Late lateral energy fractions and the

envelopment question in concert halls

M. Barron *

Department of Architecture and Civil Engineering, University of Bath, Bath, Somerset BA2 7AY, UK

Received 3 August 1999; received in revised form 11 October 1999; accepted 27 June 2000

Abstract

In concert hall acoustics, spatial perception is a crucial element of the experience, yet several

questions remain unresolved. In the 1960s, there was some work on what was then called

`room impression' caused by di€use reverberation. The possible importance of early lateral

re¯ections was proposed in 1967 by Marshall [Marshall AH. A note on the importance of

room cross-section in concert halls. Journal of Sound and Vibration 1967;5:100±12] and until

recently concern for the e€ect of early re¯ections has overshadowed study of the spatial e€ects

linked to the later sound. Bradley and Soulodre [Bradley JS, Soulodre GA. The in¯uence of

late arriving energy on spatial impression. Journal of the Acoustical Society of America

1995;97:2263±71; Bradley JS, Soulodre GA. Objective measures of listener envelopment.

Journal of the Acoustical Society of America 1995;98;2590±7] have now suggested that early

re¯ections are predominantly responsible for creating a sense of source broadening [and

apparent source width (ASW)], whereas a sense of envelopment, which had on occasions been

linked to ASW, is almost solely produced by later lateral re¯ections. Bradley and Soulodre

have proposed the late lateral energy level as a measure of listener envelopment (LEV). This

paper considers some of the history of spatial perception in concert halls and reports on

measured results made in 17 halls of the late lateral energy fraction (LLF) and the late lateral

energy level (GLL). The spread of measured values of LLF turned out to be small and GLL

was found to be predominantly determined by the total acoustic absorption of halls. # 2000

Elsevier Science Ltd. All rights reserved.

1. Introduction

Reverberation is perceived in two distinct ways Ð the temporal and the spatial.

The temporal aspect, which can be called `liveness', can be isolated by monophonic

recording or monaural listening. The decay of sound is responsible for creating an

Applied Acoustics 62 (2001) 185±202

www.elsevier.com/locate/apacoust

0003-682X/01/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.

PII: S0003-682X(00)00055-4

* Tel.: [phone]; fax: [phone].

E-mail address: [e-mail]

audible background against which the latest note in music or latest syllable in speech

is heard. The optimum value for reverberation time is largely determined by the

temporal situation.

The spatial aspect of reverberation is more intractable. Hearing reverberation

from all directions is clearly an important part of listening to music in large auditoria.

Spatial reverberation is at its most extreme in highly reverberant spaces (particularly

large church spaces and reverberation chambers), when direct sound is relatively

weak or indeed absent. In this case the listener can be without clues as to the direction

from which the sound originates. Some aspects of spatial sound with no temporal

behaviour can be studied by using continuous noise signals.

The strength of the early relative to the reverberant sound is conventionally mea-

sured by the Clarity Index, C

80

. As its name implies, the index is usually applied to

the temporal response to reverberation. It may however also have a role to play

regarding spatial response. The Clarity Index can also be considered as an inverse

measure for perceived reverberation [4].

Some aspects of the perception of spatial reverberation were studied during the

1960s which will be reviewed below. But before several important issues of spatial

hearing of reverberation were resolved, a second spatial e€ect was identi®ed which

has dominated much of the subsequent discussion. Marshall in his original publica-

tion [1] was in fact less speci®c about the subjective e€ect that he felt was crucial to

concert hall listening than many people probably imagine [5]. The e€ect of early

lateral re¯ections was quickly termed `spatial impression', whereas Marshall had

referred to `spatial responsiveness', a characteristic of the space in which the music is

performed. Two measures of spatial impression due to early re¯ections have

emerged, the early lateral energy fraction (LF) [6] and cross-correlation measures [7].

The early sound is generally taken as the ®rst 80ms after the direct. Sound level is

also considered to in¯uence perceived spatial impression, though the relative

importance of the spatial and level components is as yet unresolved [8].

In 1989, Morimoto and Maekawa [9] suggested that at least two subjective spatial

e€ects occurred. They provided evidence that a sense of being enveloped by sound

was independent of spaciousness (spatial impression caused by early re¯ections) and

that envelopment was linked to incoherence (a low interaural cross-correlation) of

the reverberant sound. Bradley and Soulodre [2,3] conducted further subjective

experiments into spatial hearing. Their experiments were conducted in an anechoic

chamber with a simulation system using ®ve (or three) loudspeakers arranged sym-

metrically in front or to the side of subjects. They found that sound from behind had

no special in¯uence on the subjective e€ects being studied, and they therefore did

not include loudspeakers behind the subjects. The simulations involved direct sound

followed by four discrete re¯ections and then reverberation whose relative level from

di€erent directions was varied.

