Cox - Engineering art the science of concert hall acoustics.pdf - AKUSTYKA - metrum

Engineering art: the science of concert

hall acoustics

TREVOR J. COX

Acoustics Research Centre, University of Salford, UK

PETER D’ANTONIO

RPG Di

ﬀ

usor Systems, Upper Marlboro, MD, USA

Modern concert hall design uses science and engineering to make an acoustic which embellishes and enhances the

artistry of the musicians. The modern discipline of concert hall acoustics is a little over a hundred years old, and

over the last century much has been learnt about how to ensure the audience receives high quality sound. During

this period, knowledge from a large number of disciplines has been exploited. It is the intention of this paper to

illustrate how disciplines as diverse as X-ray crystallography, psychology, and mobile telephony have inﬂuenced

acoustic design. The paper will concentrate on the design of acoustic diﬀusers for concert halls, as this is a topic

currently attracting considerable interest within the acoustics industry and academia.

The acoustic of a concert hall contributes an important speech sound intelligible, or to make music sound

part of the sound heard in a classical music perform- beautiful. Modern acoustic science cannot guarantee

ance; the concert hall embellishes the sound. Music a great acoustic every time, but if advice is followed,

outdoors may be popular when accompanied by ﬁre- technical knowledge should ensure that bad halls are

works, but the quality of the sound is usually poor. not built, while signiﬁcantly increasing the chance of

Move indoors and the sound comes alive, enveloping greatness being achieved. What makes a good concert

and involving the listener in the musicmaking process. hall is a combination of many acoustic and non-

Outdoors, listeners receive sound straight from the

acoustic attributes perceived by an audience member

orchestra, there are no reﬂections from walls, and the

in a complex manner. The acoustic of a concert hall

sound appears distant. When music is played in a

might be perfect, but if the audience get soaked in

room, reﬂections from the walls, ceiling, and ﬂoor

rain walking from the car park, they are unlikely to

add reverberation and other characteristics to the

rate the experience highly. So a great design is about

sound. As the conductor Sir Adrian Boult said:1 ‘The

accommodating a wide range of requirements, and not

ideal concert hall is obviously that into which you

just acoustics. This article, however, will concentrate

make a not very pleasant sound and the audience

on the acoustics. When designing a hall, the acoustic

receives something that is quite beautiful. I maintain

engineer will look at many acoustic factors: the

that this really can happen in Boston Symphony Hall;

background noise level, the amount of reverberation

it is our ideal.’ This quote is of great historical

(the decay of sound after a note has stopped being

interest, because Boston Symphony Hall was the ﬁrst

played), the amount of sound arriving from the side,

concert hall where the principles of reverberation

the reﬂections musicians receive that are necessary

were applied. These principles were developed about

for them to play in time and form a good tone, and

a hundred years ago by Wallace Sabine, who was

so on. The overall focus of this paper will be on the

the ﬁrst person to apply modern scientiﬁc principles

role of surface di

ﬀ

users.

to room design and pioneered modern concert hall

Currently there is much debate about the role

acoustics. Boston Symphony Hall is still seen as one

of surface di

ﬀ

users in concert halls. To take two

of the greatest auditoria in the world. Conversely, a

examples, one eminent concert hall designer regularly

poor hall can have a detrimental e

ﬀ

ect on the enjoy-

claims that too much di

ﬀ

usion is detrimental to the

ment of a performance, something that can a

ﬀ

ect the

sound quality of the upper strings, while in contrast

musicians as well. As the conductor Sir Simon Rattle

said of one hall (which will remain nameless): ‘The

other acoustic engineers have blamed the disappoint-

*** hall is the worst major concert arena in Europe.

ing acoustics of certain major halls on a lack of

The will to live slips away in the ﬁrst half hour of

surface di

ﬀ

usion. We will return to these contradictory

rehearsal.’2

opinions later, and will try to shed some light on why

Since Wallace Sabine’s work on room acoustics,

they arise, but ﬁrst it is necessary to describe what a

much has been learnt about what is important to get

a good acoustic, whether the requirement is to make of acoustics.

