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Acoustical criteria for concert hall stages
AppliedAcoustics 15 (1982) 321-328
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES
The Late V. L. JORDAN
Gevninge, 4000 Roskilde (Denmark)
SUMMARY
A survey of values of the inversion index (II) in a number of concert halls reveals large variations. Extreme values occur for stages of obviously quite different properties. Recent investigations have concentrated on the energy balance between direct sound energy and early refection energy for a number of concert hall stages. Some numerical results, together with the corresponding reflectograms, are commented upon.
INTRODUCTION
In view of the considerable amount of research work on the acoustical requirements of concert halls which has been undertaken during the last two decades, it is quite remarkable that the acoustical conditions which are characteristic of the stage area (the podium) of a concert hall have received much less attention. Some early studies, undertaken in the 1950s, have been reported elsewhere 1'2 and the ensuing specific criterion, the inversion index, has been studied in a number of cases. The outcome of recent work in this field should be reported before other approaches are considered.
THE CONCEPT OF INVERSION
The definition of the inversion index is dependent upon which (short time) criterion is measured. A total of four different criteria have, in fact, been applied over the years: 321 Applied Aeousties 0003-682X/82/0015-0321/$02.75 Printed in Great Britain
© Applied Science Publishers Ltd, England, 1982
322
v.L. JORDAN
(ii)RiseTime -----Average
value of rise time in the audience area Average value of rise time in the stage area
(1)
Average value of steepness in the stage area (II)st=p.... = Average value of steepness in the audience area
(2)
(II)ED T =
Average value of E D T in the audience area Average value of E D T in the stage area
(3)
Average value of clarity in the stage area (II)cl"ritY= Average value of clarity in the audience area
(4)
Numbers (1) to (3) have been illustrated with examples in reference 2. Since variations in E D T values are generally less pronounced than variations in the values of the other three criteria, the variations in values of II are less dramatic when using E D T values. The idea behind the concept of inversion is the (hypothetical but credible) judgement that the blend of different musical groups and the creation of musical impression should develop faster in the stage area than in the audience area. Thus, values of II are expected to be 1.0 or larger than 1.0, if acoustical conditions are supposed to be good. Since, nowadays, criteria such as rise time and steepness have been superseded by clarity, it has been found useful to study the actual values of II on the basis of measured values of C in a number of concert halls. The collection of halls is the same as that referred to in a recent paper in this journal. 3 To this collection has now been added hall No. 12. The data for this hall are given in Table 1 whilst a plan sketch is given in Fig. 1. The calculations of II on the basis of clarity values resulted in the figures given in TABLE 1 (See Tables 2, 3 and 4, Applied Acoustics, 14 (1981), p. 259.) Values of the criteria in concert hall no. 12
No, Seating 12
1262
Volume (m 3)
Height (m)
13000
18
RT(s) EDT(s) Empty Full Empty 2.25
2.2
2-2
Cexp (dB) C..... Empty Full Empty -2.2
-1.9
-2-4
LE
EDT" ( f )
0.390
+0.13
Variation in C-values (dB) Empty No. 12
Average -2-4
Minimum -5.9
Variation in LE values (coefficient) No. Average Minimum 12
0-390
0-165
Maximum
Maximum difference
-0.4
5.5
Maximum 0.663
Max./ Min.
Max./ Min (dB)
4.02
6.0
ACOUSTICAL
i~-
CRITERIA
FOR CONCERT
HALL
STAGES
323
., ?
F i g . 1.
Concert
H a l l N o . 12, p l a n o f l o w e r a n d u p p e r levels.
Table 2. A few examples of values based on E D T measurements have been added. The most striking fact is that practically all the halls have figures for II above the supposed critical values of 1.0. Numerical values vary between 0-99 and 2.48 with an average value (for ten halls) of 1.67. When one looks at the rather high values for the two halls (Nos 7 and 9) one starts querying the relationship between II and the TABLE VALUES OF
II
IN VARIOUS
2 CONCERT
HALLS
No.
