132 PHYSIOLOGY CHAP. 



way in which their sounds are produced ; the principal forms are 

 stringed instruments, wind instruments, and reed pipes. 



In stringed instruments the notes produced by the vibrations 

 of the strings are enormously reinforced by the resonance boxes. 

 The pitch varies with the length, tension, density, and thickness 

 of the stretched string. 



The frequency of vibration per second, on which the pitch 

 depends, is inversely proportional to the length of the string. A 

 string vibrating over its whole length gives out the deepest note ; 

 if the length is halved, the frequency of vibration is doubled, and 

 the pitch is raised an octave ; with a third of its length the 

 frequency will be three times as great, i.e. a twelfth, and so on. 



The frequency of vibration varies directly as the square root 

 of its stretching force. In order to raise by an octave the pitch 

 of the note given by the string, the tension would require to be 

 increased four times. 



The frequency of vibration varies inversely as the mass of unit- 

 lengths of the string. Thicker and heavier strings vibrate less 

 rapidly and therefore have a deeper tone. 



Wind instruments differ from stringed, since the air is here the 

 resonant body, and the walls of the pipe in which the air vibrates 

 affect only the timbre, i.e. the number and strength of the partials. 

 The pitch of the fundamental tone depends on the dimensions of 

 the pipe, and the strength of the blast of air passing through its 

 aperture. The narrower and shorter the pipe, the higher is the 

 pitch ; the greater the tension of the vibrating air molecules, the 

 more rapid are the vibrations, and the higher the frequency per 

 second. 



Keed instruments (oboe, clarinet, bassoon) only differ from 

 other wind instruments by the fact that their aperture is not 

 fixed and constant, but is formed of two vibrating tongues, which 

 rhythmically enlarge and reduce the opening by which the air 

 penetrates into the tube. According to Helmholtz the vibrations 

 of the tongues are pendular, and they can only give out simple 

 tones. The compound tones of these instruments depend on the 

 vibration of the air in the pipes ; the tongues merely regulate the 

 entrance of the air blast by rhythmically alternating the diameter 

 of the opening, which breaks up the column of air into a series of 

 rapid blasts. 



Instruments with rigid tongues must be distinguished from 

 those with soft or membranous tongues, which are represented in 

 brass instruments (trumpets, horns, etc.) by the lips of the performer. 

 In these instruments the number of the vibrations is inversely 

 proportional to the length and diameter of the vibrating membrane, 

 and directly proportional to its tension and elasticity and to the 

 strength of the air-current thrown into vibration. The width of 

 the aperture does not appear to influence the pitch of the note 