ﬀ

user is and to outline the current state of the art

Published by Maney for the Institute of Materials, Minerals and Mining

INTERDISCIPLINARY SCIENCE REVIEWS, 2003, VOL. 28, NO. 2 119

1 Spatial and temporal responses of sound reflected

from a plane flat surface (above) and a diffuser

(below)

Treatments

To alter the acoustics of an existing room, treatment

2 Temporal and frequency responses from flat

is usually placed on the boundaries, for example if

(above) and diffusing (below) surfaces

ce is too reverberant or lively, absorbent ceiling

tiles or carpet might be used to absorb and so remove

some of the acoustic energy. In concert halls, the

faithful rendition of the original sound direct from

the instrument, and less coloration will be heard.

sound can be altered by placing treatment on the

walls and ceiling (the ﬂoor already has the audience Figure 1 also shows a cross-section through a di

user,

in this case a reﬂection phase grating consisting of a

ﬀ

cult to alter). There

are three basic forms of treatment, large ﬂat surfaces,

erent depths but the same width.

There are many types of di

ﬀ

users. Absorbers, such as the ceil-

ing tiles and carpet mentioned already, are not often but in principle any non-ﬂat corrugated surface will

have some kind of di

ﬀ

user, as explained below,

used in large concert halls, because they remove sound

energy from the space. In a hall every bit of energy be constructed from a wide range of materials, such

as wood, gypsum, concrete, metal, and glass, the key

ﬀ

using ability. Di

ﬀ

users can also

must be conserved because there is a limit to how

much energy an orchestra can produce. Consequently,

feature being that the material should be hard and

acoustically non-absorbent.

the designer must choose between ﬂat surfaces or

ﬀ

users.

users are used in a variety of ways. For instance,

they can be used to reduce echoes arising from the

ﬀ

Figure 1 contrasts the spatial and temporal responses

of ﬂat and di

ﬀ

using surfaces. These describe what the

rear walls of auditoria. Sound takes a long time to

travel from the stage to the rear wall of a concert

listener would receive if they were close to one of

the surfaces, and if no other surfaces were present. hall, and if a strong reﬂection comes back from the

rear wall to the front of the hall, this may be heard

A ﬂat surface behaves like a mirror reﬂecting light,

the sound energy being preserved and concentrated as an echo. In older halls the echo problem would

have been dealt with by placing absorbent on the rear

in the specular reﬂection direction, and with equal

angles of incidence and reﬂection. The time response wall to absorb the acoustic energy, preventing the

reﬂection occurring and so curing the echo problem

shows the similarity between the direct sound and

the reﬂection: the ﬂat surface does little to the sound (such a solution was adopted in London’s Royal

Festival Hall ). However absorption removes acoustic

except change the direction in which it propagates.

Figure 2 shows the resulting frequency response. This

energy and so reduces the loudness of the orchestra.

A modern solution is therefore to use di

shows how the level (or volume) of the sound will

vary as the pitch (or frequency) of a note changes. break up and disperse the troublesome reﬂections,

which can be done without loss of acoustic energy.

ﬀ

users to

The frequency response of the ﬂat surface is uneven,

with a regularly spaced set of peaks and troughs, and An example of the use of reﬂection phase grating

is known as a comb ﬁlter response. This unevenness

means that some frequencies will be emphasised, and York, can be seen in Fig. 3. In the UK, Glyndebourne

Opera House uses convex curved surfaces on the rear

ﬀ

users, on the rear wall of Carnegie Hall in New

some deemphasised. This leads in turn to coloration

of the sound, where the timbre of notes is altered.

wall to disperse sound.

