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The Ultimate Concert Hall and Other Ultimate Truths

Jeffrey Borish

The Droid Works

P.0. Box CS-8180

San Rafael, CA 94912

ABSTRACT

There are excellent concert halls in the world, but

there are far more mediocre ones. One reason so many

disappoint is that architectural acousticians have not

fully appreciated the connection between geometry and

subjective preference. The geometry of a concert hall

controls the early reflection pattern. The image model

shows exactly how the difference in the early reflection

patterns of two commonly used shapes, tlie fan and the

rectangle, explains the perceived differences between

the two. It also suggests that a reverse fan would be

better than either, and helps to analyze several other

practical design issues. Fan-shaped concert halls are

not the only situation in which lateral reflections are

inadequate; another is domestic audio reproduction.

Stereo is incapable of adequately reproducing the early

reflections, so these sounds are omitted from recordings.

One way to correct for this distortion is to synthesize

the early reflections during playback. The image model

regulates a sequence of simplifications that preserve the

salient features of concert halls in an electronic sirnula-

tor that is remarkably simple.

Unfortunately, architectural acoustics is not the

only reality. There are several parasitic specialties.

Foremost among these is “economic acoustics.” Con-

cert halls are very expensive to build (on the order of

$30 M) and operate. Sustaining these expenses is possi-

ble only by increasing seating capacit y--and filling all

the seats. The best hall in the \torltl, the Grosscr

Musikvereinssaal in Vienna, seats only 1680. Only the

most munificent municipality coul(l consider building

such a hall today. Modern constructioii techniques ancl

architectural innovations allow the siLe of concert halls

to be increased seemingly without liiiiit, but musicians

(at least the unamplified variety) continue to output

the same acoustic power (10 Watts [I]for a full sym-

phony orchestra playing fortissimo!). l’liat means per-

formances in bigger concert halls tencl to be quieter,

producing a dissonance with psychoacoustics: there is a

preferred loudness for music. Further, halls must bc

constantly busy, and that often means designing con-

cert halls that sound as good for the Clectric Light

Orchestra as a heaxq Wagncrian orclic3sti a. Economic

acoustics also encompasses edicts siicli as “this hall

shall have a horizontal ceiling” or ‘‘llii~

INTRODUCTION

At the opening of a new concert hall, everyone

wears golden ears. Expectations that ran high during

the long gestation all too often are shattered by the

sound that reaches the audience. Acoustical flops feed

the fears of laymen that architectural acoustics is still a

black art, and to an extent they are right. Obviously,

if every design consideration in a concert liall were com-

pletely understood then every concert hall would be a

complete success, or at least would fail in precisely

predictable ways. Yet new designs continue to surprise,

and hopeful listeners are often left with an architec-

tural monument that is better seen than heard.

Great concert halls do exist, and some of them are

quite old. Of the three considered the best in the world

(the Grosser Musikvereinssaal in Vienna, the Concertge-

bouw in Amsterdam, and Symphony Mall in Boston),

the newest (Symphony Hall) is 8.5 years old. One

wonders why duplicating-indeed, surpassing-their

quality seems so difficult. After all, scientific under-

standing has advanced and new construction techniques

are available, so it ought to be possible to transcend

histt.,;ical limitations rather than merely to ape histori-

cal successes.

The great concert halls oj the past

cannot be duplicated.

Each new concert hall design is an experiment.

Unfortunately they are not ideal esperiments. They

take a long time to complete (often 5-10 years). That

means corrective feedback often arrives after other pro-

jects have been initiated on the same principles. Con-

cert halls differ in many ways, so attributing perceived

Iiall shall not

have a wooden floor” because the alternatives are too

expensive. Ineluctable economic considerations often

lead to acoustical perdition.

Then there is “political acoustics.” Architects,

who usually have greater authority, often will hand

architectural plans for a concert hall to tlie acoustician

with the directive to “make it sound good.“ As we will

see, some architectural features impose insuperable lim-

its on the acoustical characteristics. To make matters

worse, architects are usually praised most highly when

their creations are most innovative, altliough increnien-

tal changes from previous acoustical buccesses would be

less perilous. Political acoustics also suLsumes the con-

fort criterion-wider seats, more legroom, and padding.

