Loudness
I. Difference between intensity and loudness
A. Intensity = direct
measure of the magnitude of the sound
eliciting the
sensation of hearing
B. Loudness = the psychological attribute of sound assigned to
this sensation by the
listener
II. Equal loudness levels
A. Definition = the
intensity needed for tones of different
frequencies to sound
equally loud
B. Procedure: reference
tone presented at a fixed intensity while
another tone is
varied in level until it sounds equally loud to
the reference tone
1. Reference tone is usually 1000 Hz
2. Repeated for several frequencies and with reference at
several intensities
3. Resulting curves are called equal loudness contours
or
Fletcher-Munson curves
4. Phon
a. Unit of loudness level
b. Referenced to the level of a pure tone of 1000 Hz
against
the loudness of all other tones measured
c. E.g. when a 250 Hz tone at 50 dB SPL is judged to be
as
loud as a 1000 Hz tone at 40 dB SPL, the loudness
level
of the 250 Hz
tone is 40 phons
C. Shape
1. At low frequencies, curves are similar to the minimum
audible field (MAF) curves à more intensity needed to
achieve equal loudness for lower frequencies than higher
frequencies
2. At higher levels, the curves flatten à lower frequencies
grow in loudness faster than higher frequencies
3. For a real-life situation, read the stereo example on p.
339
III. Loudness scales
A. Definition = measuring relationship between loudness &
intensity using
direct scaling methods
B. Procedure: can use magnitude estimation, magnitude
production, or
cross-modality matching
1. Sone
a. Unit of loudness
b. One sone = the loudness of a 1000 Hz tone at 40 dB SPL
c. One sone also = the loudness corresponding to the
loudness level of 40 phons
2. Sone scale
a. If a sound is twice as loud as the reference, it is
assigned
a value of 2 sones
b. If a sound is half as loud as the reference, it is
assigned
a value of 0.5 sones
C. Stevens power law
1. Sone function is a straight line when plotted on log-log
scale (Fig 11.4)
2. A straight line on a log-log graph is a power function
3. Loudness can be expressed as a power of the intensity of
the stimulus by the formula:
L = k I e
where L = loudness
k = a constant
I = intensity of the stimulus
e = exponent (power)
a. A power of 1.0 means that sensation increases at the
same rate as the stimulus level
b. A power of
< 1.0 means that sensation increases at a
slower rate than the stimulus level
c. A power of
> 1.0 means that sensation increases at a
faster rate than the stimulus level
4. Although still the source of some debate, e = 0.6 (for dB
SPL) and 0.3 (for dB IL) are the most commonly used
power values for loudness in normal-hearing listeners
A. If additional sounds presented are inside the critical band,
loudness remains the
same
B. If additional sounds presented are outside the critical band,
loudness increases
V. Temporal integration
of loudness
A. Increasing the duration of the sound causes it to sound louder
B. Critical duration
1. Definition = point at which further increases in duration
do
not cause increases in loudness
2. Value is highly debated and affected very much by
methodology of study
A. Frequency = direct measure of the # of cycles per second of a
sound
B. Pitch = the psychological correlate of frequency (i.e. does it
sound high or low in
pitch ?)
II. The relationship between
frequency and pitch à pitch scales
A. Mels
1. One unit of pitch proposed by Stevens and Volkmann
which derives its name from the term melody
2. 1000 mels is the pitch of a 1000 Hz tone presented at 40
phons
3. Fig. 12.1
a. A frequency that sounds twice as a high as 1000 mels
is
assigned a value of 2000 mels
b. A frequency that sounds half as a high as 1000 mels is
assigned a value of 500 mels
c. From the figure
1) Tripling of frequency only doubles pitch
2) Tenfold increase in frequency yields only 3.5
times
increase in pitch
B. Barks
1. Bark scale is a critical band rate function
2. Bark scale relates pitch to the critical bands
a. Critical bandwidths correspond to pitch ranges of ~100-
180 mels
b. Fig. 12.2
III. Relationship between
pitch and intensity
1. Study published by Stevens (1935) shows results for
ONE SUBJECT who was a "GOOD RESPONDER!"
2. Increases in intensity increased pitch for frequencies
³ 3000 Hz but lowered pitch
for frequencies £ 1000 Hz
3. Flat response for pitches between 1-3 KHz
4. Fig 12.4
5. This data is frequently cited but is for one subject!
B. Modern view
1. Later studies did not show the large shifts in pitch with
change in intensity
2. Later studies also showed lack of consistent changes in
pitch with changes in intensity
3. Very individual results
IV. Complex pitch perception
(briefly)
A. Beats
1. When two tones of very similar but different frequencies
are played at the
same time, the sound fades in and out
2. The fading occurs at a rate equal to the difference
between
the two
frequencies
3. Above 10 Hz, separation, instead of beats you get jitter
and
then roughness
B. The case of the missing fundamental
1. Periodicity pitch
a. The pitch of a sound is based on the periodicity of
the
stimulus waveform
b. 1st proposed by Seebeck in 1841
c. Subjects match pitch to the fundamental frequency of
the
complex
2. Even if the fundamental frequency is absent, listeners
still
perceive it being there