Introduction to Acoustics

Relative response (dB)
100
90
80
70
60
50
40
0
∆O
∆O
10
∆ S
20
30
40
50
∆M
60
70 80 90 100
Input level (dB)
Fig. 13.9 Illustration of why growth of masking functions
in forward masking usually have shallow slopes. The solid
curve shows a schematic input–output function on the basilar
membrane. The relative response is plotted on a dB scale
with an arbitrary origin. When the masker is increased in
level by ∆M, this produces an increase in response of ∆O.
To restore signal threshold, the response to the signal also
has to be increased by ∆O. This requires an increase in
signal level, ∆S, which is markedly smaller than ∆M
in Fig. 13.9. It has a shallow slope for medium input
levels, but a steeper slope at very low input levels. Assume
that, for a given time delay of the signal relative to
the masker, the response evoked by the signal at threshold
is directly proportional to the response evoked by
the masker. Assume, as an example, that a masker with
a level of 40 dB produces a signal threshold of 10 dB.
Consider now what happens when the masker level is increased
by 30 dB. The increase in masker level, denoted
by ∆M in Fig. 13.9, produces a relatively small increase
in response, ∆O. To restore the signal to threshold, the
signal has to be increased in level so that the response
to it also increases by ∆O. However, this requires a relatively
small increase in signal level, ∆S, as the signal
level falls in the range where the input–output function
is relatively steep. Thus, the growth of masking function
has a shallow slope.
According to this explanation, the shallow slope of
the growth of masking function arises from the fact that
the signal level is lower than the masker level, so the
masker is subject to more compression than the signal.
The input–output function on the BM has a slope which
decreases progressively with increasing level over the
range 0 to about 50 dB. Hence the slope of the growth of
masking function should decrease with increasing difference
in level between the masker and signal. This can
Psychoacoustics 13.2 Frequency Selectivity and Masking 467
account for the progressive decrease in the slopes of the
growth of masking functions with increasing delay between
the signal and masker (see the right-hand panel
of Fig. 13.8); longer delays are associated with greater
differences in level between the signal and masker. Another
prediction is that the growth of masking function
for a given signal delay should increase in slope if the
signal level is high enough to fall in the compressive region
of the input–output function. Such an effect can be
seen in the growth of masking function for the shortest
delay time in Fig. 13.8; the function steepens for the
highest signal level.
In summary, the processes underlying forward
masking are not fully understood. Contributions from
a number of different sources may be important. Temporal
overlap of patterns of vibration on the BM may be
important, especially for small delay times between the
signal and masker. Short-term adaptation or fatigue in
the auditory nerve may also play a role. At higher neural
levels, a persistence of the excitation or inhibition
evoked by the masker may occur. The form of the growth
of masking functions can be explained, at least qualitatively,
in terms of the nonlinear input–output functions
observed on the BM.
13.2.6 Hearing Out Partials
in Complex Tones
A complex tone, such as a tone produced by a musical
instrument, usually evokes a single pitch; pitches corresponding
to the frequencies of individual partials are not
usually perceived. However, such pitches can be heard
if attention is directed appropriately. In other words, individual
partials can be heard out. Plomp [13.45] and
Plomp and Mimpen [13.46] used complex tones with 12
equal-amplitude sinusoidal components to investigate
the limits of this ability. The listener was presented with
two comparison tones, one of which was of the same frequency
as a partial in the complex; the other lay halfway
between that frequency and the frequency of the adjacent
higher or lower partial. The listener had to judge which
of these two tones was a component of the complex.
Plomp used two types of complex: a harmonic complex
containing harmonics 1 to 12, where the frequencies
of the components were integer multiples of that of
the fundamental; and a nonharmonic complex, where
the frequencies of the components were mistuned from
simple frequency ratios. He found that for both kinds of
complex, partials could only be heard out if they were
sufficiently far in frequency from neighboring partials.
The data, and other more recent data [13.47], are consis-
Part D 13.2