11 (Calculatedfrorn C)
11 (Calculatedfrom EDT)
1 2 3
1.49 1.56 1.52
----
4
--
5 6 7 8 9 10 11 12
1.86 1.56 2.48 1.48 2.09 -1.70 0.99-1.24
---1-10 1-04 -1-0 1.03
1-67
--
Average
-
324
v.L. JORDAN
'acoustics' of the stage surroundings. No. 7 is an example of a hall with a definite closed-in stage which must provide many early reflections, whereas No. 9 is an example of a hall with a rather open stage nearly integrated with the side walls of the hall. Looking more closely at the clarity values in these two cases one also finds that the value of II in case No. 7 results from very high values of clarity in the stage area, together with relatively high values of clarity in the audience area, whereas, in case No. 9, the value of II is a result of rather low values of clarity in the stage area and correspondingly lower values in the audience area. If the prime concern of our investigation is to find objective criteria associated with the acoustical conditions of a stage area it appears that, in this connection, the concept of II is not very helpful and that we must look for other (measurable) criteria. This does not mean that we should stop thinking of inversion as a factor of importance. It was proved a long time ago I that the existence of inversion in a hall was detrimental to the balance between stage and audience area, and that the problem in that particular case could be solved by providing more reflections in the stage area. A recent publication on subjectively assessed spatial impression and clarity 4 is of considerable interest in this connection. From the artificial sound fields applied in the investigation it is possible to deduce values of II (based either on values of clarity or on values of rise time). It shows that by a division into three subjective categories ('good', 'sufficient' and 'insufficient') the values of II in the first two cases are between 1.6 and 2.0 (on the basis of C-values) and 1.3 and 1.6 (on the basis of rise time values), whereas the values of II in the third case are considerably below 1.0.
O T H E R A P P R O A C H E S A N D T H E C O N C E P T OF E A R L Y E N E R G Y B A L A N C E
Returning now to the question of objective criteria for the stage area itself; within the last couple of years some approaches to this problem have been made. By experimenting with a small ensemble it was possible to reach tentative conclusions concerning the preferred interval within which reflections supporting the direct sound should arrive (evaluated by subjective assessment of the musicians themselvesS). For small groups the useful interval for early reflections seemed to have limits between 15 and 40 ms (delay with regard to the direct sound). By analysing the influence of the human directional hearing and of the directional properties of musical instruments on the resulting masking effects concerning different groups in an orchestra, Meyer and Briassoni de Serra 6 were able to establish certain rules concerning the localisation and orientation of reflecting surfaces.
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES
325
These approaches are based either on the influence of individual reflections or on directional properties (of hearing and instruments). The question arises, however, as to whether diffusing properties of the boundaries which provide the early reflections are also of importance. An early investigation by the late Tom Somerville and his coworker, Gilford 7 on the influence of breaks in the canopy ceiling of an orchestra stage showed a remarkable difference in the appearance of oscillograms of the first reflections (with and without the breaks), together with a marked difference in the subjective assessment of the musical quality of an orchestra playing on this stage. This led the author to study the oscillograms for short pulses taken at a number of different orchestra stages (from the collection of concert halls mentioned earlier). Examples from most of the halls investigated are shown in Fig. 2. As will be seen from these examples, the actual number of individual reflections and also their distribution do vary considerably from case to case. Let us now assume that the most important single aspect is not the individual reflections (their direction and delay) but the amount of diffused energy an individual musician receives within a reasonable time interval following the direct sound. This amount of diffused energy, say between 0 and 35ms, should be compared with the energy of the direct sound (within the interval 0-5 ms). The assumption is also that for the musical impression (both for the musicians and for the audience) the rapid blend of diffused sound is of importance. This then leads to the establishment of a new criterion for the stage of a concert hall: Early Energy Balance -,~ EEB = 10 log ~
(dB)
L,,0_5
with the implicit assumption that large values of the criterion are, in principle, preferable to small values. EEB should be measured with both pulse source and microphone (non-directional) on stage but with sufficient distance between them (distance larger than 'hall radius' r H -- ~ (m)). This criterion, EEB, has been tried on a number of concert hall stages and again the collection of test tapes from different halls mentioned earlier has been applied. The results are shown in Table 3. Table 3 should be studied in close connection with Fig. 2. The measured numerical values of EEB do obviously correspond to the appearance of the reflectogrammes and are reasonably well explained by them. Looking also at the dimensions of the stages and the actual possibilities of reflections off the boundaries and their delays, a comprehensive picture emerges. It is very likely that the actual number of the more prominent reflections may also have a direct connection with the degree of diffusion in the various particular cases, although definite evidence probably needs direct experimentation (both by model and full scale).
326
V. L. JORDAN
I !IP
I
5
r t: ,1~ .=
I'!ka~ljtAa, l=
i!ll!~v,,,-'!--m"'T'~
!i ~, 1]
! Fig. 2.
