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Room acoustic parameters - What's Up?

  • aQrate Acoustics Ltd.

Abstract and Figures

Room acoustic parameters are the tools to control and communicate room acoustic qualities. With over a century passed, starting from Sabine's work and the definition of reverberation time we have lots of different measures by now. The most well-known are defined in standards, yet there is still and active debate (e.g. EAA TC RBA WG6) on which to apply, how to interpret, which has more priority, what is the right form of specification, etc. This paper focuses on the practicality and the use of usual room acoustic parameters. Practicality here means not just how a parameter is easy to measure or calculate, but also how it can be interpreted and how different measures can be meaningful to clients who are hardly familiar to room acoustic theories or psychoacoustics. Presented findings of practicality are based on experience, evaluation of measurements, some simple calculations that were mostly collected during the preparation of the Technical Guidelines of Room Acoustic Design written for the Acoustic Section of the Hungarian Engineering Chamber.
Content may be subject to copyright.
Scientific Society for Optics, Acoustics,
Motion Pictures and Theatre
23-24 September 2021 Budapest Hungary
Andor T. Fürjes
aQrate Acoustics Ltd.
Abstract: Room acoustic parameters are the tools to control and communicate room acoustic qualities. With over a
century passed, starting from Sabine’s work and the definition of reverberation time we have lots of different measures
by now. The most well-known are defined in standards, yet there is still an active debate (e.g. EAA TC RBA WG6) on
which to apply, how to interpret, which has more priority, what is the right form of specification, etc.
This paper focuses on the practicality and the use of usual room acoustic parameters. Practicality here means not just
how a parameter is easy to measure or calculate, but also how it can be interpreted and how different measures can be
meaningful to clients who are hardly familiar to room acoustic theories or psychoacoustics.
Presented findings of practicality are based on experience, evaluation of measurements, some simple calculations that
were mostly collected during the preparation of the Technical Guidelines of Room Acoustic Design written for the
Acoustic Section of the Hungarian Engineering Chamber.
Keywords: room acoustics, parameters, requirements, reverberation time, strength, scattering, meta-analysis
The history of room acoustics is almost a 120-years
long story, with ever growing number of experiments,
observations, ideas and active research. Design of room
acoustics is part of the usual architectural design process
by now. We have standards, we have tools and much of
the romantic attitude still holds.
One would think, that after that long story,
fundamentals are set strong and there are only details to
clear. On the contrast, fundamental questions are still
What is room acoustics anyway? There seems to be
not much consensus in definitions. One states it is about
how sound behaves in enclosed spaces. Others include
semi-open spaces. Again, others just state, that room
acoustics is the way physical space interacts sound by
scattering and reflection. And what number of reflections
is enough to get to ‘room acoustics’?
It is for sure however, that room acoustics is about
how boundaries cause an original acoustic signal to be
repeated in an altered way and how we perceive that
series of effects. These altered repetitions change our
perceptions of the original source, space, timbre and
corrections of the original paper
We use room acoustic parameters (or RAP for short)
to describe or at least to try to describe the collection of
those effects, or just simply the quality of room acoustics.
We need parameters to characterize those qualities.
Parameters we can measure. Parameters, we can predict.
Parameters we can compare. Parameters commonly
understood. Parameters, we can talk about with the
Room acoustic parameters (RAP) are the necessary
tool to connect the subjective impression and physical
(measurable) qualities (Figure 1).
Fig.1. Illustrating the aim behind the idea of using room
acoustic parameters to connect the subjective and
objective aspects.
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This paper is not trying to be a summary of
achievements, because there are so many. This paper is
about some of the fundamental questions that are
repeatedly asked, instead.
Working Group 6 (WG6) of the Technical Committee of
Room and Building Acoustics (TC-RBA) within the
European Acoustics Association (EAA) has the title ‘Room
Acoustic Requirements’. It was motivated by a collection
of those fundamental questions (see [1]) and since the
opening in late 2020, members regularly meet and discuss
their thoughts, results and opinions. While the questions
are more general, scope of WG6 is currently limited to the
use of standardized parameters and cases of performance
Together with the evolution of measurement
methods, equipment and the collection of data on
perceptual aspects, more and more parameters were
defined and gained attention.
Still there seems to be a lack of consensus and that
people wish for a single parameter (percentage maybe?)
to describe the quality of overall impression (see e.g. [7]).
Table 1 lists ISO and EN standards that come up when
searching for the application of room acoustics
parameters. There are national standards as well. They
are not listed here, because they are basically derivatives
of parameters found here, in different interpretation and
different formats of requirements.
Table 1. Overview of standards related to the use and
requirements of room acoustic parameters.
It may sound picky, but that set of standards does not
seem to be comprehensive at all. Neither it looks like the
result of more than 100 years of exhaustive research.
We shall note, that the most types or RAPs are in
ISO 3382-1, but except for late reverberation times, those
are just found in the informative appendix. Also, there are
parameters in ISO 3382-3 based on STI (see [4]), which is
not a RAP while could be also based on a real RAP (see
[17]) or a RAP combined with noise level (see [6] and
Section 3.5).
Standards clearly do not support us with fundamental
questions, like (see [1]):
- Should the recommended values depend on culture,
flavor, genre or just psychoacoustic results?
- Which RAP should be used from ISO 3382 or more
RAPs are necessary?
- What is the optimum way to classify room purposes?
What about multipurpose halls?
- Shall be recommendations minimum, maximum, or
target values? Position dependent or averaged?
- How many positions can be allowed to be bad?
- Is there a chance to find an overall descriptor (‘overall
acoustic quality index’ AQI)?
According to an internal and initial questionnaire
within WG6 members there seems to a be a consensus in
a smaller set of topics, however:
- requirements shall be set as part of an international
standard or a guideline, but not obligatory,
- requirements shall be set as a function of
(performance) genre and main architectural attributes
(e.g. volume)
method of
limen (JND)
ISO 3382-1:2009
performance spaces
T20, T30 + (G, EDT10, C80, D50, TS,
JLF, JLFC, LJ, IACC, STearly, STlate)
X X - -
ISO 3382-2:2008
ordinary rooms T20, T30 X - - -
ISO 3382-3:2012
open plan offices Lp,A,S,4m, D2,S, rD *, rP * X - (X) -
ISO 22955:2021
open plan offices Lp,A,S,4m, D2,S, DA,S, - - X -
ISO 23591
rehearsal rooms T, G - - X -
ISO 2603:2016
interpreter booth
T- - X -
ISO 4043:2016
mobile interpreter
T- - X -
EN 12354-6:2004
sound absorption in
enclosed spaces
T, A - - - X
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- a minimum percentage of seats shall comply to
- in the first step requirements shall be based on
ISO 3382-1 room acoustic parameters.
The authors trying-to-be-provocative question was to
colleagues: “can we tell the quality of a hall just by looking
at the room acoustics parameters”? The answer was not a
straight no or yes, but a list of additional information
required (photo, floor plan, dimensions of the room,
measurement conditions, measurement positions, etc.).
The conclusion seems to be, that the answer is a rather
short “no”.
Clearly there is still a lot to be done the field.
The authors opinion of room acoustics parameters is,
that there might be some misunderstanding and little
more insight is necessary to have a set of consensual
Room acoustic parameters can be categorized in
several ways. The first is to differentiate parameters that
have a direct physical meaning to the room from
parameters that are just simply a description of the
responses between two points in the room (or acoustic
space in general).
3.1. The energy decay curve
The term “energy decay curve” (EDC) or Schroeder-
curve (see [8]) is not defined exactly in [2], but is
commonly understood as the normalized reverse-time
integrated squared impulse response (see Figure 1):
. (2)
and is the impulse response measured or
calculated in a room acoustic situation between two
Besides the visual clarity, this representation has
several advantages. A single point on the curve can mean
a duration  and an early-to-total energy ratio at the
same time, because early-to-total energy ratio is
 (3b)
Also, early-to-late and early-to-total mean the same:
Fig.1. Derivation of the energy decay curve (EDC) from
the measured impulse response.
3.2. Reverberation time
Definition of reverberation time is [2]: “duration
required for the space-averaged sound energy density in
an enclosure to decrease by 60 dB after the source
emission has stopped”.
This means a single point on the EDC (namely
 ). In the view of the author, this is
right so. However, it is often a misunderstanding, that
reverberation time was a “slope” or “rate of decay”, as it
would suggest, that the decay could be a simple single-
term exponential decay. This may be also the cause, why
T20 or T30 (see [2]) are just simple estimates of the “real”
reverberation time.
The most well-known predictions of reverberation
times are based on the classic theory of diffuse sound
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fields within an enclosure: the Sabine (or Sabine-Franklin-
Jaeger) equation:
 
