concert hall acoustic computer modeling

Acoustical Instruments and Measurements June 2015, Argentina

CONCERT HALL ACOUSTIC COMPUTER MODELING

FEDERICO DAMIS1, NAHUEL CACAVELOS

2

Universidad Nacional de Tres de Febrero (UNTREF), Buenos Aires, Argentina.

[email protected], [email protected]

2

Abstract – During the present work acoustical computer modeling and simulation techniques

were discussed, and a concert hall was simulated using EASE software. The concert hall

selected for this task was the Stadt Casino at Basel. Measured physical and acoustical

parameters of the concert hall were analyzed and then values for acoustical parameters were

obtained by means of simulation. Quantitative comparisons were made and the simulation

design procedure was described.

1. INTRODUCTION

In acoustics as in many other areas of

physics a basic question is whether the

phenomena should be described by

particles or by waves. A wave model for

sound propagation leads to more or less

efficient methods for solving the wave

equation, like the Finite Element Method

(FEM) and the Boundary Element Method

(BEM). Wave models are characterized by

creating very accurate results at single

frequencies, in fact too accurate to be

useful in relation to architectural

environments, where results in octave

bands are usually preferred. Another

problem is that the number of natural

modes in a room increases approximately

with the third power of the frequency,

which means that for practical use wave

models are typically restricted to low

frequencies and small rooms, so these

methods are not considered in the

following.

Another possibility is to describe the

sound propagation by sound particles

moving around along sound rays. Such a

geometrical model is well suited for sound

at high frequencies and the study of

interference with large, complicated

structures. For the simulation of sound in

large rooms there are two classical

geometrical methods, namely the Ray

Tracing Method and the Image Source

Method. For both methods it is a problem

that the wavelength or the frequency of the

sound is not inherent in the model. This

means that the geometrical models tend to

create high order reflections, which are

much more accurate than would possible

with a real sound wave. So, the pure

geometrical models should be limited to

relatively low order reflections and some

kind of statistical approach should be

introduced in order to model higher order

reflections. One way of introducing the

wave nature of sound into geometrical

models is by assigning a scattering

coefficient to each surface. In this way the

reflection from a surface can be modified

from a pure specular behavior into a more

or less diffuse behavior, which has proven

to be essential for the development of

computer models that can create reliable

results.

2. SIMULATION OF SOUND IN

ROOMS

2.1 THE RAY TRACING

METHOD

The Ray Tracing Method uses a large

number of particles, which are emitted in

various directions from a source point. The

particles are traced around the room

loosing energy at each reflection according

to the absorption coefficient of the surface.

When a particle hits a surface it is

reflected, which means that a new

direction of propagation is determined e.g.

according to Snell's law as known from

geometrical optics. This is called a

specular reflection. In order to obtain a

calculation result related to a specific

receiver position it is necessary either to

define an area or a volume around the

receiver in order to catch the particles

when travelling by, or the sound rays may

be considered the axis of a wedge or


pyramid. In any case there is a risk of

collecting false reflections and that some

possible reflection paths are not found.

There is a reasonable high probability that

a ray will discover a surface with the area

A after having travelled the time t if the

area of the wave front per ray is not larger

than A/2. This leads to the minimum

number of rays N:

(1)

where c is the speed of sound in air.

According to this equation a very large

number of rays is necessary for a typical

room. As an example, a minimum surface

area of 10 m2 and propagation time up to

only 600 ms lead to around 100,000 rays

as a minimum.

The development of room acoustical

ray tracing models started some thirty

years ago but the first models were mainly

meant to give plots for visual inspection of

the distribution of reflections [1]. The

method was further developed [2], and in

order to calculate a point response the rays

were transferred into circular cones with

special density functions, which should

compensate for the overlap between

neighboring cones [3]. However, it was not

possible to obtain a reasonable accuracy

with this technique. Recently, ray tracing

models have been developed that use

triangular pyramids instead of circular

cones [4], and this may be a way to

overcome the problem of overlapping

cones.

2.2 THE IMAGE SOURCE

METHOD

The Image Source Method is based on

the principle, that a specular reflection can

be constructed geometrically by mirroring

the source in the plane of the reflecting

surface. In a rectangular box-shaped room

it is very simple to construct all image

sources up to a certain order of reflection,

and from this it can be deduced that if the

volume of the room is V, the approximate

number of image sources within a radius of

ct is:

(2)

This is an estimate of the number of

reflections that will arrive at a receiver up

to the time t after sound emission, and

statistically this equation holds for any

room geometry. In a typical auditorium

there is often a higher density of early

reflections, but this will be compensated

by fewer late reflections, so on average the

number of reflections increases with time

in the third power according to (2).

