Handbook for Sound Engineers

54 Chapter 3

with RMS detectors having integration times of about
200 ms. This corresponds to the FAST setting on a
sound level meter while the SLOW setting corresponds
to an integration time of 500 ms.

3.8.6 Perception of Dynamic Changes

How sensitive is our hearing of dynamic changes? In
other words, how much intensity or level change will
lead to a perception of change of loudness? To discuss
this kind of problem, we need the concept of
just-noticeable difference (JND), which is defined as the
minimum change that can be detected. Weber’s Law
states that the JND in intensity, in general and not nec-
essarily for hearing, is proportional to the overall inten-
sity. If Weber’s Law holds, the Weber fraction in dB as
defined in Eq. 3-4 would be a constant, independent of
the overall intensity and the overall level.

(3-4)

where,

I is the intensity,

',is the JND of intensity.

Please note that the Weber fraction in dB is not the JND
of SPL ('L), which can be calculated according to Eq.
3-5.

(3-5)

If ',is much smaller than I, Eq. 3-5 is approxi-
mately

(3-6)

Fig. 3-17 shows the measurement of the Weber frac-

tion for broadband signals up to 110 dB SPL.^29 Above

30 dB, the Weber fraction in dB is indeed a constant of

about 10 dB, corresponding to a JND ('L) of 0.4 dB.

However, for weak sounds below 30 dB, the Weber

fraction in dB is higher, and can be as high as 0 dB,

corresponding to a JND ('L) of 3 dB. In other words,

our hearing is less sensitive (in level) for dynamic

changes of sounds weaker than 30 dB. Interestingly,

when measuring with pure tones, it was found that the

Weber fraction is slightly different from the broadband

signals.^30 This phenomenon is known as the near-miss

We b e r ’s L a w. Fig. 3-17 includes a more recent

measurement for pure tones,^31 which demonstrates that

the Weber fraction gradually decreases up to 85 dB SPL

and can be lower than 12 dB, corresponding to a JND

('L) less than 0.3 dB. The near-miss Weber’s Law for

pure tones is believed to be associated with the broad

excitation patterns across frequency at high levels.^32

3.9 Pitch

Pitch seems to be a very clear concept, and yet it is very

hard to give an accurate definition. The definition by the

American National Standards Institute (ANSI) is as fol-

lows: “Pitch is that attribute of auditory sensation in

terms of which sounds may be ordered on a scale

extending from low to high.”^33 Like loudness, pitch is a

subjective quantity. The ANSI standard also states:

“Pitch depends mainly on the frequency content of the

sound stimulus, but it also depends on the sound pres-

sure and the waveform of the stimulus.”^33

Roughly speaking, the sounds we perceive as pitch

are musical tones produced by a musical instrument

(except for percussion instruments) and human voice. It

is either a pure tone at a certain frequency, or a complex

tone with certain fundamentals and a series of

harmonics whose frequencies are multiples of the

Figure 3-16. Short pulses of sound must be increased in
level to sound as loud as longer pulses.

Wideband noise

30

20

10

0

10

Pure tones

Pulse width—ms

0.2 0.5 1 2 5 10 20 50 100 200 500

Change in sound pressure levelto maintain same loudness—dB

Weber fraction in dB 10 'I^

I

= log©¹§·-------

=constant

'L 10 1 'I

I

= log©¹§·----- -+

'L 4.35 1 'I

I

= ©¹§·----- -+

Figure 3-17. Just-noticeable difference (JND) for a broad-

band noise and for a 1 kHz tone. (After Plack, Reference

15; data from Miller, Reference 29, and Viemeister and

Bacon, Reference 31.)

Pedestal level—dB SPL

Weber fraction—dB

Miller (wideband noise)

Viemeister and Bacon (pure tone)