2 PROCEEDINGS OF THE AMERICAN ACADEMY 



was provided with a circle of holes near the circumference, hetween 

 a vibrating tuning-fork and a resonator, the number of beats per 

 second being of course greater as the speed of the disk was greater. 

 Hence the sound-wave reaching the ear was not at all a compound 

 wave due to the superposition on one another of two simple sound- 

 waves slightly differing in length, as in ordinary beats, but merely 

 a series of simple waves with gaps, as it were; while the passage 

 from maximum to minimum intensity in the sound reaching the 

 ear was very different in its character from that actually occurring 

 with ordinary beats. In referring to such beats as those studied 

 by Mayer, we shall for the sake of brevity designate them as " in- 

 terruptional beats," and the ordinary beats we shall call "inter- 

 ference beats." 



We have thought it desirable to ascertain what results would be 

 reached in different registers with interference beats, such as are 

 present in actual dissonances. It was of course necessary to em- 

 ploy simple tones. Our method was a direct one, viz. to produce 

 two such tones simultaneously, and to vary the pitch of one of these 

 by known amounts, estimating by the ear when the sound became 

 the harshest. 



As a source of sound we employed the cylindrical resonators of 

 Koenig, which were sounded by gently blowing across the opening 

 a stream of air from the brass, slit-shaped "universal embouchure " 

 made by the same maker. We found these tones to be very pure 

 and loud, while their pitch could be varied with great readiness 

 without altering the intensity of the sound emitted. The set of 

 resonators employed ranged from Solx to Ml h , the ranges of succes- 

 sive resonators overlapping slightly. The two embouchures were 

 connected to a Y by rubber tubes, and placed on adjustable sup- 

 ports in suitable relation to the apertures of the two resonators to 

 be sounded. The strength of the blast was regulated by a stopcock, 

 and the bore of each rubber tube could be closed more or less by a 

 clamp, so that the force of the jet of air at each resonator could be 

 adjusted with all needed delicacy. Thus the intensity of the notes 

 given out by the two resonators could be adjusted so that they were 

 exactly equal in loudness. This was done by causing the tones to 

 beat slowly, and so adjusting the apparatus that there was ap- 

 parently an absolute silence when the sound fell to its minimum 

 intensity. No difficulty was found from any whirring of the sheet 

 of air as it struck the edges of the aperture, since by proper adjust- 

 ment this could be made quite inappreciable. Having once made 



