Acoustic ambience of two roman theatres in the Cartaginensis province of Hispania

Depósito de investigación de la Universidad de Sevilla https://idus.us.es/ Esta es la versión aceptada del artículo publicado en: This is an accepted manuscript of a paper published in: Building and Environment (2021): 15/01/2025 DOI: https://doi.org/10.1016/j.buildenv.2021.107653 Copyright: © 2021 Elsevier Ltd. All rights reserved. El acceso a la versión publicada del artículo puede requerir la suscripción de la revista. Access to the published version may require subscription. “This is an Accepted Manuscript of an article published by Elsevier in [Building and Environment] on [2021], available at https://doi.org/10.1016/j.buildenv.2021.107653” ” 1 Acoustic ambience of two Roman theatres in the Cartaginensis province of Hispania *S. Girón, M. Galindo, J. A. Romero-Odero, J. Alayón, F. J. Nieves. Instituto Universitario de Arquitectura y Ciencias de la Construcción (IUACC) y Departamento de Física Aplicada II, Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, Avenida Reina Mercedes 2, 41012-Seville, Spain. [email protected], [email protected], [email protected], [email protected], nie[email protected]. Corresponding author: S. Girón • E-mail address: [email protected] • Postal address: Instituto Universitario de Arquitectura y Ciencias de la Construcción (IUACC), Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, Av. Reina Mercedes 2, 41012-Seville, Spain. Tel. +34 954 557129 (*) Parts of this work have been presented in Acústica2020 Faro, Portugal. 2 Abstract The period of Romanisation of Hispania runs from 218 BC (Romans landing in Ampurias) to the beginning of the 5th century (entry of the Visigoths into the Iberian Peninsula, replacing the authority of Rome). Throughout this extensive period spanning seven centuries, the territory would be marked with the unmistakable imprint of Roman culture and customs. The imperial era of Roman civilisation witnessed not only the greatest upsurge in the construction of the theatre, but also the export of its model from Rome to the provinces. This work studies the acoustic environment of two Roman theatres of Hispania (present-day Spain and Portugal) located on the east coast of the peninsula that were reference cities of the Cartaginensis province: the theatre of Carthago Nova and the theatre of Saguntum. The acoustic characterisation encompasses a parametric and spatial description of their sound fields and a comparison of their acoustic atmospheres justified by their different states of recovery-rehabilitation. Both theatres especially that of Saguntum, present long reverberation times compared to other theatres of Roman Hispania. As a consequence, their energy descriptors show noticeable differences in the two theatres, whereby the most unfavourable perceptual conditions are presented in the Saguntum theatre with its completely rebuilt stage front. The parametric results are corrobarated through tridimensional energy plots carried out by IRIS diagrams imported into 3D geometrical models of the performance spaces, and therefore further indicate the importance of certain zones in the acoustics of the theatres. Keywords: Historical Acoustics, Acoustic Heritage, Classical theatre acoustics, 3D impulse responses, Roman Hispania, Energy diagrams. 1. Introduction 3 Greco-Latin culture refers to the mix of knowledge, ideas, traditions, and customs that were formed from the fusion of the Greeks and Romans, which combined Roman ideals with Greek development. The Roman theatre is commonly interpreted as the continuity of the taste for Greek performances, which Roman culture included in its leisure activities: ludi circenses, ludi scaenici, and munera. These activities had specifically designated spaces where these events took place; the first took place in the circus, the second in the theatre, and the third in the amphitheatre. The imperial era of Roman civilisation witnessed not only the greatest upsurge in the construction of theatre, but also the export of the model from Rome to the provinces. In addition to being a symbol of Rome, the theatre must be recognised both as an instrument of the new imperial ideology, and as a means for its political, religious, and propaganda content to be disseminated. In fact, the Roman theatre identifies a whole series of transformations with respect to the old Greek-Hellenic structures according to this new conception and functionality. Research on the acoustics of ancient theatres has proliferated in recent decades, where the Greek theatre of Epidaurus (Greece) [1, 2] and the Roman theatre of Aspendos (Turkey) [3] have provided the focus of the majority of these studies due to their marvellous state of preservation. The techniques employed range from a basic interpretation of the sound propagation made by Vitruvius [4] (2nd century BC) to the modern computer techniques of measurement and acoustic simulation. This development is due in part to European research projects: the ERATO (Identification, Evaluation, and Revival of the Acoustical Heritage of Ancient Theatres and Odea) project [3], and the Italian project ATLAS (Ancient Theatres Lighting and Acoustics Support) [5]. Two other events worthy of mention include the International Congress held in the University of Patras (Greece): The Acoustics of Ancient Theatres (2011) [6], and the 4 special Volume 1 of the year 2013, of the Acta Acustica United with Acustica journal [7], where the most relevant research of the previous congress is published. Most of the published pieces of research perform computer simulations, where hypothetical scenarios