Introduction to Acoustics

480 Part D Hearing and Signal Processing
Part D 13.5
there are at least two dimensions to musical pitch. One
aspect is related monotonically to frequency (for a pure
tone) and is known as tone height. The other is related
to pitch class (i. e., the name of the note) and is called
tone chroma [13.107, 108]. For example, two sinusoids
with frequencies of 220 and 440 Hz would have the same
tone chroma (they would both be called A on the musical
scale) but, as they are separated by an octave, they would
have different tone heights.
If subjects are presented with a pure tone of a given
frequency, f1, and are asked to adjust the frequency, f2
of a second tone (presented so as to alternate in time
with the fixed tone) so that it appears to be an octave
higher in pitch, they generally adjust f2 to be roughly
twice f1. However,when f1 lies above 2.5kHz,sothat
f2 would lie above 5 kHz, octave matches become very
erratic [13.109]. It appears that the musical interval of
an octave is only clearly perceived when both tones are
below 5 kHz.
Other aspects of the perception of pitch also change
above 5 kHz. A sequence of pure tones above 5 kHz does
not produce a clear sense of melody [13.110]. It is possible
to hear that the pitch changes when the frequency is
changed, but the musical intervals are not heard clearly.
Also, subjects with absolute pitch (the ability to assign
names to notes without reference to other notes) are very
poor at naming notes above 4–5 kHz [13.111].
These results are consistent with the idea that the
pitch of pure tones is determined by different mechanisms
above and below 5 kHz, specifically, by a temporal
mechanism at low frequencies and a place mechanism
at high frequencies. It appears that the perceptual dimension
of tone height persists over the whole audible
frequency range, but tone chroma only occurs in the frequency
range below 5 kHz. Musical intervals are only
clearly perceived when the frequencies of the tones lie
in the range where temporal information is available.
The Effect of Level on Pitch
The pitch of a pure tone is primarily determined by its
frequency. However, sound level also plays a small role.
On average, the pitch of tones with frequencies below
about 2 kHz decreases with increasing level, while the
pitch of tones with frequencies above about 4 kHz increases
with increasing sound level. The early data of
Stevens [13.112] showed rather large effects of sound
level on pitch, but other data generally show much
smaller effects [13.113]. For tones with frequencies
between 1 and 2 kHz, changes in pitch with level are
generally less than 1%. For tones of lower and higher
frequencies, the changes can be larger (up to 5%). There
are also considerable individual differences both in the
size of the pitch shifts with level, and in the direction of
the shifts [13.113].
13.5.3 The Perception of the Pitch
of Complex Tones
The Phenomenon of the Missing Fundamental
For complex tones the pitch does not, in general, correspond
to the position of maximum excitation on the
basilar membrane. Consider, as an example, a sound
consisting of short impulses (clicks) occurring 200 times
per second. This sound contains harmonics with frequencies
at integer multiples of 200 Hz (200, 400, 600,
800 ... Hz). The harmonic at 200 Hz is called the fundamental
frequency. The sound has a low pitch, which
is very close to the pitch of its fundamental component
(200 Hz), and a sharp timbre (a buzzy tone quality).
However, if the sound is filtered so as to remove the fundamental
component, the pitch does not alter; the only
result is a slight change in timbre. This is called the
phenomenon of the missing fundamental [13.99, 114].
Indeed, all except a small group of mid-frequency harmonics
can be eliminated, and the low pitch remains the
same, although the timbre becomes markedly different.
Schouten [13.99,115] called the low pitch associated
with a group of high harmonics the residue. Several other
names have been used to describe this pitch, including
periodicity pitch, virtual pitch, andlow pitch. Theterm
low pitch will be used here. Schouten pointed out that
it is possible to hear the change produced by removing
the fundamental component and then reintroducing it.
Indeed, when the fundamental component is present, it
is possible to hear it out as a separate sound. The pitch
of that component is almost the same as the pitch of the
whole sound. Therefore, the presence or absence of the
fundamental component does not markedly affect the
pitch of the whole sound.
The perception of a low pitch does not require activity
at the point on the basilar membrane which would
respond maximally to the fundamental component. Licklider
[13.116] showed that the low pitch could be heard
when low-frequency noise was present that would mask
any component at the fundamental frequency. Even
when the fundamental component of a complex tone
is present, the pitch of the tone is usually determined by
harmonics other than the fundamental.
The phenomenon of the missing fundamental is not
consistent with a simple place model of pitch based on
the idea that pitch is determined by the position of the
peak excitation on the basilar membrane. However, more