"This research project encompasses the ﬁelds of live sound and architectural
acoustics in ancient theatres. The hypothesis which drives the analysis of the data is
that point source subwoofer arrays are better suited to the combined acoustical
metrics of Roman theatres than other possible conﬁgurations. Three subwoofer arrays
are measured: point source, centre and left-right. The acoustical metrics of frequency
response, SPL, phase, and coherence are discussed and compared. The investigation
possesses two aims: to provide relevant data to the scientiﬁc community, and to
present the subwoofer conﬁguration which oﬀers the most favourable results in order
to deliver the best performance to the audience, increasing this way the interest of the
general public towards culture and the Roman civilisation. The hypothesis is
conﬁrmed as results indicate that the point source array achieves preferable combined
"El presente proyecto de investigación abarca los campos de sonido en directo
y acústica arquitectónica. La hipótesis que dirige el análisis de los datos obtenidos es
que: un arreglo de subgraves de un punto de origen se adapta mejor a la combinación
de métricas acústicas de los teatro romanos que otra conﬁguración posible. Se miden
tres arreglos: un punto de origen, en el centro siguiendo la línea del escenario e
izquierda y derecha. Las métricas acústicas analizadas y comparadas son: respuesta
de frecuencia, nivel de presión sonora (SPL), fase y coherencia. Esta investigación
posee dos objetivos: aportar información relevante a la comunidad cientíﬁca y
presentar el arreglo que ofrece los mejores resultados para, de esta manera, aumentar
el interés del público hacia la cultura y el mundo romano. La hipótesis se conﬁrma ya
que los resultados indican que el arreglo de puntos de origen produce los mejores
valores para las métricas acústicas aquí estudiadas.$
Table of contents
2. Literature Review
2.1 Ancient theatres !
"2.1.1 Brief historical background!
"2.1.2 International and Spanish national projects!
2.2 Architectural acoustics and live sound !
"2.2.1 Frequency cut at 125 Hz in acoustic measurements!
2.3 Subwoofers in live sound!
"2.3.1 Room acoustical metrics Vs. Combined acoustical metrics!
"2.3.2 Uses of subwoofers in sound reinforcement!
"2.3.3 Gradient loudspeakers!
"2.3.4 Democracy of sound. Subwoofer arrays: positioning, spacing, and " "
""directivity" " !
"2.3.5 Flown Vs. Ground-stacked subwoofer conﬁgurations. The optimal array!
"2.3.6 System Performance Quantiﬁcation!
3. Methodology """"""""" !
3.1 Hypothesis recall !
3.2 Equipment used!
3.3 Project phases!
"3.3.1 Phase 1. Measurements!
"3.3.2 Phase 2. Data analysis!
3.4 Limitations and scope of the project!
4. Results of in situ measurements """""""!
"4.1.1. Array Performance Rating!
"4.1.2. Point source array!
"4.1.3. Centre array!
"4.1.4. Left-Right array!
5. Conclusion and future research!
Appendices [A-G] """""""!
Appendix A: Previous Spanish national research projects!
Appendix B: Guide: how to interpret Smaart graphs!
Appendix C: Technical speciﬁcations of the equipment used!
Appendix D: Raw measurements data!
Appendix E: APR Excel Workbook!
Appendix F: Meteorological conditions record!
List of ﬁgures / List of graphs and charts / List of formulas
Figure 1: Ancient theatres in Europe and North Africa
Figure 2: Comparison of T30 (vertical axis) over frequency (horizontal axis) in theatres
and odea. Longer reverberation times in theatres are shown
Figure 3: Superposition of the cavea’s layout and the overhead view of the current
state. Theatre of Cádiz, where a virtual reconstruction was needed
Figure 4: In situ measurements in the Roman theatre of Medellín
Figure 5: Introduction of bi-ampliﬁcation by Altec, where a dedicated signal was fed to
the ‘woofer’ to improve low frequency reproduction. A-7 Cabinet
Figure 6: Zero-order gradient source and polar pattern
Figure 7: First-order gradient source and polar pattern. 1/4 Wavelength delay (left) and
full wavelength delay (right)
Figure 8: First-order gradient source and polar pattern
Figure 9: Second-order gradient source and polar pattern
Figure 10: Royal Albert Hall’s main PA system
Figure 11: Electronic delay applied to point source array for different degrees of
Figure 12: Acoustic centre. Pressure contours and ﬂow lines at 10 Hz
Figure 13: Centre array with 900 of electronic delay & cardioid cabinets
Figure 14: LR in end-ﬁre array conﬁguration
Figure 15: Frequency response and polar pattern Beyerdynamic MM1
Figure 16: Measurement positions grouped in rows (left) and sections (right)
Figure 17: Point source array (left speaker not in use)
Figure 18: Centre array conﬁguration
Figure 19: Left - Right conﬁguration
Figure 20: Radiation pattern simulation over frequency for all subwoofer arrays
Graph 1: Reverberation time, Cádiz
Graph 2: Reverberation time, Medellín
Graph 3: Reverberation time, Segobriga
Graph 4: Reverberation time, Italica
Graph 5: Reverberation time, Regina Turdulorum
Graph 6: Point source array. Magnitude response of rows
Graph 7: Point source array. Magnitude response of sections
Graph 8: Point source array phase response. Rows (left) Sections (right)
Graph 9: Point source array: Cavea, orchestra, and stage. Coherence over frequency
Graph 10: Centre array. Magnitude response of rows
Graph 11: Centre array. Magnitude response of sections
Graph 12: Centre array phase response. Rows (left), Sections (right)
Graph 13: Centre array: Cavea, orchestra, and stage. Coherence over frequency
Graph 14: LR array. Magnitude response of rows
Graph 15: LR array. Magnitude response of sections
Graph 16: LR array phase response. Rows (left), Sections (right)
Graph 17: LR array: Cavea, orchestra, and stage. Coherence over frequency
Graph 18: Magnitude response at point 6. Centre array. Cancellations at 45 and 60 Hz
Graph 19: Magnitude response at point 9. LR array. Cancellation at 60 Hz
Graph 20: Phase responses - All arrays
Graph 21: Coherence responses - All arrays
Graph 22: Examples of coherence issues
Chart 1: Array Performance Rating chart
Chart 2: APR Results for FOH Point 5
Chart 3: APR Results for FOH Point 4
Formula 1: Tonal Consistency
Formula 2: Acceptable System Headroom
Formula 3: Level Consistency Audience/FOH
Formula 4: Array Performance Rating equation
18, 26, 37!
"Sound democratisation is the primary objective of any sound reinforcement
system. The act of providing an even coverage of sound pressure levels (SPL) and
frequency response throughout the audience area comprises complex sub-tasks
which require from dedicated time. Having this allocated time to optimise the system
can be considered a comfort that is not always possible, specially in large productions
where time constraints are usually present (McCarthy, 2016) (Hill et al., 2010).!
"Adding to the tightness of schedules, productions are hosted in numerous
spaces which diﬀer in size, materials, and architectonic elements such as roofs and
walls. These diﬀerences have to be taken into account when deploying a system as
wavelengths can be compared to the size of many venues at low frequencies, creating
undesirable room modes and cancellations. This, and high SPL leakages disturbing
close neighbourhoods in open-air locations, resulted in the need for controlling the
propagation pattern of sound systems.!
"Based on the acoustic fundamentals of constructive and destructive
interferences, there are several subwoofer conﬁgurations that carefully implement this
concept in order to radiate energy in a particular direction. At its simplest form, two
loudspeakers positioned one behind the other at a speciﬁc distance cause waves to
sum in the front and cancel out in the back. Manufacturers visioned its practicality and
merged both cabinets, resulting in cardioid subwoofers. This principle can be scaled
up by grouping them in diﬀerent conﬁgurations (arrays) depending on the venue’s
"An example of the diversity of venues are ancient theatres, which are well-
known because of their excellent acoustics. These buildings were originally designed
for propagating the human voice over a large audience area and due to written
evidences, researchers are able to know the advanced knowledge that they had on
acoustics at the time. Unfortunately, some of the theatres have lost some of their parts
due to natural phenomena or human activities.!
"Multiple vestiges of Roman cities can be found in the mediterranean countries.