The advantage of the image source

method is that it is very accurate, but if the

room is not a simple rectangular box there

is a problem. With n surfaces there will be

n possible image sources of first order and

each of these can create (n -1) second order

image sources. Up to the reflection order i

the number of possible image sources Nsou

will be:

( )(( ) )

( ) (3)

As an example we consider a 15,000 m3

room modelled by 30 surfaces. The mean

free path will be around 16 m which means

that in order to calculate reflections up to

600 ms a reflection order of i = 13 is

needed. Thus equation (3) shows that the

number of possible image sources is

approximately Nsou = 2913

1019

. The

calculations explode because of the

exponential increase with reflection order.

If a specific receiver position is considered

it turns out that most of the image sources

do not contribute reflections, so most of

the calculation efforts will be in vain. From

equation (2) it appears that less than 2500

of the 1019

image sources are valid for a

specific receiver. For this reason image

source models are only used for simple

rectangular rooms or in such cases where

low order reflections are sufficient, e.g. for

design of loudspeaker systems in non-

reverberant enclosures. [5] [6]

2.3 HYBRYD METHODS

The disadvantages of the two classical

methods have led to the development of


hybrid models, which combine the best

features of both methods [7] [8] [9]. The

idea is that an efficient way to find image

sources having high probabilities of being

valid is to trace rays from the source and

note the surfaces they hit. The reflection

sequences thus generated are then tested as

to whether they give a contribution at the

chosen receiver position. This is called a

visibility test and it can be performed as a

tracing back from the receiver towards the

image source. This leads to a sequence of

reflections, which must be the reverse of

the sequence of reflecting walls creating

the image source. Once 'backtracing' has

found an image to be valid, then the level

of the corresponding reflection is simply

the product of the energy reflection

coefficients of the walls involved and the

level of the source in the relevant direction

of radiation. The distance to the image

source gives the arrival time of the

reflection.

It is, of course, common for more than

one ray to follow the same sequence of

surfaces, and discover the same potentially

valid images. It is necessary to ensure that

each valid image is only accepted once;

otherwise duplicate reflections would

appear in the reflectogram and cause

errors. Therefore it is necessary to keep

track of the early reflection images found,

by building an 'image tree'.

Figure 1. Principle of a hybrid model. The

rays create image sources for early reflections

and secondary sources on the walls for late

reflectios.

For a given image source to be

discovered, it is necessary for at least one

ray to follow the sequence which define it.

The finite number of rays used places an

upper limit on the length of accurate

reflectogram obtainable. Thereafter, some

other method has to be used to generate a

reverberation tail. This part of the task is

the focus of much effort, and numerous

approaches have been suggested, usually

based on statistical properties of the room's

geometry and absorption.

3. DIFFUSION OF SOUND IN

COMPUTER MODELS

The scattering of sound from surfaces

can be quantified by a scattering

coefficient, which may be defined as

follows: the scattering coefficient s of a

surface is the ratio between reflected sound

power in non-specular directions and the

total reflected sound power. The definition

applies for a certain angle of incidence,

and the reflected power is supposed to be

either specularly reflected or scattered. The

scattering coefficient may take values

between 0 and 1, where s = 0 means purely

specular reflection and s = 1 means, that all

reflected power is scattered according to

some kind of 'ideal' diffusivity. One

weakness of the definition is, that it does

not say how the directional distribution of

the scattered power is; even if s = 1 the

directional distribution could be very

uneven.

Figure 2. Snell’s law reflection (left) vs

Lambert’s law reflection (right).

Diffuse reflections can be simulated in

computer models by statistical methods

[10]. Using random numbers the direction

of a diffuse reflection is calculated with a

probability function according to

Lambert's cosine-law, while the direction


of a specular reflection is calculated

according to Snell's law (Fig.2). A

scattering coefficient between 0 and 1 is

then used as a weighting factor in

averaging the co-ordinates of the two

directional vectors, which correspond to

diffuse or specular reflection, respectively

An example of ray reflections with

different values of the scattering

coefficient is shown in Fig. 3. For

simplicity the example is shown in two

dimensions, but the scattering is three-

dimensional. All surfaces are assigned the

same scattering coefficient. Without

scattering the ray tracing displays a simple

geometrical pattern due to specular

reflections. A scattering coefficient of 0,20

is sufficient to obtain a more diffuse result.

Figure 3. Reflection of rays with different

scattering coefficients of the surfaces. a) s=0;

b) s=0,2; c) s=1.

