1880.] 



Notes of Observations on Musical Beats. 



531 



forms of dissidences which should beat 4 in a second have also been 

 investigated : Fifth 3 : 2, Fourth 4 : 3, Major Third 5 : 4, Minor Third 

 6 : 5, Major Sixth 5 : 3, Sub-Fifth 7 : 5, Super-Fourth 10 : 7, Super- 

 major Third 9 : 7, Sub-minor Sixth 14 : 9, Sub-minor Third 7 : 6, 

 Super-major Sixth 12 : 7, Sub-minor or Harmonic Seventh 7 : 4, Super- 

 major Second 8 : 7, Major Tone 9 : 8, Minor Tone 10 : 9, Small Major 

 Seventh 9: 5, and Diatomic Semitone 16:15. The latter was most 

 difficult, on account of the great roughness of the intervening beats, 

 and succeeded best in the highest case, reeds 480 and 512. The Major 

 Sevenths 16 : 9 and 15 : 8, however, baffled me, from the excessive 

 roughness of the other beats. I have frequently shown these effects to 

 others, and as the instruments are accessible at the South Kensington 

 Museum, they can easily be repeated.* 



In counting the beats of the reeds with forks, I was unable to use 

 the octaves of the forks, as they were entirely drowned by the primes 

 of the reeds, and hence above reed 440 I was obliged to use other forks 

 which had been previously counted with the octaves of Scheibler's 

 forks; but below reed 220 I always counted by the partials of the 

 reeds. By this means I was able to determine the pitch as far as 12 

 vib. in a sec, with tolerable certainty. Occasionally I determined the 

 pitch of a single reed by means of several partials, beating, of course, 

 with the primes of different forks. The following table gives the 

 nominal numbers of some of these low reeds, with the partials used, 

 the mean pitch determined, and the decimals of a vibration determined 

 from the different partials, showing the close agreement of the several 

 determinations. 



Nominal 

 number 



of vi- 

 brations. 



Mean number 

 of vibrations in 



Partials used, of 



Decimals of the numbers of 

 vibrations of the prime as 

 calculated from the pitch 

 of the partials. 



the prime by 

 Scheibler's 

 forks. 



which the pitch was 

 determined. 



88 



87-34 



3, 4, 5 



•34, -33, 36 



72 



71-46 



4, 5, 6 



•45, -45, '47 



64 



6352 



4, 5, 6 



•52, -52, -53 



48 



4768 



5, 6, 7, 8, 9 



•67, -68, -67, -69, '71 



40 



39-92 



6, 7, 8, 9, 10, 11 



•91, -93, -90, -92, -93, "93 

 •73, -73, -73, -735, -745, -74 



36 



35-74 



7, 8, 9, 10, 11, 12 



32 



31-47 



7, 8, 8, 9, 10, 11, 12, 13 



•47, -48, -46, -47, "49, '45, 

 • -47, -45 



23 



22-88 



13, 19 



•88, -88 



16 



15-94 



25, 27, 25 



•94, -94, -92 



13 • 



12-90 



20, 25 



•89, 91 



12 



11-90 



20, 28 



•88, -91 



* Since this paper was sent in to the Eoyal Society, I have handed to the Secre- 

 tary of the Science and Art Department for the use of the South Kensington 

 Museum, a detailed account of the method of making these experiments, with tables 

 showing how to bring the proper reeds into action. — June 15, 1880. 



VOL. XXX. 2 P 



