Visual assessments of the surface di€usion

properties of concert halls

Fergus R. Fricke*

Department of Architectural and Design Science, University of Sydney, NSW 2006, Australia

Received 17 September 1999; received in revised form 15 October 1999; accepted 1 November 1999

Abstract

The di€usion of sound in concert halls has been recognized as signi®cant in determining the

acoustic quality of halls. The di€usion of sound in rooms is dicult to assess as are the dif-

fusing properties of surfaces. The collective di€using properties of the walls, ¯oor and ceiling

in a hall would seem to be almost impossible to assess objectively but such an assessment is

needed for the design of concert halls. In this paper it is shown, indirectly, that visual assess-

ments of the di€usion of concert hall interiors appears to be repeatable and reproducible to a

degree which will allow halls to be designed to one of three broad classi®cations; ``excellent'',

``good'' or ``fair''. # 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction

It has been suggested by Beranek [1] that there are six orthogonal acoustic prop-

erties of auditoria: IACC

E3

, t

I

, EDT, G

mid

, BR and SDI. IACC

E3

is the average

early interaural correlation coecient, t

I

is the time delay between the direct and

®rst re¯ected sound at the centre of the main seating area, EDT is the early decay

time in the hall, G

mid

is a measure of the average sound level in a hall at mid-fre-

quencies, BR is the bass ratio, i.e. the ratio of the reverberation time at low to mid

frequencies and SDI is the surface di€usivity index of the hall surfaces, i.e. a mea-

sure of the di€using properties of the interior surfaces. SDI, like di€usion, is a dif-

®cult quantity to estimate or measure for a particular surface and to get a

representative value for a concert hall would seem even more dicult. This paper

investigates the ecacy of using visual assessments of the acoustic di€usion of sur-

faces for the assessment of concert halls.

Applied Acoustics 60 (2000) 253±261

www.elsevier.com/locate/apacoust

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PII: S0003-682X(99)00060-2

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

E-mail address: [e-mail] (F.R. Fricke).

Visual assessments of the acoustic di€usion properties of surfaces in concert halls

have been made but the repeatability and reproducibility of these has not been

assessed. The paper by Haan and Fricke [2] was based on one person's assessments

of the acoustic di€usion properties and there was only indirect evidence of the dif-

fusion properties of the surfaces surveyed; there was no direct linking of assessed

di€usion and the actual di€usion. Such a comparison would be extremely valuable but is

unlikely to occur because of the amount of work involved and the diculty in assessing

the di€usion of seating areas and balconies and the interaction of the various elements

making up a concert hall.

Another approach to the evaluation was taken by Fricke and Han [3] when they

used assessed values of the level of ``discontinuities'' in surfaces in a neural network

analysis to predict the acoustic quality of concert halls. They used 10 inputs to the

neural network; room volume, surface area, maximum length, width and height, the

number of seats, the mean rake angle of the seating, the stage height, a stage enclo-

sure index and a SDI. The last two of these inputs were estimated by a group of

practicing architects from photos and drawings of the halls.

This approach [2] was an indirect way of linking the assessed surface di€usion

values to acoustic quality. It does not indicate whether the visual assessments of

di€usion do in fact a€ect acoustic di€usion (nor does it help substantiate Beranek's

concert hall acoustic model as geometric inputs, rather than acoustic inputs, were

used.). Theirs was a realistic attempt to assess the importance of di€usion but it

assumes, amongst other things, that visual assessments of ``discontinuities'' in surfaces

are related to the acoustic di€using properties of those surfaces. It also assumes that

the visual assessments are reproducible and that surface treatments are the main

producers of di€usion and not factors like the seating, the shape of the halls and hall

reverberation characteristics. No account was taken of the patterns of asperities or

``roughness'' elements on surfaces that will in¯uence the di€usion of sound. The

e€ect of curved surfaces on di€usion was also dicult to assess.

This paper takes another approach. If visual assessments are going to work then

they must be repeatable and consistent, amongst individuals or groups which make

them. The paper investigates these aspects. It also uses surface di€usion data toge-

ther with other orthogonal measures of the acoustics of auditoria [EDT, t

I

, G

mid

, BR

and (1-IACC

E3

)] (see Beranek [1], p. 517) to estimate the acoustic quality of halls

using neural network analysis. Besides being an indirect way of assessing whether

visual assessments of concert hall di€usion can be used to predict the acoustic

quality of halls the neural network analysis developed should also be a valuable

semi-independent evaluation of whether Beranek's six orthogonal variables can be

used to predict the performance of halls.