The best-preserved example in the Iberian Peninsula is the city of Baelo Claudia,
where elementary characteristics of Roman urbanism can be found (Torres-Ruiz, 2007)
The archaeological complex is a reference site to an international level because of its
distinct characteristics (McDougall, Pliego-Sanchez, 2007).!
"Resulting from its geographical location, the Strait of Gibraltar beneﬁted the
city of Baelo Claudia from key commercial routes with Africa and port cities in the
Mediterranean sea. This helped to export its most expensive and appreciated product:
the garum, which was a ﬁsh sauce made mostly from tuna (McDougall, Pliego-
"Although the Roman theatre of Baelo Claudia is not one of the best-preserved
in Spain, it is an example of the diversity across venues where shows are hosted. A
common characteristic amongst open-air venues in the Strait of Gibraltar is the
presence of strong winds, which can be detrimental to the performance of the system.
Despite this fact, the annual programme displays favourable levels of attendance.!
"The aim of this project is to provide data of the low-frequency range in Roman
theatres. It is an area of the spectrum which is not usually studied although being
highly relevant for performances that require sound reinforcement. Furthermore, the
outcome of the study intends to improve the audience’s experience in the architectural
complex, promoting culture and contributing to a better understanding of the Roman
life. All of this through a more vivid and real experience of what a dramatic
representation in Ancient Rome was.!
"The present paper presents the ﬁrst research project related to the acoustics of
the Roman theatre of Baelo Claudia, in which in situ measurements of three subwoofer
arrays (point source, centre, and left-and-right) are evaluated in order to assess their
suitability to the acoustical metrics of the venue.!
"The research structure is guided by the question: which subwoofer
conﬁguration delivers the best results in the Roman theatre of Baelo Claudia? To focus
on the matter, the outcome will conﬁrm or deny the following hypothesis: !
Point source subwoofer arrays are better suited to the combined acoustical metrics of
Roman theatres than any other possible conﬁguration!
"The paper will start with a brief introduction to Roman theatres and the
previous studies carried out to international and Spanish national levels. Then, the
diﬀerences between the relevant acoustic parameters in architectural acoustics and
live sound will be presented in order to demonstrate the value of the data gathered in
this project. Once the targeted acoustic metrics are stated, an insight on the physics
of subwoofers and waves behaviour is given to then, enumerate the diﬀerent
subwoofer arrays that will be studied.!
"Next, the research methods used in the investigation are explained as well as
the data intended to be collected from them. Following the methodology, results of the
in situ measurements are showcased. Lastly, they will be discussed and the diﬀerent
subwoofer conﬁgurations will be compared in order to verify or refute the hypothesis.$
2 Literature Review
2.1 Ancient theatres
2.1.1 Brief historical background!
"Ancient Roman civilisation has left several vestiges such as the Roman law and
outstanding architecture as the Colosseum. One of the best written-remains through
which contemporary researchers in the scientiﬁc community can understand the level
of knowledge this civilisation had at a technical level more than 2,000 years ago is 'Ten
books on architecture'%(Vitruvius Pollio, NA) (Haddad, Akasheh, 2009). The ancient
Roman architect Vitruvius is the author, and in his ﬁfth book, he describes how
theatres had to be built for optimal audience sight and listening%(Iannace, Trematerra,
"Roman theatres are an evolution of the classical Greek theatre model. Vitruvius
did a compilation of the existent Greek knowledge on theatre architecture and
acoustics, plus his improvements and additions due to his knowledge in the ﬁeld.
Vitruvian norms are found in Roman theatres all over the territories that once were part
of the Roman Empire. One example of this is the theatre in%Cádiz, Southern Spain,
which dimensions resemble the ones in Rome and is connected to the ancient city
of%Baelo Claudia, where the theatre subject to study for this project is located%(Álvarez-
Corbacho et al., 2018).%&
"As mentioned earlier, numerous theatres were built across the Empire, and
most of them are located in countries next to the Mediterranean Sea. Jordan and
Turkey hold the best-preserved examples of these buildings%(Iannace, Trematerra,
2017, p.2). Resulting from the ongoing research and increasing attention to the
acoustics of these constructions, the scientiﬁc community alongside with
governmental bodies have conducted important investigation projects%(Álvarez-
Corbacho et al., 2019).%!
Figure 1: Ancient theatres in Europe and North Africa (Ancient Theatre Archive, NA).
2.1.2 International and Spanish national projects!
"The European Commission ﬁnanced the ERATO Project (ERATO, 2006). It had
a duration of three years in which one of the aims was to study the acoustics of the
odea and open-air theatres utilising computer models of the performance spaces and
to reconstruct them virtually according with archaeological remains%(Rindel, 2013).!
"Romans are presumed to have been using several buildings for diﬀerent
theatrical acts. Amphitheatre, theatre and odeon hosted ﬁghts, speech, and music
performance, respectively%(Sear, 2006, p. 37). The last two represented events which
required speciﬁc acoustic conditions. These particularities are discussed in the ERATO
Project, which studied selected the theatres in Aspendos, Jerash and Syracuse, and
the odea in Aosta and Aphrodisias%(Rindel, 2011).!
"The ERATO Project analyses the room acoustical parameters%of the diﬀerent
spaces. These are: Reverberation time (T30), Strength, Clarity (C80), and Speech
Transmission Index (STI). Those parameters will indicate the reverberation, perceived
sound, the balance between early- and late-arriving energy and degree of amplitude
variation of speech in the audience area%(ISO 3382, 2009, p.12) (McCarthy, 2016, p.31)
(Rindel, Nielsen, 2006, p. 4).&
"The project concluded with meaningful results, conﬁrming the presumption
that Romans uses diﬀerent spaces for distinct acts. Theatres presented remarkable
longer reverberation times than the odea, and the acoustic reconstruction displayed
high clarity levels and low strength of sound in open-air theatres (Figure 2)%(Rindel,
Nielsen, 2006, p. 11).!
Figure 2: Comparison of T30 (vertical axis) over frequency (horizontal axis) in theatres and odea. Longer reverberation times in theatres
are shown (Rindel, Nielsen, 2006).
-Previous studies on the acoustics of Roman theatres in Spain!
"Research projects have been carried out in several Roman theatres present in
the Iberian Peninsula. These studies also focus on room acoustical metrics. Although
none of the measured parameters are directly related to the present study, their
outcomes show a connection between the preservation status and the acoustic
characteristics. A connection which is relevant to this project. For example, high
reverberation times because of the theatre’s large dimensions and the oyster ﬁnishing
stone (Álvarez-Corbacho et al., 2018). Other theatres achieve shorter reverberation
times caused by the lack of the stage front (Álvarez-Corbacho et al., 2019).&
"Two methods of gathering data are presented in these studies: in situ
measurements where possible, and virtual reconstructions for the cases in which the
preservation conditions are not ideal for the tests to be carried out.!
"More detailed information about the methods and outcomes from each ancient
theatre in Spain can be found in Appendix A.!
Figure 3: Superposition of the cavea’s layout and the overhead view of
the current state. Theatre of Cádiz, where a virtual reconstruction was
needed (Álvarez-Corbacho et al., 2018).
Figure 4: In situ measurements in the Roman theatre of Medellín
(Barragán-Pullido et al., 2014).
2.2 Architectural acoustics and live sound
2.2.1 Frequency cut at 125 Hz in acoustic measurements!
"It is of signiﬁcant importance to mention that almost all investigations on the
acoustics of Roman theatres do not study below the frequency of 125 Hz. It is a
logical decision from the researchers, but their ﬁndings do not enter into the scope of
"The answer to why the authors of these studies do not contemplate the
frequency content below 125 Hz varies from case to case. However, one of the main
reasons is because they refer to the ISO 3382 standard%(Álvarez-Corbacho, 2020)
(Astolﬁ, 2020) (Iannace, 2020), which speciﬁes that for engineering and other
precision-methodology purposes, at least the 125 Hz to 4,000 Hz frequency range
would need to be covered%(ISO 3382, 2009, p.6).!
Graph 2: Reverberation time, Medellín (Barragán-
Pullido et al., 2014).
Graph 5: Reverberation time, Regina Turdulorum (Álvarez-
Corbacho et al., 2015).
Graph 3: Reverberation time, Segobriga (Álvarez-
Corbacho et al., 2019).
