Handbook for Sound Engineers

166 Chapter 7

in Fig. 7-6, it becomes evident that the room volume
must not fall short of a certain minimum if the desired
reverberation time is to be achieved with the planned
audience capacity.
For enabling a tentative estimate of the acoustically
effective room size required with regard to its specific
use, there serves the volume index k, which indicates
the minimum room volume in m³/listener seat, Table
7-8. In case an auditorium is used for concert events, the
volume of the concert enclosure is added to the volume
of the auditorium without increasing, however, the
seating capacity of the auditorium by the number of the
additional performers (orchestra, choir). For theater
functions the volume of the stage house behind the
portal is left out of account.
The minimum required acoustically effective room
volume is calculated as follows:

(7-46)
where,
V is the acoustically effective room volume in m^3 ,
k is the volume index according to Table 7-5 in m^3 /seat,
N is the seating capacity in the audience area.

If a given room is to be evaluated regarding its suit-
ability for acoustic performances, the volume index may

be useful for providing a rough estimate and simultane-

ously for determining the scope of additional

sound-absorptive measures.

If the volume index falls short of the established

guide values, the desirable reverberation time cannot be

achieved by natural acoustics. With very small rooms,

especially orchestra rehearsal rooms, it is moreover

possible that loudness results in excessive fortissimo (in

a rehearsal room of 400 m³ (14,000 ft^3 ) volume and with

25 musicians, may reach up to 120 dB in the diffuse

field). In rooms of less than 100 m³ (3500 ft^3 ) the eigen-

frequency density results are insufficient.^2 This leads to

a very unbalanced frequency transmission function of

the room giving rise to inadmissible timbre changes.

Excessive loudness values require additional

sound-absorptive measures, which may bring about too

heavy a loudness reduction for low-level sound sources.

On the other hand, it is not possible to increase

seating capacity and room volume just as you like,

because of the increase of the equivalent sound absorp-

tion area and the unavoidable air absorption, Fig. 7-4.

The attainable sound energy density in the diffuse field

decreases as well as the performance loudness (see Eq.

7-8). Moreover the distances within the performance

area and to the listener are dissatisfactory expanded this

way. For these reasons it is possible to establish an

upper volume limit for rooms without electroacoustic

sound reinforcement equipment (i.e., with natural

acoustics) that should not be exceeded, Table 7-2. These

Table 7-6. T30,mid, BR, and TR1 for Outstanding and
Excellent Concert Halls

Room (in Alphabetical

Order)

T30,mid in s BR TR1 Primary

Structure

Amsterdam Concertgebouw 2.0 1.09 0.77 Rectangle

Basel, Stadt-Casino 1.8 1.18 0.74 Rectangle

Berlin, Konzerthaus 2.05 1.08 0.79 Rectangle

Boston Symphony Hall 1.85 1.03 0.78 Rectangle

Cardiff, David’s Hall 1.95 0.98 0.87 Polygon

New York Carnegie Hall 1.8 1.14 0.78 Rectangle

Tokyo Hamarikyu Asahi 1.7 0.93 1.04 Rectangle

Vienna Musikvereinssaal 2.0 1.11 0.77 Rectangle

Zürich Tonhallensaal 2.05 1.32 0.58 Rectangle

Table 7-7. Brilliance Ratio for 36 Examined Concert
Halls

Room shape Number of

Examined

Halls

Average

Value TR 1

Confidence

Range TR 1

Limit

Values TR 1

Rectangle 12 0.75 r0.05 0.70–0.80

Polygon 10 0.91 r0.05 0.86–0.97

Circle 5 0.75 r0.16 0.59–0.91

Trapezoidal 9 0.75 r0.15 0.63–0.86

VkN= u

Table 7-8. Volume Index k versus Room Volume

No. Main use Volume

Index k in

m³/seat

(in ft^3 /Seat)

Maximum

Effective

Room

Volume with

Natural

Acoustics in

m³ (ft^3 )

1 Speech performances—e.g.,

spoken drama, congress hall

and auditorium, lecture room,

room for audiovisual perfor-

mances

3–6

(110–210)

5000

(180,000)

2 Music and speech perfor-

mances—e.g., musical theater,

multi-purpose hall, town hall

5–8

(180–280)

15,000

(550,000)

3 Music performances—e.g.,

concert hall

7–12

(250–420)

25,000

(900,000)

4 Rooms for oratorios and organ

music

10–14

(350–500)

30,000

(1,100,000)

5 Orchestra rehearsal rooms 25–30

(900–1100)