2. Neural network analysis of concert hall quality using acoustic measures

There seems to be reasonable agreement on the need for acoustic measures of

auditoria and concert halls. It is recognized too that there are optimum values of

these measures but there does not appear to have been any attempt to check whether

254

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

combinations of less than optimal acoustic measures can still result in a highly

regarded concert hall. Nor does there appear to be a substantiation of how much

each of the six orthogonal measures contributes to the overall perception of the

acoustics of a hall [1,3]. Beranek suggests that the contribution of each parameter is

(1-IACC

E3

): 25%, EDT: 25%, SDI: 15%, G

mid

: 15%, t

I

: 10% and BR: 10% but

there is no compelling evidence that these percentages are correct for all combina-

tions of acoustic measures or that the contribution of each of these factors can be

summed linearly. Neural network analysis (described in texts such as [4] and [5])

provides a possible method of investigating whether the relationship between

acoustic quality and the acoustic parameters is linear or non-linear. It could also

provide a more objective assessment of the contribution of each parameter to the

overall acoustic quality. In this paper neural network analysis is used to investigate

the importance of surface di€usion only.

For the neural network analysis Beranek's data was used. The inputs were as

above. The outputs were grouped as in Beranek's work (A+, A: categorized as

``excellent'', B+: categorized as ``good'' and B, C+, C: categorized as ``fair''. For

training the network the majority of halls were in the ``good'' category (18) while in

the ``excellent'' category there were seven and the ``fair'' category there were ®ve.

Two halls from each category were used for validation. Thus 24 halls were used for

training the network and six for validation. The number of halls for the training and

validation are minimal and are one of the limitations of the present work.

The neural network software, ``Brainmaker'' [6], was used with three layers of

neurons and with three neurons in the hidden layer. Training was undertaken to a

tolerance of 0.35 (this level of training tolerance is governed by the three categories

of acoustic quality that were used.) The validation resulted in the correct categor-

ization of four of the six halls. Such a result does not seem good but as the training

tolerance was large this is a reasonable result, especially as both of the ``excellent''

halls were correctly predicted. One of the two incorrectly predicted halls (Lie-

derhalle, Stuttgart) was a borderline case and a change of 10% in the assessment of

SDI resulted in the correct prediction of acoustic category (This is an important

result and will be dealt with below.). The second incorrectly predicted hall result was

for the Barbican Concert Hall in London. The neural network analysis prediction

indicated that this hall would be classed as ``good'' whereas Beranek put it in the

lowest of his three acoustic categories. While this miscategorization may be a result

of the failure of the neural network analysis it may also be an indication of limita-

tions of the six input parameter model or the assessment of the acoustic quality.

Despite the result for the Barbican Concert Hall the neural network approach seems

to support Beranek's six parameter model.

It seems then that we have a useful method of predicting the acoustic quality of

concert halls using Beranek's six acoustic quantities as inputs. This assessment can

be undertaken using Beranek's procedure or using neural network analysis, which

does not rely on weightings or on a linear summation, to obtain an acoustic eva-

luation. The neural network analysis can also be used to determine how sensitive

the analysis is to changes in SDI and hence how accurately SDI needs to be

determined.

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

255

The neural network analysis shows that:

1. Using Beranek's six acoustic parameters as inputs (and his SDI values of hall

surfaces) better concert halls are achieved with higher SDI values, as suggested

by Beranek [1], Haan [7, 8] and others.

2. That the importance of SDI varies from hall to hall. There are some halls that

are relatively insensitive to SDI change, except at very high or very low values

of SDI, while other halls show a fairly steady change over the whole range of

SDI values. For instance, the Concertgebouw, Amsterdam, and Colston Hall,

Bristol are predicted to have the highest of the three Beranek hall acoustic

ratings for 0.4<SDI<1.0. Boston Symphony Hall is only a top rating hall if

the SDI is unity. No amount of di€usion would seem to improve the Royal

Albert Hall, or the Roy Thompson Hall. The DeDoelen and Costa Mesa halls

show that the amount of di€usion has a more uniform e€ect and the halls

could fall into the lowest, middle or highest acoustic categories, depending on

the amount of surface di€usion.

3. In some cases a relatively small error in assessing the SDI value could result in

a hall being ranked at the opposite end of the quality scale. For example, the

Concertgebouw would change from the highest ranking to the lowest if its SDI

changed from 0.3 to 0. As was indicated above, the Liederhalle, Stuttgart was

sensitive to a 10% change in the SDI. This is, to some extent, an artifact of

classifying halls into one of three groups and would not be as much an issue if

a continuous scale was used.