 (5)
and the Eyring (or Norris-Eyring) equation:
 
 (6)
where is the speed of sound, is the volume of the
room, is the total surface area of the room, is
the absorbing power of the boundaries and is the air
attenuation in dB per unit length.
The above formulas suggest, that overall
reverberation times of enclosures are the functions of
 or . But actually, the
equations could also be better interpreted as:
 
 (7)
 
where  
is the statistical mean of lengths of paths
between two reflections.
It may just seem as a game with letters, but it also can
mean, that the real driving forces or causes behind the
decay process are a delay (or inertia) of sound
propagation and the loss of energy.
From that we can conclude, that reverberation time is
not a cause, but rather a consequence, where real causes
are repeated reflections, reflections and propagation are
the only sources of energy losses, the time
between reflections and the absorption at reflections (
assuming a continuous decay or  when
assuming a stepwise decay) plus the absorption
during propagation.
While this approach seems reasonable, it seems odd,
that or the  
ratio is almost never listed next to the
lists of rankings or comparisons of different halls. Also,
usually only functions are studied and displayed,
perhaps just because they seem easier to communicate.
The difference in interpretation might be more
obvious when noting, that while an overall reverberation
time could hardly be applied in a non-closed situation,
decay rates or slopes of responses like T20 or T30 are still
possible to use.
3.3. Strength
Strength is basically a measure of level of the response
(, in dB) within the hall, using the free field sound
pressure level of same sound source at 10 m distance
( in dB) as the reference:
    (9)
In the classical theory of diffuse sound field, total
sound level is the sum of the direct sound and the diffusely
reverberant sound (see p 268 [14]):
 
where is the sound power level of the source, is the
directivity factor, is the distance of the observer from
the source,  is the room constant. If is
small, then . If the source is omnidirectional
, expression in (9) turns into:
  
where the effect of reverberation (last term) seems to be
constant over positions, according the condition that the
diffuse field is isotropic and homogenous within the
A series of theoretical experiments of the author [12]
shows, that
- if sound power is uniformly distributed along the
surface of a boundary, expected (or average) sound
level within the box will be uniform (see Figure 2),
independently from the theoretical directivity of the
secondary/virtual sources along the boundary;
- if aiming of the sound sources along the boundary are
not stable (e.g. facets of a rough surface), the field will
behave the same as if the sources were
omnidirectional into the half-space.
Another calculation also shows, that the level within
the boundary will depend only on the surface area and not
on the volume or the mean path length. In Figure 3 scatter
plots show the expected sound levels along the center axis
of 500 rectangular boxes with randomly chosen
dimensions (  ). From the results it is
clear, that sound level correlates to surface area.
According to the graph, the correlating expression for unit
total power level is (R2>0.98):
 (12)
When adding the effect of absorption as a sum of the
 geometric series and the
directivity factor ( ) of sources along the
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 (13).
Experience shows however, that reverberating energy
decays with distance and that a revised theory (see [11])
approximates measurements more accurately. Rewriting
equation (13) from [11] using (11b) above, we can get:
  