Bradley and Soulodre basically agreed with Morimoto and Maekawa that there

were two spatial e€ects which had in the past often been confused. Bradley and

Soulodre called the two e€ects: source broadening and listener envelopment (LEV);

this nomenclature will be used here. (The expression `spaciousness' has been used to

mean di€erent things by di€erent authors and will only be used here in quotations.)

186

M. Barron / Applied Acoustics 62 (2001) 185±202

Source broadening can be measured by the perceived apparent source width (ASW).

Their experiments showed that ASW is predominantly determined by the early

sound, whereas envelopment is governed by the late sound. Most earlier work had

concentrated on source broadening, referring to it as spatial impression. Just as

perceived source broadening is in¯uenced by sound level, so Bradley and Soulodre

also found sound level to be signi®cant for LEV.

Bradley and Soulodre [3] proposed as an objective measure for LEV the late lateral

sound level, LG

1

80

or more simply GLL:

LG

1

80

…GLL† ˆ 10 log

…

1

0:08

p

2

F

…t†:dt=

…

1

0

p

2

A

…t†:dt

; dB

…1†

where p

F

t

… † is the pressure measured at a listener position with a ®gure-of-eight

microphone with the null pointing at the source and p

A

t

… † is the omni-directional

response to the same source at a distance of 10 m in a free ®eld. Time t is measured

relative to the arrival time of the direct sound. The late lateral sound level is

measured at four octave frequencies (125±1000 Hz) and averaged.

Sound direction in the horizontal plane can be simply divided into frontal, lateral

left and right and from the rear. In the case of source broadening, experiments have

shown that re¯ections from the rear produce the same e€ect as re¯ections which

arrive from in front with the same angle to the axis through the listeners ears [6,10];

listeners cannot perceive the sound as coming from behind them.

Bradley and Soulodre consider that for LEV listeners have the same insensitivity

to whether sound arrives from in front or behind, but there is, of course, a subjective

di€erence here: source broadening is heard in front of the listener whereas listener

envelopment involves feeling surrounded by sound, including the sense of receiving

sound from behind. Some researchers are unhappy with the notion that sound can

be perceived from behind when in reality no sound arrives at the listener from that

direction.

This paper ®rstly reconsiders some work on spatial perception of reverberation

from the 1960s. The remaining discussion considers measured values of the late lateral

energy fraction (LLF) and the late lateral level (GLL) and what design consequences

result if the GLL is to be optimised.

2. Room impression as studied in the 1960s

In the 1960s, German authors used the word `Raumeindruck' for the spatial

aspect of reverberation. This seems best translated as `room impression' to distin-

guish it from spatial impression generally used for the e€ect of early re¯ections.

Most experimental work in the 1960s involved simulations which produced di€use

reverberant sound ®elds. It is thus reasonable to equate the room impression from

these experiments with listener envelopment.

A key experience in simulations of concert hall acoustics is to vary the ratio of

direct to reverberant energy. Reichardt and Schmidt [11] quanti®ed the transition

M. Barron / Applied Acoustics 62 (2001) 185±202

187

from maximum room impression to zero perceived spatial reverberation in a paper

whose title can be translated as ``The audible steps of room impression with music''.

Subjects were presented with direct sound and reverberation from a reverberation

plate (reverberation time 2 s). Four incoherent reverberation signals were fed to four

loudspeakers arranged at 45

and 135

in azimuth relative to straight ahead of

the subject. The onset of reverberation was delayed 50 ms after the direct sound. The

reverberant separation, H (Hallabstand), was varied while the total level was kept

constant; H is the direct sound level relative to the reverberant. It is equivalent to

C

50

in this experiment.

Subjects determined just noticeable di€erences (jnd) which led to a 15 point scale

of room impression (Fig. 1). However the range of room impression used in this

experiment is much larger than encountered in concert halls. A proposed preferred

range for C

80

is between 2 dB [12], which is only three steps of room impression.

Slightly larger ranges of C

80

are found in actual halls so one can conclude that only

four or ®ve steps are perceived in practice.

Schmidt [13] subsequently extended the experiment using the same apparatus but

varying both the reverberant separation H and the reverberation time. The experi-

ment showed that H was not a unique measure of room impression. An attempt by

Reichardt [14] to resolve the question of room impression for impulse responses

containing both early re¯ections and reverberation did not prove entirely successful

since two measures emerged, one more successful in reverberant ®elds and the other

in unreverberant sound ®elds. In retrospect, one can interpret Reichardt's diculties

to a lack of understanding of the role of early lateral re¯ections.

Major experimental work relating to room impression was also conducted at

GoÈttingen. Damaske [15] investigated what was required in order to simulate the

Fig. 1. Perceived room impression as a function of reverberant separation (direct relative to reverberant

level) after Reichardt and Schmidt [11]. One unit of room impression corresponds to one just noticeable

di€erence.