Pulse oscillograms for concert halls Nos 1, 2, 5, 7, 8, 9, 11 and 12. Time interval: 5 ms per division.
327
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES TABLE 3 V A L U E S OF
Concert Hall No.
rn (m)
Mean width
EEB
FOR V A R I O U S C O N C E R T H A L L STAGES
Depth (m)
Total area
(m) 1 2 5 7 8 9 11 12
Height (m)
Distance EEB Comments source-receiver (dB)
(m 2)
(m)
4.26 4.26 4-24 4.24 4.37 4.37 4.15 4.15 5.65 5.65
20 20 15 15 22-5 22.5 16.7 16-7 17.3 17.3
9.5 9.5 9.5 9.5 12 12 9 9 11.7 11.7
215 215 150 150 270 270 130 130 210 210
16 16 9-10 9-10 9-15 9-15 5-7 5-7 19 19
5-13 5"13 5.13 4-44 4.44
17.7 17.7 17.7 15 15
11.7 11.7 11.7 13"2 13.2
210 210 210 200 200
11 11 11 11"5 11,5
4.34 4.34 4.34 4.34
15.3 15.3 15-3 15-3
11"6 11"6 11"6 11 '6
160 160 160 160
17 17 17 17
9"5 12.0 10.2 8'9 11"1 14-1 15"2 11"6 9.4 9,7 9.7 9.8 10-5 11.2 9.6 9.6 9-6 5.2 5-3 11.5 10.5
Average value of EEB for eight Concert Halls
7.0 5.5 5.2 7-9 9.5 5-5 11.7 10.9 5.0 6.3 4.5 2.6 2.8 2.6 4.1 4.0 4.6 3.7 5-1 6.4 6.8
(1)
(2) (3)
6.2dB
(1) Horizontal reflectors at approximately 7 m height above stage level. (2) Horizontal reflectors at approximately 10 m height above stage level. (3) Peripheral barriers of 1 m height. PRELIMINARY CONCLUSIONS T h e v e r y e a r l y i n t e r v a l o f d i r e c t s o u n d a n d e a r l y reflections m u s t be o f c o n s i d e r a b l e significance for the a c o u s t i c a l c o n d i t i o n s for the m u s i c i a n s . T h e d i m e n s i o n s o f the o r c h e s t r a stage, t o g e t h e r w i t h t h e d i f f u s i n g p r o p e r t i e s o f its b o u n d a r i e s , s h o u l d be s t u d i e d m o r e closely u s i n g E a r l y E n e r g y B a l a n c e o r s i m i l a r c o n c e p t s . T h e r a n g e o f n u m e r i c a l v a l u e s o f E E B f o r the e i g h t c o n c e r t halls i n v e s t i g a t e d is c o n s i d e r a b l e , b e i n g f r o m 2.6 to I 1 - 7 d B , w i t h an a v e r a g e v a l u e a r o u n d 6 . 2 d B . T h e i n v e r s i o n i n d e x is still o f i m p o r t a n c e w i t h r e g a r d to t h e s u b j e c t i v e e v a l u a t i o n o f listeners o c c u p y i n g d i f f e r e n t p o s i t i o n s b u t has o n l y l i m i t e d significance f o r the p r o p e r t i e s o f the s t a g e a r e a itself.
REFERENCES 1. V. L. JORDAN,The building-up process of sound pulses, Proc 1CA 1H, 1959. 2. V. L. JORI~AN,Acousticaldesign of concert halls and theatres, Applied Science Publishers, London, 1980.
328
V . L . JORDAN
3. V. L. JORDAN, A group of objective acoustical criteria for concert halls, J. Appl. Acoustics, 14 (1981), pp. 253--66. 4. W. RE1CnARDr U. LEHMANN, Optimierung yon Raumeindruck und Durchsichtigkeit, Acustica, 48 (1981), p. 174. 5. A. H. MARSHALL, D. GOTTLOB and AHLRUTZ, Acoustical conditions preferred for ensemble, J.A.S.A., 64 (1978), pp. 1437-42. 6. J. MEYERand F. C. BRIASSONIDE SERRA,Zum Verdedungseffekt bei Instrumentalmusikern, Acustica, 46 (1980), pp. 130-40. 7. T. SOMERVILLE and C. S. GILEORD, Effects of reflectors in concert halls, J. Sound & Vib., 3 (1966), p. 127.