 
Please note, that the above expression deliberately
avoids involving reverberation time from the simplified
expression of (5) as  
and that . The
logic behind is to show, that reverberation time is a
consequence, and not a cause. Causes are again:
geometric constraints ( and ) and absorption ( or
better  ).
The non-homogenous reverberating sound level is
probably due to the non-homogenous irradiation of the
boundaries, which is not considered by the classic theory.
This can also explain, why attempts to approximate
measurements require involving geometrical data
(distance or distance from floor e.g. [13], etc.) and why
computer models considering irradiation (e.g. by using the
Lambert reflectance model) do fit.
Fig.2. Expected SPL vs. distance from the center of a
20×20×20 m rectangular boundary if sound sources along
the boundary (r = 10 m) are aimed perpendicular to the
boundary surface (see [12]).
It may be worth to note, that strength is actually a
form of the direct-to-reverberant ratio (DRR):
  (15a)
, (15b)
where DRR is also the first drop in the EDC:
  
, (16)
because    if  is the end of the direct sound
in the response.
Fig.3. Mean of mean (o) and median (.) SPLs within
random rectangular boundaries vs. mean path length
(top), volume (middle) and surface area (bottom) of the
rectangle with reference to unit total power. Results from
a Monte Carlo experiment of random dipole sound source
distributions along a rectangular boundary aimed
perpendicular to surfaces.
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3.4. Other parameters on the EDC
In the standard ISO 3382-1 ([2]), most of the
parameters can be derived from the EDC.
Clarity measures, like C80 or D50 denote one exact point
on EDC with  and  respectively.
The idea behind early-late and early-total ratios is, that
early part of the response is more characteristic to the
direct sound, while later part is more characteristic to the
reverberant sound in accordance with perception. The
role and importance of different early parts (or
“perceptual time periods”) of the response are well
summed up in [15].
Early stage support is based on three points on EDC:
 
 (17a)
Late stage support is based on four points on EDC:
 
