92 C. Barns — Combination Tones of the Siren, etc. 



and siren give a difference tone shown by the line (OP— OS) 

 of the chart. This also escaped me. 



I come now to the right half of the diagram (t> 8), in which 

 the ascending cadence of difference tones of the first order 

 (D\) has already been recognized. Here the siren, /S 7/ , is con- 

 tinually above f" and the result is a distinct descending cadence 

 of difference tones of the first order (OP/ = OP—S), due to 

 the combination of the first overtone, f'", of the organ pipe 

 and the siren. This is the continuation of the train not heard in 

 the preceding section. OD x ' is fainter than Z\, but otherwise 

 like it, finally vanishing into not very distinct beats at £=16 of 

 the abscissa. These two first orders of difference tones, as a 

 rule about equally strong, intersect above t = 12, in/*, which 

 being an octave below/ 7 '' of the organ pipe and heard together 

 with the fifth C f " of the siren, is a landmark in this region of 

 difference tones. It is upon this note, f\ that the two ascend- 

 ing and descending cadences (D\ and OjD\) chromatically con- 

 verge, thereupon again to diverge. 



But there must be another phenomenon here, namely the 

 difference tones of the third order (Z> 3 = OP/—P/ and P 3 = 

 P/ — OD/) due to the combination of the two difference tones of 

 the first order in this region. With these the difference tone (D s 

 = P-(OS- OP) and (D 3 ' = (OS-OP)-P) would completely 

 coincide. But I have only been able to recognize the third 

 order of difference tones through faint beats at t = 12, at which 

 the two steep diagonals D 3 and D % ' converge because of the 

 unison of the component notes in f. The train (OS— OP) 

 also eluded me. Finally reference to overtones* above the 

 first seemed in every way superfluous. 



Brown University, Providence, K. I. 



* The relative strength of the different cadences will clearly depend on the rela- 

 tive strengths of the fundamental and overtones. Thus with a pipe Z/the cadences 

 of the second half of the diagram came out more clearly, etc. 