Graph 4: Reverberation time, Italica
(Álvarez-Corbacho et al., 2014).
Graph 1: Reverberation time, Cádiz (Álvarez-
Corbacho et al., 2018).
Other reasons include:!
1. High uncertainty of collecting accurate data when measuring low frequencies
in open-air spaces%(Bo, 2020).!
2. Problems related to obtaining reliable results with the virtual simulation
software used%(Tatlas, 2020).!
3. No relevance of responses in that area as the fundamental frequency of the
male voice is around 125 Hz%(Lokki, 2020).!
"Despite this, it is understandable that acoustic engineers just need, as the
object of study, the middle and high frequencies since Roman theatres were initially
designed for speech%(Haddad, 2006), and the acoustic parameters which analyse
vocal quality are based upon data from the high end of the sonic spectrum.!
"However, in the live sound industry, the range from 20 Hz to 125 Hz is an
essential frequency band for sound systems in most applications, mainly because
each room has unique acoustic characteristics%(Kaiser, 2020) (Nutty, 2020) (Raynolds,
2020). For this reason, the low end of the frequency spectrum has to be measured and
studied. The next section will discuss this topic in depth.!
"Finally, there is a relevant on-topic discussion from Naif Haddad which debates
the use that is currently given to ancient theatres. In his discourse, Haddad presents
how modern acts damage, to a certain extent, the natural acoustics of the building.
Moreover, some of these performances do not suite the theatres because of the short
reverberation times that some of them possess, which may aﬀect the perception of
the audience on the overall experience%(Haddad, 2006).!
2.3 Subwoofers in live sound
2.3.1 Uses of subwoofers in sound reinforcement
"As discussed by Haddad in the previous section, Roman theatres are used for
many diﬀerent purposes, and not all acts are designed for these spaces. This remains
true for numerous venues, which nowadays tend to host any kind of shows regardless
of their compatibility. For this reason, there is a need to understand and to control the
directivity of sound systems.&
"Simultaneously, the sound reinforcement scene has suﬀered from an incredibly
fast sophistication in the techniques used to manufacture and to control the
components inside loudspeakers. This reﬁnement in technology has enabled
engineers to manage, in an easier way, the coverage of the audience, leading to a
more designed sound ﬁeld. The ability to control the directivity of subwoofers is
integral to the design of the systems%(Rumsey, 2017, p. 1051).!
"Since subwoofers were initially used in the late 1970s, there has been an
increasing ongoing demand for more SPL and so, new issues arose: feedback
generated by the omnidirectional nature of low frequencies. This problem did not only
lead to the manufacturing of cardioid cabinets, but also to more sophisticated time
alignment processing, and the introduction of computer modelling softwares%(Hill et
al., 2010, p. 2-3) (Small, 1972)%(Small, 1973) (Thiele, 1971).!
Figure 5: Introduction of bi-ampliﬁcation by Altec, where a dedicated signal was fed to the ‘woofer’ to improve low-
frequency reproduction. A-7 Cabinet (Audio-Database, 1977).
2.3.2 Room acoustical metrics Vs. Combined acoustical metrics
"Almost all research projects carried out in Roman theatres focus on room
acoustical metrics, which are parameters used to describe a space without any sound
system and therefore, they are of minor relevance compared to what live sound
engineers need to know from a venue. Similarly, there are values called speaker
acoustical metrics to purely measure the behaviour of a loudspeaker in free-ﬁeld,
which does not apply either to the current project%(McCarthy, 2016, pp. 31,32).!
"Consequently, it is needed a blend of both parameters. Combined, room and
loudspeaker acoustical metrics provide the necessary information about the
performance of a sound system in a room%(McCarthy, 2016, pp. 34). The combined
acoustical parameters used in this project are presented and discussed in the
methodology (p. 20).!
2.3.3 Gradient Loudspeakers
"Olson introduced the concept of gradient loudspeakers in 1973. The founding
principle is the knowledge on microphone directionality applied in reverse to
speakers%(Olson, 1973). This technique is the most common for controlling low-
frequency directionality%(Hill et al., 2010, p. 3).!
"According to Olson, a gradient loudspeaker is made out of at least two
unattached speakers working with opposite phase or equivalent combination of
phases between them. Gradient loudspeakers are also referred to as diﬀerential
loudspeakers%(Olson, 1973, p. 86).!
"He presents diﬀerent conﬁgurations which provide low-frequency polar pattern
"The most simple is called a zero-order gradient source. It is made of one
drive which radiates equal energy, creating an omnidirectional pattern%(Hill, Hawksford,
Figure 6: Zero-order gradient source and polar pattern (Hill, Hawksford, 2010).
"If two zero-order gradient sources are combined, phase-reversed, and
separated in space then, it is called ﬁrst-order gradient source. It can also be called
dipole because of the shape of its polar pattern. Depending on the separation
between each source, it produces diﬀerent patterns: two lobes when a quarter of the
wavelength is applied, and four lobes with a full wavelength separation%(Hill,
"Moreover, it is possible to produce cardioid-like patterns by adding delay to
the second unit%(Hill, Hawksford, 2010).!
"Furthermore, the cardioid radiation pattern of ﬁrst-order gradient sources
introduced by Olson was later on veriﬁed as the ratio between the applied delay, the
acoustic wavelength, and the distance separating the cabinets (Thompson et al.,
"This veriﬁcation conceives simple sources as a sphere pulsating in free space.
The concept is determined by a complex formula, which is used to deﬁne the pressure
that a simple source or, a simple point source, radiates. As long as the multiple
sources present the same characteristics, they can be combined (forming a point
source array), and their generated sound ﬁeld can be predicted (Thompson et al.,
Figure 7: First-order gradient source and polar pattern. 1/4 wavelength delay (left) and full
wavelength delay (right) (Hill, Hawksford, 2010).
Figure 8: First-order gradient source and polar pattern (Hill, Hawksford, 2010).
"The simple-source concept is generally used to anticipate the sound ﬁeld
generated by a subwoofer. This idea can be scaled up with the intention of predicting
the radiation pattern of a subwoofer array (Thompson et al., 2012).!
"Second-order gradient sources are the result of combining two ﬁrst-order
sources and delaying the second ﬁrst-order by the equivalent to the physical distance
in between them%(Hill, Hawksford, 2010).!
"This is the concept applied in point source arrays, were cabinets are
progressively delayed towards the sides. Higher-order gradient sources can be
reached by combining the previous conﬁgurations through an analogous process%(Hill,
"Additional investigations with gradient sources have been conducted to
improve the in-room response%(Backman, 2003)%and how the cabinet itself contributes
to the total radiated pressure%(Bastyr, Capone, 2003).!
Figure 9: Second-order gradient source and polar pattern (Hill, Hawksford, 2010).
2.3.4 Democracy of sound. Subwoofer arrays: positioning, spacing, and directivity
"Arrayability is the phenomena caused by the interactions between the radiation
pattern of a distinct speaker cabinet and the ones adjacent. It has always been a
challenge to get it right since diﬀerent combinations of cabinets will result in some
losses of tonal balance across the audience%(Mochimaru et al., 2011).&
"Moreover, there has been a recent topic within the live sound community:
sound democracy. The whole audience should hear the same content, regardless of
their seat in the venue. Unless having a complicated system, it is understandable that
having the same SPL values across the attendees is not possible due to propagation
loss. However, consistent tonality is expected in all seats%(Hill, 2018).!
"An example of the implementation of sound democracy is the recently
deployed sound system in the Royal Albert Hall. With over 400 loudspeakers, this
system has become the largest, permanently installed concert hall d&b speaker-
system in the world%(Jeﬀery, 2019).!
"Deploying a well-designed sound system in a venue can provide optimal
audience coverage and reduce leakage onto the stage and outside the building%(Hill,
2017). A democratised sound is achieved by implementing the right system design for
a venue. Rephrasing the hypothesis, point source arrays provide a more democratised
sound in Roman theatres than any other possible subwoofer conﬁguration.!
Figure 10: Royal Albert Hall’s main system (Paradise, 2019).
Point Source Array !