By comparison of computer simulations

and measured reverberation times in some

cases where the absorption coefficient is

known, it has been found that the

scattering coefficient should normally be

set to around 0.1 for large, plane surfaces

and to around 0.7 for highly irregular

surfaces. Scattering coefficients as low as

0.02 have been found in studies of a

reverberation chamber without diffusing

elements. The extreme values of 0 and 1

should be avoided in computer

simulations, as they are not realistic. In

principle the scattering coefficient varies

with the frequency - scattering due to the

finite size of a surface is most pronounced

at low frequencies, whereas scattering due

to irregularities of the surface occurs at

high frequencies.

4. ACOUSTICAL SIMULATION:

STADT CASINO

During the present work a virtual

acoustical model was proposed for an

arbitrarily selected concert hall. In this

case, the choice was the Stadt Casino,

located in Basel, Switzerland. The Stadt

Casino is a globally acclaimed concert

hall, due to its acoustical characteristics

and its visually appealing architecture as

well. It was built in 1876 under the

direction of Ar. Johann Jacob Stehlin-

Burkhardt and it is nowadays the local

venue for most performances of the

‘Sinfonieorchester Basel’ (Basel’s

Symphonic Orchestra). Also the Basel

Chamber Orchestra and the Basel

Sinfonietta usually organize their

symphonic concerts in this hall [11].

Figure 4: Outside view of the Stadt Casino.

The Stadt Casino is a typical

rectangular hall with a flat coffered ceiling

that connects to the side walls with a

sloping cornice [12]. The audience area

consists of a flat main floor and shallow

balconies. The widths of both are nearly

the same (21m) making the room very

intimate acoustically. Visually, the

balconies are surrounded by large and

sumptuous crystal windows, necessary at

the moment it was built due of the lack of

artificial lightning and air conditioning.

Four ornate chandeliers decorate the

ceiling.


Figure 5. Inside view of the Stadt Casino.

Its characteristic large organ stands

above the highest stage riser on which the

percussion or the organ console

customarily sit. The interior is plaster with

a small amount of wood and baroque

columns and ornamentation, which

according to acoustic designers, is

responsible for bass warmth and brilliance

of the higher registers in this case. The

floor surface consists of parquet over a

solid base, without any type of carpet. The

stage floor surface is made up of heavy

wood over airspace, which rises 91 cm

over the main floor. The sets are partially

upholstered at the top of seat bottoms and

the front of the backrests; the underseats

are made of solid metal.

Figure 6. Floor plan of the main floor (1) and

balconies (2).

Figure 7. Cross section of the Stadt Casino.

The hall responds well to the music in

general and musicians often positively

criticize the venue, even though it is too

small for full orchestra. Musicians and

audience who know the hall well often

recognize that all music that is properly

scaled to the size of the Stadt Casino

sounds very good. The seating capacity is

890 for the main floor and 558 for both

balconies, leaving a total seating capacity

of 1448. The total volume of the venue is

10,500 m3

while the total audience area is

584 m2; thus leaving an amount of 7,25

m3/0.404 m

2 per seat. The stage area totals

160 m2 and the acoustical absorption area,

891 m2. [13]

Volume (V) 10,500 m3

Capacity (N) 1448

Audience Area (Sa) 584 m2

Stage Area (So) 160 m2

Absorption Area (St) 891 m2

V/N 7,25 m3

Sa/N 0,404 m2

Avg Height (H) 15,2 m

Avg Width (W) 21 m

Avg Length (L) 23,5 m

H/W 0,72

L/W 1,12 Table 1. Physical dimensions of the Stadt

Casino.

The average room height, measured

from main floor to ceiling is also an

important distance to recognize, since it

has influence on the time delay of the first

ceiling reflection, which may be long

relative to the arrival of the direct sound

when the reflection goes to a main floor


seat and much shorter when it goes to a

balcony seat. This average distance is 15,2

m. Similarly, the average width, measured

between sidewalls in the audience area on

the main floor, disregarding any balcony

overhang, is an indication of the ‘intimacy’

of the hall. The first reflection after the

direct sound that reaches a listener on the

main floor may come from a balcony face.

However, most side balconies are only a

few rows deep, so that the average width

between sidewalls is a more general

indication of the ‘intimacy’ factor. On the

other side, the average room length,

measured from the stage front to the

average of the back wall positions at all

levels, is a general indication of the

magnitude of the fall-off in loudness with

distance from the stage. The overall

relevant physical dimensions can be

observed in Table 1.