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES
The Late V. L. JORDAN
Gevninge, 4000 Roskilde (Denmark)
SUMMARY
A survey of values of the inversion index (II) in a number of concert halls reveals large variations. Extreme values occur for stages of obviously quite different properties. Recent investigations have concentrated on the energy balance between direct sound energy and early refection energy for a number of concert hall stages. Some numerical results, together with the corresponding reflectograms, are commented upon.
INTRODUCTION
In view of the considerable amount of research work on the acoustical requirements of concert halls which has been undertaken during the last two decades, it is quite remarkable that the acoustical conditions which are characteristic of the stage area (the podium) of a concert hall have received much less attention. Some early studies, undertaken in the 1950s, have been reported elsewhere 1'2 and the ensuing specific criterion, the inversion index, has been studied in a number of cases. The outcome of recent work in this field should be reported before other approaches are considered.
THE CONCEPT OF INVERSION
The definition of the inversion index is dependent upon which (short time) criterion is measured. A total of four different criteria have, in fact, been applied over the years: 321 Applied Aeousties 0003-682X/82/0015-0321/$02.75 Printed in Great Britain
© Applied Science Publishers Ltd, England, 1982
322
v.L. JORDAN
(ii)RiseTime -----Average
value of rise time in the audience area Average value of rise time in the stage area
(1)
Average value of steepness in the stage area (II)st=p.... = Average value of steepness in the audience area
(2)
(II)ED T =
Average value of E D T in the audience area Average value of E D T in the stage area
(3)
Average value of clarity in the stage area (II)cl"ritY= Average value of clarity in the audience area
(4)
Numbers (1) to (3) have been illustrated with examples in reference 2. Since variations in E D T values are generally less pronounced than variations in the values of the other three criteria, the variations in values of II are less dramatic when using E D T values. The idea behind the concept of inversion is the (hypothetical but credible) judgement that the blend of different musical groups and the creation of musical impression should develop faster in the stage area than in the audience area. Thus, values of II are expected to be 1.0 or larger than 1.0, if acoustical conditions are supposed to be good. Since, nowadays, criteria such as rise time and steepness have been superseded by clarity, it has been found useful to study the actual values of II on the basis of measured values of C in a number of concert halls. The collection of halls is the same as that referred to in a recent paper in this journal. 3 To this collection has now been added hall No. 12. The data for this hall are given in Table 1 whilst a plan sketch is given in Fig. 1. The calculations of II on the basis of clarity values resulted in the figures given in TABLE 1 (See Tables 2, 3 and 4, Applied Acoustics, 14 (1981), p. 259.) Values of the criteria in concert hall no. 12
No, Seating 12
1262
Volume (m 3)
Height (m)
13000
18
RT(s) EDT(s) Empty Full Empty 2.25
2.2
2-2
Cexp (dB) C..... Empty Full Empty -2.2
-1.9
-2-4
LE
EDT" ( f )
0.390
+0.13
Variation in C-values (dB) Empty No. 12
Average -2-4
Minimum -5.9
Variation in LE values (coefficient) No. Average Minimum 12
0-390
0-165
Maximum
Maximum difference
-0.4
5.5
Maximum 0.663
Max./ Min.
Max./ Min (dB)
4.02
6.0
ACOUSTICAL
i~-
CRITERIA
FOR CONCERT
HALL
STAGES
323
., ?
F i g . 1.
Concert
H a l l N o . 12, p l a n o f l o w e r a n d u p p e r levels.
Table 2. A few examples of values based on E D T measurements have been added. The most striking fact is that practically all the halls have figures for II above the supposed critical values of 1.0. Numerical values vary between 0-99 and 2.48 with an average value (for ten halls) of 1.67. When one looks at the rather high values for the two halls (Nos 7 and 9) one starts querying the relationship between II and the TABLE VALUES OF
II
IN VARIOUS
2 CONCERT
HALLS
No.