At this stage of the research there are no reliable statistics on the errors to be

expected from miscategorizing SDI values but it would seem that about 70 to 80%

of halls would be correctly categorized using an SDI which was within ‹0.2 and

about 90% if the SDI was within ‹0.1. This is of concern because it is unlikely that

two people would rank the SDI of halls in the same way even if they were given the

same instructions and same photographs. The following section looks at the possible

variations in the assessment of SDI values.

3. Surface di€usion assessments

This part of the present study is concerned with comparing the assessments made

of the SDIs of di€erent halls. Data on the surface di€usion index was obtained from

four sources:

1. Haan's data [8].

2. Beranek's data [1].

3. Han's data [9].

4. Current work (identi®ed as Clarke/Fricke in the rest of this paper).

The SDI assessments of Haan, Han and the current study were all done using

photographs and drawings. In the cases of Haan and Clarke/Fricke this was an

independently assessed SDI using three categories; ``low,'' ``medium'' and ``high''

256

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

di€usion. The walls and the ceiling of each hall were independently assessed using

these three categories and then a hall SDI was determined in ®ve categories. The ®ve

categories were ``low±low'' (low wall and ceiling di€usion), ``low±medium'' (low wall

di€usion and medium ceiling di€usion or low ceiling di€usion and medium wall

di€usion), ``medium±medium'' (medium wall and ceiling di€usion), ``medium±high''

(medium wall di€usion and high ceiling di€usion or medium ceiling di€usion and

high wall di€usion) and ``high±high'' (high wall and ceiling di€usion). A situation

where the ceiling had ``low'' di€usion and the walls had ``high'' di€usion (``low±

high'') was classi®ed the same as ``medium±medium''). No weighting, based on the

area of the walls and ceiling, was undertaken. Haan [2] developed a description of

surfaces that ®tted into each of these three surface categories but his categories were

not used by Clarke/Fricke. Haan's SDI evaluations, together with those of Beranek,

Han, Clarke and Fricke are shown in Table 1.

The Clarke/Fricke assessments were undertaken independently by two people.

Clarke was an independent researcher with architectural training but with limited

expertise in the area of concert hall acoustics. She was asked to ®nd photographs

and drawings of 61 halls and, based upon those, make her judgements. She found

sucient information on 58 halls to make judgements. A year later she was asked to

reassess these halls, using the same methodology. A similar assessment procedure

was used by the author. The assessments of Clarke and Fricke are presented inde-

pendently in Table 1.

The assessment of surface di€usion by Han [9,10], should be less idiosyncratic than

those of the other SDI assessors. Practicing architects in Australia and Korea were

shown photographs and drawings of halls and asked to rate the walls and the ceiling

as either ``¯at'', ``small discontinuities'', ``medium discontinuities'' or ``large dis-

continuities''. The choice of the word ``discontinuities'' was unfortunate as curved

surfaces could have been judged as ``¯at'' even though they had signi®cant di€using

qualities. As these questions, together with others on the same questionnaire, were self-

administered, there is no knowing how these questions were interpreted. For instance,

it is not known whether the respondents referred only to the surfaces or took into

account balconies, caryatids, etc. On the positive side, the four categories for each

surface gave the potential for a ®ner determination of the di€usion rating for halls.

Beranek's evaluations of SDI appear to have been made visually, in a similar way to

that of Haan and Clarke/Fricke, although the details of his 11 point scale are not

known. In order to compare the di€erent assessments of SDIs, Beranek's data was

grouped: 0 and 0.1 were classed as ``0'', 0.2 and 0.3 were classi®ed as ``0.3'', 0.4, 0.5 and

0.6 were classi®ed as ``0.5'', 0.7 and 0.8 were classi®ed as ``0.8'' and 0.9 and 1 were

classi®ed as ``1''. Han's scale was grouped in the same way. A correlation analysis of the

di€erent SDI assessments was carried out using Statistica software [11].

4. Results

The results of the SDI assessments of concert halls are presented in Table 1. Not

every assessor has information on all the halls so that there are some blanks in the table.

