432 Dr. R. Konig on the Simultaneous 



the secondary beats sound in conjunction with the loud rattle 

 of the primary beats somewhat in the manner that I have de- 

 scribed above in the simultaneous sounding of 80 : 144 v. s. 

 At G :e, however, where the rattle of the primary beats is 

 already much weaker, it disappears before the secondary beats ; 

 and the same thing occurs at the fifth c : g. 



In the intervals with the fundamental note e, the whole system 

 of secondary beats can be very fully observed. The beats of 

 the unison of the beat-notes can not only be numerously and 

 clearly heard in the intervals 2 : 3, where they can be followed 

 till they change to a rattle of from 12 to 16, at 2 : 5, 2 : 7, and 

 even at 2 : 9 to the number of about 4, but also in the octave 

 formed by m and m! at 3 : 4, 3 : 5 to about 6 or 8, at 3 : 7 and 

 3 : 8 (the former weaker than the latter) to about 4, and at 

 3 : 1 1 in the third period to 3 or 4. The beats of the twelfth 

 of in and mf are only perceptible in the first period at the in- 

 tervals 4 : 5 and 4:7, and can only be followed to about 3 

 or 4. 



In the intervals with the fundamental note c' the vibrations 

 of my tuning-forks are somewhat less favourable than in those 

 just mentioned with the fundamental note c. Consequently the 

 secondary beats at the unison of the beat-notes m and mf in the 

 first three periods were really quite distinctly audible in the 

 intervals 2 : 3, 2 : 5, and 2:7; and when they formed together 

 the octave, in the first period only, at 3 : 4 and 3:5. 



In the first period of the interval with the fundamental note c", 

 the secondary beats can be perceived in all intervals in which 

 the beat-notes stand in the ratio of 1 : 1, 1 : 2, and 1 : 3 to one 

 another ; in the second period, however, only a few distinct 

 beats at 2 : 5 and some very weak ones at 3 : 7 can be dis- 

 tinguished. 



Intervals with the fundamental note c" f are formed in the 

 first period by a powerful tuning-fork for the fundamental note, 

 and weaker forks for the upper notes. Here the secondary beats 

 are only heard clearly at 2 : 3, and further at 3 : 4 and 3 : 5. 

 Above the octave, however, with the powerful forks of the 

 octave c IV to c v , the beats of the beat-notes are heard not only 

 at 2 : 5 and 2 : 7 and at 3 : 8, but even at 4 : 9. 



Experiments on all these intervals formed from very high 

 notes are already very fatiguing to the ear ; and this is still 

 more the case in the intervals of the octave of c ly to c v . I 

 succeeded, however, in distinguishing besides the secondary 

 beats of the fifth, and the fourth and sixth, also those of the 

 third and of the ratio 4:7. The extraordinary intensity of 

 the notes of my forks for this octave proved itself especially 

 valuable in the intervals 8 : 11 and 8 : 13. 



