### Error Significance

In one study, young normal listeners exhibited a standard deviation in
their measured auditory bandwidths (based on notched-noise masking
experiments) on the order of 10% of center frequency [178].
Therefore, a 20% peak error in mapped bandwidth (typical for sampling
rates approaching 40 kHz) could be considered significant. However, the
*range* of auditory-filter bandwidths measured in 93 young normal
subjects at 2 kHz [178] was 230 to 410 Hz, which is -26% to +32%
relative to 310 Hz. In [298], 40 subjects were measured,
yielding auditory-filter bandwidths between -33% and +65%, with a
standard deviation of 18%. It may thus be concluded that a worst-case
mapping error on the order of 20%, while probably detectable by ``golden
ears'' listeners, lies well within the range of experimental deviations in
the empirical measurement of auditory bandwidth.

As a worst-case example of how the 18% peak bandwidth-mapping error in
Fig.E.7 might correspond to an audible distortion, consider one
critical band of noise centered at the frequency of maximum negative
mapping error, scaled to be the same loudness as a single critical band of
noise centered at the frequency of maximum positive error. The systematic
nature of the mapping error results in a narrowing of the lower band and
expansion of the upper band by about 1.7 dB. As a result, over the warped
frequency axis, the upper band will be effectively *emphasized* over
the lower band by about 3 dB.

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Bark Relative Bandwidth Mapping Error