Considering the influence of these para5itic specialties

leads us to our first ultimate truth:

differences to particular architectural features is diffi-

cult. Furthermore, the ultimate gauge of acoustical

qualities is subjective, introducing uncertainties due to

personal preference. Also, subjective comparisons

depend on acoustical memory, which is taxed by the

long delays in traveling from one concert hall to

another. These complications in performing and

analyzing experiments make it impossible to extract as

much benefit as would be desirable from each experi-

ment, inevitably slowing progress.

response. As a result, the two regions of reverberation

have different subjective effects. The early reflections

give listeners a sense of immersion in the sound field;

the later reflections add warmth and fullness and con-

tribute to the sense that the performance is taking

place in an enclosed space. The characteristics of early

reverberation cannot be encapsulated in a convenient

closed-form expression as is done for late reverberation.

However, the image model neatly tackles the problem.

We start by considering how souiid travels from a

.I88

-98

Fig. 1. A perspective kiew (A) is the most straightfor-

ward presentation. It shows the concert hall sur-

rounded by the virtual sources. Also shown are three

imaginary walls upon which have been drawn the pro-

jections along each of the coordinate axes. The “angle

plane” (B) shows the directions of the virtual sources as

a function of their azimuth and elevation; the size of

the x gives an indication of their strength. Finally, the

polar plot (C) shows sound intensity as a function of

azimuth. Both (B) and (C) define 0” azimuth as the

direction of the actual source.

A different approach is to develop new analytical

techniques. One technique that has proven useful is

computer modeling. Like all models, a computer model

is a simplified representation of reality, but thoughtful

simplifications often reveal deeper truths. In any case,

siniple models can be enhanced when deficiencies are

discovered. Because problems still arise in concert hall

design, the conventional model-a reverberation time

formula--must be inadequate. A coinputer model will

also be found inadequate for some problems, but though

simplistic, it can provide some new insights. The ines-

capable ultimate truth is:

source to a listener. When a sound is emitted in an

enclosed space it follows many paths, changing in a

unique way on each one. One changc is the delay

incurred because paths involving reflection are longer

than the direct path. Second, there is an attenuation

attributable to two causes, dilution---the inverse pro-

portion between sound pressure and distance in a spher-

ically propagating wave-and absorption--the absorp-

tion of energy by reflecting boundaries and by the air

itself. Third, there is the change in direction-many of

the reflections reach the listener from a different direc-

tion than the direct sound. There are many other

changes as well: spectral changes (absorption depends

on frequency); dispersion (velocity depends on frc-

quency); diffusion (reflections are not specular); diffrac-

tion. Accurately modeling every effcct is impossible,

but rather than defeatism we choose reductionism and

produce some worthwhile insights into concert hall

design.

The reduction we pursue is to focus on the first

three characteristics of the early reflectioiis: delay time,

attenuation factor, and direction. The first two depend

on the length of the path. If we assunie that a wall

reflects sound like a mirror reflects light, then we can

treat a path involving reflections as a straight path

from a “virtual” source located symnictrically behind

the surface. Computers enable us to esteiid this fami-

liar idea to three dimension and to a polyhedron with

any number of sides 131. The program also allows the

user to specify the position of the SOUI~CC and listener,

and the acoustical properties of tlic 1 eflecting boun-

daries. F ig. 1 shows three ways of presenting the

The ultimate concert hall model

is a concert hall.

1. Image Model

One computer model that has proven useful in

gaining new insights into concert hall acoustics is the

image model. The image model prohides a convenient

way of analyzing details of the early rcf’lection pattern.

Traditional analytic tools have focussed on the later

reverberation which is characterized bj, two properties:

incoherence, and a gradual decay. Statistical measures

are adequate for this phase of the re\erlcration because

of the high temporal density of the sounds that reach

listeners. The early reflections, on tlic other hand, are

infrequent enough that our hearing is able to resolve

each one to an extent, so the particular time, ampli-

tude, and direction can influence our subjective

results of the analysis. The virtual source positions are

sufficient for determining the three most important

characteristics of the early reflections. Next we will

show how these results can be used in analytical studies

or for simulating concert halls.

spatial impression. The reverse fan, on the other hand,

extracts greater benefit from the virlual sources by

positioning them even more laterally than the rectangu-

lar hall. The reverse fan has never been applied in

practice so no empirical evidence exists.