"A point source array is made of individual cabinets positioned in a curved line,
broadening the coverage pattern this way. It can be arched physically; however, an
electronic delay is used in most cases because of space constraints%(Excelsior Audio
"As mentioned in page 11, the radiation pattern generated by a point source
can be predicted; however, where exactly is this propagation radiating from?!
"After an investigation carried out by John Vanderkooy, the term acoustic centre
was introduced. It is the physical point in space from which the radiation of a
loudspeaker emanates. Opposite to what most people think, the radiation point in
subwoofers is not in the centre of the cone but instead, somewhere forward. For
example, for a 10 Hz sine wave, the acoustic centre is located 14.54 cm in front of the
"The acoustic centre is a crucial component when designing and working with
subwoofer arrays as it has to be taken into account in order to minimise coverage
problems%(Vanderkooy, Rousseau, 2009) (Thompson et al., 2012).!
Figure 11: Electronic delay applied to point source array for diﬀerent degrees of curvature (Excelsior Audio
Figure 12: Acoustic centre. Pressure contours and ﬂow lines at 10 Hz (Vanderkooy, 2010).
"Centre array is a conﬁguration in which the subwoofers are distributed across
the front of the stage, or below the stage in permanent installations, and there is no
delay applied to them. According to Bob McCarthy, the cabinets can be separated up
to two metres apart in this conﬁguration. It presents combing, which denotes a zone
with considerable variance in SPL, causing the frequency response to look as a wave
(McCarthy, 2016, p. 376, 564).!
Left & Right Array!
"This conﬁguration is very common to see, where loudspeakers are placed to
the sides of the stage. It can be as simple as one subwoofer per side or scaled up
massively. In terms of eﬀectiveness and practicality, four elements per side is the
optimum conﬁguration (McCarthy, 2016, pp. 320, 321).
Figure 13: Centre array with 900 electronic delay & cardioid cabinets (Excelsior Audio Design, 2011).
Figure 14: LR in end-ﬁre array conﬁguration (Excelsior Audio Design, 2011).
"Moreover, using multiple subwoofers instead of one (or one point source array,
by inference) can be beneﬁcial to tonal balance because it helps reducing destructive
interferences across the audience area (Martens, 1999) (Rämo et al., 2012) (Welti,
Devantier, 2006). Furthermore, feeding a stereo signal to subwoofers when physically
distanced seems to also help with cancellation problems (Hill, Hawksford, 2013, p. 6).!
"Lastly, studies show that placing directional subwoofers below the stage or
right in front of it, will partially or fully destroy the unit’s directivity. What is more, it will
create high pressure levels on the stage creating a resonance box below it, being it
detrimental for the musicians or performers as well as making the working
environment uncomfortable (Hill, Paul, 2016). For this reason, system engineers pay
special attention to subwoofer placement and their polar patterns.!
2.3.5 Flown Vs. Ground-staked subwoofer conﬁgurations. The optimal array.
"In order to conserve a stable frequency response when adding a subwoofer
system to the main PA, the ﬁrst should provide matching front-to-back SPL, and
summation coherence of phase with the main system across the listening
area%(Corteel et al., 2018).&
"Ground-stacked subwoofer arrays show problems to fulﬁl these requirements
since the conﬁgurations provide high front-to-back SPL variance, and the physical
distance between both systems causes compromises in the alignment%(Corteel et al.,
"In contrast, ﬂown subwoofers oﬀer modest front-to-back SPL variance,
reducing considerably the energy in the ﬁrst rows, and phase alignment is coherent
since the physical distance between them is negligible. For this reason, it is preferable
to use ﬂown subwoofer conﬁgurations and if necessary, support the ﬂown system with
ground-stacked subwoofer conﬁgurations%(Corteel et al., 2018) (Milan, Amate, 2011).!
"Note: Although ﬂown subwoofer conﬁgurations are out of the scope of this
project due to rigging structures constraints, it is mentioned as more and more
productions decide to implement it. An example of this is L-ISA (L-Acoustics L-ISA,
2.3.6 System Performance Quantiﬁcation
"Diverse compromises have to be done during the optimisation of a sound
system. These can vary from physical elements such as the number of cabinets
available and positioning, to trade-oﬀs between FOH SPL and coverage width, and, of
course, time constrains which make it diﬃcult to ﬁne tune the system (Hill, 2018).!
"To save time, system optimisation should be done using the manufacturer’s
ecosystem (Hill, 2018). For example, L-Acoustics is innovating and manufacturing new
products each year to make the process of designing and optimising a system the
easiest and fastest way possible whilst maintaining the audio quality (L-Acoustics
"Three main targets are connected to subwoofer systems performance and
provide quantitative data of the system’s performance:!
"It measures the spatial variation (SV) in magnitude response across the
audience area. It is expressed in decibels.!
"Although it is a complex expression, it does not take into consideration
propagation loss. For this reason, magnitude responses have to be normalised;
process that can be done via software such as MATLAB and Excel (Hill, 2018) (Matlab,
2020) (Microsoft, 2020).!
"Acceptable system’s headroom is measured as the diﬀerence between
targeted and achieved FOH SPL.!
"If the diﬀerence is less than zero, then the target has been achieved. If it is zero
or greater, there is insuﬃcient headroom to operate the system (Hill, 2018).!
Formula 1: Tonal Consistency (Hill, 2018).
Formula 2: Acceptable System Headroom (Hill, 2018).
Audience to FOH level consistency!
"Usually, if FOH position is right in the centre axis in front of the stage and the
subwoofer system is not optimised, then the engineer will suﬀer from more SPL on
low frequencies due to the power alley generated by the speakers (Hill, 2018). It is
important that the engineer knows what the audience is listening to. The diﬀerence
should be as little as possible.!
Array performance rating (APR)!
"The individual equations previously mentioned can be combined in order to
provide a ﬁnal value to the performance of the system. It is given by:!
"In this equation, WSV, WHR, and WAUD indicate the individual weighting (W) of
SV, ΔHR, and ΔAUD, respectively. The user can prioritise any value by assigning them
a weighting from zero to one. The total sum has to be one. Eventually, it will indicate
the performance of the system in a linear scale, following the next chart (Hill, 2018).!
Formula 3: Level Consistency Audience/FOH (Hill, 2018).
Formula 4: Array performance rating equation (Hill, 2018).
Chart 1: Array Performance Rating chart (Hill, 2018).
New solutions to system optimisation!
"Following the increasing demand on software-based live sound measurements,
researchers have studied new ways to optimise a system in the best way possible in
the shortest time, or in the smartest way. !
"For instance, a diﬀerent approach to the usual workﬂow is to tune the system
during rehearsals and important parameters such as intelligibility or clarity can be
reviewed live or even optimised (Ahnert et al., 2006) (Ahnert et al., 2007).!
"Another method which is becoming popular due to the lack of time to tune the
system, is to optimise it live. It uses complex algorithms working in real time to adjust
the optimisation to what is acoustically happening at that particular moment with
music playing. Instead of playing pink noise, the software measures the diﬀerence
between the delayed signal outputted by the desk and what is reproduced by the
speakers (Shabalina et al., 2013).$
3.1 Hypothesis recall
"In order to answer the research question: which subwoofer array delivers the
best results in the Roman theatre of Baelo Claudia?, these quantitative methods were
used: In situ measurements to provide data of combined acoustical metrics
(Frequency response, SPL, phase, and coherence), and the analysis and comparison
of the collected information for the diﬀerent conﬁgurations. !
"Given the semicircle-shape of Roman theatres, the project starts from the
Point source subwoofer arrays are better suited to the combined
acoustical metrics of Roman theatres than any other possible subwoofer
"This reasoning is based upon the radiation pattern generated by point sources,
discussed in section 2.3.3. !
"The project will follow as close as possible the guidelines given by the ISO
3382 standard. As shown in the Literature Review, the ISO 3382 does not fully suit the
necessities of the study as the output of the same cannot be obtained with the
suggested parameters presented in the standard. For this reason, several scientiﬁc
papers will support the decisions made during the process.!
3.2 Equipment used
"To collect the necessary data, the measurement software Smaart V8 was used
in transfer function mode (TF), providing phase, frequency response, and SPL for each
measurement location (Please see Appendix B for a guide on how to interpret the data
presented in this paper). Phase and Magnitude resolution were set to 1/24 Octave as
recommended by Bob McCarthy to better identify key information (McCarthy, 2016,
"The microphone Beyerdynamic MM1 was used as it complies with the
requirements set by the ISO 3382 (Omnidirectional polar pattern and ±1.5dB deviation
in frequency response) (ISO 3382, 2009, p.3) (McCarthy, 2016, p.383).!