188

M. Barron / Applied Acoustics 62 (2001) 185±202

e€ect of a di€use reverberant ®eld, without the hundreds of interfering re¯ections

which exist in real rooms. Most of his experiments were undertaken with continuous

noise signals. Fig. 2 illustrates the results of two experiments using (a) two and (b)

four incoherent noise signals; subjects were required to indicate the areas in the

hemispherical space above them from which they heard sound.

One can conclude from Fig. 2 that, except for sound arriving only in the median

plane [last diagram in Fig. 2(a)], sound is perceived as arriving from the region

between the various directions of the incident sound. The directional acuity of lis-

teners is seen not to be large but, for a sense of subjective di€useness, sound must

arrive from four principal directions. Unfortunately no result is presented for sound

from the front, back and two sides.

The importance of Damaske's work at the time is recorded by Kuttru€ ([16]

p. 197): ``For a long time it was common belief among acousticians that spacious-

ness (i.e. a sense of subjective di€useness) was a direct function of the uniformity of

the directional distribution in the sound ®eld: the higher the di€usion, the higher the

degree of spaciousness. This belief originated from the fact that many old and highly

renowned concert halls are decorated with statuettes, pillars, co€ered ceilings and

other projections which supposedly re¯ect the sound rather in a di€use manner than

specularly. It was the introduction of synthetic sound ®elds as a research tool which

led to the insight that the uniformity of the stationary directional distribution is not

a primary cause of spaciousness''.

In retrospect, one might question generalising from Damaske's result, which used

noise signals, to the case of music in concert halls. But the design solution with all

surfaces highly di€using (as in the Beethovenhalle, Bonn of 1959 [12]) has only

rarely been used since.

Neither of the studies from the 1960s is conclusive regarding room impression

(envelopment) but, reviewing this work in 1970, one would have probably concluded

that spatial reverberation depended on sound arriving from all four key directions

and that the magnitude of perceived room impression was determined by the ratio of

early to reverberant sound.

3. Measurement procedures in British concert halls

Objective measurements have been made in 17 unoccupied British halls which are

used for concert performance (Table 1). Detailed accounts of the individual halls

are to be found in [12]. The survey used an omni-directional loudspeaker at a central

position close to the front of the stage and a microphone of variable directivity

placed at ear height in audience locations. On average, 11 microphone positions

were used per hall. The source was placed 3 m from the stage front. The survey used

single cycle sine pulses as signals with the impulse responses being recorded on

analogue tape. The microphone used was an AKG C414EB; careful calibration of

the relative sensitivities of the ®gure-of-eight and omni-directional characteristics is

needed with this sort of microphone. The expressions for the early lateral energy

fraction (LF) and late lateral energy fraction (LLF) are:

M. Barron / Applied Acoustics 62 (2001) 185±202

189

Fig. 2. Perceived areas in the hemisphere above subjects listening to incoherent noise signals in an

anechoic chamber after Damaske [15]. Arrows indicate the positions of loudspeakers with (a) two loud-

speakers and (b) four loudspeakers.

190

M. Barron / Applied Acoustics 62 (2001) 185±202

LF ˆ

…

0:08

0:005

p

2

F

…t†:dt=

…

0:08

0

p

2

O

…t†:dt LLF ˆ

…

T

0:08

p

2

F

…t†:dt=

…

T

0:08

p

2

O

…t†:dt;

…2†

where p

F

t

… † is the pressure measured at the listener position with the ®gure-of-eight

characteristic with the null pointing at the source and p

O

t

… † is the pressure measured

with the omni-directional characteristic. Time t ˆ 0 is the arrival time of the direct

sound; the limiting time, T, for integration for the LLF was taken as 0.4 rever-

beration time to ensure sucient accuracy without contamination by background

noise. The responses were analysed by computer to produce results in the four

octaves between 125 and 1000 Hz.

To calculate the late lateral level (GLL), a measurement is also required of the

total relative sound level (G). The total sound level is measured with the same

loudspeaker fed with calibrated octave noise signals, while the sound level in the

same seat locations was measured with sound level meters. Further details about the

measurement procedure are given in [17].