Presumably the reason reverse fans have not been

applied has to do with their practical limitations.

Reverse fans sacrifice seats that uould have had

acceptable sightlines, and in this era of fiscal famine

maximizing the number of seats is tlic name of the

game. Furthermore, the reverse splay of the walls

would probably create aesthetic problems. But it still

might be interesting to find a suitable fan and reverse

the positions of orchestra and audience, just to test the

theory.

2. Designing the Ultimate Concert Hall

The concert halls widely regarded as the best in

the world are all rectangular. Other shapes have been

used, but they never work as well. Although specific

details may account for some differences, the con-

sistency suggests that there is an ultimate truth lurk-

ing.

In some ways architectural acousticians have

become remarkably proficient. One important way is in

designing for a desirable reverberation time. Rever-

beration time is known to be a significant attribute of a

concert hall [3]. The fact that some concert halls with

ideal reverberation times still do not sound good proves

that other factors are significant. One other factor

that has been shown to be important is the proportion

of the early sound energy reaching the listener from th?

:i.

::: 1::

+ +hi

+++++++++

+,+++++++

++* +

++ +*+ ++

Fig. 2. In the rectangular hall (A) the xirtual sources

spread to the sides along straight lines. But when the

walls splay outward (B), the virtual sources curve

toward the front, decreasing spatial impression. Con-

versely, a reverse splay increases spatial impression by

reversing the curvature (C). This pattern explains why

rectangular halls sound better than fans, and suggests

that reverse fans would be better still.

side. The more lateral and loud tlie delayed sounds,

the more “spatial impression” 141. Because this param-

eter is related to the details of the early reflection pat-

tern, the image model is an ideal tool for studying the

differences that arise from different concert hall

geometries.

The walls are obviously an important factor in con-

trolling the lateral energy fraction (though not the only

one). Using the image model, we can compute the posi-

tions of the virtual sources for a sequence of concert

halls in which the only difference is the splay of the

walls (Fig. 2). Viewing the virtual sources from directly

above reveals an interesting pattern. In the fan shape

the virtual sources curve toward the front; in the rec-

tangular hall they extend outward along straight lines;

and in the reverse fan they curve rearnard. Because

the fan deflects the virtual sources toward the front of

the hall, it has the least spatial impression. Empirical

differences between fans and rectangles, it should be

noted, are completely consistent uith a difference in

An objective measure provides furtlicr confirmation

for this heuristic analysis. Fig. 3 shows a sequence 0:

halls in which the splay of the walls is changed in 10

steps. The listener moves along a straight line some-

what off center. Fig. 4 shows the comparison of spatial

impression. Spatial impression is aluayS lower at the

front than the rear because there the direct sound doni-

inates. We can also see that, as expected, spatial

impression is uniformly greater for tlie reverse fan than

the rectangle, which in turn is greater than the fan.

The just noticeable difference for spatial impression is

1.4 dB [1], so the 10” increments span two subjective

units.

One way it might be possible to combine the

acoustical advantages of the reverse fan with the prac-

tical advantages of the fan is to segnieiit the side walls.

Each segment would be positioned according to an

overall fan shape, but oriented according to a reverse

10" steps. The source is positioned at the + and the

listener moves from the rear to near the source along a

line that is 11 m from the nearer wall.

+ +++ +

-3T

Fig. 5. To correct for the acoustical deficiencies of a

fan we can segment the walls and orient the segments

in accordance with a reverse fail (A). The virtual

sources show the same rearward curvature (B) as in the

simple reverse fan so the two should have comparable

spatial impression.

-4

Fig. 4. The plot of spatial impression as a function of

distance from the rear of the hall for six different splay

angles. As expected, spatial impression is always lower

in the front of the hall. We can also clearly see how

spatial impression is reduced by increasing the splay.