11 (Calculatedfrorn C)
11 (Calculatedfrom EDT)
1 2 3
1.49 1.56 1.52
----
4
--
5 6 7 8 9 10 11 12
1.86 1.56 2.48 1.48 2.09 -1.70 0.99-1.24
---1-10 1-04 -1-0 1.03
1-67
--
Average
-
324
v.L. JORDAN
'acoustics' of the stage surroundings. No. 7 is an example of a hall with a definite closed-in stage which must provide many early reflections, whereas No. 9 is an example of a hall with a rather open stage nearly integrated with the side walls of the hall. Looking more closely at the clarity values in these two cases one also finds that the value of II in case No. 7 results from very high values of clarity in the stage area, together with relatively high values of clarity in the audience area, whereas, in case No. 9, the value of II is a result of rather low values of clarity in the stage area and correspondingly lower values in the audience area. If the prime concern of our investigation is to find objective criteria associated with the acoustical conditions of a stage area it appears that, in this connection, the concept of II is not very helpful and that we must look for other (measurable) criteria. This does not mean that we should stop thinking of inversion as a factor of importance. It was proved a long time ago I that the existence of inversion in a hall was detrimental to the balance between stage and audience area, and that the problem in that particular case could be solved by providing more reflections in the stage area. A recent publication on subjectively assessed spatial impression and clarity 4 is of considerable interest in this connection. From the artificial sound fields applied in the investigation it is possible to deduce values of II (based either on values of clarity or on values of rise time). It shows that by a division into three subjective categories ('good', 'sufficient' and 'insufficient') the values of II in the first two cases are between 1.6 and 2.0 (on the basis of C-values) and 1.3 and 1.6 (on the basis of rise time values), whereas the values of II in the third case are considerably below 1.0.
O T H E R A P P R O A C H E S A N D T H E C O N C E P T OF E A R L Y E N E R G Y B A L A N C E
Returning now to the question of objective criteria for the stage area itself; within the last couple of years some approaches to this problem have been made. By experimenting with a small ensemble it was possible to reach tentative conclusions concerning the preferred interval within which reflections supporting the direct sound should arrive (evaluated by subjective assessment of the musicians themselvesS). For small groups the useful interval for early reflections seemed to have limits between 15 and 40 ms (delay with regard to the direct sound). By analysing the influence of the human directional hearing and of the directional properties of musical instruments on the resulting masking effects concerning different groups in an orchestra, Meyer and Briassoni de Serra 6 were able to establish certain rules concerning the localisation and orientation of reflecting surfaces.
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES
325
These approaches are based either on the influence of individual reflections or on directional properties (of hearing and instruments). The question arises, however, as to whether diffusing properties of the boundaries which provide the early reflections are also of importance. An early investigation by the late Tom Somerville and his coworker, Gilford 7 on the influence of breaks in the canopy ceiling of an orchestra stage showed a remarkable difference in the appearance of oscillograms of the first reflections (with and without the breaks), together with a marked difference in the subjective assessment of the musical quality of an orchestra playing on this stage. This led the author to study the oscillograms for short pulses taken at a number of different orchestra stages (from the collection of concert halls mentioned earlier). Examples from most of the halls investigated are shown in Fig. 2. As will be seen from these examples, the actual number of individual reflections and also their distribution do vary considerably from case to case. Let us now assume that the most important single aspect is not the individual reflections (their direction and delay) but the amount of diffused energy an individual musician receives within a reasonable time interval following the direct sound. This amount of diffused energy, say between 0 and 35ms, should be compared with the energy of the direct sound (within the interval 0-5 ms). The assumption is also that for the musical impression (both for the musicians and for the audience) the rapid blend of diffused sound is of importance. This then leads to the establishment of a new criterion for the stage of a concert hall: Early Energy Balance -,~ EEB = 10 log ~
(dB)
L,,0_5
with the implicit assumption that large values of the criterion are, in principle, preferable to small values. EEB should be measured with both pulse source and microphone (non-directional) on stage but with sufficient distance between them (distance larger than 'hall radius' r H -- ~ (m)). This criterion, EEB, has been tried on a number of concert hall stages and again the collection of test tapes from different halls mentioned earlier has been applied. The results are shown in Table 3. Table 3 should be studied in close connection with Fig. 2. The measured numerical values of EEB do obviously correspond to the appearance of the reflectogrammes and are reasonably well explained by them. Looking also at the dimensions of the stages and the actual possibilities of reflections off the boundaries and their delays, a comprehensive picture emerges. It is very likely that the actual number of the more prominent reflections may also have a direct connection with the degree of diffusion in the various particular cases, although definite evidence probably needs direct experimentation (both by model and full scale).
326
V. L. JORDAN
I !IP
I
5
r t: ,1~ .=
I'!ka~ljtAa, l=
i!ll!~v,,,-'!--m"'T'~
!i ~, 1]
! Fig. 2.
