HEARING 407 



The quality of a musical note depends upon the number 

 and relative loudness of its overtones. When several notes 

 are sounded simultaneously, they blend into a chord or har- 

 mony, provided the intervals which separate them are equal 

 to the intervals which separate the simpler overtones. Each 

 of the notes yields overtones. The tones blend into a concord. 

 Their partials are in unison. The variations in air-pressure 

 of the compound tone are strictly periodic. If the ratios of 

 the frequencies of its constituent notes are simple the product 

 is a rich, full sound, such as a common chord. 



At least one other character of the pulsations of sound must 

 be taken into consideration if we wish to picture the nature 

 of the force to which the ear responds. Tones which reach it 

 from several instruments simultaneously are not necessarily in 

 unison, or even in harmony. The overtones of a single note 

 sounded on a piano or violin the statement does not hold 

 good for bells, nor is it strictly true of flutes or horns must 

 necessarily bear a simple proportional relation to their prime 

 tone. They divide the grand pulsation into fractions " with- 

 out a remainder." But the vibrations of two tuning-forks 

 which are slightly out of unison interfere one with the other at 

 regular intervals. They produce " beats." Everyone is familiar 

 with the curious effect which is produced upon the eye when 

 one row of railings is seen through another, or one expanse of 

 wire-netting behind another. Sets of lines which occupy 

 nearly the same positions in the line of sight combine to make 

 a large pattern, which overlies the smaller pattern of the rails 

 or netting. The same thing happens with sounds which coin- 

 cide at considerable intervals, although in the case of sounds 

 interference is as marked as reinforcement. If whilst a tuning- 

 fork yielding 101 vibrations per second is singing another of 100 

 vibrations is brought into play, the vibrations of the second 

 fork are superposed on those of the first. At a certain moment 

 the forward movement of molecules of air induced by the first 

 fork is reinforced by a forward push from the second. But 

 half a second after this coincidence of phase an opposite result is 

 produced 50 1 vibrations of No. 1 have passed, but only 50 of 

 No. 2. No. 2 is going backwards (inwards), whilst No. 1 is 

 moving forwards (outwards). The same molecules are im- 

 pelled backwards by No. 2 and forwards by No. 1. The result 