As regards its acoustical parameters,

measurements inside the Stadt Casino were

made in the past by Takenaka and Beranek

in 1993 and 1965 respectively. [13] These

acoustical evaluations were made for

parameters such as reverberation time and

early decay time, interaural cross-

correlation, musical clarity and strength.

Values obtained are shown in Table 2.

Parameters 125 250 500 1000 2000 4000

RT -unoccupied-

(s) 2,78 2,74 2,31 2,31 2,23 1,90

RT -occupied-

(s) 2,20 2,00 1,80 1,75 1,60 1,50

EDT -unoccupied-

(s) 2,55 2,62 2,19 2,20 2,13 1,79

IACCa -unoccupied-

0,90 0,72 0,22 0,13 0,17 0,18

IACCe -unoccupied-

0,89 0,78 0,46 0,34 0,33 0,29

IACCl -unoccupied-

0,90 0,69 0,17 0,09 0,07 0,06

C80 -unoccupied-

(dB) -4,10 -4,50 -3,20 -2,00 -1,70 -0,70

G -unoccupied-

(dB) 9,10 8,90 7,90 8,30 7,70 7,20

Table 2. Acoustical parameters measured at the

Stadt Casino.

An acoustical simulation was proposed

and elaborated using EASE v4.3.8

software (Enhanced Acoustic Simulator for

Engineers) in order to compare the values

obtained by simulation to those obtained

by real measurements such as those in

Table 2.

5. MODEL DEVELOPMENT AND

RESULTS

5.1 DESIGN

Prior to the development of the EASE

acoustical model, it was necessary to draw

three-dimensionally the venue in a 3D

design software such as Google Sketchup.

This task was carefully done by

referencing to the floor plan and cross-

section from Figs. 6-7, and taking into

account the functioning and workflow

from EASE.

The 3D model was then imported to

EASE and some corrections were made,

since the importation algorithm from

EASE can be troublesome. For that matter,

surface color was assigned differently (as it

can be seen on Figs. 8-9) according to the

absorption and scattering coefficients

proposed for each sector.

Figure 8. 3D model of the Stadt Casino.

Figure 9. 3D model of the Stadt Casino.

Seven different surfaces were modeled

to simulate seven different

materials/conditions inside the room: wood

on 2cm of air, plaster, windows, two


different wood floors, people seated and

the organ. Absorption coefficients for each

material can be seen on Table 3.

Table 3. Absorption coefficient of the materials

used in the simulation model.

Both the total modeled room volume

and room dimensions were very important

in the design phase, since reverberation

time is calculated by means of

Sabine/Eyring Equation in EASE. Table 5

shows data comparison between real and

modeled reverberation time.

Parameter Real Model

Volume 10.500 m3 10.509 m

3

Height 15,2 m 15,2 m

Widh 21 m 21 m

Large 23,5 m 25, 07m

Distance stage to

listener 24,4 m 24,5 m

Table 4. Comparison of physical atributes

between the reals values and simulation model

values.

Figure 10. Main dimensions for the simulated

model.

Octave

Band

Rev. time [s]

measured

by Beranek

Rev. time [s]

calculated

with Eyring

equation

125 2,20 2,09

250 2,00 1,93

500 1,80 1,72

1000 1,75 1,56

2000 1,60 1,50

4000 1,50 1,44 Table 5 – Reverberation time comparison

between measurements made by Beranek and

theoretical values from Eyring formula

Weather conditions were set by default

on the simulation, namely: 60% humidity,

constant temperature of 20°C and an

atmospheric pressure of 1013 hPa.

5.2 SOURCE AND LISTENER

POSITIONS

After the software checked that the

model had met the necessary requirements

for calculation, 10 listening positions were

defined within the room, which the

software used to calculate ray tracing

impact. Besides, two source positions on

the stage were chosen in order to obtain

values as uniformly and spatially

distributed as possible.

A modeled source of constant

omnidirectional response at all frequencies

and angles was chosen. The sound level of

the source was set to the maximum

allowable of 96,78dB at 1m. Phase rotation

was set to 0 °.