4. Mean values and distributions of lateral energy fractions

Table 2 lists the mean values and standard deviations for the 189 early and late

lateral energy fractions measured in the 17 halls. The early lateral energy fraction

Table 1

Basic details of the 17 British concert spaces

Hall

Label Year of

completion

Seating

capacity

a

Volume

(m

3

)

Mean

width

(m)

Plan

form

Royal Festival Hall, London

F

1951

2645+256 21 950

32

Parallel-sided

Royal Albert Hall, London

A

1871

4670+419 86 650

47

Queen Elizabeth Hall, London

Q

1967

1106

9600

23

Parallel-sided

Barbican Concert Hall, London

R

1982

2026

17 750

34

Wigmore Hall, London

G

1901

544

2900

13

Parallel-sided

Fair®eld Hall, Croydon

C

1962

1539+250 15 400

26

Wessex Hall, Poole

P

1978

1473+120 12 430

30

Parallel-sided

Colston Hall, Bristol

B

1951

1940+182 13 450

22

Parallel-sided

St. David's Hall, Cardi€

D

1982

1687+270 22 000

34

Assembly Hall, Watford

W

1940

1586

11 600

22

Music School Auditorium,

Cambridge

S

1977

496

4100

20

Parallel-sided

Royal Concert Hall, Nottingham N

1982

2315+196 17 510

26

Free Trade Hall, Manchester

M

1951

2529

15 400

22

Philharmonic Hall, Liverpool

L

1939

1767+184 13 560

27

Parallel-sided

Usher Hall, Edinburgh

E

1914

2217+333 16 000

29

Conference Centre, Wembley

Y

1976

2511

24 000

50

Fan-shape

Butterworth Hall,

Warwick University

K

1981

1152+177 12 100

30

Parallel-sided

a

The second number refers to choir seating.

M. Barron / Applied Acoustics 62 (2001) 185±202

191

results are discussed in more detail elsewhere [8]. One observes that the mean early

fraction is signi®cantly lower than the late. A major reason for this is surely that the early

sound contains the direct sound which by de®nition is not lateral. The mean value of the

late lateral energy fraction at 0.31 is very close to the theoretical value for a di€use sound

®eld of 0.33. The scatter of measured values is small for the late lateral energy fraction.

Fig. 3 shows the distributions of both the early and late lateral energy fractions.

Tests on the statistical normality of each set of data using the

2

test show the early

lateral energy fraction to be ``almost certainly not normal'' with a con®dence limit of

over 0.1%. On the other hand the

2

test on the late lateral energy fraction shows

that the data is ``highly normal'' (signi®cantly less than the P=10% value).

Fig. 4 shows the means and standard deviations of measurements of the early and

late lateral energy fractions as a function of frequency. Though the mean of the early

Table 2

Means and standard deviations of measured early and late lateral energy fractions

a

Early lateral

energy fraction

Late lateral

energy fraction

Di€use

Mean

0.19

0.31

0.33

Standard deviation

0.085

0.047

±

Distribution

Not normal

Highly normal

±

a

Data set of 189 values.

Fig. 3. Distributions of the early and late lateral energy fractions as measured at 189 receiver positions.

192

M. Barron / Applied Acoustics 62 (2001) 185±202

fraction is constant with frequency, the late fraction has lower values at the lower

frequencies. Since the measurement systems for both fractions were identical, and

indeed the two fractions were derived from the same impulses responses, these lower

values of the late fraction at low frequencies would seem to be either a feature of

sound ®elds or a consequence of the measuring process. The second looks unlikely

since consideration of the di€erences between the character of early and late sound

does not obviously lead to this conclusion. (This could be checked by rotating the

®gure-of-eight microphone through 90 degrees and measuring the late frontal energy

fraction.)

Nor is there an obvious reason why the directional character of the late sound

®eld should vary with frequency. For instance, a major in¯uence on low frequency

sound is attenuation at grazing incidence, also known as the seat dip e€ect, but if the

late sound ®eld is di€use, we would expect attenuation at grazing incidence to e€ect

both frontal and lateral sound and thus have a neutral e€ect on the late lateral

energy fraction. It is just possible that the low values of late fraction at low fre-

quencies indicate less di€use sound ®elds at these frequencies.

The other feature to note in Fig. 4 is that the scatter of measured values of both

the early and late lateral fractions is smallest at mid-frequencies (500/1000 Hz) and

largest at 125 Hz.

Apart from unresolved details regarding frequency, the conclusion regarding the

late lateral energy fraction is that it is randomly distributed with a small degree of

scatter around a mean, which is close to the value expected in a di€use sound ®eld.

Fig. 4. Octave means 1 standard deviation for the measured early and late lateral energy fractions.

M. Barron / Applied Acoustics 62 (2001) 185±202

193

5. Late lateral energy fractions averaged by hall

When late lateral energy fractions are averaged by hall, the hall means only vary

between 0.25 and 0.34, a range of 0.09 compared with a range of 0.20 for the early

lateral energy fraction [8].

The hall mean values have been compared to various hall parameters by regression

analysis. The following were considered but found to be unrelated to the mean late

lateral energy fraction (LLF): auditorium volume, seat capacity and mid-frequency

reverberation time. The only parameter found to correlate with mean LLF was hall

width, with a correlation coecient of r ˆ ÿ0:55 signi®cant at the 5% level. (The

corresponding coecient for the early lateral energy fraction is ÿ0.59, signi®cance

level <2%.) Mean LLF is plotted in Fig. 5 against hall width.

