Sounding of two Notes. 433 



As I have already stated, the simultaneous sound of 4096 

 (c IV ) and 5632 v. a. (8:11) allows m = 768 beats {g") and 



m 



/ 



1280 beats (e' f/ ) to be distinctly heard, besides which a 

 quite distinct c", which is =512 v. d., that is, =1280 — 768 

 v. d., may be perceived ; and the same result is obtained by a 

 simultaneous sound of 4096 and 6656 v. s. (8 : 13) when 

 m = 1280 and??/ = 768 beats. The note c" may also be clearly 

 perceived here ; so that the secondary beats, if their number 

 and strength are sufficient, melt into one note like the primary 

 beats. 



I only observed the secondary beat-notes in these two cases ; 

 but there they were quite clear and distinct. In the deeper 

 octave, where the same intervals produce the distinctly audi- 

 ble beat-notes g f and e // , the latter, in consequence of the 

 greater weakness of the primary notes, does not allow the c', 

 which ought to be there, to be heard. 



With regard to the general observation of the secondary 

 beats, it may be remarked that the weaker they are, the less 

 must they exceed a certain number if they are to be clearly 

 distinguished ; it must not, therefore, be forgotten when the 

 higher primary note is put out of tune in order to bring them 

 out, that if this note is put out of tune by one double vibra- 

 tion, 2, 3, or 4 secondary beats are produced. In the inter- 

 val c : e for instance, therefore, the latter note must only be put 

 out of tune by one double vibration at the outside if the se- 

 condary beats are to be clearly perceptible ; otherwise nothing 

 more is heard of them ; at least when I have struck these 

 notes together I have never distinguished more than four. At 

 the simultaneous sound of c iy and e IY the secondary beats are 

 also most distinctly heard when they are about four in num- 

 ber. My e iy fork weighs about 560 grammes; and even a little 

 lump of wax weighing about a decigramme attached to the 

 end of one of its prongs puts it out of tune to the extent of 



double vibration, and thereby allows the four secondary 

 beats to be heard. From this example we may see how 

 easily it may often happen that the secondary beats cannot be 

 perceived merely because the interval of the two primary 

 notes is too much out of tune. 



I have already remarked, while on the subject of pure har- 

 monic intervals, that until now all beats of wider intervals 

 have been traced back to the beats of two notes near the uni- 

 son. It was supposed that the first difference note of the 

 primary notes again produced difference notes with these pri- 

 nary notes, that these produced others with the primary notes 

 wid the first difference note, and so it was continued until two 

 of the notes near the unison were reached, which would then 



Phil. Mag. S. 5. Vol. 1. No. 6. June 1876. 2 G 



