Sounding of two Notes. 517 



proportionally far greater intensity than the deeper ones, 

 their beat-notes are also much more powerful than the beat- 

 notes of the same pitch which are produced by wider intervals 

 of deeper notes, and that it is therefore much easier to produce 

 very deep clearly audible beat-notes from them than from 

 deeper primary notes. 



I have stated above that the clang of c : g, even when very 

 powerful tuning-forks and resonators are used, only allows a 

 scarcely audible C (128 v. s.) to be perceived, and deeper beat- 

 notes in the lower parts of the scale I could not directly observe 

 at all ; but with high forks it is possible to produce even the 

 double C of 32 complete vibrations, which lies on the furthest 

 limits of audibility. 



The first series of tuning-forks which I made use of for this 

 experiment were tuned to notes between V" and c IV ; as, how- 

 ever, these forks only allowed the beat-notes of 40 and 36 com- 

 plete vibrations (double E and double D) to be heard as faintly 

 as possible, I constructed a second series for notes between 

 b lv and e r , which gave a proportionally far greater intensity. 

 Such powerful beat-notes are produced by the latter, that not 

 only are, for example, c and C distinctly to be heard at a con- 

 siderable distance, but also all the notes of the deep octave to 

 double C can be clearly distinguished. This latter is produced 

 by the notes 4064 and 4096 v. s., which stand in the ratio of 

 127 : 128, and form thus an interval far smaller than a comma 

 (80 : 81). 



The following Table contains all the tuning-forks which 

 form the two just mentioned series, with their ratios, and the 

 beat-notes formed from them. 



V. s. 



3840 : 



V. s. 



4096 



15: 



16 



Beats. JNote. 



128 =a 



3904 : 



j? 



61: 



64 



96 =G. 



3936 : 



?? 



123: 



128 



80 =E. 



3968 : 



?« 



31: 



32 



64 =C. 



3976 : 



jj 



497: 



512 



60 = Double B. 



3989-3; 



j? 



187: 



192 



53-3= „ A, 



4000 : 



jj 



125: 



128 



48 = „ G 



4010-7: 



j? 



47: 



48 



42-7= „ F. 



4016 : 



j? 



251: 



256 



40 = „ E. 



4024 : 



j? 



503: 



512 



36 = „ D. 



7936 : 



8192 



31: 



32 



128 =C. 



8064 : 



?? 



63: 



64 



64 =a 



8096 : 



;j 



253: 



256 



48 = Double G. 



8106-7: 



jj 



95: 



96 



42-7= „ F. 



8112 : 



jj 



507: 



512 



40 = „ E. 



8120 : 



j? 



1015: 



1024 



36 == „ D. 



8128 : 



?5 



127: 



128 



32 = „ C. 