One observes in Fig. 5 that the narrowest hall (G, Wigmore Hall, London) is one

of three halls with the highest measured LLF, whereas the widest (Y, Wembley

Conference Centre) has the lowest LLF. The Wembley hall is semicircular in plan,

which is an extreme form of fan-shape; one notes that it sits below the regression line

in Fig. 5. On the other hand, the Royal Albert Hall, London (A) behaves well for its

width with regard to LLF. In spite of its well-known faults [12], the Royal Albert

Hall does have a particularly good dynamic response with extremely smooth tran-

sitions during crescendos. A good dynamic response is thought to be a characteristic

of di€use sound ®elds and the result here regarding the mean hall LLF provides

objective evidence to corroborate this subjective observation.

Another outlier in Fig. 5 deserves comment: the Assembly Hall, Watford (W) has a

low mean LLF value for its width. This rectangular-plan hall has six large windows

along each side wall which are covered with curtains; this surely in¯uences lateral

re¯ections and therefore lateral fractions.

Fig. 5. Hall mean late lateral energy fractions as a function of hall width. Hall labels according to second

column of Table 1.

194

M. Barron / Applied Acoustics 62 (2001) 185±202

6. Late lateral energy fractions within halls

The standard deviation (S.D.) for LLF measurements within halls ranges from

0.02 to 0.06, with a mean S.D. of 0.04. Again this is smaller than the within hall

mean standard deviation of 0.06 for the early lateral fraction.

An interesting observation can be made on the halls with the lowest standard

deviations for the LLF; there are four halls with a standard deviation of 0.03 or

0.02. Two of these halls are the smallest in volume and seating capacity of the 17

measured: Cambridge Music School and the Wigmore Hall, London. The other two

halls with low scatter of LLF are St. David's Hall, Cardi€ and the Butterworth Hall,

Warwick University. Both these halls have designs which are likely to promote a

di€use sound ®eld [12]. In the case of St. David's Hall, the audience seating is

arranged in ``vineyard terraces'' and the ceiling is highly di€using; both character-

istics are good for di€use late sound. The Warwick University hall also has a highly

di€using ceiling.

Within each hall, the behaviour of the late lateral energy fraction has been com-

pared with two distances: the source-receiver distance and the lateral distance, the

distance of the measurement position from the axis of symmetry. In three (out of the

17 halls) there is a positive correlation (at the 10%) level between source-receiver

distance and LLF, whereas there is one hall with a negative correlation at the 10%

level. Three other halls exhibit positive correlations of LLF with lateral distance.

None of this behaviour is very consistent nor is there any correlation between LLF

values and either source-receiver distance or lateral distance for the whole data set.

7. Comparison between measured early and late lateral energy fractions

Fig. 6 is a scatter diagram for the 189 measured values of the early and late lateral

energy fractions. The correlation coecient is 0.45. Though this correlation is statis-

tically signi®cant (at the 0.1% level), there is probably a considerable random element.

We would not expect a good correlation since the early and late sound have di€erent

characters. The late sound consists of many interfering re¯ections with an approxi-

mately di€use directional distribution. The early sound is dominated by the direct

sound and discrete early re¯ections; the relative level of the direct sound is a function of

source±receiver distance and the early re¯ections are determined by the hall geometry.

In the light of the above, it comes as a surprise to observe the relationship between

hall mean early and late energy fractions (Fig. 7). With a correlation coecient of

0.80 signi®cant at the 0.1% level, one concludes that the hall average LLF is

strongly determined by the average early lateral fraction. The regression equation is:

Mean late lateral fraction=0.37 * Mean early lateral fraction+0.24
In view of the relationship between hall mean lateral fractions, the correlation

between both hall mean fractions and hall width mentioned in Section 5 is expected.

Regarding the relationship in Fig. 7, the surprise arises due to the di€erent direc-

tional distributions of early and late sound incident on room surfaces. Late re¯ections

M. Barron / Applied Acoustics 62 (2001) 185±202

195

arriving at listeners from the side have been incident on the side wall surfaces from

all directions. The early sound is generally dominated by the ®rst-order re¯ections,

which have originated from the source only. Thus, a small plane surface which

provides ®rst-order early lateral re¯ections will only provide late lateral re¯ections

Fig. 6. Late versus early lateral energy fractions in 17 concert spaces.

Fig. 7. Mean hall late versus mean hall early lateral energy fractions. Hall labels according to second

column of Table 1.

196

M. Barron / Applied Acoustics 62 (2001) 185±202

for sound which originates from the stage area; the surface does not produce late

lateral re¯ections for sound originating from elsewhere.

