300 AUDITORY BIOPHYSICS 



tensile equilibrium is attained in 0.010 to 0.016 second with the tympanic 

 muscular contraction predominating at high frequencies and high inten- 

 sities. Under these conditions the coupling action of the aural mecha- 

 nism is small and will as a result exclude any surges in the transmitted 

 energy. If the coupling is large because of loose ossicle connections, 

 and if the time of adjustment is long, the surges set up in the system may 

 produce aural harmonics. 



Aural Harmonics 



A harmonic is a component of a complex periodic disturbance possess- 

 ing a frequency which is an integral multiple of the fundamental fre- 

 quency. Aural harmonics are subjective tones. They are heard when 

 very loud tones are impressed on the eardrum. They are introduced as a 

 result of the nonlinear and asymmetric transmission characteristics of 

 the mechanism of the middle ear and cochlea. 



When, for example, the source of sound is a 200-cycle pure sinusoidal 

 wave of sufficient intensity (30 db), a careful observer can, in addition to 

 the fundamental pitch, identify the pitches corresponding with the 

 harmonic frequencies 400 and 600 cycles. When two simple harmonic 

 frequencies excite the aural mechanism simultaneously, it is possible to 

 experience a group of subjective combination tones in addition to the two 

 fundamental tones. They are the aural harmonics called summation 

 and difference tones. 



Aural Harmonics as Conditioned by Intensity 



It was shown by Fletcher [1929] that when a pure tone of 256 cycles 

 was presented to the ear the second harmonic was identified when the 

 intensity of the fundamental reached a sensation level of 30 db, the fourth 

 at about 48 db, and the fifth at about 60 db above threshold. For fre- 

 quencies above 1000 cycles no harmonics were heard until the sensation 

 level had reached 50 db above threshold. 



Owing to the fact that the threshold-of-hearing curve (Fig. VII-19) 

 is concave upward, a constant physical intensity level at different fre- 

 quencies represents different sensory loudness levels, so that at low fre- 

 quencies the higher harmonics are heard relatively more pronounced 

 because the ear is more sensitive to them than to the lower fundamental. 

 If the fundamental has a high frequency, the aural harmonics accom- 

 panying it fall in the very high-pitch range where the ear is less sensitive; 

 hence, one hears them less loud than the fundamental. 



Direct measurements of the magnitude of the aural harmonics were 

 obtained by Stevens and Newman [1936] by observing the micro- 