Figure 15: Frequency response and polar pattern Beyerdynamic MM1 (Beyerdynamic MM1, 2019).
"The condenser microphone was placed vertically, as indicated by the
manufacturer. The microphone was calibrated at 94 dB using the Peaktech 8010
sound level calibrator before starting the measurements (Peaktech, 2020).!
"The analog-to-digital converter Focusrite Scarlett 2i2 (Focusrite, 2020)
connected the measurement microphone to the computer and sent pink noise to the
sound system. For the latter, four L-Acoustics SB28 subwoofers driven by the LA8
ampliﬁer and controlled by LA Network Manager were deployed. The signal was sent
directly from the sound card to the ampliﬁer to minimise any potential deviation
created by an external device.!
"To measure the requested weather conditions by the ISO 3382, the
anemometer Skywatch Xplorer 2 and the thermohygrometer Trotec BC06 were used;
all complying with the acceptable measurement deviations (Skyview, 2020) (Trotec,
2020) (ISO 3382, 2009, p.3).!
Please, refer to Appendix C for more detailed speciﬁcations of the equipment used.!
3.3 Project phases
3.3.1 Phase 1. Measurements
"32 measurement positions were distributed across the audience area (Cavea
and Orchestra), and three more in a straight line on the stage. Positions remained the
same for the three conﬁgurations.!
"Also, reception points followed an alike zebra pattern. This distribution is
recommended to accurately represent the direct sound characterisation and any
potential strong room reﬂections (L-Acoustics White Paper 2, 2020).!
Figure 16: Measurement positions grouped in rows (left) and sections (right).
"For the reception points, the microphone’s capsule was placed 1.2 metres
above the ﬂoor, representing the height of the audience’s ear when seated, which is
the usual set up in the theatre of Baelo Claudia (ISO 3382, 2009).!
"Three diﬀerent subwoofer arrays were deployed:!
Point Source subwoofer array!
"Three milliseconds of delay was applied to both, left and right speakers, taking
as reference the centre cabinet in order to create an electronic arch and direct the
coverage to the audience area in a 160 degrees, creating cancellations to the sides.!
Centre subwoofer array!
"Speakers were spaced out equally to 1.8 metres across the front of the stage.
No delay was applied. With this conﬁguration, it is intended to show that it creates
comb ﬁltering. This happens because at the distance of 1.8 metres (which is more
than 1/2 the wavelength of the crossover frequency: 100 Hz), the subwoofers no
longer constitute a point source conﬁguration, but they start to behave as individual
Figure 17: Point source array (left speaker not in use).
Figure 18: Centre array conﬁguration.
Left-Right subwoofer Array!
"As seen in the section 2.3.4, it is a very common conﬁguration. One of the
reasons is because it does not obstruct the visibility, which in the case of ancient
theatres, is proposed to keep the scaena frons architecture visible.!
"The Roman City of Baelo Claudia is located in the Strait of Gibraltar. It is the
connection point between the Atlantic Ocean and the Mediterranean Sea, and due to
the fast temperature changes, strong winds are always present and changing
direction. For this reason, if strong winds occurred during the measurements, a
windshield would be used as it does not aﬀect the microphone’s frequency response
and polar pattern at low frequencies (Brixten, 2005) (Schneider, 2004).
"Ambient atmospheric conditions such as wind can have a negative impact on
acoustic measurements and on the overall performance of the sound system (Corteel
et al., 2017), and there are several strategies to reduce these issues as acclimatisation
of the equipment to the ambient, and regular calibration (Chapman, 2014).!
Figure 19: Left - Right array.
3.3.2 Phase two. Analysis
"The raw data gathered from the in situ measurements (Available in Appendix d)
will be analysed in two steps in order to obtain as much information as possible from
the subwoofer conﬁgurations. !
"Firstly, the Array Performance Rating (APR) proposed by Adam J. Hill (p. 17)
will be used as a starting point. It will provide an overall quantiﬁcation of the system’s
performance by looking at three key indicators:!
"Tonal consistency will serve to determine how much is the magnitude response
variance over the diﬀerent measurement points. All data collected has to be
normalised in order for the formula to take into account the propagation loss caused
by the audience’s widespread area (This process is explained in Appendix G). The
second measure is the acceptable system headroom, which calculates the diﬀerence
between targeted and achieved front of house (FOH) SPL. Finally, the consistency
between the audience and FOH SPL is assessed. The APR result will follow a grading
scale which ranges from zero to one, being one the best score.!
"Secondly, after the APR outcome, a more careful and detailed examination will
be done to each of the arrays, providing a second point of view to the results. For this
purpose, measurements will be treated individually and grouped-wise to extract
conclusions of possible trends or isolated facts within each speaker conﬁguration and
then, compared to the other arrays. The groups will be shown as rows and as sections
(ﬁgure 16). Reception points were distributed so that all locations within a row were
equidistant to the centre.!
"To conclude this study, results will be discussed to determine which
conﬁguration suits best the acoustical metrics of the Roman theatre of Baelo Claudia.!
3.4 Limitations and scope of the project
"This project is intended to obtain the combined acoustical metrics of the
Roman theatre of Baelo Claudia. Therefore, the conclusions here presented are
inherent to the studied theatre. Further connections or assumptions related to other
Roman theatres should be made carefully as the acoustic properties at low
frequencies may change the same way as with the high frequencies showcased in
previous studies (Section 2.1.2).!
"One day was suﬃcient to collect all necessary data. However, a second one
with similar or even better atmospheric conditions would have been beneﬁcial to
double check the information obtained from the ﬁrst day. This was not possible due to
the previously mentioned strong winds in the area, restricted openings of cultural
places due to COVID-19 lockdown (hence timeframe to complete the project), and
"The ﬂown subwoofer array was not contemplated to be deployed in this
theatre because of the lack of rigging points.!
"Since the SB28’s frequency range extends up to 100 Hz, frequencies between
100 Hz and 125 Hz (which is where the other research projects start from) were not
discussed in the project. A potential solution to this issue is given in the conclusion as
part of the future research.$
4. Results of in situ measurements
4.1.1 Results - Array Performance Rating
"Results for APR do not show considerable diﬀerences between the three
conﬁgurations. All achieve a Grade C, which means that they are not the best systems
as starting points, and can certainly be improved. !
"The LR array achieved the best results out of the three (0.59) and the centre
array, the worst (0.52) (See Chart 2). In fact, the point source and left-right
conﬁgurations have similar APR, varying in only 0.018 points. (Please, notice that
results showcased in Chart 2 have been approximated in order to follow the rating
chart format. Raw data and Excel Workbook can be found in Appendices D and E).!
"The LR array has an APR of 0.589. Its Spatial Variance (SV) is the lowest out of
the three, meaning that this conﬁguration provides a more even coverage thought the
audience than the others; leading to no signiﬁcant deviations over the magnitude
response. The acceptable system headroom (ΔHR) is positive as the SPL targeted at
FOH is superior than the achieved SPL. To represent that there is no suﬃcient
headroom to run the system, the result is set to inﬁnite, which in the APR equation
term derives in zero for the change in system headroom. Lastly, the consistency level
between the audience and FOH (ΔAUD) is the highest, which will result in a worse
representation to the FOH engineer of what the audience is hearing.!
"The point source array has an APR of 0.571. The SV is the highest, resulting in
a bigger diﬀerence of magnitude response across the audience. The ΔHR is also
positive, meaning that the system runs out of headroom to operate it. The ΔAUD
metric has a slightly better result compared to the LR conﬁguration, giving the sound
engineer a better picture of what the audience is listening to.!
Chart 1: Array Performance Rating chart (Hill, 2018).
Left - Right
Chart 2: APR results for FOH Point 5.
"The centre array has an APR of 0.517, which gives it the closest grade to D of
the three layouts. The SV metric falls between the other two arrays, but there is still a
diﬀerence of magnitude response across the audience area. The system runs out of
headroom as well, resulting in a value of inﬁnite for the ΔHR metric. Interestingly, this
conﬁguration provides the best value of diﬀerence between the audience and FOH.!
