Handbook for Sound Engineers

1396 Chapter 36

means of traditional statistical acoustics, it is not
possible to accurately estimate, on a statistical basis, the
early and late reflection fields. (To do this requires a
computer model of the space and ray-tracing/reflection
analysis program.)
Prior to such techniques being available, a number of
statistically based intelligibility prediction methods
based on calculation of the direct and reverberant fields
were developed and are still useful in order to provide a
quick ball park review of a design or idea. They have
greater accuracy when applied to center cluster or point
source systems as opposed to distributed loudspeaker
systems (particularly high-density distributed systems).
The best known equation is that of Peutz as later
modified by Klein and is the articulation loss of conso-
nants equation (%Alcons). Peutz related intelligibility to
a loss of information. For a loudspeaker-based system in
a reverberant room, the following factors are involved:

• Loudspeaker directivity (Q).


• Quantity of loudspeakers operating in the space (n).


• Reverberation time (RT 60 ).


• Distance between listener and loudspeaker (D).


• Volume of the space (V).

(36-1)

The %Alcons scale is unusual in that the smaller the
number, the better the intelligibility. From Eq. 36-1 it
can be seen that the intelligibility in a reverberant space
is in fact proportional to the volume of the space and the
directivity (Q) of the loudspeaker, (i.e., increasing either
of these parameters while maintaining the others con-
stant will improve the intelligibility). From the equation
it can also be seen that intelligibility is inversely propor-
tional to the squares of reverberation time and distance
between the listener and the loudspeaker.
The equation was subsequently modified to take
account of talker articulation and the effect that an
absorbing surface has on the area covered by the loud-
speakers.

(36-2)

where,
m is the critical distance modifier, taking into account
higher than average absorption of the floor with an
audience, for example,

m is (1 –a)e(1 –ac) where a is the average absorption

coefficient, ac is the absorption in the area covered by

the loudspeaker,

k is the listener/talker correction constant typically 1–3,

but for poor listeners/talkers can increase to 12.5%.

Peutz found that the limit for successful communica-

tion was around 15% Alcons. From 10 to 5% intelligi-

bility is generally rated as good and below 5% the

intelligibility can be regarded as excellent. A limiting

condition

(36-3)

was also found to occur by Peutz.

Although not immediately obvious from the equa-

tions, they are effectively calculating the direct-to-

reverberant ratio. By rearranging the equation, the effect

of the direct-to-reverberant ratio on %Alcons can be

plotted with respect to reverberation time. This is shown

in Fig. 36-21. From the figure, the potential intelligibil-

ity can be directly read from the graph as a function of

D/R and rverberation time. (By reference to Fig. 36-13

the effect of background noise SNR can also be incorpo-

rated.)

The Peutz equations assume that the octave band

centered at 2 kHz is the most important in determining

intelligibility and uses the values for the direct level,

reverberation time, and Q to be measured in this band.

There is also an assumption that there are no audible

echoes and that the room or space supports a statistical

sound field being free of other acoustic anomalies such

as sound focusing.

In the mid-1980s Peutz redefined the %Alcons equa-

tions and presented them in terms of direct and reverber-

ant levels and background noise level.

(36-4)

where,

%Alcons

200*D

2

T 60

2

n 1+

QV

=----------------------------------------------------

* use 656 for American units

Alcons

200*D^2 T 602 n 1+

QVma

= ----------------------------------------------------+K

* use 656 for American units

Alcons 9 Tk+=

%Alcons=100 10 2–^ ABC+ –ABC +0.015

A 0.32

LR+LN

10 LD++LR LN

–= log--------------------------------------

for A 1let t A 1=

B 0.32

LN

10 LR+LN

–= log-------------------------

for B 1let t B 1=

C 0.50

RT 60

12

–= log©¹§·------------