sixth the notes 

 form a rough clang, through which, between the sixth and 

 seventh, a more distinct roll begins to appear, which at the 

 seventh changes to single perceptible beats, and at 496 v. s. 

 (8 beats) to single computable beats, which disappear at the 

 octave c : c f . 



In the second period, c : d to c :g f , even at 584 v. s. only a 

 roughness can be perceived ; and at 608 v. s. the two notes 

 already form a completely undisturbed clang, which only at 

 704 v. s. again becomes rough, and at 720 v. s. changes to a 

 roll, that then melts into the single beats, which disappear at 

 the twelfth, eg' (1 : 3). 



In the third period, of c : g' to c : c" the last traces of the 

 roughness produced by the increasing numbers of the lower 

 beats disappear so soon as at 820 v. s. The two notes form, 

 from this point to 976 v. s., an undisturbed simultaneous sound, 

 which at 984 v. s. (20 beats, m!) become rough, and then again 

 allows the single beats to be heard, which disappear at the 

 double octave, c : c" (1 : 4). 



