50 Chapter 3
ity—namely, harmonic distortion and combination
tones. Harmonic distortion can be easily achieved by
simply distorting a sine-tone. The added new compo-
nents are harmonics of the original signal. A combina-
tion tone happens when there are at least two
frequencies in the input. The output might include com-
bination tones according to
(3-2)where,
fc is the frequency of a combination tone,
f 1 and f 2 are the two input frequencies, and n and m are
any integer numbers.
For example, when two tones at 600 and 700 Hz are
input, the output might have frequencies such as 100 Hz
(= 700600 Hz), 500 Hz (= 2 × 600700 Hz), and
400 Hz (= 3 × 6002 × 700 Hz), etc.
Because the harmonic distortion does not change the
perception of pitch, it would not be surprising if we are
less tolerant of the combination tones.
Furthermore, because the auditory system is active,
even in a completely quiet environment, the inner ear
might generate tones. These otoacoustic emissions^23 are
a sign of a healthy and functioning inner ear, and quite
different from the tinnitus resulting from exposure to
dangerously high sound pressure levels.
3.5 Perception of PhaseThe complete description of a given sound includes
both an amplitude spectrum and a phase spectrum.
People normally pay a lot of attention to the amplitude
spectrum, while caring less for the phase spectrum. Yet
academic researchers, hi-fi enthusiasts, and audio engi-
neers all have asked, “Is the ear able to detect phase dif-
ferences?” About the middle of the last century, G. S.
Ohm wrote, “Aural perception depends only on the
amplitude spectrum of a sound and is independent of
the phase angles of the various components contained in
the spectrum.” Many apparent confirmations of Ohm’s
law of acoustics have later been traced to crude measur-
ing techniques and equipment.
Actually, the phase spectrum sometimes can be very
important for the perception of timbre. For example, an
impulse and white noise sound quite different, but they
have identical amplitude spectrum. The only difference
occurs in the phase spectrum. Another common
example is speech: if one scrambles the relative phases
in the spectrum of a speech signal, it will not be intelli-
gible. Now, with experimental evidence, we can
confirm that our ear is capable of detecting phase infor-
mation. For example, the neural firing of the auditory
nerve happens at a certain phase, which is called the
phase-locking, up to about 5 kHz.^24 The phase-locking
is important for pitch perception. In the brainstem, the
information from left and right ears is integrated, and
the interaural phase difference can be detected, which is
important for spatial hearing. These phenomena will be
discussed in more detail in Sections 3.9 and 3.11.3.6 Auditory Area and ThresholdsThe auditory area depicted in Fig. 3-12 describes, in a
technical sense, the limits of our aural perception. This
area is bounded at low sound levels by our threshold of
hearing. The softest sounds that can be heard fall on the
threshold of hearing curve. Above this line the air mole-
cule movement is sufficient to elicit a response. If, at
any given frequency, the sound pressure level is
increased sufficiently, a point is reached at which a tick-
ling sensation is felt in the ears. If the level is increased
substantially above this threshold of feeling, it becomes
painful. These are the lower and upper boundaries of
the auditory area. There are also frequency limitations
below about 20 Hz and above about 16 kHz, limitations
that (like the two thresholds) vary considerably from
individual to individual. We are less concerned here
about specific numbers than we are about principles. On
the auditory area of Fig. 3-12, all the sounds of life areFigure 3-11. A plot of critical bandwidths (calculated ERBs)
of the human auditory system compared to constant per-
centage bandwidths of filter sets commonly used in acousti-
cal measurements.
1000500200100502010Bandwidth—HzCenter frequency—Hz100 200 500 1k 2k 5k 10k1 octave Critical band (ERB)1 /^3 octave1 /^6octavefc= nfu 1 mfur 2