"APR results, alongside data interpretations of each subwoofer conﬁguration
and potential solutions to improve the system’s performance will be presented in the
4.1.2. Results - Point source array
"This was the ﬁrst measured conﬁguration. Started at 12:30, there was an
average temperature of 32.50C, average wind speed of 5.2 km/h, and relative humidity
of 54% (Please see Appendix F for full meteorological conditions record).!
Frequency response and SPL!
"The magnitude response graphs for this conﬁguration follow the same
triangular shape and present strong consistency between levels. The traces can be
divided into four segments. In the ﬁrst one, between 20 Hz and 35 Hz, the level
ascends until it reaches a peak located in the 35-40 Hz region. Then, it slowly starts to
descend towards the 100 Hz, meeting a small peak at 75 Hz.!
Graph 6: Point source array. Magnitude response of rows.
"In terms of SPL, almost the entire spectrum is situated over the 94 dB line (0
dB is calibrated to 94 dB). Only the frequencies below 25 Hz show negative values.
The 35-40 Hz area reaches an average of 109 dB. On the stage, levels drop by
approximately 15 dB, this time presenting its peak at 33 Hz and the overall trace
below 94 dB.!
"When the measurement points were grouped in sections, similar trends
appeared: ascendent ﬁrst, peak in the 35-40 Hz region, and descendent until 100 Hz.
The main diﬀerence between this view and the previous one is that in this case, levels
are more spread apart. The traces start to separate very early. From 25 Hz, the centre
of the cavea and the centre of the orchestra follow a very similar path, and the left and
right sections show discrepancies such as the left side having a higher SPL than the
Phase and coherence!
"In the left hand-side graph, rows are divided into two parts. The ﬁrst one
consists of row one and two, being them very late or phase-shifted compared to the
other rows, which form the second part of the phase traces. !
Graph 7: Point source array. Magnitude response of sections.
Graph 8: Point source array phase response. Rows (left) Sections (right).
"The right hand-side graph, visualises the phase in sections. There are three
diﬀerentiated groups. Firstly, cavea left and orchestra left show similar behaviours,
having the closest phase shift to zero of all sections. Secondly, cavea centre,
orchestra centre, present almost identical trends, and cavea right is also within the
same degree range. Finally, orchestra right is distanced approximately 300 degrees
from the other traces. !
"Coherence for the measurements have been averaged to display the three
diﬀerent parts of the theatre measured: cavea, orchestra, and stage.!
"The average coherence value for the cavea is 0.961, 0.960 for the orchestra,
and 0.916 for the stage. These graphs show more favourable levels where the SPL
was higher and therefore, a higher ratio between the measured signal and the
background noise, than for example on the stage, where SPL was considerable lower.!
Graph 9: Point source array: Cavea, orchestra, and stage. Coherence over frequency.
20" 40" 60" " 80 " 100
20" 40" 60" " 80 " 100
20" 40" 60" " 80 " 100
4.1.3. Results - Centre array
"This was the second-measured conﬁguration. Started at 13:30, there was an
average temperature of 35.60C, average wind speed of 5.1 km/h, and relative humidity
of 49.5% (Please see Appendix F for full meteorological conditions record).!
Frequency response and SPL!
"The magnitude response chart for the in-line conﬁguration shows three main
characteristics. The ﬁrst one is that it also presents the triangular shape. The levels of
the individual frequencies rise from 20 Hz until the 35-40 Hz region. There, the graph
achieves its peak and slowly descends towards the 100 Hz. However, there are two
considerable falls in the graph, which make up the second characteristic. One of them
at 45 Hz and the other at 60 Hz. This is a trend present in all traces. However, the
amount of incidence changes. For example, the ﬁfth row presents high level
diﬀerences compared to the ﬁrst or second, which have more even values.!
"Lastly, this subwoofer conﬁguration shows prominent changes in SPL levels
across the diﬀerent rows. The third row has the lowest SPL, which is similar to the
stage trace. The ﬁfth and sixth rows present one of the highest levels, and very close
to them are the ﬁrst and fourth. The peak of the graph reaches 110 dB in the ﬁfth row.
The dips in the frequency response reach a reduction of 6 dB.!
Graph 10: Centre array. Magnitude response of rows.
"When the raw data is displayed in sections, similar trends occur although the
frequency drops present a much higher reduction (of up to 9 dB in case of the third
row). There are also level diﬀerences such as the ones of the second and ﬁfth rows,
which switch positions in the chart. The fourth and sixth rows follow a very similar
path. The centre of the cavea shows a higher level, which may be caused by the
power alley generated by the system.!
Phase and coherence!
"Phase traces for the centre array are spread out in a wide area, and this made
the visualisation window to be vertical and the scale to be extended. In the left hand-
side visualisation, there are three diﬀerentiated groups. Most of the traces are located
between -120 and -480 degrees, these include the ﬁrst, fourth, and ﬁfth rows. The
sixth row has a positive value, and the second and third negative ones, presenting the
latest arrival and showing similar trends.!
Graph 11: Centre array. Magnitude response of sections.
Graph 12: Centre array phase response. Rows (left), Sections (right).
"In the sections visualisation there are three groups as well, maintaining the
same degree ranges as before. Both sides of the cavea present similar phases up to
45 Hz and the centre shows a phase shift of approximately 330 degrees over the
spectrum. A similar case occurs in the orchestra, where the centre and the right side
display similar trends in phase, and the left side shows a phase shift of 330 degrees as
"The stage showcases a considerably fast change in phase, varying in over 630
"Coherence wise, the cavea has achieved a value of 0.956, 0.977 for the
orchestra, and 0.959 for the stage. The orchestra trace is more unstable, presenting a
‘fade’ shape in both extremes, which achieve considerable low levels in certain
Graph 13: Centre array: cavea, orchestra, and stage. Coherence over frequency.
20" 40" 60" " 80 " 100
20" 40" 60" " 80 " 100
20" 40" 60" " 80 " 100
4.1.4. Results - Left-Right array
"This was the third-measured conﬁguration. Started at 14:20, there was an
average temperature of 36.50C, average wind speed of 6 km/h, and relative humidity
of 45.6% (Please see Appendix F for full meteorological conditions record).!
Frequency response and SPL!
"The magnitude response for the LR conﬁguration displays a trapezium shape
rather than a triangle, and it can still be divided into three sections. The ﬁrst one is an
increase in levels from 20 Hz to 30 Hz. Secondly, the graph stabilises until the 80 Hz
region. Within this segment there is small boost in levels around the 35-40 Hz area for
some rows. A general behaviour amongst the traces are the cancellations at 45 Hz
and 60 Hz, being more pronounced for example in the ﬁfth row and less in the third.!
"SPL levels show a considerable diﬀerence between traces. The ﬁrst row
achieves a peak at 40 Hz of 112 dB, whilst the third is the lowest of all audience
traces, and has a peak of 102 dB at 38 Hz. The levels of this last row can be
compared with the ones on stage. For cancellations, values fall up to 9 dB in cases
like the ﬁfth row.!
Graph 14: LR array. Magnitude Response of rows.
"If looked as sections, there is also a trapezium shape but traces diﬀer. The
centre of the orchestra presents an uneven response. The 35-40 Hz region has only
boosts in the centre and right of the cavea, and in the centre of the orchestra. Levels
are considerable closer to the ones on stage.!
Phase and coherence!
"There are visible trends over both of the visualisations. Traces are grouped in
three. On the left hand-side, the second and ﬁfth rows have positive values, being
near zero degrees of phase shift between 50 Hz and 100 Hz. Within the negative
values, the third, fourth, and sixth also share similar regions, although the sixth
changes abruptly at 45 Hz and reaches up to -1K degrees. Lastly, the ﬁrst row is
isolated from the rest.!
Graph 15: LR array. Magnitude response of sections.
Graph 16: LR array phase. Rows (left), Sections (right).
"On the right hand-side, the grouping in of three repeats. In this case, values are
much closer to zero. The left side of the orchestra has positive values and is isolated
from the centre and the right side, which move between 150 and -90 degrees.!