Frecuency

bandOrgan

Generic, Wood

Grid, 35mm x 15

mm, on 2 cm of

Air

Generic,

Plaster on

Lath, Rough

Finish, SSE

Generic,

People, in Fully

Covered Seats,

per Person

Generic, Glass,

Window,

Plate, 0,25 inch

thk, Heavy

Large Panes

Generic,

Floor,

Wood, on

Beams

Generic,

Floor, Wood

on Concrete

100Hz 0.31 0.01 0.02 0.22 0.21 0.20 0.02

125Hz 0.30 0.01 0.02 0.25 0.18 0.20 0.02

160Hz 0.28 0.02 0.02 0.30 0.14 0.18 0.02

200Hz 0.27 0.04 0.02 0.35 0.10 0.17 0.03

250Hz 0.25 0.05 0.02 0.40 0.06 0.15 0.03

315Hz 0.23 0.06 0.02 0.45 0.05 0.13 0.03

400Hz 0.22 0.07 0.03 0.50 0.05 0.12 0.03

500Hz 0.20 0.08 0.03 0.55 0.04 0.10 0.03

630Hz 0.19 0.08 0.03 0.58 0.04 0.09 0.03

800Hz 0.18 0.09 0.04 0.62 0.03 0.09 0.03

1000Hz 0.17 0.09 0.04 0.65 0.03 0.08 0.03

1250Hz 0.16 0.09 0.04 0.65 0.03 0.08 0.03

1600Hz 0.16 0.09 0.04 0.65 0.02 0.08 0.03

2000Hz 0.15 0.09 0.04 0.65 0.02 0.08 0.03

2500Hz 0.13 0.09 0.04 0.63 0.02 0.07 0.03

3150Hz 0.12 0.09 0.03 0.62 0.02 0.06 0.03

4000Hz 0.10 0.09 0.03 0.60 0.02 0.05 0.03

5000Hz 0.09 0.09 0.03 0.59 0.02 0.05 0.03

6300Hz 0.09 0.09 0.03 0.58 0.02 0.05 0.03

8000Hz 0.08 0.09 0.03 0.57 0.02 0.05 0.03

10000Hz 0.08 0.09 0.03 0.57 0.02 0.05 0.03


Figure 11. Above: positioning of sources

and microphones (cross section); Below:

positioning of sources and microphones (floor

plan).

Fig. 11 shows listening positions

(represented as chairs) designed with the S

prefix and their corresponding numerical

number. The height of all listening

positions was 1.20 m above ground level,

according to the standardized height of the

audience. Analogously, source positions

can be identified with the letter L. L1 was

established at a height of 0.5m, supposing

the height of a percussion instrument

within a typical formation of an orchestra.

The height of the L2 position was

established according to the average height

of a violin executed by a soloist, that is,

around 1,5 m.

Figure 12. 3D rendering of the concert hall

(EASE).

5.3 RAY TRACING SETUP

EASE aims to assess enclosure data

using the ray tracing method, that is,

calculating the amount of impacts that

cross each zone of analysis (listener

positions), defined as a sphere. Thereby it

intends to calculate some of the parameters

commonly taken into account in the design

of concert halls.

Time impact analysis was set as 300ms,

since the ray tracing method is only valid

for the behavior of early reflections. The

average free path time was set as 20 ms,

thus indicating the average time between

the direct sound and the first reflection

estimated. The amount of rays emitted by

the source was increased so that the odds

of impact exceeded 95%. The processing

time was 6 hours approximately, for two

source positions and 10 listening positions.

Impulse responses were obtained for

each listening position after the tracing

simulation. Each impulse response was

added a statistical tail. It was necessary to

manually adjust the level of this random

tail and the noise associated to it, until both

curves matched. Fig. 13 illustrates this

procedure from a reflectogram signal at a

frequency of 1 kHz.

Figure 13 – Procedure to add random

reverberation tail

Once the impulse responses were

obtained, it was possible to calculate

acoustical parameters such as EDT and

Lateral Fraction, since these parameters

could not be evaluated by the simulation

program used. Impulse responses were

extracted as audio wave files in order to be

evaluated later using other software.


To be able to calculate LF it was

necessary to obtain two different types of

microphone polar patterns in the responses

of each position; the EARS module was

used for that matter. This module can

apply different filters corresponding to

different polar patterns to the three-

dimensional impulse response, as it can be

seen on Fig. 14.

.

Figure 14 – Above: Three-dimensional Impulse

Response; Middle: Omnidirectional polar

pattern; Below: Lumbert Side Cosine polar

pattern.

Lateral Fraction is defined as the ratio

between the energy received by a figure-

of-eight microphone with its null pointing

at the source and the energy received by an

omni-directional microphone at the same

position. Lumbert Side polar patterns were

used to simulate the response of figure-of-

eight microphones, even though they do

not represent exactly a figure-of-eight

polar pattern. Moreover, they only

represent half of the polar pattern needed,

so it was necessary to sum two audio wave

files with different and opposing Lumbert

Side patterns. These audio waves files, in

addition to the regular impulse responses

obtained beforehand (omnidirectional)

were processed to obtain LF values.