 (17b)
Both are meant to describe the quality of stage
acoustics and for that reason the selection of
measurement points is limited, compared to other
Reverberation times in the standard are all derived
from regression of EDC values between given two points
of the EDC:
- early decay time EDT10: time of the start of the direct
sound  and the time where EDC reaches the -10 dB
- late reverberation time T20 and T30: from the time
where EDC reaches the -5 dB level to the times where
EDC reaches the -25 dB or -35 dB level respectively.
The problem with these definitions is, that they do not
necessarily provide robust and expressible results,
- all try to compare the decay to a single exponential
decay (“best-fit linear regression”), which is not true
in a lot of cases
- early decay time is hard to interpret, if DRR is high
and there is an abrupt drop in EDC accordingly right
after the direct sound ends (see Figure 4).
Evaluating a large set of measurement (see [17])
showed, that results of regression-based EDT10 values
have the same tendencies but much larger variations
compared to the direct reads from 0/-10 dB points of the
EDC. While this change of definition may seem to be just
a simplification, a direct read makes EDT10 actually a
single-point-on-EDC type or early-late descriptor.
Importance of EDT10 seems to be acknowledged and
not just in room acoustics (see e.g. [18]). This is rightful so,
because while T20 and T30 characterize only the last 32%
(after -5dB) of the response, EDT10 is based on the first and
more important 90% of the response.
Fig.4. Regressive evaluation of EDT10 as per ISO 3382-1 is
problematic if D/R is high. A direct evaluation based on
0 dB and -10 dB points provides a robust evaluation.
Figure taken from [16].
3.5. More standard parameters
Remaining parameters in ISO 3382-1 are either loosely
coupled to EDC or are not related at all.
Lateral energy ratios (JLF, JLFC, LJ) are comparing early
parts (from  to  ) of the lateral part of
response to the early ( to  ) or late ( to
 ) total energies. Here  is assumed to be 
 . Here the lateral incidence is the result of
spatial filtering by a figure of 8 (or dipole) microphone
coincident to the omnidirectional microphone (MS stereo
configuration). The null plane of the figure of 8
characteristics shall aim to the direct sound or stage
center, so that the figure of 8 will pick up mainly the lateral
reflected sound.
Interaural cross-correlation coefficient (IACC) requires
using a dummy-head to simulate the effects of the head-
related-transfer functions (HRTF) as well.
IACC and lateral ratios tend to correlate, but it is
argued, which is better for the purpose (see e.g. [16] and
[19]). It is for sure, however, that measurement of lateral
energies is more straightforward and aiming of the figure
of 8 pattern can be done after doing the measurements
automatically by processing B-format Ambisonic
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measurements by applying a direction-of-arrival (DOA)
Center time (TS) is basically the first moment of the
energetic impulse response, which correlates the length
of the decay time if the decay is a simple exponential
decay. Next to the other parameters, center time seems
to have lost its significance.
Parameters in ISO 3382-3 (see [3]) are meant to
describe the way room acoustics helps to reduce
disturbance of adjacent or nearby workplaces in open
office areas. Disturbance is expressed by either sound
levels (Lp,A,S,4m) or spatial decay rate of speech (D2,S) and by
distraction distance (rD) and privacy distance (rP).
The first two parameters can be derived from G, but
the last two parameters are based on STI (see [4]), which
is problematic in several ways. STI was originally meant to
describe overall speech intelligibility when the
(electroacoustic) system is noisy and nonlinear, and also
models nonlinear subjective phenomena such as spectral
and level masking or empirical corrections for aged, or
non-native listeners. Due to the above, calculation and
measurement of STI is based on only spectral (and not
temporal) characteristics of the response.
Despite fundamental dissimilarities STI is often
compared to room acoustic parameters to prove that STI
is needed to complete room acoustics specifications.
Actually, STI correlates real room acoustics parameters
like D50, C80 or even EDT10 convincingly (see [17]), making
it redundant. In case the effect of noise level is of concern,
D50 can be extended by a noise level term (see U50, e.g.
[20]). The latest ISO 22955:2021 seem to make rD and rP
technically obsolete.
3.7. Mother and Father
A paper ([10]) calls reverberation time the mother of
all room acoustic parameters, because using only
reverberation time , volume and the distance from
the source, one can predict other parameters using just
simple empirical formula surprisingly well. In the authors
view however, such a set of empirical formulas would be
interesting truly, if the set of cases were more diverse.
Concert halls are regarded as having reverberant, diffuse
sound fields, 14…18 m mean path lengths and an
absorptive floor (audience area), hence they might be not
very different after all.
On the other hand, the name ‘mother of all room
acoustics parameters’ seems right in the sense, that if
reverberation time is the finish or length of the decay, it
will certainly limit the ‘playground’ for the other
Figure 5 illustrates, that reverberation time is indeed a
limit for speech transmission index: a certain
reverberation time will guarantee that intelligibility will
not be worse than a certain limit value [21]:
   (18)
where  is the mean reverberation time as the
arithmetic average of T20,500 Hz and T20,1 kHz.
Reverberation time does not correlate parameters like
STI, because within those limits set by T, STI can be
anything, depending on the distance of the source and
listener and the directivity of the source or receiver (see
also [4] Annex L).
Fig.5. When reverberation time does not correlate to a
parameter (here: STI), but clearly shows its nature in
limiting possible values of the same parameter.
To continue that analogy, G may be regarded as the
“father of all room acoustic parameters”, because it sets
DRR at the very start of the EDC.
Together G and T will then hold the two points, within
which EDC can theoretically have an unlimited number of
forms with non-positive slopes, yet the set of physically
feasible forms (i.e. combinations of RAPs) is certainly
smaller (see Figure 6).
One of the fundamental aims in engineering using
objective parameters is to differentiate “optimum” from
“not-optimum” or at least to differentiate “good” from
“bad”. This section weighs in a collection of topics just to
illustrate some issues.
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Fig.6. If T60 was the “mother” then G could be the “father”
of all room acoustic parameters, as they set the limits
of the playground, where other room acoustic
parameters can occur.
4.1. Value ranges, means, averages…
Suggested ranges of values for RAPs do exist in reports
(e.g. [1], [23]), papers and now even in international
standards (e.g. [20], [22]). Most of the work is done in
concert halls, rehearsal rooms, open offices and
It is not always clear, however, which attitude is viable
when formulating the requirements:
a) is the range targeting a so-called “optimum”
b) is the range avoiding a “surely bad” or “risky”
These two certainly are very different. In the view of
the author, option b) should be pursued in the first place,
because a definition of “optimum” will always be argued.
ISO 3382-1 suggests means and averages to be used as
single figure values (500 Hz+1 kHz in most cases), but
other standards and especially national standards tend to
use more frequency bands to calculate a mean value.
A collection of measurement results from [25] shows
(see Figure 7), that except for a small bias, using 4
frequency bands instead of 2 frequency bands has no real
advantage, just makes measurements more complicated
(e.g. measurement by handclapping is seldom working
below the 500 Hz band).
4.2. Requirements vs. volume
It is typical to see reverberation time requirements or