"Coherence values for this conﬁgurations are 0.952 for the cavea, 0.968 for the
orchestra, and 0.929 for the stage. The cavea trace is the most unstable of the
audience area, and the stage shows severe depressions on the high end of the
Graph 17: LR array: Cavea, orchestra, and stage. Coherence over frequency.
20" 40" 60" 80 " 100
20" 40" 60" 80 " 100
20" 40" 60" 80 " 100
"In the Literature Review section (page 7), the need for combined acoustical
metrics has been presented. Then, in the methodology (page 20), this project’s
approach in order to obtain the metrics was introduced so that the hypothesis could
be conﬁrmed or denied with the provided results.!
"The present section will discus the data gathered from the measurements and
will display which subwoofer conﬁguration best meets the metrics of frequency
response, SPL, phase, and coherence in the Roman theatre of Baelo Claudia.!
Improvement of the Array Performance Rate!
"APR values display relevant insights on the performance of the systems. All
three conﬁgurations achieve a grade C, which is a favourable outcome if it is taken as
a starting point from which to initiate optimising the system. Although system
optimisation is out of the scope of this project, it can signiﬁcantly improve the
"Interestingly, if it is taken a closer look at the equation proposed by Hill, these
APR results can be modiﬁed and improved as well: !
"All terms in the equation were given the same weight (W = 1/3). This means
that each of them will have a value between 0 and 0.3 periodic. Let’s have a closer
look at them:!
"This metric analyses the variations in all frequencies across the audience area.
So, the closer the value is to zero, the less diﬀerences there are amongst the
measured points, hence achieving a more democratised sound coverage.!
"As this term takes into consideration the SPL levels gathered, there is no room
for improvement in the outcome unless changing the system’s design itself. However,
the value of the last two terms can be modiﬁed.!
Formula 4: Array Performance Rating equation (Hill, 2018).
ΔHR and ΔAUD!
"These two terms in the equation have a common element which is the
achieved SPL at FOH. This value will depend on the chosen FOH position. As a
clariﬁcation, point ﬁve was used in order to represent (up to a certain extent) the real
FOH location, which is oﬀ the centre axis, between points ﬁve and six.!
"In order to achieve a favourable result of ΔHR, the diﬀerence between targeted
SPL and achieved SPL should be negative. This means that the target was met and
that the system has enough headroom to operate. Initially, the target SPL was set to
114 dB. However, considering the type of performances that are put on in the theatre,
the target SPL could be set to 110 dB.!
"The maximum SPL achieved by the conﬁgurations were 112 dB at point four in
the point source design; 110.2 dB at point four in the centre design; and 109 dB at
point 17 in the LR design (This conﬁguration achieves 108 dB at point four).
Consequently, if point four was chosen as common FOH position, the ﬁrst two
conﬁgurations would beneﬁt of +0.33 in the equation.!
"Lastly, ΔAUD also depends on the achieved SPL value at FOH therefore the
diﬀerence between this level and the average audience level will be aﬀected.
Calculating once more the APR equation with the new values results in the following
"With only a change of the FOH position, the point source array has achieved
grade A; grade B for centre array; and grade C for LR array. The ΔAUD values have
dropped because there is more diﬀerence now between FOH and the audience than
before (with point ﬁve as FOH). However, the Array Performance Rating has been
considerably improved for two of the three system conﬁgurations.!
Chart 1: Array performance rating chart (Hill, 2018).
Left - Right
Chart 3: APR Results. FOH Point 4.
Suitability of the combined acoustical metrics gathered!
As showcased in the APR results’ chart, there are considerable diﬀerences
between the three conﬁgurations. These facts are also visible in Smaart:!
Frequency response and SPL!
"The point source conﬁguration appears to have the less issues in drop levels
out of the three. Due to its radiation pattern, it presents more subtle frequency
alterations from the centre to the sides. In the graph below, there is a simulation of the
sound systems in Soundvision showcasing the coverage pattern over frequency. It
should be interpreted as a visual reference and not as factual information since the
software only takes into account average temperature, relative humidity, and air
"Recalling the triangular shape of the traces presented in the results, the
analysis will be divided in three segments: increase in levels from 20 Hz to 35-40 Hz,
maximum levels at 35-40 Hz, and decrease towards the 100 Hz.!
"In the low end of the spectrum, the point source array creates slightly more
SPL because of the constructive interaction between the cabinets. However, all
conﬁgurations produce a similar output. This is the reason why the three frequency
responses start with low levels at 20 Hz and then, they increase towards the 35-40 Hz
region where the graphs reach their peak.
Figure 20: Radiation pattern simulation over frequency for all subwoofer arrays.
The results of the point source conﬁguration show that this system has the
highest frequency boost out of the three designs. As displayed in the snapshots above
(ﬁgure 20), the system itself could be the cause of the level build up in this region. The
centre and LR layouts also present comparable values for these frequencies. However,
their radiation patterns spread over a larger area while increasing the frequency. This
greater propagation would be beneﬁcial if there were no cancellations, which leads
onto the last characteristic of the systems.!
"Due to the destructive interferences created by the physical distance between
cabinets in the centre and LR conﬁgurations, there are the so called ‘valleys’ with low
SPL levels across the audience. Contrary to the valleys, there are the ‘power alleys’ or
‘lobes’ formed by the constructive interferences. These interactions cause the
frequency response to suﬀer from abrupt level variances, as the ones present in points
six and nine of the centre and LR conﬁguration, respectively. The point source array
does not present severe cancellations.!
Graph 18: Magnitude response at point 6. Centre array.
Cancellations at 45 and 60 Hz.
Graph 19: Magnitude response at point 9. LR array.
Cancellation at 60 Hz.
Phase and coherence!
""In terms of phase, the point source array is considerably smoother and
consistent if compared to the centre and LR systems. In the last two, there are more
deviations in the slope of the traces, specially in row six.!
"Lastly, there are relevant connections regarding coherence values across the
diﬀerent arrays. Measurement positions located next to walls or other architectonic
structures present lower coherence values. The graphs below display the coherence
responses. Although coherence is given in values from zero to one, in the next graphs,
the vertical axis has been enlarged in order to properly capture the variations.!
Graph 21: Coherence responses - All arrays.
Graph 20: Phase responses - All arrays.
"According to Smaart, the decrease in coherence values indicate a problem
with the measurement system, contamination from environmental noise, or
reverberation (Smaart V8, 2018, p.121). In the case of this project, the system was
operating normally and meteorological conditions were favourable. Therefore, it might
indicate that the constructional shape of the theatre creates strong reﬂections at
locations next to the surfaces. These reﬂections could be the cause of the
cancellations at 45 Hz and 60 Hz. However, the present project is not intended to
research this topic as its complexity would require a dedicated study. The next graphs
show examples of the relation between frequency response and coherence in
locations next to surfaces."
Graph 22: Examples of coherence issues.
"The complex process of designing and optimising a subwoofer system for a
speciﬁc venue is sometimes simpliﬁed due to time constraints and practicality. This is
the reason why the present project can be relevant to the live sound community. This
paper has exposed relevant acoustic characteristics of the L-Acoustics SB28’s
performance in the theatre of Baelo Claudia, in particular, the metrics of frequency
response, SPL, phase, and coherence have been presented. !
"As conﬁrmed by the acoustical metrics gathered in this investigation, the
hypothesis Point source subwoofer arrays are better suited to the combined
acoustical metrics of Roman theatres than any other possible subwoofer array
conﬁguration has been validated.!
"Firstly, the importance of the acoustic characteristics of ancient theatres to the
scientiﬁc and archaeological community were evidenced by presenting previous
studies in the ﬁeld. Following this, the project’s relevance to the current necessities of
sound reinforcement productions was supported by previous research.!
"Then, the methods implemented in the project used to generate valuable data
from the three subwoofer conﬁgurations were described. The results of the acoustic
measurements showed four features. First, all designs presented a boost on the
frequency response around 35-40 Hz, having the point source conﬁguration the
highest values. Second, there are considerable cancellations across the audience area
at 45 Hz and 60 Hz in the centre and LR arrays. Third, SPL levels were more
consistent in the point source array, showing a smoother variance from the centre to
the sides. Lastly, the ratio audience-to-stage levels displayed similar values in the
centre and LR conﬁgurations, achieving a higher separation in the point source array.!
