Fundamentals of Psychoacoustics
169
direct methods
pitch
frequency JND
subjective scale for pitch
mel
Experimental curves similar to that reported in figure 4 show in many cases
significant deviations from (14). For instance, the relation between intensity and
loudness is more similar to
L
3
I ,
(15)
as three doublings of intensity are needed for approximating one doubling in
loudness.
Power laws such as the (15) are the natural outcome of the so called direct
methods of psychophysical experimentation, where it is the sensation itself that
is the unit for measuring other sensations. Such experimental paradigm was
largely established by Stevens
, and it is the one in use when the experimenter
asks the subject to double or half the perceived loudness of a tone, or when a
direct magnitude production or estimation is used.
C.3
Pitch
Periodic tones elicit a sensation of pitch, thus meaning that they can be ordered
on a scale from low to high. Many aperiodic or even stochastic sounds can elicit
pitch sensations, with different degrees of strength.
If we stick with pure tones for this section, pitch is the sensorial correlate
of frequency, and it makes sense to measure the frequency JND using the tools
of psychophysics. For instance, if a pure tone is slowly modulated in frequency
we may seek for the threshold of modulation audibility. The resulting curve of
average results would look similar to figure 5.
1
10
100
1000
10000
JND in Hz
Central frequency in Hz
JND in frequency for a modulated pure tone
JND
3% resolution
1% resolution
0.6% resolution
0.5% resolution
Figure 5: JND in frequency for a slowly modulated pure tone.
Again, from the curve of figure 5 we notice a significant deviation from the
Weber's law f f . The physiological interpretation is that there is more
internal noise in the frequency detection in the very-low range.
If we integrate
1
f (f )
we obtain a curve such as that of figure 6 that can be
interpreted as a subjective scale for pitch, whose unit is called mel. Convention-
ally 1000 Hz corresponds to 1000 mel. This curve shouldn't be confused with the
3
Stanley Smith Stevens (1906-1973).