Introduction to Acoustics

750 Part E Music, Speech, Electroacoustics
Part E 18.2
filter bank. The brain does not see the wide-band audio
signal arriving at the ear, as it might appear on an oscilloscope,
but instead processes the outputs of the basilar
membrane filter bank, subject to effective half-wave rectification
and loss of high-frequency synchrony by the
neurons (Fig. 18.6). Output neural signals from each ear
are ultimately processed by multiple areas of the brain.
So, it is not surprising that issues of timing are a little
ill-defined, and that there are a number of time constants
associated with different aspects of hearing.
For starters, there is the basic ability of the neurons
in the auditory nerve to follow the individual cycles of
audio impinging on the basilar membrane; i.e. to exhibit
phase locking. Current research seems to put the upper
frequency of this activity at about 5 kHz, although
this seems somewhat at odds with lateralization of sine
waves on the basic of interaural time difference, which
only extends up to about 1500 Hz.
The ability to follow individual cycles of audio may
aid in pitch perception, as the effective shapes of the
basilar membrane filters appear too broad to account for
the observed pitch resolution. However, the physiological
mechanisms for how this might be accomplished are
still the subject of some debate.
Other time constants appear to apply to the aggregate
audio, regardless of the presence of a filter bank
at the input. Already noted are the masking time constants,
which substantially extend only 1–2 ms prior to
the onset of a loud sound, but continue for several tens
of milliseconds after its cessation.
Each of these may be related to a more fundamental
time constant. The short time constant of about 1–2 ms
may represent the shortest time one can perceive without
relying on spectral cues, while the post-masking interval
may be related to the fusion time. The fusion time
in particular seems to represent a kind of acoustic integration
time, or the limit of primary acoustic memory,
typically on the order of 30–50 ms, and appears to be associated
with the lower frequency limit of the audio band
(20–30 Hz). It also seems to explain why echoes are only
heard as such in large cathedral-like rooms, as they are
integrated with the direct arrivals in normal-size rooms.
Table 18.1 Summary of approximate perceptual time/amplitude
limits
Parameter Range JND
Amplitude 120 dB 0.25 dB
Premask N/A 2ms
Postmask N/A 30–50ms
Binaural timing 700 µs 10 µs
On the other hand, binaural timing clearly exhibits
higher resolution, as differences of interaural timing on
the order of 10 ms may be audible.
18.2.4 Spatial Acuity
Strictly speaking, the spatiality of a sound field is not
perceived directly, but is instead derived from analysis
of the physical attributes already described. However,
given its importance to audio and electroacoustics, it is
nonetheless useful to review the processes involved.
Specification of the position of a sound source
relative to a listener in three-space requires three coordinates.
From the mechanisms used by the human ear,
the natural selection is to use a combination of azimuth,
elevation, and distance. Of these, distance is generally
considered to be an inferred metric, based on the amplitude,
spectral balance, and reverberation content of
a source relative to other sources, and is not especially
accurate in any absolute sense.
This leaves directional estimation as the primary
localization task. It appears that the ear uses separate
processes to determine direction in a left/right sense and
a front/top/back sense. Given the physical placement of
the ears, it is not surprising that the left/right decision
is the more direct and accurate, depending on the interaural
amplitude difference (IAD) and interaural time
difference (ITD) localization cues.
Although the ear is sensitive to IAD at all audible
frequencies, as can be verified by headphone listening,
the head provides little shadowing effect at low frequencies,
since the wavelengths become much longer than
the size of the head, so IAD is mostly useful at middle
to high frequencies.
The JND for IAD is about 1 dB, corresponding to
about 1 degree of an arc for a front/centered highfrequency
source. As a sound moves around to the side
of the head, the absolute IAD will tend to increase, and
the differential IAD per degree will decrease, causing
the angular JND to decrease accordingly.
The ITD lateralization cue has a rather astonishing
JND of just 10 ms, for a source on the centerline between
the ears, corresponding to an angle of about 1 degree.
For signals off to one side, the ITD will typically reach
a maximum value of just 750 ms – 3/4 of a millisecond.
As with the IAD cue, the sensitivity of the ITD cue
declines as a source moves around to the side of the
head.
Also like IAD, this cue is usable at all frequencies,
albeit with a key qualification. At frequencies below
about 1500 Hz, the neural response from the basilar