In two situations, one can argue that hall design features would promote both

early and late lateral re¯ections. If the side wall surfaces are highly di€using, then

the angle of incidence on these surfaces is irrelevant and we could expect the strength

of both early and late lateral sound to be similarly in¯uenced by the location of these

surfaces. Likewise, a large side wall surface will provide lateral re¯ections to listeners

both for sound originating at the source and sound from other directions ``visible''

from the side wall surface. Only a few of the 17 halls measured have particularly

di€using side walls but many have large side wall surfaces.

It can be concluded that design for good early lateral re¯ections is on average

good for late lateral re¯ections. However, the di€erences between the mean values of

the late lateral fraction for halls are small.

8. Determinants of the late lateral level

As discussed in Section 1, Bradley and Soulodre [3] have proposed the late lateral

level (GLL) as a measure for perceived listener envelopment (LEV). In practice, the

late lateral level is likely to be calculated from measured values of three quantities: the

total relative sound level (G), the early-to-late sound index (C

80

) and the late lateral

energy fraction (LLF). The calculation uses the logarithmic version of the late lateral

energy fraction, which can be called the late lateral index [LLI=10. log(LLF)].

Late lateral level; GLL ˆ Late level ‡ 10: log LLF

…

†

ˆ G ÿ 10: log 1 ‡ 10

C

80

=10

ÿ

‡ 10: log LLF

…

†

…3†

In other words, the late lateral level is the sum of a level term (the late level G

L

)

and a directional term based on the late lateral energy fraction. It is of interest to

establish the relative importance of level and late re¯ection directivity for the late

lateral level. With knowledge of their relative importance, it may be possible to

establish the design implications to achieve a high late lateral level.

As part of the original acoustic survey of British auditoria, both C

80

and G were

measured [17]. Octave results for each measure were combined into two frequency

bands: a bass frequency (125 and 250 Hz octaves) and mid-frequency band (500,

1000 and 2000 Hz). From these the bass and mid-frequency late levels have been

calculated. These two levels have been averaged by taking antilogs, averaging and

taking logarithms to give a mean late level. The late lateral energy fraction is mea-

sured over the frequency range 125±1000 Hz. The minor discrepancy in frequency

range for the late level is very unlikely to be of signi®cance. The measurements in

halls were made in unoccupied auditoria and no corrections for occupancy have

been made; the validity of the arguments below is not likely to be a€ected by this

either. Levels are quoted relative to the level of the direct sound at 10 m from the

omni-directional source.

M. Barron / Applied Acoustics 62 (2001) 185±202

197

Table 3 lists the basic statistics of the measured components in Eq. (3). Bradley

and Soulodre [3] quote a measured range from ÿ14.4 to +0.8 dB for GLL, which is

in good agreement with the range in British halls. One notices in Table 3 that the

standard deviation for the late lateral index is much smaller than that for the late

level. The ratio of these two standard deviations can provide us with the information

we are seeking: the relative importance of the late level, G

L

, and directivity, LLI,

towards the late lateral level, GLL. However one condition needs to be ful®lled for

this ratio to be used, it is necessary that the G

L

and LLI are independent of one

another. The very low correlation coecient between them of 0.073 suggests that

they are independent. A better check involves normalising G

L

, LLI and GLL by

subtracting the relevant mean value in each case. The sums of squares for each

normalised quantity is calculated, as is the sum of the cross-products between G

L

and LLI. The sum of squares for GLL is 2157 and the sum of cross-products is 30,

which is considered small enough to indicate independence between G

L

and LLI.

The relative importance of G

L

compared with LLI for the late lateral level is thus

3.27/0.68=4.8. In other words, the level G

L

contributes to 83% of the variation of

the late lateral level and the late lateral index only contributes towards 17% of the

variation. Inspection of the correlation coecients in ®nal row of Table 3 provides

qualitative support for this conclusion. The late lateral level is thus in practice

principally determined by the level of the late sound. Though the late lateral energy

fraction was found to be related to hall width and the mean hall early lateral energy

fraction, these variations have only a small in¯uence on the proposed measure, the

late lateral level.

The discussion now turns to the late level and what are the main determinants of

the late level. Two theoretical values are considered for comparison with the mea-

sured late levels: the traditional re¯ected sound level and the late sound level

according to revised theory [12]. For both theoretical values, linear regressions have

been conducted with measured values. The results of the regression analysis are

presented in Table 4.

Details of revised theory are given in the Appendix. The comparison of measured

with prediction according to revised theory is shown in Fig. 8. Agreement is good

with a regression line with a slope of unity. The reasons for the level di€erence of

0.9 dB have already been discussed in detail; they include such things as the e€ects

Table 3

Measured means, standard deviations and range of values for the components in Eq. (3)

a

Late level

(G

L

)

Late lateral

index (LLI)

Late lateral

level (GLL)

Mean (dB)

0.3

ÿ5.2

ÿ4.8

Standard deviation (dB)

3.27

0.68

3.39

Range (dB)

ÿ8.4 to +8.2

ÿ7.2 toÿ3.4

ÿ14.1 to +3.4

Correlation coecient for regression with GLL

0.98

0.27

(1.00)

a

Data set of 189 values.