5.4 SCATTERING COEFFICENTS

In order to evaluate the behavior of the

enclosure in a more realistic way,

scattering coefficients were added.

Since scattering values of the materials

used were not available at the moment of

the simulation, it was decided to estimate

these values according to the surface

geometry that was arranged in each

material.

The modeling software offers a

scattering prediction tool for certain

geometric shapes and surfaces.

Figure 15. EASE scattering calculation tool.


Different scattering curves were

calculated for each surface. Scattering

values for the organ were predicted

differently to other materials, because the

scattering prediction tools did not present

an option for this case. These values were

obtained from a table provided in the book

Acoustic Absorbers and Diffusers (shown

in Table 6) [16]. While the description of

these values does not exactly fit the

geometry of the organ, the choice was a

reliable approximation.

Table 6. Scattering coefficient table. Acoustic

Absorbers and Diffusers, Trevor J. Cox.

A full detailed view of the scattering

coefficients used for the project can be

seen on Table 7. This table describes the

scattering coefficients as a function of

frequency and the material used.

Table 7. Scattering coefficent values of each

material.

6. RESULTS AND DISCUSSION

In order to compare and contrast the

influence of scattering on the models, two

different simulations were made: one

without considering scattering at all, and

one using the above mentioned

coefficients.

6.1 SIMULATION WITHOUT

SCATTERING

6.1.1 REVERBERATION TIME

After the ray tracing analysis was

carried out, various impulse response audio

wave files were obtained. The T30 values

were obtained by averaging 20 impulse

responses (10 seating position and 2 source

position) using the software Aurora 4.3.

Octave

Band

Rev time [s]

measured

for Beranek

Rev. time [s]

calculated

from IR

125 2,20 2,38

250 2,00 2,18

500 1,80 1,94

1000 1,75 1,76

2000 1,60 1,68

4000 1,50 1,59 Table 8. Comparison between RT measured by

Beranek and RT calculated with simulation.

As it can be seen on Table 8, the values

are closer to the ones measured by Beranek

in 1965. It is important to note that the ray

tracing method cannot make a good

approximation for low frequencies

considering the wave nature of sound at

these frequencies.

6.1.2 EARLY DECAY TIME

Similarly to the RT, EDT was

calculated.

Octave

Band

EDT [s]

measured

for

Takenaka

EDT [s]

calculated

from IR

125 2,55 3,93

250 2,62 2,92

500 2,19 2,05

1000 2,20 1,88

2000 2,13 1,77

4000 1,79 1,70

Table 9. Comparison between EDT values

measured from Takenaka in 1993 and EDT

values calculated from simulation.

Frecuency

bandOrgan

Generic, Wood

Grid, 35mm x 15

mm, on 2 cm of

Air

Generic,

Plaster on

Lath, Rough

Finish, SSE

Generic,

People, in Fully

Covered Seats,

per Person

Generic, Glass,

Window,

Plate, 0,25 inch

thk, Heavy

Large Panes

Generic,

Floor,

Wood, on

Beams

Generic,

Floor, Wood

on Concrete

100Hz 0.13 0.10 0.50 0.60 0.10 0.10 0.10

125Hz 0.22 0.10 0.50 0.60 0.10 0.10 0.10

160Hz 0.38 0.10 0.50 0.63 0.10 0.10 0.10

200Hz 0.50 0.10 0.50 0.67 0.10 0.10 0.10

250Hz 0.57 0.10 0.50 0.70 0.10 0.10 0.10

315Hz 0.67 0.20 0.41 0.73 0.10 0.10 0.10

400Hz 0.79 0.30 0.33 0.77 0.10 0.10 0.10

500Hz 0.85 0.40 0.25 0.80 0.10 0.10 0.10

630Hz 0.85 0.40 0.19 0.80 0.10 0.10 0.10

800Hz 0.76 0.40 0.12 0.80 0.10 0.10 0.10

1000Hz 0.69 0.40 0.10 0.80 0.10 0.10 0.10

1250Hz 0.75 0.40 0.10 0.80 0.10 0.10 0.10

1600Hz 0.77 0.40 0.10 0.80 0.10 0.10 0.10

2000Hz 0.75 0.40 0.10 0.80 0.10 0.10 0.10

2500Hz 0.79 0.40 0.10 0.74 0.10 0.10 0.10

3150Hz 0.85 0.40 0.10 0.67 0.10 0.10 0.10

4000Hz 0.81 0.40 0.10 0.60 0.10 0.10 0.10

5000Hz 0.78 0.40 0.10 0.60 0.10 0.10 0.10

6300Hz 0.78 0.40 0.10 0.60 0.10 0.10 0.10

8000Hz 0.78 0.40 0.10 0.60 0.10 0.10 0.10

10000Hz 0.78 0.40 0.10 0.60 0.10 0.10 0.10


Contrary to RT, the values obtained for

EDT vary strikingly with the ones

measured by Takenaka. It should be

clarified that these values have been

measured without audience; the simulation

corresponds to an occupied room with

added audience absorption. The acoustic

characteristics of the seating area in a

concert hall are circumstantially influential

in the acoustics of the room. This is mainly

due to the large area occupied by them. It

is proposed as a future work then, to

consider the empty room conditions in the

simulated concert hall.