user, on the other hand, disperses the reﬂection

both temporally and spatially. The time response

ﬀ

Architectural trends

is greatly altered, with reﬂections arriving over a

longer period, and the frequency response shows less

In older, pre-twentieth century halls, such as the

Grosser Musikvereinssaal in Vienna, ornamentation

evidence of comb ﬁltering than the plane surface,

the peaks and troughs being uneven and randomly appeared in a hall because it was the architectural

style of the day. Such walls were therefore naturally

spaced. This means that the reﬂected sound is a more

120 INTERDISCIPLINARY SCIENCE REVIEWS, 2003, VOL. 28, NO. 2

an o

and seating on it, and so is di

series of wells of di

absorbers, and di

Adi

3 Schroeder diffusers (QRDs) applied to the rear

wall of Carnegie Hall to prevent echoes

using; large ﬂat surfaces were very rare. The

Grosser Musikvereinssaal is an interesting example

to acousticians, because it is often cited as one of the

best halls in the world. The hall sound is thought to

have inﬂuenced composers including Brahms, Bruckner,

and Mahler. In the Grosser Musikvereinssaal the

inﬂuence of the surface di

ﬀ

usion on the sound is very

use sound resulting.

In the twentieth century, however, architectural trends

changed and large expanses of ﬂat areas appeared

in many concert halls. The UK has many post-war

concert halls which have very little ornamentation,

such as the Colston Hall in Bristol. The style of the

day was to produce clean lines following a modernist

style, but these surfaces then had little or no di

ﬀ

using

capability. The expanse of ﬂat surfaces can lead to

distortion in the sound heard as a result of comb

ﬁltering, echoes, and other mechanisms. It is worth

noting, however, that it is also possible to design

very successful halls with ﬂat surfaces, a good UK

example being Symphony Hall in Birmingham, which

has relatively little surface di

ﬀ

usion.

user design is to ﬁnd forms

that complement the architectural trends of the

The key to good di

ﬀ

4 Three different Schroeder diffusers: the original

day. The di

ﬀ

user must not only meet the acoustic

design (top), a fractal design (middle), and an

speciﬁcation, it must ﬁt in with the visual scheme

active diffuser (bottom); the diffusers are 0·6m

wide, 0·6m high and about 0·2m deep

required by the architect. As discussed below, modern

user designs have successfully been developed to

complement modern architectural forms.

ﬀ

Fowler Centre, New Zealand.4,5 Figure 5 illustrates this

application. Marshall and Hyde used large overhead

Schroeder diffusers

reﬂectors to provide early reﬂections to the audience

in the balconies in a revolutionary design. This was

user began with

pioneering work by Manfred Schroeder, one of the

ﬀ

a layout whereby a hall could have good clarity, and

yet maintain a large volume for reverberation. The

twentieth century’s greatest acoustic engineers. In

the 1970s, Schroeder developed the phase grating large volume partly comes from the space behind

the di

user. An

example of the original design can be seen in Fig. 4 the hall, it had been established that lateral reﬂections

were important in concert halls as they promote a

ﬀ

user,3 also known as the Schroeder di

ﬀ

users. Not many years before the design of

ered just what acoustic

designers were looking for, deﬁned acoustic perform-

ﬀ

users o

ﬀ

sense of envelopment or spatial impression in rooms.6

The evidence for the beneﬁcial e

ance based on very simple design equations; for while

it is know that ornamentation produces di

ﬀ

ects of lateral

ﬀ

usion, it

reﬂections came from laboratory measurements on

human perception, which followed techniques pioneered

does this in an ill deﬁned and haphazard fashion.

One of the pioneering applications of Schroeder

in experimental psychology. These measurements

showed that lateral reﬂections are important to get a

ﬀ

users was by Marshall and Hyde in the Michael

INTERDISCIPLINARY SCIENCE REVIEWS, 2003, VOL. 28, NO. 2 121

obvious, with a di

The development of the modern di

(top). These di

5 Schroeder diffusers in the Michael Fowler

Centre, New Zealand (photo courtesy Dr Harold

Marshall of Marshall Day Acoustics)

sense of involvement with the music. The need for

6 Scattered levels from a Schroeder diffuser

(left) and a plane surface (right) of the same

dimensions

lateral reﬂections inﬂuenced Marshall and Hyde to

apply di

users to the large overhead surfaces rather

than using ﬂat reﬂectors.