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

257

Table 1

Five visual assessments of the surface di€usivity indices of concert halls

a

Name of hall

SDI

FF

SC

YH

CH

LB

Festspielhaus, Salzburg, Austria

0.8

1

0.5

0.8

1

Grosser Musikvereinssaal, Vienna, Austria

0.8

1

0.3

1

1

Palais des Beaux-Arts, Brussels, Belgium

0.5

0.5

0.5

0.3

Radiohuset Studio 1, Copenhagen, Denmark

0.5

0.3

0.5

0.3

0.5

Tivoli Koncertsal, Copenhagen, Denmark

0.5

0.5

0.3

0.5

Carl Nielsen Hall, Odense, Denmark

0.5

0.5

0.3

0.5

National Concert Hall, Dublin, Eire

1

1

0.3

0.5

Berliner Philharmonie Hall, Berlin, Germany

0.5

0.5

0.5

0.5

0.8

Beethovenhalle, Bonn, Germany

0.8

0.8

0.5

0.3

Gewandhaus, Leipzig, Germany

0.5

0.5

0.5

1

Herkulessaal, Munich, Germany

0.5

0.5

0.3

0.8

Gasteig Philharmonie Hall, Munich, Germany

1

1

0.8

0.5

0.8

Liederhalle, Beethovensaal, Stuttgart, Germany

0.3

0.5

0.5

0.3

0.5

Frederic R. Mann Auditorium, Tel Aviv, Israel

0.5

0.3

0.5

Concertgebouw, Amsterdam, Netherlands

1

1

0.3

1

1

Concert Hall De Doelen, Rotterdam, Netherlands

1

0.8

0.5

1

1

Music Center, Utrecht, Netherlands

0.8

0.8

0.5

0.3

Berwald Hall, Stockholm, Sweden

0.8

0.8

0.3

0.5

Stadt-Casino, Basel, Switzerland

0.8

1

0.3

0.8

0.8

Grosser Tonhallesaal, Zurich, Switzerland

0.8

1

0.5

0.8

1

Colston Hall, Bristol, UK

0.3

0.3

0.5

0.3

0.3

St. David's Hall, Cardi€, UK

0.8

0.5

0.5

0.5

0.5

Usher Hall, Edinburgh, UK

0.8

0.8

0.3

0.5

Philharmonic Hall, Liverpool, UK

0.5

0.5

0.5

0.3

0.5

Royal Festival Hall, London, UK

0.8

0.5

0.5

0.3

0.5

Barbican Concert Hall, London, UK

0.8

0.5

0.5

0.3

0.3

Derngate Centre, Northampton, UK

0.8

0.8

0.3

0.5

Royal Concert Hall, Nottingham, UK

0.5

0.5

0.5

0.5

Free Trade Hall, Manchester, UK

0.5

0.5

0.3

0.5

Lyric Theatre, Baltimore, USA

0.5

0.5

0.3

0.8

Boston Symphony Hall, Boston, USA

1

1

0.3

1

1

Orchestra Hall, Chicago, USA

0.5

0.5

0.3

0.5

Severance Hall, Cleveland, USA

0.5

0.5

0.5

0.8

0.8

Boettcher Concert Hall, Denver, CO, USA

0.5

0.5

0.5

0.3

Avery Fisher Hall, New York, USA

1

0.8

0.3

0.3

0.8

Carnegie Hall, New York, USA

0.8

0.8

0.5

0.8

Academy of Music, Philadelphia, USA

0.8

1

0.5

0.5

Eastman Theatre, Rochester, New York, USA

0.8

0.8

0.3

0.5

L. M. Davies Symphony Hall, San Francisco, USA

1

1

0.5

0.8

0.8

War Memorial Opera House, San Francisco, USA

0.5

0.5

0.5

0.5

The Grand Hall, Worcester, MA, USA

1

1

0.3

0.8

0.8

Roy Thomson Hall, Toronto, Canada

0.8

1

0.5

0.3

Concert Hall, Sydney Opera House, Australia

1

1

0.5

0.5

The Melbourne Concert Hall, Melbourne, Aust.

0.5

0.5

0.5

a

FF, Fricke's assessments; SC, Clarke's assessments; YH, the ®ve-category, modi®ed Han assessments;

CH, Haan's assessments; LB, the ®ve-category, modi®ed Beranek assessments.

258

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

The results of the correlation analysis are shown in Table 2. The correlation values were

obtained using the 20 cases that are in common to each of the SDI assessments. The

values in bold in Table 2 indicate that the correlations are signi®cant at the 5% level.

Han's results are not signi®cantly correlated with any of the other evaluations and so

it would seem that better guidelines would need to be provided if assessments of surface

di€usivity were to be made by architects or members of other non-cognate professions.

