On the Beats of Mistimed Consonances. 69 



self. For Mr. Bosanquefs sake I regret that the tone of his 

 letter leaves me no alternative but to produce the evidence 

 upon which I deliberately assigned priority to Dr. Konig. 



Mr. Bosanquet appears to have read Konig's papers ; for he 

 savs he " knew " them " intimately/' and that " there was no 

 vestige of guidance in them on the subject ;" that " Konig 

 never analyzed his beats, and never enunciated any opinion 

 whatever as to the notes of whose variation the beats consist, 

 except in the one case of the octave .... where he says that 

 fundamental and octave are heard alternately." 



There lie before me at this moment the Annalen of Poggen- 

 dorff for the year 1876 (Bd. clvii.) It is true that Konig 

 states therein that the two primaries are alternately heard ; 

 but that he traced this alternation to its true cause is shown 

 bv the very paragraph in which this statement occurs. I quote 

 from p. 188 of the volume of the Annalen, italicizing the words 

 which Mr. Bosanquet appears to have overlooked when he savs 

 that Konig did not analyze or enunciate any opinion, and that 

 Konig only touched the case of the octave. 



" Erne Eigenthiiinlichkeit der Stosse harmonischer Intervalle 

 besteht noch darin, das die beiden prirnaren Tone abwechselnd her- 

 vortreten. Lasst man neben dem starken, grossen C das nur urn 

 einen geringen Theil einer Schwingung verstimmte kleine c ertb'nen, 

 so dass sich sehr langsame Stosse bilden, so hort man abwechselnd 

 einmal den Grimdton und einmal die Octave so deutlich herror- 

 treten, dass man, wenn das kleine c sebr stark ist, mitunter geneigt 

 sevn konnte, jede Schwebung doppelt zu zahlen. Ist das Tcleme e 

 dag eg en schv:ac~h, so hbrt -man nur den Grimdton abweehselnd starker 

 und schwacher iverden. Granz dieselbe Beobachtung habe ich auch 

 bei den sehr langsamen Stossen der Duodecimo, und der Doppdoctave, 

 C: g und O : c' machen ko'nnen, aber bei nur einigermassen schnellen 

 Schwebungen lasst sich das periodische Hervortreten des hoheren 

 Tones nieht mehr wahrnebmen." 



It is the more remarkable that Konig' s insight into the 

 cause of the alternation mentioned in the first sentence of the 

 paragraph quoted above should have escaped Mr. Bosanquet's 

 notice, since three months before the publication of Mr. Bosan- 

 quet's paper in the Philosophical Magazine Konig had pub- 

 lished another very important paper in Wiedemann's Annalen 

 (Bd. xii. 1881, p. 337), in which the results of a reexamina- 

 tian of the very point in question are most unequivocally laid 

 down. I quote the passage from p. 311, again italicizing the 

 important words. 



" Eegulirt man ferner die Intensitat der beiden Tone eines alte- 

 rirten harmonischen Intervalls in der AVeise, dass die Stosse am 

 deutlicbsienhervortreten, so miissten, wenn sie durch den hdheren 

 primaren Ton und einen im Obre erzeugten harmonischen Oberton 