Pulse oscillograms for concert halls Nos 1, 2, 5, 7, 8, 9, 11 and 12. Time interval: 5 ms per division.
327
ACOUSTICAL CRITERIA FOR CONCERT HALL STAGES TABLE 3 V A L U E S OF
Concert Hall No.
rn (m)
Mean width
EEB
FOR V A R I O U S C O N C E R T H A L L STAGES
Depth (m)
Total area
(m) 1 2 5 7 8 9 11 12
Height (m)
Distance EEB Comments source-receiver (dB)
(m 2)
(m)
4.26 4.26 4-24 4.24 4.37 4.37 4.15 4.15 5.65 5.65
20 20 15 15 22-5 22.5 16.7 16-7 17.3 17.3
9.5 9.5 9.5 9.5 12 12 9 9 11.7 11.7
215 215 150 150 270 270 130 130 210 210
16 16 9-10 9-10 9-15 9-15 5-7 5-7 19 19
5-13 5"13 5.13 4-44 4.44
17.7 17.7 17.7 15 15
11.7 11.7 11.7 13"2 13.2
210 210 210 200 200
11 11 11 11"5 11,5
4.34 4.34 4.34 4.34
15.3 15.3 15-3 15-3
11"6 11"6 11"6 11 '6
160 160 160 160
17 17 17 17
9"5 12.0 10.2 8'9 11"1 14-1 15"2 11"6 9.4 9,7 9.7 9.8 10-5 11.2 9.6 9.6 9-6 5.2 5-3 11.5 10.5
Average value of EEB for eight Concert Halls
7.0 5.5 5.2 7-9 9.5 5-5 11.7 10.9 5.0 6.3 4.5 2.6 2.8 2.6 4.1 4.0 4.6 3.7 5-1 6.4 6.8
(1)
(2) (3)
6.2dB
(1) Horizontal reflectors at approximately 7 m height above stage level. (2) Horizontal reflectors at approximately 10 m height above stage level. (3) Peripheral barriers of 1 m height. PRELIMINARY CONCLUSIONS T h e v e r y e a r l y i n t e r v a l o f d i r e c t s o u n d a n d e a r l y reflections m u s t be o f c o n s i d e r a b l e significance for the a c o u s t i c a l c o n d i t i o n s for the m u s i c i a n s . T h e d i m e n s i o n s o f the o r c h e s t r a stage, t o g e t h e r w i t h t h e d i f f u s i n g p r o p e r t i e s o f its b o u n d a r i e s , s h o u l d be s t u d i e d m o r e closely u s i n g E a r l y E n e r g y B a l a n c e o r s i m i l a r c o n c e p t s . T h e r a n g e o f n u m e r i c a l v a l u e s o f E E B f o r the e i g h t c o n c e r t halls i n v e s t i g a t e d is c o n s i d e r a b l e , b e i n g f r o m 2.6 to I 1 - 7 d B , w i t h an a v e r a g e v a l u e a r o u n d 6 . 2 d B . T h e i n v e r s i o n i n d e x is still o f i m p o r t a n c e w i t h r e g a r d to t h e s u b j e c t i v e e v a l u a t i o n o f listeners o c c u p y i n g d i f f e r e n t p o s i t i o n s b u t has o n l y l i m i t e d significance f o r the p r o p e r t i e s o f the s t a g e a r e a itself.
REFERENCES 1. V. L. JORDAN,The building-up process of sound pulses, Proc 1CA 1H, 1959. 2. V. L. JORI~AN,Acousticaldesign of concert halls and theatres, Applied Science Publishers, London, 1980.
328
V . L . JORDAN
3. V. L. JORDAN, A group of objective acoustical criteria for concert halls, J. Appl. Acoustics, 14 (1981), pp. 253--66. 4. W. RE1CnARDr U. LEHMANN, Optimierung yon Raumeindruck und Durchsichtigkeit, Acustica, 48 (1981), p. 174. 5. A. H. MARSHALL, D. GOTTLOB and AHLRUTZ, Acoustical conditions preferred for ensemble, J.A.S.A., 64 (1978), pp. 1437-42. 6. J. MEYERand F. C. BRIASSONIDE SERRA,Zum Verdedungseffekt bei Instrumentalmusikern, Acustica, 46 (1980), pp. 130-40. 7. T. SOMERVILLE and C. S. GILEORD, Effects of reflectors in concert halls, J. Sound & Vib., 3 (1966), p. 127.