516 Dr. R. Konig on the Simultaneous 



sliding weights in front of large suitable sounding-boxes open 

 at both ends, the rattle of the third was still more powerful, 

 and that of the fifth also much louder. The 64 beats of the 

 third c' \ cf, which with the tuning-forks and resonators only 

 allow a mere roughness to be heard, changed by means 

 of the tuning-forks on sounding-boxes to a positive rattle ; 

 and even the fifth cf : g f allowed a trace of the roughness pro- 

 duced by 128 boats to be heard. 



"When a note is produced in a closed space, it is well known 

 that, by the combination of the direct sound-waves and those 

 that reverberate from the walls, nodes and ventral segments are 

 formed. In very loud simple notes, of which the sound-waves 

 are tolerably long, the difference of intensity at these different 

 points is so remarkable that in the above-mentioned experi- 

 ments, in which it is above all necessary that the ear should 

 receive both notes very strongly, we must be careful to place 

 it for both notes at the same node. The ear must there- 

 fore be placed in the best position for one note, and then the 

 other fork moved away till its note also is heard with the 

 greatest intensity. The higher we go in the scale, the easier 

 it is to produce very powerful piercing notes ; and while the 

 interval of the fifth cf : g r , which with ordinarily powerful 

 notes allows no trace of roughness to be perceived, must be 

 produced by notes more powerful than can be found in any 

 musical instrument in order that its 128 beats may be per- 

 ceived, for the notes V" \ c IV the reeds of a harmonium suffice 

 to make the same number of beats audible. 



Helmholtz, who states this last fact, lays, in order to 

 explain it, particular weight upon the smallness of the in- 

 terval (Tonempfind. p. 263); but, as will be seen from the 

 above-mentioned experiments with deep and very powerful 

 notes, it is only necessary to make use of primary notes of 

 sufficient intensity in order to obtain the same phenomenon 

 with much greater intervals, while on the other hand, again, 

 with sufficiently faint high notes very small intervals may be 

 formed which do not allow it to be perceived. 



As the small intervals of higher notes, with regard to the 

 audibility of the single beats, cannot be distinguished from 

 wider intervals of sufficiently powerful deeper notes which 

 are separated from one another by an equal absolute number 

 of vibrations, so also they show no difference in the manner 

 in which beat-notes are formed. Two tuning-forks, h" f , c IV 

 (15 : 16), with a tolerably intense rattle of 128 beats, allow 

 the note c to be heard, just as with the very powerful notes cf 

 and g'\ besides the roughness a faint c is perceived ; but it 

 must be observed that, as these high primary notes possess a 