suggestions in figures as a function of volume, but except
for the trends and main categories (e.g. genre or room
purpose) there is not much agreement.
There are also formulas, that would make the
representation easier:
where and are the parameters of the form, or
  (20)
where and are the parameters of the form of the
function. The latter formula is more often used in several
standards (e.g. [22], [24]).
Fig.7. Comparison of mean reverberation times Tm2
(500 Hz+1 kHz) and Tm4 (250 Hz+500 Hz +1 kHz+2 kHz)
from a large set of measurements.
When discussing this topic in WG6, an interesting
argument came up based on aspects discussed in [26]:
setting target reverberation times in the form of (20) can
suggest unreasonable values at low volumes (the required
mean absorption to match reverberation time would
increase with lower volumes).
The author suggested another approach: instead of
forcing a  vs. volume formula, simply just the mean
absorption coefficient should be set. Using classic
formulas (5) or (6) the  will then show itself
implicitly. This very simple and informative way is not new
actually (e.g. in ÖNORM B 8115-3, [27]), but values of
for specific cases are not yet defined anywhere.
4.3. Orthogonality
Importance of a parameter can be judged upon their
relationships to other parameters. Correlation between
RAPs is often checked to see, which parameter is
independent from others (i.e. more important) and which
parameters are correlating to others (i.e. can be omitted).
As an example, a series of calculations in [21] of
extreme settings resulted in a correlation matrix shown in
Table 2. The emphasis was to check relationship of
ISO 3382 parameters to STI and which single number
rating would fit best to others. The results here show, that
STI is best correlated to C50,mf values, while other
parameters are really independent and important on their
time (sec)
T60 as Mother
G as Father
playground for the others
-60 dB
-10 -8 -6 -4 -2 0246810 12 14 16 18 20
gyakoriság (%)
Tm4 relatív eltérése Tm2-től %, 100×(Tm4-Tm2)/Tm2
occurence (%)
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Specifications shall use only parameters that have a
real added value when describing qualities.
Table 2. Relation of different parameters expressed by
coefficients of determination, calculated at 10% diffuse
settings of different distributions of absorptions of
theoretical cases [21] (mf is the mean value from
500 Hz+1 kHz+2 kHz average, A is the wide band A-
weighted evaluation).
4.4. Architectural parameters: guidelines, instructions
or requirements?
It is obvious, that characteristic dimensions of a room
will fundamentally affect its potentials in acoustic
qualities. It would be hard however to state, that typical
architectural aspects like length/width/height or the
shape of a room are “room acoustic parameters”. In
addition, an ultimate “optimum” specification would limit
the freedom in architectural design.
For that reason, it is important to decide, that any
requirements of architectural dimensions or shapes shall
be taken as guidelines, instructions or requirements?
Relations like in the case of concert halls
 and
 (21)
are really useful and do not limit the freedom of design.
There are situations however, where room acoustic
consideration will lead to real limitations. Figure 8
illustrates the result of a simple acoustic constraint: what
length and width is allowed if reflections from all walls
must arrive within 35 ms or 50 ms of the arrival of the
direct sound? These time limits are based on typical early-
late limits related to speech intelligibility and the
assumption, that the speaker can turn in any direction and
can be anywhere along the center line of the room (i.e.
reflections from all walls are of equal importance).
This simple constraint resulted reasonable
architectural constraints explaining why the maximum
floor area of a classroom shall not be larger than approx.
90 m2 (which is the case actually). It also supports to
design smaller rooms (with fewer students) if more focus
is necessary.
Fig.8. Classroom sizing chart, based on minimum required
number of early wall-reflections (source S is in front
center, receivers R within 1m of walls) [24].
4.5. Effects of operational variables
Typical room acoustic specifications are set for the
unoccupied, furnished situation for a given set of
constraints. One shall not forget however, that during
normal operation of the room, there are objects within
the room, that will affect room acoustic qualities
significantly and there might be different uses that would
require different room acoustic qualities.
It is more important so, if there can be an “optimum”
value for a parameter but the unkown nature of objects
(number of listeners in a room, type of instrument in a
rehearsal room, number of plush animals in a
kindergarten room) or purposes introduce a set of
uncontrolled variables.
Even safely designing to the worst-case scenario might
lead to “overdesign” and a less comfortable operational
condition for a higher price. Figure 9 shows real
measurements of acoustically untreated, unoccupied,
furnished and inhabited kindergarten rooms. If the room
was acoustically treated, reverberation times could be
even halved, while optimum reverberation times are
known to be around 0.5 s for speech in the occupied
situation [30]. If we add the possibility that children or
students might want to sing in kindergarten rooms or
mf Amf Amf Amf A avg avg-dev
- 1,00 0,96 0,89 0,83 0,27 0,14 0,34 0,23 0,52 0,67
log 1,00 0,95 0,90 0,84 0,29 0,15 0,36 0,25 0,55 0,69
- - 1,00 0,94 0,90 0,19 0,07 0,38 0,27 0,58 0,77
log - 1,00 0,95 0,91 0,21 0,07 0,41 0,29 0,60 0,79
- - - 1,00 0,98 0,30 0,12 0,56 0,42 0,73 0,83
log - - 1,00 0,98 0,33 0,14 0,58 0,44 0,75 0,84
- - - - 1,00 0,31 0,12 0,64 0,51 0,80 0,84
log - - - 1,00 0,32 0,12 0,66 0,52 0,82 0,85
mf - - - - - 1,00 0,92 0,43 0,37 0,43 0,14
A - - - - - - 1,00 0,19 0,15 0,18 0,02
mf - - - - - - - 1,00 0,98 0,96 0,64
A - - - - - - - - 1,00 0,89 0,54
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classrooms, a reverberation time of <0.4 s is surely not
Fig.9. Reverberation time measurement results in
acoustically untreated rooms of kindergartens in a
Hungarian small city, showing the significance of
objects and that additional room acoustic treatment
could also reduce quality [25].
Building multipurpose halls and rooms is often desired
due to economic or financial reasons. The usual practice is
sometimes to design for the most often occurring
situation and tries to introduce some compromise or
variability in the construction to fit other situations. Even
then, the repertoire might change over time, shifting
preferences to where architectural acoustics will be no
longer optimal in most of the events.
The conclusion is, that room acoustic specification
shall therefore leave some room for such variables or the
involvement of the client.
In this section a couple of thoughts are highlighted,
where certainly more research is necessary.
5.1. Listener aspects
For the purpose of using room acoustic parameters
ISO 3382-1 suggests which perceptual factors are
described by which RAP:
- subjective level of sound: G
- perceived reverberance: EDT10
- perceived clarity: C80, D50, TS
- apparent source width (ASW): JLF, JLFC
- listener envelopment (LEV): LJ.
Current research uses a much broader range of
perceptual factors (localization, engagement, timbre,
crispness, harshness, etc.) to differentiate room acoustic
experience further. It is certain, that there are more
parameters needed in addition to the standard ones.
Research in important listener aspects may even result
to omit existing parameters.
New parameters based on findings of psychoacoustic
aspects (e.g. [15], [31]) can already fill some of the gaps,
where existing (or better: regular) RAPs are not able to
differentiate qualities.
An example illustrates this in Figure 10: the task was to
find the problem causing intelligibility problems in a small
theatre at certain rows. ISO 3382 parameters and STI did
not reveal any characteristic difference along the
audience area. The problem could be localized only using
an early-to-direct energy ratio parameter (here called
 