6.1.3 SPEECH INTELLIGIBILITY

Fig. 16 shows the calculated STI

mapping for the audience area on the

simulated hall.

Figure 16. STI mapping on the audience area.

It is noticeable that the value of STI is

proportional to the distance from the

source, which is related to the reduction in

level of direct sound and the increasing

level of reflections from surfaces.

Nevertheless, the STI values range within

a fair amount for nearly all audience areas.

It is possible to interpret the STI values in

a simple way in terms of a proposal made

by Barnett. [14] [15]

Figure 17. Barnett qualification of STI.

On the other hand, it can be seen that

for audience areas located on the first floor

(balcony) EASE was unable to determine

STI values since there is no direct path

from the source to the top of the audience

area. For this reason, a speech

intelligibility analysis was performed only

for the listening positions on the main

floor, including STI and %ALcons

(percentage of articulation loss of

consonants) values. Results can be seen on

Table 10.

Position STI %ALcons

1 0,509 10,80%

2 0,513 10,60%

3 0,515 10,47%

4 0,536 9,32%

5 0,556 8,36%

6 0,513 10,60%

7 0,512 10,66%

8 0,551 8,61%

9 0,507 10,95%

10 0,511 10,68%

Avg 0,5223 10,11% Table 10. STI and %ALcons values obtained

from simulation.

Both the simulated STI and %ALcons

values show coherence between each

other, and fall below expected values for

this type of rooms, even though concert

halls are not designed for speech uses. It is

usually considered that when %ALcons

values are more than 10%, the

intelligibility is poor. In learning

environments and voice-focused systems,

the desired value is 5% or less. 15% is

usually the maximum acceptable loss.

6.1.4 LATERAL FRACTION (LF)

Results for LF were obtained by means

of averaging the 20 omnidirectional

impulse responses and the 20 figure-of-

eight impulse responses (as described in

section 5.3). Table 11 shows the average

LF values calculated as a function of

frequency.

125

Hz

250

Hz

500

Hz

1000

Hz

2000

Hz

4000

Hz

0,19 0,26 0,24 0,20 0,20 0,21

Table 11. Lateral Fraction values.

Since LF values measured in situ could

not be obtained, it was not possible to

make a comparison in these terms.

Otherwise, it is possible to note that this

parameter has no significant variations

between each octave band. It remains

approximately constant at 0.22 times the


direct relationship between early lateral

energy and total energy early.

6.1.5 ECHO SPEECH AND ECHO

MUSIC

Echo speech projects how seriously

delayed energy spikes will degrade speech

intelligibility. It is derived by applying a

weighting function (proposed by Dietsch

and Kraak) to the Energy Time Curve

(ETC). Computed values greater than 1 are

likely to be problematic and values greater

than 0,9 are marginal.

Figure 18. Echo speech curves obtained for the

simulation.

Echo music projects how seriously delayed

energy spikes will degrade the quality of

music. It is also derived by applying a

weighting function (proposed by Dietsch

and Kraak) to the Energy Time Curve

(ETC). Computed values greater than 1,8

are likely to be problematic and values

greater than 1,5 are marginal.

Figure 19. Echo music curves obtained for the

simulation.

Figs. 18-19 show obtained curves for echo

music and echo speech as a function of

time. Each graph consists of different

curves for different frequencies and one

full IR echo curve. All of the computed

values are far from being problematic

according to the ranges described above.

This indicates the absence of problematic

echoes (in terms of music and speech) for

the listener positions analyzed. The results

in this case were analyzed using EASERA

software.

6.2 SIMULATION WITH

ESTIMATED SCATTERING

COEFFICENTS

After completing the previous

simulation, the evaluation of acoustical

parameters including scattering coefficient

values was carried out. The evaluation

method for obtaining these values was

similar as the one explained in the previous

section. The results for Early Decay Time

(EDT) and Reverberation Time (RT) are

exposed below.

