Handbook for Sound Engineers

Psychoacoustics 51

played out—low frequency or high, very soft or very
intense. Speech does not utilize the entire auditory area.
Its dynamic range and frequency range are quite lim-
ited. Music has both a greater dynamic range than
speech and a greater frequency range. But even music
does not utilize the entire auditory area.

3.7 Hearing Over Time

If our ear was like an ideal Fourier analyzer, in order to

translate a waveform into a spectrum, the ear would

have to integrate over the entire time domain, which is

not practical and, of course, not the case. Actually, our

ear only integrates over a limited time window (i.e., a

filter on the time axis), and thus we can hear changes of

pitch, timbre, and dynamics over time, which can be

shown on a spectrogram instead of a simple spectrum.

Mathematically, it is a wavelet analysis instead of a

Fourier analysis. Experiments on gap detection between

tones at different frequencies indicate that our temporal

resolution is on the order of 100 ms,^25 which is a good

estimate of the time window of our auditory system. For

many perspectives (e.g., perceptions on loudness, pitch,

timbre), our auditory system integrates acoustical infor-

mation within this time window.

3.8 Loudness

Unlike level or intensity, which are physical or objec-

tive quantities, loudness is a listener’s subjective per-

ception. As the example in Section 3.3, even if the SPL

meter reads the same level, a sound with a wider band-

width might sound much louder than a sound with a

smaller bandwidth. Even for a pure tone, although loud-

ness follows somewhat with level, it is actually a quite

complicated function, depending on frequency. A tone

at 40 dB SPL is not necessarily twice as loud as another

sound at 20 dB SPL. Furthermore, loudness also varies

among listeners. For example, a listener who has lost

some sensitivity in a certain critical band will perceive

any signal in that band to be at a lower level relative to

someone with normal hearing.

Although there is no meter to directly measure a

subjective quantity such as loudness, psycho-physical

scaling can be used to investigate loudness across

subjects. Subjects can be given matching tasks, where

they are asked to adjust the level of signals until they

match, or comparative tasks, where they are asked to

compare two signals and estimate the scales for

loudness.

3.8.1 Equal Loudness Contours and Loudness Level

By conducting experiments using pure tones with a

large population, Fletcher and Munson at Bell Labs

(1933) derived equal loudness contours, also known as

the Fletcher-Munson curves. Fig. 3-13 shows the equal

loudness contours later refined by Robinson and

Dadson, which have been recognized as an international

standard. On the figure, the points on each curve corre-

spond to pure tones, giving the same loudness to an

average listener. For example, a pure tone at 50 Hz at

60 dB SPL is on the same curve as a tone at 1 kHz at

30 dB. This means that these two tones have identical

loudness to an average listener. Obviously, the level for

the 50 Hz tone is 30 dB higher than the level of the

60 Hz tone, which means that we are much less sensi-

tive to the 50 Hz tone. Based on the equal loudness con-

tours, loudness level, in phons, is introduced. It is

always referenced to a pure tone at 1 kHz. The loudness

level of a pure tone (at any frequency) is defined as the

level of a 1 kHz tone that has identical loudness to the

given tone for an average listener. For the above exam-

ple, the loudness of the 50 Hz pure tone is 30 phons,

which means it is as loud as a 30 dB pure tone at 1 kHz.

The lowest curve marked with “minimum audible” is

the hearing threshold. Although many normal listeners

can hear tones weaker than this threshold at some fre-

Figure 3-12. All sounds perceived by humans of average

hearing acuity fall within the auditory area. This area is

defined by the threshold of hearing and the threshold of

feeling (pain) and by the low and high frequency limits of

hearing. Music and speech do not utilize the entire auditory

area available, but music has the greater dynamic range

(vertical) and frequency demands (horizontal).

Threshold of feeling

Sound pressure level—dB

120

100

80

60

40

20

0

20 50 100 500 1k 5k 10k 20k

Speech

Music

Threshold

of hearing

Frequency—Hz