Fig. 6. Allowing the segments to rotate provides a

direct control of spatial impression.

vary the amount of absorbing material in the concert

hall, thereby changing the reverberation time. Because

the late reverberation is audible primarily when the

direct sound stops, changing the rate at nhich it decays

is detectable relatively rarely. The early reflections, on

the other hand, are audible almost all the time. There-

fore, a more effective control of tlie acoustics would

vary spatial impression. Fig. 7 slio\\s how spatial

impression varies as a function of the oricntation of the

wall segments. The rotations are for 2 and 4 . Only

a 4' rotation is required for a subjectively significant

change in spatial impression. Note that this method of

changing the spatial impression docs riot change the

fan. As shown in Fig. 5, the virtual sources show the

same tendency as in the reverse fan to curve toward the

rear, so the two would be expected to dcinonstrate simi-

lar acoustical characteristics.

Allowing these panels to rotate (Fig. 6) would

introduce an intriguing acoustical adjustment. Adju-

stable acoustics are desirable because they allow the

acoustics of the hall to be suited to the style of music

or even the size of the audience. Typically adjustments

Fig. 3. To quantify the dependence of .;play angle on

spatial impression we will plot spatial impression as a

function of position for 6 angles from -10" to +io" in

+ Lt

total absorption in the hall nor the volume so the rever-

beration time should remain approximately constant.

Combining rotatable panels with retractable absorbers

suspended from the ceiling would provide independent

control of both portions of the reverberation.

A practical consideration is how high the segments

have to be. Economic constraints dictate boxes or bal-

conies along the side walls, complicating the design of

the rotatable panels. If regions of thc wall were not

used to support reflections, they could be anchored.

Fig. 8 shows where reflections hit in a rectangular hall

for the same sequence of listener positions as in Fig. 3.

The size of the circle suggests the relative intensity of

the sound hitting the wall at that point. Even if we

were willing to dispense with reflections too weak to

appear as a circle, few regions are available for a bal-

cony without interfering with some important lateral

reflections. Fig. 9 clinches the matter by showing what

happens as a listener moves across the liall. The entire

wall is required when the entire audience is considered,

ruling out the possibility of seats along the walls.

Because economic pressures dictate that audience seat-

ing capacity be maximized, we are led to another ulti-

mate truth:

duce a dependence on frequency. Also tlie absorption

coefficient varies with frequency as well as direction of

incidence. Many surfaces are not locally reacting. The

long catalog can continue, but the poiiit is that the

image model is not the final word. Ll’hile the simple

image model provides many useful iiwiglits into concert

hall acoustics, further refinements might reveal new and

important effects. So we are forced to concede the

somewhat discouraging-r

cliallengirig-ultimate truth:

In architectural acoustics,

there are no ultimate truths.

3. Designing the Ultimate Electronic Concert

Hall Simulator

It is not only poorly designed concert halls that

suppress early lateral reflections, stereo recordings do as

well. They must. When early reflections reach a

listener from the wrong direction they produce a dif-

ferent subjective effect. In stereo the range of direc-

tions is limited to the sector Letneen the two

speakers-too narrow to accurately reproduce the early

lateral reflections of a concert hall. \\’ere these reflec-

tions to be presented from the front speakers along with

the direct sound the result would be an overly-

reverberant quality familiar to anyone who has ever

recorded a conference with a portable tape recorder.

The ultimate concert hall

will never be built.

The image model is only a starting point. It

ignores many physical processes, some of which might

be subjectively significant [5]. For example, the image

model does not completely solve the boundary-value

problem except in a small number of pal ticular shapes;

diffraction waves are usually required to complete the

solution. Edge diffraction arises at surface discontinui-

ties such as balcony fronts. Reflections are not gen-

erally specular but diffuse 161. All these effects intro-

. ....... D

(.In)

dt-isn c

(mct<r>)

Fig. 8. Here we see a plot of where on Lhe wall lateral

reflections strike for many positions of the listener as he

moves along the same line parallel to thc wall. The size

of the circle indicates the relative strength of the

corresponding sound. This figure shows what. regions of

the wall are actively supporting lateral reflections. We

can see that there are inactive regions where balconies

could be positioned without interfering with the lateral

reflections.

Fig. 7. Changing the orientation of the panels directly

affects spatial impression. “rX” means a reverse fan

with splay X” ; “K” is fan with splay So. A mere 4 ’

rotation produces a subjectively significant change.

Fig. 9. In this plot we see where sound hits the wall as

the listener moves across the hall. Siniilar plots can be

generated for different latitudes but the point is clear:

different listener locations require different portions of

the surface to provide lateral reflections; tlie entire wall

must be available to cover the entire audience.

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