moves around the surface on a semicircle. A series of

lobes are seen, eleven in this case, which are grating

user technology

entering wide use was its commercialisation by an lobes generated by the periodicity of the surface

structure. Imagine viewing this polar response end

ﬀ

usor Systems Inc.,

whose interest lay in studio design. Around the time on so that a set of eleven bright spots are seen; it is

this type of image that X-ray crystallographers use

ﬀ

user, a

new design regime for listening and monitoring rooms

ﬀ

to determine crystal structures. The problem posed in

the acoustic case is however somewhat di

was invented. This was the Live End Dead End

(LEDE) layout,7 which was later reﬁned into the

ﬀ

erent from

the crystallographic challenge: in crystallography, the

users are

used in small spaces to disperse reﬂections that would mine an unknown structure, whereas in the acoustic

case, the problem to be solved is how to determine

ﬀ

raction patterns of the X-rays are used to deter-

otherwise arrive early and at a high level and so cause

coloration of the timbre of the sound. This is some-

the correct surface structure to achieve a desired

polar response (or di

times referred to as acoustic glare, and is again caused

by comb ﬁltering. Just when studio designers were

ﬀ

raction pattern). But before

explaining how Schroeder solved this problem, it is

necessary to explain how di

users to achieve this design, by happy

coincidence Schroeder di

ﬀ

users scatter sound.

users became available.

At that time, one of the founders of RPG, and

ﬀ

Huygens

also one of the authors of this paper, Peter D’Antonio,

wasadi

ﬀ

raction physicist at the Laboratory for the The Huygens construction used in optics is one way

of explaining how di

Structure of Matter at the Naval Research Laboratory

in Washington, DC. Knowing of his interest in music,

ﬀ

using surfaces scatter, though it

is only approximate in many acoustic cases. Consider

a planar surface, the situation illustrated in the upper

a colleague handed him the latest issue of Physics

Today with a cover photo of Manfred Schroeder half of Fig. 7. When illuminated by a sound source,

a set of secondary sources is generated on the surface,

seated in an anechoic chamber. The associated article

suggested using Schroeder’s number theoretic di

ﬀ

users

and these are shown as stars in Fig. 7. Each of these

secondary sources then radiates semicircular waves.

in concert halls. It became apparent that the reﬂection

phase gratings suggested by Schroeder were in e

ﬀ

ect By connecting points on these waves which are in

phase with each other, it is possible to visualise the

two-dimensional sonic crystals, which scatter sound

in the same way that three-dimensional crystal lattices waves that are reﬂected from the surface. (These are

rather like ripples on the surface of water created

raction

theory employed in X-ray crystallographic studies when a stone is thrown into the water.) In this

situation, a simple plane wave at right angles to the

ﬀ

was also applicable to reﬂection phase gratings, it was

straightforward to model and design the reﬂection surface is generated. The planar surface is acting like

an acoustic mirror, and the wave is unaltered on

phase gratings using techniques ﬁrst developed in

crystallography.

reﬂection (except in its direction). The lower part of

Fig. 7 shows the case for a semicircular surface. In

Figure 6 ( left) shows the scattering from a

Schroeder di

ﬀ

user in a polar response. A source

this case, the reﬂected waves are now semicircular in

shape. The wave has been altered by the surface, being

illuminates the surface, normal to the surface and

from the right. The polar response shows the energy dispersed so that the sound reﬂects in all directions,

a characteristic desirable in a di

scattered from the surface (in decibels) as a receiver

ﬀ

user.

122 INTERDISCIPLINARY SCIENCE REVIEWS, 2003, VOL. 28, NO. 2

ﬀ

Another reason for this new di

American company, RPG Di

that Schroeder was developing the new di

Reﬂection Free Zone (RFZ) design. Di

looking for di

scatter electromagnetic waves. Since the di

7 Huygens constructions for a plane wave reflected

method, Schroeder turned to his favourite subject of

number theory, at ﬁrst glance a rather obscure form

of abstract mathematics which studies the properties

of natural numbers, but which in practice has proved

to be very useful to scientists and engineers.

