430 Dr. R. Konig on the Simultaneous 



n 



m is much greater than -, and the coexistence of m and mf is 



observable when m approaches -. For example, c IV : d iy (8 : 9) 



z 



only allows m=l = 6 / to be heard; c IV : b™ (8:15) only 

 m' = l = c' ; and at c IV : 6656 v. s. (8:13) both m = 5=e'" and 

 mf =.?>=g ff are to be heard. 



II. Secondary Beats and Beat-notes. 



In the foregoing section I have endeavoured to describe 

 connectedly the operations of the upper and lower beats, as 

 they appear in the different intervals when these are formed, 

 first from the deepest notes, then from higher and higher up 

 to highest, and so as not to disturb their connexion. There 

 yet remains a class of phenomena which I will now describe. 



We have seen above that in the clang of the two notes 80 

 and 148 v. s., the roll of the 34 lower beats m, and the single 

 audible 6 upper beats m' can be separately heard, that in the 

 neighbourhood of the fifth C:Ga strong confused rattle is 

 caused by the coexistence of these two kinds of beats, and 

 that finally in the high octaves, as also in the intervals 



n : hn + m, if m approaches to -, both the beat-notes m and 



a 



mf can be observed together. These two beat-notes, which 

 appear side by side, are in the same relation to each other as 

 would be the case with two equal primary notes of the same 

 intensity : i. e. if they are near the unison they allow strong 

 beats to be heard ; if they form almost the interval of an oc- 

 tave they also produce beats, which, however, are weaker ; and 

 in the same way their broken twelfth will also allow beats 

 to be heard. 



In the intervals n :hn + m the two beat-notes m and mf are 



in unison if m = -, therefore in the intervals 2 : 3, 2 : 5, 2 : 7. 



Z 



If, however, m=-+l, then n— m — -— 1, and we obtain 



Z "Z 



two beats. 



The upper beat-note mf is the higher octave of the lower 



beat-note m if w=o> & n d therefore in the intervals 3:4, 3:7.... 

 o 



If, however, m — -+l, then n— m= — — 1, and we obtain 

 o o 



(-— + 2 ) — (-15 — 1 )> ••?• three beats. 



The lower beat-note is the higher octave of the upper beat- 



