532 



Notes of Observations on Musical Beats. [June 17, 



After reed 12 the results were very uncertain. After reed 32 the 

 primes were scarcely audible, and after reed 15 they were utterly 

 inaudible. All that could be distinguished was the thumping of the 

 beats of the upper partials, and these became gradually fainter and 

 fainter, but were always audible even for reed 8. 



The mode of finding the proper forks for any partials of reeds was 

 simple, since the approximate pitch of the reed and the actual pitch of 

 the fork were known. Thus for reed 12, the 20th partial would be 

 nearly 20 x 12=240, and hence would lie between the forks 239*66 and 

 235'G9. On trial I found the beats to be respectively 2*00 and 1*96 

 (the last a mean of several counts). Then 239*66 — 20 X reed 12 = 

 2*00, and 20 x reed 12-235'69=l-96. These give 20 x reed 12 = 

 237*66 and 237*65 respectively, and consequently reed 12=11*88 

 vibrations. The ease and certainty with which the partials could thus 

 be picked out was delightful to observe. As no resonance boxes or 

 jars were used for the reeds, the objection sometimes made, that 

 such partials are created by multiple resonances within the resonance 

 cavity itself, falls to the ground, and the practical objective existence 

 of the partials is established. The practical coincidence of the values 

 of the prime from several distinct partials shows that there was no 

 error in assigning the pitch to the proper partial. In the case of the 

 four last reeds, 11, 10, 9, 8 only, where successive partials are so very 

 close, did I feel any uncertainty, and hence I have not cited these 

 results. It was for these cases extremely difficult to hear any beats 

 at all, as distinct from the beats of the partials of the single notes 

 themselves, as the partials that had to be used were very high and 

 very weak. From and after reed 32 there were no musical sounds 

 at all ; indeed, even reed 64 scarcely deserved the name of a musical 

 sound, so strong were the beats of the upper partials. 



As the coefficient of temperature for reeds is unknown, a suspicion 

 of error to a small amount attaches to all these determinations 

 of pitch, which were made at artificial temperatures varying from 

 45° to 55° F. This want of correction for temperature, and liability 

 to lose pitch from unknown circumstances, militate against the use of 

 the reed tonometer for scientific purposes, but on account of its 

 mumerous partials it is admirably adapted for many purposes which 

 the stabler tuning-fork, with its small number of available partials, 

 cannot subserve. How stable tuning-forks are, it is difficult to say. 

 The lowest and highest forks of Scheibler's tonometer do not seem to 

 have varied, by so much as the twentieth of a vibration since 1837, 

 judging by my own measurements and by Professor McLeod's 

 measurements of a fork in absolute union with the highest. A good 

 fork, marked 438 simple vibrations (that is, 219 double vibrations) in 

 Scheibler's own handwriting, probably about fifty years ago, is now 

 considerably rusty, but I measure it as 218*77 double vibrations, 