198

M. Barron / Applied Acoustics 62 (2001) 185±202

of balcony overhangs [18], absorption in the stage area [17], a fan-shaped hall [12]

and attenuation at grazing incidence in the bass [19].

Revised theory was developed in response to the observed reduction in sound level

in concert halls as one moves away from the source. The theory matches measured

behaviour well on average. The expression for the theoretical late sound according

to revised theory contains three terms:

Theoretical G

L

ˆ 10: log

31200:T

V

ÿ

482

T

ÿ

0174:r

T

…4†

where T is the reverberation time, V the auditorium volume and r the source±receiver

distance. The ®rst term is the traditional one for the re¯ected sound level (assuming

Table 4

Results of linear regression between measured and theoretical late levels

a

Slope

Di€erence of

means (dB)

Correlation

coecient, r

Standard error of

estimate (dB)

Correlation of measured with:

Late sound according to revised theory

0.99

ÿ0.9

0.89

1.5

Traditional re¯ected sound level

1.04

ÿ5.8

0.82

1.9

a

Data set of 189 values.

Fig. 8. Measured late sound level relative to the theoretical late sound level according to Eq. (4), includ-

ing line of best ®t.

M. Barron / Applied Acoustics 62 (2001) 185±202

199

Sabine's reverberation time equation is valid). The second term relates to it being the

late sound arriving more than 80 ms after the direct sound. The third term takes

account of the arrival time of the direct sound after it is emitted from the source; this

term provides the variation in level with position. The theoretical late level accord-

ing to Eq. (4) is used in Fig. 8.

One question of interest in concert halls is whether the sense of envelopment varies

with distance from the source. The variation in late level with distance in a typical hall is

2.6 dB (30 m range, RT=2 s). If the late lateral level is the relevant measure, then we

expect the sense of envelopment to reduce as we move away from the source; the 2.6 dB

range should be compared with the total measured range for the late lateral level of

17.5 dB. On this basis, the variation with distance may not be subjectively signi®cant.

Eq. (4) contains three variables on the right hand side. Can we usefully reduce the

correlation of measured late levels to a single objective measure? Table 4 also

includes the correlation between the measured late level and the traditional expression

for the re¯ected sound [the ®rst term in Eq. (4)]. The correlation between the mea-

sured value and traditional theory is still good with a standard error of 1.9 as

opposed to 1.5 dB for revised theory.

The conclusion therefore regarding the major in¯uence on the late lateral level has

to be that it is the ratio of reverberation time to auditorium volume, in other words

the total acoustic absorption. We would thus expect the sense of envelopment to be

high in small halls and low in large halls.

Sound level for the listener is also determined by the performance and ¯uctuates during

a piece of music. For comparison between halls it is appropriate to compare halls when

used with similar musical forces. We can expect on the basis of the late lateral level to

experience the greatest sense of envelopment when a large orchestra plays in a small hall.

9. Conclusions

The proposal by Bradley and Soulodre on spatial hearing in rooms is a major

advance in our understanding of auditorium acoustics. They have clari®ed the dis-

tinction between the spatial e€ects created by early and late re¯ections. Their work

led them to propose a speci®c measure, the late lateral sound level (GLL), as relating

to listener envelopment (LEV).

The aim of this paper was to determine what were the design implications of the

late lateral level and to consider whether there was any evidence that the late lateral

level might not be the ®nal answer to the envelopment question.

The late lateral level can be considered as the sum of two components: a directional

component based on the late lateral energy fraction (LLF) and a level component.

Analysis of measured values collected from 17 British music spaces showed that the

LLF does not vary much between or within halls. The late lateral level was dis-

covered to be substantially determined by the late level. And the late level itself was

found to be principally linked to the total acoustic absorption in halls. This leads

one to the conclusion that listener envelopment should be high in small halls and

low in large ones. Subjective studies at real concerts would be welcome to establish

200

M. Barron / Applied Acoustics 62 (2001) 185±202

whether this simple conclusion is valid, and also to ®nd out whether there are sig-

ni®cant changes in perceived LEV within halls. It is possible that the late lateral level

is biased too far towards the level component. Is the design criterion for good

envelopment just to optimise sound level?

Objective measures involving energy are either absolute or relative. Sound level is

an absolute measure, as is the proposed late lateral level; other components of the

sound excluded from the late lateral level are assumed not to in¯uence the subjective

e€ect. A relative measure involves the balance between one component and another,

as in the Clarity Index, C

80

. A relative measure takes into account the masking of

one sound component by another. Using a very simple impulse response, Reichardt

and Schmidt found that room impression, which is surely equivalent to envelopment,

was determined by the balance between direct and reverberant sound. (They used a

relative measure but in fact, because total level was kept constant in their experi-

ment, an absolute measure of reverberant sound level would have worked as well!)

