176 Chapter 7
w is the width of the rear wall,
h is the height of the rear wall,
D is the enclosure depth.
Optimum conditions for the mutual hearing of the
musicians are achieved for a concert stage enclosure in
the shape of a truncated pyramid, Fig. 7-36, with K d
0.3.^36
The more pronounced the diffuse subdivision of the
inner surfaces of the concert stage enclosure, the
smaller results the dependence of the room-acoustical
parameters on the inclination index K.
If the platform boundaries are not formed by acousti-
cally favorable solid wall and ceiling surfaces, addi-
tional elements have to be installed. The surface-related
mass of the planking of these platform boundary
surfaces should be chosen in such a way that the sound
energy reduction by absorption results as little as
possible. (The thinner the boundary walls the higher the
low-frequency absorption.) To this effect, area-related
masses of about 20 kg/m^2 (0.85 lbs/ft^2 ) are generally
sufficient, in the neighborhood of bass instruments
about 40 kg/m^2 (1.7 lbs/ft^2 ).
The vibration ability of the platform floor has only
an insignificant influence on its sound radiation. With a
relatively thin platform floor (12.5 mm (0.5 in)
plywood^37 there may well result a sound amplification
of between 3 dB to 5 dB in the lower-frequency range,
but one should also not forget in this respect the positive
psychological feedback of a vibrating floor on the
players.^3 As a rule, the area-related mass of the platform
floor should not fall below 40 kg/m^2.
By comparison with a rigid floor, a vibrating plat-
form floor has, for the sound radiation of the bass string
instruments with pizzicato play (faster decay resulting in
a dry sound), the disadvantage of a reduced airborne
sound energy, which can, however, be technically
compensated with bow strokes.^3 This is why the plat-
form floor should be frequency-tuned as low as possible.
The platform boundary surfaces should be struc-
tured in such a way that the mutual hearing of the musi-
cians is supported, disturbing echo phenomena (e.g., by
parallel wall surfaces) are avoided, and a well-mixed
sound pattern gets radiated into the audience area.
Obtaining a thorough mixing of the sound pattern
requires a frequency-independent substructure of the
boundary surfaces.
The space required per musician is about 1.4 m^2
(15 ft^2 ) for high-pitched string and brass instruments,
1.7 m^2 (18 ft^2 ) for low-pitched string instruments,
1.2 m^2 (13 ft^2 ) for woodwind instruments and 2.5 m^2
(27 ft^2 ) for the percussion. From this one can infer that,
with due consideration of the participation of soloists
(tail piano, etc.), the area of a concert platform (without
choir) should generally not fall much below 200 m^2
(2200 ft^2 ), in which case the width should be about
18 m (60 ft) at the level of the high-pitched strings, and
the maximum depth about 11 m (36 ft).
Depending on the sloping of tiers in the audience
area (see Section 7.3.3.3.1), a vertical staggering of the
orchestra is necessary especially if the audience area in
the parquet is level or only slightly sloping. In the
Musikvereinssaal Vienna the level difference on the
platform is 1.8 m (6 ft), in the Berliner Philharmonie,
which was destroyed during WWII, it was 2.8 m
(9.2 ft). In such a case it is necessary to have one step in
the string group approximately 250 mm (10 in), the
following steps to and between the two rows of wood-
wind instruments should each be 500 mm (20 in) high.
For the brass instruments or the percussion a further
step of about 150 mm (6 in) is sufficient.
A choir, which in the staging of a grand concert, is
normally lined up behind the orchestra, can profit only
from the lateral wall surfaces and the ceiling of the
room with regard to clarity-enhancing sound reflections,
the floor area is shaded. Since according to Meyer^3 the
main radiation axis of the singers’ strongest sound frac-
tions is inclined about 20° downwards, the choir line-up
should be relatively steeply staggered in order to insure
clarity and definition of articulation in the choir sound.
With a flat line-up, however, only reverberance is
increased. This is perceived as disturbing in rooms with
a long reverberation time, whereas it may be rather
desirable in reverberation-poor rooms. The optimum
value of vertical staggering within a choir is about
45°—i.e., the steps should be equal in breadth and
height in order to enable simultaneously an unhindered
sound radiation to the lateral boundary surfaces of the
room.^3Figure 7-36. Geometrical parameters of a concert
enclosure.
WDWHh