  in dB) calculated for W, X, Y and
Z channels of B-format room impulse responses.
Fig.10. An attempt to find a parameter to differentiate
perceptual problems. Top: early-late (or clarity)
measure vs. distance (and other regular) parameters
did not show any deviation. Bottom: an early-total
parameter could show and localize the problem in
accordance of perception.
5.2. Scattering
The diffuse sound field is something, that most
formulas and derivations assume, but it is not really
defined, how one can check or measure if diffuse
assumptions hold, or what consequences can it have.
There is a standard ([32], [33]) to describe scattering
properties of samples, but how this information can be
used or applied in situ is not really settled (e.g. [36]).
63 125 250 500 1000 2000 4000 8000
lecsengési idő (sec)
frekvencia (1/1 oktávsáv, Hz)
min max átlag szórás medián
mean stdev. medianmax
measured reverberation time (T20, s)
frequency (1/1 octave, Hz)
0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0
távolság (m)
distance (m)
early-late (C50,A, dB)
0,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0
távolság (m)
distance (m)
early-direct (M5-25,A, dB)
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Despite difficulties in the application of scattering
coefficients, a simple derivation might be used to
formulate a general requirement on average scattering
coefficient in a room.
Let us assume, that energy decay can be approximated
by the function:
 
where is time, is the speed of sound, is the average
absorption coefficient and is the mean free path length
between reflections. The purely specular part is then
 
where is the average scattering coefficient of the room.
We may assume, that once a part of the specular
incident energy is scattered (spatially and/or temporally),
it will stay scattered, then the total energy is the sum of
the purely specular and the non-specular (or scattered)
energies at any moment. The diffuse and specular parts
are equal when
 