In the late eighteenth century, Carl Friedrich

Gauss developed the law of quadratic reciprocity,

well known to mathematicians working in number

theory. Dedekind was a doctoral student of Gauss

and wrote a ﬁne description of his supervisor:8

… usually he sat in a comfortable attitude, looking down,

slightly stooped, with hands folded above his lap. He

spoke quite freely, very clearly, simply and plainly: but

when he wanted to emphasise a new viewpoint … then

he lifted his head, turned to one of those sitting next to

him, and gazed at him with his beautiful, penetrating

blue eyes during the emphatic speech.… If he proceeded

from a flat surface (above) and a curved surface

from an explanation of principles to the development of

(below): normal incidence source with incident

wavefronts excluded for clarity and secondary

mathematical formulae, then he got up, and in a stately

very upright posture he wrote on a blackboard beside

sources shown as stars on the surface

him in his peculiarly beautiful handwriting: he always

succeeded through economy and deliberate arrangement

in making do with a rather small space. For numerical

Figure 8 shows the case for a simpliﬁed reﬂection

phase grating. In this situation, the reﬂected waves

examples, on whose careful completion he placed special

are delayed because the waves must travel down

value, he brought along the requisite data on little slips

of paper.

each well and back up again before reﬂection. The

Although best known to modern physicists for

secondary sources have di

ﬀ

erent delays (phases)

Gauss’s Law, which explains the properties of the

because of the di

ﬀ

erent well depths, and this alters

electric ﬁeld, it is Gauss’s number theory work

the reﬂected wave. This again generates dispersion.

which is of most interest here, because it leads to

the quadratic residue sequence used in the design of

Sequences

user (QRD), an example

of which is shown in Fig. 4 (top). The formulation of a

ﬀ

In many ways, a reﬂection phase grating is acting

quadratic residue sequence is based on a prime number.

like an optical di

ﬀ

raction grating. In the acoustic

For the di

ﬀ

user in Fig. 4 (top), the prime number is

case, the designer has control over the phases of the

7. The depth of the n th well is then proportional to

sound waves. To design a reﬂection phase grating, a

n 2 modulo 7, where modulo indicates the smallest

method is required to determine an appropriate well

non-negative remainder. So the third well has a depth

depth sequence, which then generates a phase distri-

proportional to 32 modulo 7, in other words 2. The

bution on the surface of the di

ﬀ

user to give the

sequence mapped out in this case is 0, 1, 4, 2, 2, 4, 1,

desired reﬂected wavefronts. In inventing such a

which can be seen in Fig. 4. (The quadratic residue

user in Fig. 4 has zero depth wells on both ends,

but these are half the width of the others, a useful

sleight of hand to make manufacturing and ﬁtting

easier). If this quadratic residue sequence is used to

construct the di

raction or grating

lobes generated all have the same energy, as shown

in Fig. 6 ( left).

There are many other sequences that can be used.

Another popular one is the primitive root sequence.

The depth of the n th well is then proportional to r n

modulo N , where r is a ‘primitive root’ of N and N

must be a prime. For r to be a primitive root, the

sequence generated must contain every integer from

1to N

ﬀ

user, then the di

ﬀ

3isa

primitive root, which generates the sequence 1, 3, 2,

6, 4, 5. If this sequence is used to make a di

−

1 without repeat. Thus for N

7, r

user,

the central (specular) lobe will be suppressed, while

the others remain at the same level.

ﬀ

8 Huygens constructions for a plane wave reflected

from a simplified Schroeder diffuser: the upper

This sequence generation technique is an advanced

plot shows wavefronts from two wells only

for clarity

form of the number games sometimes played by

children: with some simple generation rules, fantastic

INTERDISCIPLINARY SCIENCE REVIEWS, 2003, VOL. 28, NO. 2 123

the quadratic residue di

ﬀ

Cox - Engineering art the science of concert hall acoustics.pdf

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