"There are still numerous topics that can be subject of future research. One of
them being the implementation of a full PA system and measure of the medium- and
high-end of the spectrum. This will encompass positioning and conﬁguration of the
main system as well as phase-alignment with the subwoofer system. Another case to
study could be how the acoustic metrics vary when the theatre is occupied with
audience. Because of the special geographical location of the Roman city, a research
on how wind gusts interact with the architectural shape of the theatre and how it
eventually aﬀects the speech intelligibility index and performance of the PA system
could be beneﬁcial for future performances.!
"In addition, improvements to the methods used in this project can be
implemented in future investigations. For example, the use of a dedicated SPL meter,
which will give ﬂexibility to Smaart readings when adjusting the measurement signal’s
gain to stay within the recommended SPL range established by Rational Acoustics. In
addition, other manufacturer’s subwoofers could be compared to the ones of L-
Acoustics to better understand if the acoustic characteristics presented in this project
were created by the system or by any resonant frequency that the theatre might have.!
"Finally, the present paper is the beginning of future investigations that the
author would like to carry out in a bigger scale. Broadening the scope of the research
to encompass all Roman theatres in the Autonomous Community of Andalusia, will
provide new information about these ancient performance spaces and potentially
extrapolate the results in order to establish connections and trends amongst the
diﬀerent theatres. This will not only help touring productions, but also the scientiﬁc
community and the archaeological complexes to provide a higher quality experience
"Mr. Ángel Muñoz, Chief of the Department of Protection of the Historical
Patrimony in Cádiz, and Mrs. Mercedes Colombo, Territorial Delegate in Cádiz for
granting the permit so that the project could be carried out, and Mr. Iván García, Chief
of the Conservation and Investigation Area in the Archaeological Complex of Baelo
Claudia for the excellent reception and help during the stay in the Complex.!
"Also, special thanks to Luís López from Concert Sound, who provided the
sound system for the project, and assisted during the process.!
"Al Sr. Ángel Muñoz, Jefe del Departamento de Protección del Patrimonio
Histórico en Cádiz y a la Sra. Mercedes Colombo, Delegada Territorial en Cádiz, por
conceder el permiso para la realización del proyecto. También al Sr. Iván García,
encargado del Área de Conservación e Investigación del Conjunto Arqueológico de
Baelo Claudia por la excelente bienvenida y ayuda durante la estancia en el Complejo. !
"Por último, pero no por ello menos importante, gracias a Luís López, de
Concert Sound, por proveer el equipo de sonido y su gran ayuda durante el proceso."
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Appendix A: Previous Spanish national research projects.!
"The%theatre of#Cádiz%was built in the 1st century B.C. and has a calculated
audience capacity of more than 10,000 people, which makes it the oldest and second-
largest Roman theatre in the peninsula. Because of the preservation conditions, the
full structure is not available, and for this reason, virtual simulations with diﬀerent
occupancy states were created and measured. The simulations considered the source
located in the%proscaenium#(S0), and 27 reception points scattered across the
audience area%(Álvarez-Corbacho et al., 2018).!
"The simulated parameters were T30, Early Decay Time (EDT), G, and C80. These
shown highly reverberant times because of the theatre's large dimensions and the
oyster ﬁnishing stone%(Álvarez-Corbacho et al., 2018).!
"The%Roman theatre of#Medellín, built in the late-Republican or pre-Augustan
age had a capacity for 3,000 spectators. This time, the project used two methods.
Firstly, in situ measurements such as SPL, background noise and reverberation time
were taken for then, compare, calibrate, and validate the computer model
parameters%(Barragán-Pullido et al., 2014, p.1).!
Figure X: Superposition of the layout of the cavea and the overhead view
of its current state (Álvarez-Corbacho et al., 2018).
Figure X: Floor plan of the source (blue) and receiver
positions (red) (Álvarez-Corbacho et al., 2018).
Figure X: In situ measurements in the Roman theatre of Medellín (Barragán-Pullido et al.,
"The%theatre of Segobriga%has one of the best-preserved%cavea%of Spain
although there are some missing structures such as the%scaenae frons. It was built in
the years 79 A.D. and had a capacity of 2,500 people. This work presents the analysis
and results of in situ monoaural and binaural recorded acoustic parameters via
impulse responses. Diﬀerent combinations of three source positions and nineteen
reception points are discussed%(Álvarez-Corbacho et al., 2019).!
"Because of the previously mentioned missing-stage front, there are short
reverberation times across the audience. Nevertheless, the author states that the
theatre presents optimal conditions for performing acts%(Álvarez-Corbacho et al.,
"The%Roman theatre of#Italica, Seville, dates from between the ﬁrst century
B.C. and the beginnings of the ﬁrst century A.D. and has an audience capacity for
3,000 people. The workﬂow employed was ﬁrst to measure the reverberation times
and be able to calibrate the virtual model then, to simulate the real acoustic ﬁeld
Figure X: Roman theatre of Segobriga, Cuenca, Spain (Álvarez-
Corbacho et al., 2019).
Figure X: Floor plan of source (blue) and reception points (red) in the
theatre of Segobriga (Álvarez-Corbacho et al., 2019).
Figure X: Virtual model of the Roman theatre of Italica
(Álvarez-Corbacho et al., 2014).
Figure X: Roman theatre of Italica
(Álvarez-Corbacho et al., 2014).
"Results show coherence between the software simulation and in situ
measurements, and the author states potential research areas for future projects.!
"Lastly, the%theatre of Regina Turdulorum,%built during the second half of the
1st century A.D., presents an exceptional preservation state and can be considered of
almost perfect construction, in line with the canon rules. The same approach, as in the
theatre of%Medellín, was implemented in this project. In order to adapt the virtual
model to the real world, the data collected from in-situ measurements were used to
eventually, adequately capture the parameters: T30, EDT, C50, D50, T, and
IACCE%(Álvarez-Corbacho et al., 2015).!
Figure X: Roman theatre of Regina Turduloum
(Álvarez-Corbacho et al., 2015).
Figure X: Virtual model of the Roman theatre of
Regina Turduloum (Álvarez-Corbacho et al., 2015).
Appendix B: Guide: how to interpret Smaart graphs.!
"Chapter 6 of the Smaart V8 Users guide provides all the necessary information
regarding concepts, terminologies and workﬂow of Transfer Function Measurements in
Smaart, as well as details about the Magnitude Response, Phase, and Coherence.!
"Full guide: https://www.rationalacoustics.com/download/Smaart-v8-User-
Guide.pdf (Accessed 25 September 2020).!
"Please, note that the graphs presented in the results and the discussion
displaying the averages in coherence do not belong to Smaart itself. They are graphs
created in Excel from the raw data provided by Smaart. More information about the
averages of data and the Excel sheet can be found in Appendix E!
(Rational Acoustics, 2018)
Appendix C: Technical speciﬁcations of the equipment used.!
Measurement microphone BEYERDYNAMIC MM1
(Rational Acoustics, 2018)
Microphone calibrator PEAKTECH 8010
A/D Converter FOCUSRITE SCARLETT 2i2
Subwoofer L-ACOUSTICS SB28
(L-Acoustics Products, 2020)
(L-Acoustics Products, 2020)
Software LA NETWORK MANAGER
(L-Acoustics Products, 2020)
Thermohygrometer TROTEC BC06
Anemometer SKYWATCH XPLORER 2
Appendix D: Raw measurements data.!
"The data shown in this appendix are the individual traces of Smaart. These are
105 measurements which would take a lot of space in this Appendix. For this reason,
if you would like to see the data, please contact one of the emails in the title page and
the author of the project will be more than happy to send you a copy of the Smaart
Appendix E: APR Excel sheet.!
"Within the ‘Appendices’ folder included with the Major Project, there are the
diﬀerent Excel Workbooks. These are:!
-Raw data for Point Source Array!
-Raw data for Centre Array!
-Raw data for LR Array!
-APR for Point Source Array!
-APR for Centre Array!
-APR for LR Array!
-Coherence for Point Source Array!
-Coherence for Centre Array!
-Coherence for LR Array!
"Please, contact one of the emails in the title page to have a copy of the Excel’s
Appendix F: Meteorological conditions record.!
(Excel Workbook can be found in the folder ‘Appendices’)!