which yields
 
 (25)
where  is the time, where purely specular and non-
specular energies are in balance. Please note, that this
time is not the mixing time often used to separate
diffusely random part of a single responses.
If we require to have more diffuse energy than
specular energy by the time when EDC reaches the -5 dB
point (see definition of T20 and T30), the requirement is
 , which can turn into
  (26)
if  is calculated using (6).
The result of this thread is shown in Figure 11. This
derivation seems useful and reasonable as a requirement
overall, but the fundamental problem still holds: there is
no tool to check average scattering coefficient in a room
and the definition of a diffuse field does not work
completely even in concert halls, as we saw in 3.3.
It is interesting to see, how different aspects of
“diffuseness” are tried to be described by different
methods. Isotropy can be measured using intensity
probes, homogeneity or uniformity can be measured
using a large number of measurement positions, temporal
randomness can be checked by creating sparsity
parameters [34], perceptual aspects and sensitivity can be
assessed by virtual experiments [35], effects of different
interpretations can be examined by checking different
models [36].
It is an unavoidable and important next step to find the
practical and consensual way of expressing, measuring,
calculating and applying diffusing properties of complex
surfaces (e.g. objects).
Fig.11. Required minimum average scattering coefficient
to ensure more scattered energy than specular energy
from the -5 dB or -10 dB of the decay as the function of
the average absorption coefficient
5.3. New types of situations, new challenges
Perhaps it does not need any consideration, but
obviously there are new types of situations, that might
introduce new kinds of challenges.
Multipurpose halls are more often equipped with
some kind of physical or electroacoustic system that
change room acoustics to fit the needs of actual event.
Changing or coupling volumes is one way, varying or
hiding sound absorbing properties by moving elements is
the other way of physical solutions. Electroacoustic
systems are another type of challenge, and especially
regenerative systems require more careful initial room
acoustic design. Feasibility and acoustic realities should be
reflected in RAPs and their requirements. Even new types
of parameters could be developed to describe the
qualities of such systems.
Teleconferencing in small and large scales is another
challenge nowadays, which is actually the case of
electroacoustically coupled rooms [37].
5.4. Low frequency behavior
Room acoustics research pays a somewhat less
attention to low frequency behavior, perhaps because it is
not in the comfort zone of statistical acoustics and most
situations do not need special considerations due to the
23-24 September 2021 Budapest Hungary
large volumes (e.g. concert halls) or due to the type of
sources (e.g. speech spectra).
Mechanical, electroacoustic or musical sources of
sounds, however occur in smaller environments, well
below the threshold often identified by the Schroeder
There are a number of papers on preferred situations,
most of which are based on rectangular or nearly
rectangular enclosures and its analytical solutions (e.g.
Figure 12 shows an additional attempt to map quality
of low frequency behavior of different room dimension
ratios. Here instead of looking at the global response of
the room, responses of random source-receiver positions
only near the floor (+1…2 m) were evaluated based on the
image source theory and a qualifier was set up based on
the smoothness of the response. This approach seems to
have a somewhat different result than earlier works.
Fig.12. Preferred ratios using a different qualifier of low
frequency response within a room [28].
Low frequency behavior is interesting from other
aspects as well:
- how can we measure and simulate low frequency
reflection and scattering from real structures (current
standards and practices are hardly applicable below
100 Hz),
- how long bursts of low frequency excitations are
necessary to consider modal behavior (not all sound
sources are stationary),
- how loud excitations will cause significant differences
in perception (nonlinear behavior of hearing),
- how air-borne induced structure-borne sensations
affect our perception of room acoustics (advantage of
hollow floor structures in concert halls).
5.5. Just noticeable vs. meaningful differences
ISO 3382-1 sets basically consensual just noticeable
differences (JND) as limens of perceptibility. JNDs are
useful as thresholds in evaluation, and because JNDs are
dimensionless values, they are candidates to express a
change in percentage (they way some clients prefer to
communicate quality).
JNDs on the other hand are of hardly any use when
trying to express what a client will experience as a real
difference. This is because an untrained client in real
situations will most probably not able to differentiate JND
(e.g. 5% change in reverberation time).
It would be useful to find the just meaningful
differences (JMD) to communicate real differences,
because in agreement with [29] the author argues, that
noticeability, meaningfulness, and importance need be
carefully distinguished.
Research of room acoustics and room acoustic
parameters go hand in hand for over a century by now,
but it is obvious, that there are more questions open than
This paper tries to give an overview, but could show
only snippets on what is going on, in the personal view of
the author.
EAA TC-RBA WG6 is currently working to find tangible
resolutions to some of the fundamental questions.
One final suggestion is based on the observation, that
even if there is a huge amount of data from more and
more precise measurement and experience available,
they are not accessible to the scientific public in a regular
format, which makes stand-alone evaluations and
conclusions fragmented and of limited applicability.
The author encourages colleagues therefore to initiate
an open database, where researchers can access
measurement data and not just evaluated end results
from published papers and reports. As one colleague
pointed out, this approach is normal in medical research
and is called meta-analysis. Obviously, some kind of
anonymity would be required, because not all
measurements show that everything is great, while all
event halls and concert halls want to be the best in its
With all the technology currently available, there is
surely a hope, that all current and former efforts can end
up in a consensual set of room acoustic parameters and
guidelines on how to use them.
golden ratio
golden ratio
Walker:1, Rindel: A Rindel: B Rindel: C
0.1 < L/H - W/H < 0.2
1.0 < L/H - W/H < 1.1
2.8 < L/H + W/H < 2.9
H < 4 m
23-24 September 2021 Budapest Hungary
The author would like to thank the work of all the
pioneers in the field of room acoustics for their
enthusiasm and endurance in times, when measurement,
processing and theoretical background was so much more
challenging than it is today.
[1.] U. M. Stephenson: Requirements for Room
Acoustical Parameters A proposal for
structuring the questions on how to define them,
[2.] EN ISO 3382-1:2009 Acoustics. Measurement of
room acoustic parameters. Part 1: Performance
[3.] EN ISO 3382-3:2012 Acoustics. Measurement of
room acoustic parameters. Part 3: Open plan
[4.] EN 60268-16:2020 Sound System Equipment. Part
16: Objective rating of speech intelligibility index
[5.] EN ISO 3382-2:2012 Acoustics. Measurement of
room acoustic parameters. Part 3: Open plan
[6.] Y. Choi: Comparison of Two Types of Combined
Measures, STI and U50, for Predicting Speech
Intelligibility in Classrooms, Archives of Acoustics
Vol. 42, pp 527-532, 2017
[7.] M. Skålevik: Can concert hall preference be