Octave

Band

Rev time

[s]

measured

by

Beranek

Rev. time

[s]

calculated

from IR

125 2,20 1,14

250 2,00 1,07

500 1,80 1,13

1000 1,75 1,20

2000 1,60 1,18

4000 1,50 1,16 Table 12. Comparison between RT measured

by Beranek in 1995 and RT calculated with

simulation.

Octave

Band

EDT [s]

measured

for

Takenaka

EDT [s]

calculated

from IR

125 2,55 0,86

250 2,62 0,81

500 2,19 0,82

1000 2,20 0,86

2000 2,13 0,87

4000 1,79 0,96 Table 13. Comparison between EDT measured

by Takenaka in 1993 and EDT calculated with

simulation.

As it can be seen on Table 12-13 the

values obtained for RT and EDT were

reduced in great amount for all octave

bands. This situation is given by the fact

that it is very difficult to determine the

right amount of scattering for each surface,

since it does not only depend on the

material (roughness) but it also depends on

the detailed geometry of the surface.

Therefore, it is proposed as future work to

specify each surface individually with


more detailed scattering values related to

its geometry.

Since the values of RT and EDT did not

represent faithfully the real acoustical

conditions of the concert hall, all other

acoustic parameters were not evaluated

since they will also lack coherence and

they will not be suitable to comparisons

with the measured values.

7. CONCLUSION

Acoustical modeling software offers

diverse tools to predict the acoustical

behavior of enclosures, but require great

effort in order to obtain trustworthy results.

It must be taken into consideration also

that software models require large time to

process and reprocess data and this can be

a limiting issue in determined projects.

Apart from that, they can successfully

complement the acoustical designer’s work

and they can offer the unique possibility to

listen (via auralization) the outcome of a

concert hall prior to its construction. Hence

the importance of these systems and the

development of the technology used by

them can be crucial to the fate of the

development of room acoustics in the near

future.

8. REFERENCES

[1] A. Krokstad, S. Stroem, & S. Soersdal.

Calculating the Acoustical Room Response

by the use of a Ray Tracing Technique J.

Sound Vib. 8, 118-125 (1968).

[2] A. Kulowski. Algorithmic

Representation of the Ray Tracing

Technique. Applied Acoustics 18, 449-469

(1985).

[3] J.P. Vian, & D. van Maercke.

Calculation of the Room Impulse Response

using a Ray-Tracing Method. Proc. ICA

Symposium on Acoustics and Theatre

Planning for the Performing Arts,

Vancouver, Canada (1986) pp. 74.

[4]. T. Lewers. A Combined Beam Tracing

and Radiant Exchange Computer Model of

Room Acoustics. Applied Acoustics 38,

161-178 (1993).

[5] J.B. Allen, & D.A. Berkley. Image

method for efficiently simulating small-

room acoustics. J. Acoust. Soc. Am. 65,

943-950 (1979).

[6] J. Borish. Extension of the image model

to arbitrary polyhedral. J. Acoust. Soc.

Am. 75, 1827-1836 (1984).

[7]. M. Vorländer. Simulation of the

transient and steadystate sound

propagation in rooms using a new

combined ray-tracing/image-source

algorithm. J. Acoust. Soc. Am.

86, 172-178 (1989).

[8] G.M. Naylor. ODEON - Another

Hybrid Room Acoustical Model. Applied

Acoustics 38, 131-143(1993).

[9] G.M. Naylor. Treatment of Early and

Late Reflections in a Hybrid Computer

Model for Room Acoustics. 124th ASA

Meeting, New Orleans (1992) Paper

3aAA2.

[10] U. Stephenson. Eine Schallteilchen-

computersimulation zur Berechnung für

die Hörsamkeit in Konzertsälen

massgebenden Parameter. Acustica 59, 1-

20 (1985).

[11] Sinfonieorchester Basel. Wikimedia

Foundation. Web. 5 June 2015.

[12] W. Furrer, Raum- und Bauakustik,

Larmabwehr , 2nd

Edition, Birkhauser

Verlag, Basel and Stuttgart (1961).

[13] Beranek, L. (2004). Concert halls and

opera houses: music, acoustics, and

architecture. Springer Science & Business

Media.

[14] Barnett, P. W. and Knight, R.D.

(1995). The Common Intelligibility Scale,

Proc. I.O.A. Vol 17, part 7.

[15] Barnett, P. W. (1999). Overview of

speech intelligibility Proc. I.O.A Vol 21

Part 5.


[16] Cox, T. J., & D'antonio, P. (2009).

Acoustic absorbers and diffusers: theory,

design and application. CRC Press.

concert hall acoustic computer modeling

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