490 



HEARING, VOICE AND SPEECH 



tion during the period. The more frequent the vibrations in a unit of time 

 i. e., the shorter the period the higher is the tone. 



For an exposition of the fundamental facts of this subject it is very con- 

 venient to have a special apparatus, like the siren (Fig. 193), which permits 

 an easy determination of the number of atmospheric vibrations producing 

 different tones. 



A is a thin disk of pasteboard or metal which is provided with holes in 

 several concentric rows and at equal distances from each other in the same row. 

 It can be set in rapid rotation by means of the string f which runs over the 

 pulley fc. By means of the tube c a blast of air of proper strength is directed 

 toward one of the rows of holes. Each hole therefore as it passes the mouth of 

 the tube lets out a single puff of air and thus when the disk is rotated rapidly 

 enough a tone is produced whose pitch depends upon the number of holes 



blown through in a second of time. 

 This number can be found by count- 

 ing the rotations. 



Now experiment has shown that 

 pitch is entirely independent of the 

 size of the holes or the strength of 

 the blast and thus it is proved that 

 pitch depends only on the number 

 of vibrations. 



The nearer the row of holes to 

 the center of the disk i. e., the 

 smaller the number blown through 



in a single rotation the lower will be the tone, the rate of rotation remaining 

 the same. If one row with 8 and another with 16 be employed the tone pro- 

 duced by the latter is the octave of that produced by the former i. e., the 

 tone which constitutes the higher octave of the other contains within a given 

 time exactly twice as many vibrations as the other, and the ratio of the two 

 is as 1 : 2. 



In the same way the following ratios have been found to obtain between 

 the number of vibrations of the different tones used in music : 1 : 2 = octave ; 

 2 : 3 = a fifth ; 3 : 4 = a fourth ; 4 : 5 = major third ; 5:6= minor third ; 

 5:8=: minor sixth ; 3 : 5 = major sixth. These are all consonant intervals 

 i. e., in the octave every second vibration of the upper note begins at the 

 same time with one of the lower; in the fifth, every third; in the fourth, 

 every fourth, etc. 



There is an upper and a lower limit to the frequency of periodic vibrations 

 capable of exciting the auditory organ. 



The smallest number per second which can be heard by the human ear is 

 given by Preyer as 15-24, by Helmholtz as 28, by Bezold using highly improved 

 experimental methods as 11 ; but sounds only begin to acquire a definite musical 

 pitch at about 40 vibrations per second. The highest number which can be 

 heard as a distinct sound according to Edelmann is in the neighborhood of 50,000. 

 The whole range of perceptible sounds (11-50,000) amounts therefore in the 

 most favorable case to over 12 octaves. In music only about 7 octaves (40-4,700 

 vibrations) are used. 



FIG. 193. Seebeck's siren. 