Most of the other correlations are low though the majority of the assessments are

within ‹0.1 of each other. These low correlations are, to some extent, a result of the

way in which the results of Haan and Beranek have been modi®ed to allow com-

parisons to be made with those of Fricke and Clarke (when, for instance, Beranek's

assessments of SDIs are correlated with the modi®ed form used here the correlation

is only 0.81.).

One encouraging result was that there was no signi®cant di€erence between Clar-

ke's two assessments which were separated by about a year (r=0.926). Also,

although the correlations between assessments are sometimes low any of these

assessments can still be used to make predictions of SDI, and hence of concert hall

acoustic quality, using a neural network trained on these assessed values. However,

the analysis would not be the same as that based on the SDI values of Beranek.

5. Conclusions

It seems, from the results of the neural network analysis, that Beranek's approach

to the prediction of the acoustic performance of concert halls is valid (a better way

though, of predicting the acoustic performance, may be to train a neural network).

However there are some diculties associated with it such as the variation of

quantities such as IACC, G and EDT throughout the hall, the diculty of comput-

ing some of these quantities, especially at the early stage of a design, and the

inability to assess SDI values in a reproducible way.

Visual determination of SDI seems to be the only viable method at present. If

visual determination is to be of use it must be de®nable and repeatable to within

satisfactory limits. What are these limits? From the present work it looks like SDI

must be determined to ‹0.1 or possibly ‹0.2 in order to get acceptable predictions

of acoustic quality of halls. If ‹0.2 is acceptable hall surfaces must be placed into

Table 2

Correlation matrix for ®ve independent assessments of the SDI of 20 halls

ab

FF

SC

YH

CH

LB

FF

1.00

0.78

ÿ0.24

0.54

0.59

SC

0.78

1.00

ÿ0.31

0.75

0.82

YH

ÿ0.24

ÿ0.31

1.00

ÿ0.41

ÿ0.32

CH

0.54

0.75

ÿ0.41

1.00

0.86

LB

0.59

0.82

ÿ0.32

0.86

1.00

a

For explanation of initials, see Table 1 footnote.

b

The signi®cant correlations are shown in bold.

F.R. Fricke / Applied Acoustics 60 (2000) 253±261

259

one of ®ve SDI categories. This seems possible but a 10 category evaluation to achieve

‹0.1 does not without knowing more about how much the ceiling, walls and seating

contribute to the di€usion, whether area weighted values of di€erent surface SDIs

should be used and whether surfaces, partially obscured by balconies, should carry the

same weighting as those surfaces which are more exposed. In some halls it is dicult to

distinguish the walls from the ceiling (e.g. the Concert Hall of the Sydney Opera House)

while in others there are marked di€erences in the ®nishes of the walls and ceiling and so

a re®nement of the visual assessment of SDI would be dicult.

The previous paragraph also indicates some of the limitations of the ®ve category

SDI evaluation used in the present work. There are other limitations such as those

introduced because di€erent camera lenses and angles used as well as di€erent

lighting conditions for the photos on which the evaluations were carried out. Dif-

ferent instructions given to subjects assessing surfaces are also likely to a€ect the

SDI evaluations. And then there are the unknown e€ects of factors such di€erent

types of di€using elements on surfaces, their interaction and the in¯uence of factors

other than surface treatments, on the di€usivity achieved in halls. All this means of

course there is plenty of scope for further work.

More work needs to undertaken on a better de®nition of what constitutes various

di€usion categories. Reliable statistics on how important the errors in the assess-

ment of SDI are on the evaluation of concert hall acoustics need to be obtained.

Instructions on how to recognize small-scale di€usion elements and determine their

importance need to be produced. What form should the di€usion elements take, e.g.

what is the di€erence in di€usion properties between regular and irregular placed

elements, should also be investigated.

Whether the visual assessments of di€usion have any correspondence to actual

di€usion is also of concern. This needs to be investigated though for the analysis of

how good a room is acoustically this does not seem to be an important issue as the

visual assessments appear to be satisfactory if a neural network analysis is used and

halls placed into one of three acoustic categories.

It may well be that visual assessments are not the way to go but until there is a

more ``appropriate'' way it is worth persevering with the visual assessments and

trying to identify the limitations of this method.

Acknowledgements

The work of Sue Clarke, a Research Assistant in the Department of Architecture,

Planning and Allied Arts at the University of Sydney, in searching for photographic

material on halls and assessing the di€usion of surfaces, is gratefully acknowledged.

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