THE SENSK OF HEARING 



225 



To produce the highest tones, the opening ol' (lie cylinder /' must lie 

 brought near the mouth of the pipe /,' by means of the micrometer snv\\ /,', 

 which is empirically graduated. 



To obtain uniform sounds, it is nei vs>ary to employ an air-current of 

 constant intensity. For this purpose a bellows, or better still a blast of 

 constant pressure, must be used. 



Just as the scale of perceptible tones is circumscribed within 

 a minimum and maximum number of vibrations in the time-unit, 

 so the capacity of the ear for distinguishing 

 the difference between two notes of different 

 pitch is also limited. It is only when the 

 difference between two tones exceeds a 

 certain minimum that we are capable of 

 distinguishing them as different in pitch. 



After a few experiments by Delezenne 

 (1825) and Seebeck (1846), Preyer (1876) 

 was the first to solve the problem of the 

 liminal threshold of tone-discrimination by 

 a number of systematic researches with a 

 set of metal tongues. He was able to prove 

 that a trained musical ear is capable of dis- 

 tinguishing between two tones of 500 and 

 500-3 vibrations, or of 1000 and 1000'5 

 vil irations ; while two tones that differ by 

 0'2 vibrations only cannot be distinguished 

 with any certainty. Luft (1888) confirmed 

 Preyer's results by a series of tuning-forks 

 with resonators. In the lowest tones the 

 discriminative capacity is less, even for the 

 trained ear. Preyer observed that below 40 

 vibrations it is not easy to distinguish two 

 tones that vary by one whole vibration ; 

 Luft found the threshold of difference for 

 very low tones to be 044 vibrations. 

 Persons who are untrained make errors of 

 several vibrations in estimating the differ- 

 ence between very low notes. 



Generally speaking, it may be said that the mean power of 

 discrimination of pitch is much lower than the recognised 

 optimum. Stumpf (1889) found that many people are unable to 

 say which of two tones is the higher, even when they differ by an 

 interval of a third, a fourth, or even a fifth. 



It is very doubtful whether the limit of capacity for perceiv- 

 ing the difference between two tones follows Weber's law, i.e. is pro- 

 portional to the number of the vibrations. According to Scripture, 

 very gradual alterations in pitch may amount to a whole tone, 

 without detection even by a musical ear. 



VOL. iv Q 



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i m ::EII;I])!: 



FIG. 89. Gallon's Whistle ; 

 Kitelmuim's IH-W model. 



