AUDITORY PERCEPTIONS. 



tial tones, which will be considered presently) produce beats that number 

 about 33 in the second. 



Finally, two simple tones or musical tones sounded together may give 

 rise to new tones if they sound simultaneously and in suitable intensity. 

 In addition to these two primary tones or musical sounds, a third new 

 tone is heard on listening intently, the number of whose vibrations is 

 equal to the difference between the two primary tones. These tones 

 are called differential tones, or Andreas Sorge's or Tatini's tones. 



If, for example, two tones in the relation of the fifth (2 : 3) or of the fourth 

 (3 : 4) or of the third (4 15), are sounded, the fundamental tone = i is heard as 

 a differential tone. Musical tones that are rich in overtones yield differential 

 tones of higher order. Thus, if the third (produced by two metal bars) in a high 

 register, namely 16:20 (=4: 5) is sounded, the tone = 4 (fundamental tone) 

 is readily heard as the first differential tone. This tone 4 forms, however, with 

 1 6 another differential tone of second order, that isi6 4=12. In fact, with 

 the aid of resonators the differential tone of third order may be heard, namely 

 12 4 =8. 



Helmholtz showed, further, that new tones may also result through 

 addition of their vibration-numbers (so-called summation- tones). 

 These are difficult to hear, though best when the two primary tones be- 

 long to the middle and lower register, and are rich in overtones. 



When musical tones are sounded together, the harmony of the differential 

 tones must also be taken into account. In the major chord these are consonant; 

 in the minor chord there is dissonance of the differential tones. Therefore, the 

 first have a finished, complete, satisfying character, while the latter produce a 

 feeling of unsatisfactoriness, melancholy, contention, which requires a resolution 

 into more finished consonant harmonies. 



AUDITORY PERCEPTION. FATIGUE OF THE EAR. OBJECTIVE 



AND SUBJECTIVE HEARING. ASSOCIATED SENSATIONS. 



AUDITORY AFTER-SENSATIONS. 



When the stimulations of the nerve-endings in the labyrinth are 

 referred, by a psychical act, to the source of the sound in the outer 

 world, there result objective auditory perceptions. Only such stimu- 

 lations, however, are referred outward as are transmitted to the tympanic 

 membrane by vibrations of the air. This is proved by the fact that, 

 when the head is held under water, so that the external auditory 

 canals are rilled, all sound-vibrations will be heard as if originating 

 in the head; the same is true of one's own voice, if the auditory canals 

 are held closed, and also of sound-waves conducted through the bones of 

 the skull. 



As to the direction from which a sound comes a judgment is formed 

 from the relation of the auditory canals to the source of the sound, espe- 

 cially if this direction is estimated from time to time by turning the head. 

 The direction from which musical tones combined with noises come is 

 more easily recognized than that from which simple tones come. With 

 equally strong stimulation of both ears, the source of sound is referred 

 to the median plane in front as a single sound ; but if one ear is more 

 strongly affected, the sound is referred to that side. The position of the 

 auricles, which act as collecting funnels for the sound-waves, is naturally 

 important in judging the direction from which these come. According 

 to Eduard Weber it is much more difficult to determine the direction 

 when the auricles are held firmly pressed against the head. This ob- 

 server states that if the hands are placed over the ears in such a manner 