predicted with physical quantities? AIA-DAGA,
[8.] M. R. Schroeder: New Method of measuring
Reverberation time, J. Acoust. Soc. Am., Vol. 37 p.
409, 1965
[9.] EN 12354-6: 2004 Estimation of acoustic
performance of buildings from the performance
of elements. Part 6: Sound absorption in enclosed
[10.] M. Skålevik: Reverberation Time the mother of
all room acoustical parameters, BNAM, 2010
[11.] M. Barron: Theory and measurement of early, late
and total sound levels in rooms, J. Acoust. Soc.
Am. Vol 137 p. 3087, 2015
[12.] A. T. Fürjes: Investigating properties of random
sound source constellations, Forum Acusticum
[13.] C. Wang, H. Ma, Y Wu, J. Kang: Characteristics and
prediction of sound level in extra-large spaces,
Applied Acoustics Vol 134, 2018
[14.] A. D. Pierce: Acoustics An introduction to its
Physical Principles and Applications, ISBN 0-
[15.] E. Green, E. Kahle, V. Berrier, E. Carayol: Beyond
80ms: The Subjective Effects of Sound Energy
Arriving Shortly After the “Early” Sound Period,
ISRA 2019
[16.] J. S. Bradley: Review of the objective room
acoustics measures and future needs, Applied
Acoustics 72 p713-720, 2011
[17.] A. T. Fürjes, A. Nagy: Tales of more than One
Thousand and One Measurements (STI vs. room
acoustic parameters -a study on extensive
measurement data),,
2020 (last visited on the 29th of Sept 2021) DOI:
[18.] P. Brown, P. Mapp: Early Decay Time as a System
Performance Benchmark, https://www.
time-as-a-system-performance-benchmark/ (last
visited on the 29th of Sept. 2021)
[19.] T. Okano, T. Hidaka, L. L. Beranek: Relations among
interaural cross-correlation coefficient (IACC(E)),
lateral fraction (LFE) and apparent source width
(ASW) in concert halls, J. Acoust. Soc. Am., Vol. 104
p. 255, 1998
[20.] EN ISO 22955:2021 Acoustics Acoustic quality of
open office spaces
[21.] A. T. Fürjes: Exploring and alternative scheme of
room acoustics specification, Forum Acusticum
[22.] ISO 23591:2020 Acoustic quality criteria for music
rehearsal rooms and spaces
[23.] M. Barron: Using thee standard on objective
measures for concert auditoria, ISO 3382, to give
reliable results, Acoust. Sci. & Tech. 26, 2, 2005
[24.] MSZ 2080:2020 Acoustics. Specifications and
recommendations for room acoustic design
[25.] FAP-2019/112AT: Teremakusztikai méretezés
gyakran előforduló szituációkban (Design of room
acoustics in usual situations), a technical guideline
of the Acoustical Division of the Chamber of the
Hungarian Engineers.
[26.] B. Støfringsdal, A. C. Gade: The music rehearsal
room - for work and leisure, ISRA 2019
[27.] ÖNORM B 8115-3:2005 Schallschutz und
Raumakustik im Hochbau - Teil 3: Raumakustik
[28.] A. T. Fürjes: Examples of constraint-based
specification of room acoustic parameters,
Euronoise 2021
[29.] D. McShefferty, W. M. Whitmer, M. A. Akeroyd:
The Just-Meaningful Difference in Speech-to-
Noise Ratio, Trends in Hearing Vol. 20:I-II, 2016
[30.] D. Pelegrín-García, J. Brunskog: Classroom
acoustics design guidelines based on the
optimization of speaker conditions, Euronoise
[31.] D. Griesinger: Localization, Loudness, and
Proximity, IOA 2018
[32.] ISO 17497-1:2004 Acoustics Sound-scattering
properties of surfaces Part 1: Measurement of
the random-incidence scattering coefficient in a
reverberation room
23-24 September 2021 Budapest Hungary
[33.] ISO 17497-2:2012 Acoustics Sound-scattering
properties of surfaces Part 2: Measurement of
the directional diffusion coefficient in a free field
[34.] H. P. Tukuljac, V. Pulkki, H. Gamper, I. Tashev: A
Sparsity Measure for Echo Density Growth in
General Environments, ICASSP 2019
[35.] L. Shtrepi, S. Di Blasio, A. Astolfi: Listeners
Sensitivity to Different Locations of Diffusive
Surfaces in Performance Spaces: The Case of a
Schoebox Concert Hall, Applied Sciences Vol. 10,
[36.] L. Shtrepi, A. Astolfi, S. Pelzer, R. Vitale: Objective
and perceptual assessment of the scattered sound
field in a simulated concert hall, The Journal of the
Acoustical Society of America 138(3):1485-1497,
[37.] U. P. Svensson, J. L. Nielsen: Room acoustical
parameters of two electronically connected
rooms, J. Acoust. Soc. Am., Vol. 138(4) p. 2235,
[38.] J. H. Rindel: Preferred dimension ratios of small
rectangular rooms, J. Acoust. Soc. Am Express
Letter 1 (2), 021601, 2021
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Acoustic scattering audibility thresholds are needed for the efficient design of performance spaces and to increase the accuracy of geometric room acoustic models. This paper focuses on the evaluation of the perceptual thresholds of the scattering coefficient through listening tests in simulated concert halls. It also deals with an investigation on the sensitivity of room acoustic parameters to scattering coefficients. A rectangular concert hall has been simulated with three prediction models, in which scattering coefficients of 0.1, 0.3, 0.5, 0.6, 0.7, and 0.9 were applied to the ceiling and walls in six different configurations. The analysis was performed comparing the results of the three-alternative forced choice listening tests and considering the objective parameters T 30, early decay time (EDT), C 80, and G. An increase in EDT and a decrease in C 80 have been observed for increasing scattering coefficient values for all three types of software, while no similar trend was observed for the other parameters. The perceptual evaluation has shown that differences of ∼0.4, relative to an anchor value of 0.9 of the scattering coefficient, were perceived in the listening test conducted with one of the three kinds of software, while no clear differences in auralizations were perceived with the other two kinds.
This paper aims to examine sound fields in extra-large spaces, which are defined in this paper as spaces used by people, with a volume approximately larger than 125,000m 3 and absorption coefficient less than 0.7. In such spaces inhomogeneous reverberant energy caused by uneven early reflections with increasing volume has a significant effect on sound fields. Measurements were conducted in four spaces to examine the attenuation of the total and reverberant energy with increasing source-receiver distance, which was then validated by the simulations with image-source method. Results show that the reasons for the total energy's exponential decrease are not only the direct sound, but also the reverberant energy. The prediction difference of total sound pressure level (SPL) between classical formula and the image-source method increases with the volume and decreases with the surface absorption, based on which a critical line separating extra-large spaces from large ones is proposed. Moreover, a newly modified model based on the importance of first reflection from floor is proposed, showing more advantages of sound level prediction in extra-large spaces.
The acoustical properties of two rooms that are one-way connected electroacoustically, e.g., in a telephone/video conference, can be analyzed through the total impulse response from a source in one room to the receiver in the other room. The total impulse response is a convolution of the two involved room impulse responses, and such a model is analyzed in this paper. The room impulse response model used here facilitates convolution analysis as the model is quite simple and composed of two terms only, a direct sound term and an exponentially decaying random Gaussian noise term. Analytical expressions have been derived for the energy decay function, leading to estimates of room acoustical parameters like clarity and the modulation transfer functions for such convolved impulse responses. Background noise expressions are also introduced to allow signal-to-noise ratio studies. Estimates of acoustic parameter values have been compared with measurements to evaluate the model used and verify the results achieved.