Is listener envelopment really immune to the relative level of early sound, for

instance? Bradley and Soulodre [2,3] provide evidence that variations in C

80

have

some in¯uence on perceived LEV, but reject it as a major in¯uence.

The ®nal question concerns the role of sound from behind. To this author, the

presence or absence of sound from behind can be perceived in concert halls. The

proposal that sound from behind is irrelevant to the sense of feeling surrounded by

sound is surprising.

Acknowledgements

I am grateful to the managements of the various halls for allowing access to make

measurements in their halls. The measurement work was undertaken while the

author was at the Martin Centre for Architectural and Urban Studies, Cambridge,

with the assistance of Lee-Jong Lee. The measurement programme was supported

by the Science and Engineering Research Council.

Appendix. Revised theoretical level for late sound

Energies are expressed relative to the direct sound at 10 m from the omni-directional

source. The expression for the direct sound is the traditional one with the direct

energy=100/r

2

, where r is the distance from the source. According to revised theory,

the late sound energy, l, arriving later than 80ms after the direct sound is [17]:

l ˆ 31200T=V

…

†e

ÿ1:11=T

:e

ÿ0:04r=T

:

where V is the auditorium volume, T the reverberation time. Hence the late level is

Theoretical G

L

ˆ 10: log

31200:T

V

ÿ

482

T

ÿ

0174:r

T

dB:

M. Barron / Applied Acoustics 62 (2001) 185±202

201

References

[1] Marshall AH. A note on the importance of room cross-section in concert halls. Journal of Sound

and Vibration 1967;5:100±12.

[2] Bradley JS, Soulodre GA. The in¯uence of late arriving energy on spatial impression. Journal of the

Acoustical Society of America 1995;97:2263±71.

[3] Bradley JS, Soulodre GA. Objective measures of listener envelopment. Journal of the Acoustical

Society of America 1995;98:2590±7.

[4] Barron M. The Gulbenkian Great Hall, Lisbon, II: an acoustic study of a concert hall with variable

stage. Journal of Sound and Vibration 1978;59:481±502.

[5] Marshall AH, Barron M. Spatial responsiveness in concert halls and the origins of spatial impres-

sion. Applied Acoustics, 2000;62(2):91±108.

[6] Barron M, Marshall AH. Spatial impression due to early lateral re¯ections in concert halls: the

derivation of a physical measure. Journal of Sound and Vibration 1981;77:211±32.

[7] Keet W de V. The in¯uence of early lateral re¯ections on the spatial impression. Proc 6th Interna-

tional Congress on Acoustics, Tokyo, 1968, paper E-2-4.

[8] Barron M. Measured early energy fractions in concert halls and opera houses. Journal of Sound and

Vibration, 2000;232:79±100.

[9] Morimoto M, Maekawa Z. Auditory spaciousness and envelopment. Proc 13th International Con-

gress on Acoustics, Belgrade, 1989;2:215±8.

[10] Morimoto M, Iida K, Sakagami K. The role of re¯ections from behind the listener in spatial

impression. Applied Acoustics, 2000;62(2):109±24.

[11] Reichardt W, Schmidt W. Die hoÈrbaren Stufen des Raumeindruckes bei Musik. Acustica

1966;17:175±8.

[12] Barron M. Auditorium acoustics and architectural design. London: E & FN Spon, 1993.

[13] Schmidt W. Zusammenhang zwischen Hallabstand und Nachhallzeit fuÈr den Raumeindruck (Hal-

ligkeit und RaÈumlichkeit bei Musik). Hochfrequenz und Electroakustik 1968;77:37±42.

[14] Reichardt W. Der Impuls-Schalltest und seine raumakustische Beurteilung. In: Proc 6th Interna-

tional Congress on Acoustics, Tokyo, 1968, paper GP-2-2 p. GP11±20.

[15] Damaske P. Subjektive Untersuchungen von Schallfeldern. Acustica 1967;19:199±213.

[16] Kuttru€ H. Room acoustics. 3rd ed. London: Elsevier Applied Science, 1991.

[17] Barron M, Lee L-J. Energy relations in concert auditoriums, I. Journal of the Acoustical Society of

America 1988;84:618±28.

[18] Barron M. Balcony overhangs in concert auditoria. Journal of the Acoustical Society of America

1995;98:2580±9.

[19] Barron M. Bass sound in concert auditoria. Journal of the Acoustical Society of America

1995;97:1088±98.

202

M. Barron / Applied Acoustics 62 (2001) 185±202