are studied, such as the influence of the audience [8, 9], the acoustic evolution of a specific theatre [10], and the examination, in terms of acoustics, of the evolution of the ancient theatres, from the early Classic Greek, the Hellenistic, and the Roman theatre types and performance styles [11]. Other authors also study the diffraction of sound waves in the cavea seats of the theatres and the amplification of sound due to the periodicity of rows at high frequencies, which are essential for speech intelligibility [12, 13]. In other cases, based on measurements of background noise and reverberation times in the venue, the virtual model was adjusted to recreate a model in order to explore differences in acoustic conditions through the smart design of various elements of the scenery [14]; likewise, simulation was carried out to understand whether velaria can affect the acoustics of the theatres [15]. Altenatively, in other cases, onsite measurements and simulations are combined in order to validate the results of the simulations, and to study possible reconstructions, such as the existence of a ceiling in the odeons [16], which are currently all unroofed theatres. In the work by Bo et al. [17], an assessment is carried out of the performance of two simulation software applications to outdoor unconventional environments. By means of measurements in situ and scale models, Farnetani et al. [18] provide an acoustic evolution of Ancient Greek and Roman theatres in five theatres. With the same approach, Prodi et al. [19] investigated the possible benefits and limits of passive strategies in the adaptation of ancient theatres to modern performances. Moreover, Astolfi et al. [20] highlight whether the measurement protocol recommended in the ISO standard 5 [21] and universally used in these performance buildings [22] should be applied to these spaces, which lack original architectural elements and ceilings. A number of researchers also investigate the subjective criteria of the acoustic quality of these theatres by using questionnaires distributed to the spectators of performances or to listeners of recreated sounds under lab conditions [23-25], and by using similar metrics as in closed enclosures with different reverberation times [26]. However, despite the boom in studies and projects concerning the acoustics of western ancient theatres especially those appearing after the year 2000, acoustic characterisation work based on Roman theatres remains sparse. This is surprising considering that, according to Mourjopoulos and Fausti [7], there are 425 theatres and 46 documented odeons that belong to the Roman era, and, of the 191 theatres in Italy that are still architecturally identifiable as theatrical structures, almost half are in use today for drama, dance, and musical festivals [16]. Along these lines, of the 198 Roman theatres around the world reported by Girón et al. [22], only on 20 has some kind of acoustic study been carried out. This lack of coverage, see for example the case of Gaul (France), in terms of knowledge of this intangible heritage of these historic venues or of improving the efficiency of the natural acoustics of theatres in contemporary performances, is limited to the environment of the theatre itself and the surrounding soundscape. It is appropriate to take into consideration the competing background noise at the sites, whose location is, in many cases, in the close proximity of urban areas. In this work, the results and discussion of the acoustic atmosphere of two theatres in the Roman province of Hispania are described and discussed while combining parametric and spatial acoustic information of the two venues. The theatres under investigation are part of the case studies of the research project PIAATRE [27], funded by the Spanish 6 government to analyse the intangible acoustic and environmental heritage of Roman theatres built in Hispania. 2. Roman Hispania The Roman conquest of the Iberian Peninsula was a process in which territories were seized that had previously been held under the control of native Celtiberian tribes and the Carthaginian Empire. This conquest covers the historical period between the Roman landing in Ampurias (218 BC, Figure 1), (this wall was built around 100 BC with a delimiting purpose rather than defensive), and the conclusion, by Caesar Augustus (19 BC), of the Roman conquest of the Iberian Peninsula with the end of the Cantabrian wars. The peninsula was inhabited by various ethnic groups and a large number of tribes. The Carthaginian territories in the south and east of the peninsula were conquered in 206 BC during the Second Punic War (218-201 BC) between Carthage and Rome: this war was sparked off by an attack by Hannibal on Saguntum, after which the Carthaginian forces left the peninsula. In 197 BC, at the end of the first phase of the Roman conquest, the first structuring of Hispania into provinces occurred: • Hispania Citerior: the closest to Rome, the Mediterranean strip along the southeast coast to Castulo (present-day Linares, Jaen) in the interior. •Hispania Ulterior: the rest of the future Andalusia now called Baetica. Over the next 170 years, following the second Punic War, the Roman Republic slowly expanded its control over Hispania by means of a gradual process of pacification and assimilation of the local tribes into the Roman world and its economic system. 7 This process changed at the end of the Roman Republic and on the establishment of rule by emperors in Rome. After the Roman victory in the Cantabrian Wars (the last rebellion against the Romans in Hispania) in the north of the peninsula, Augustus reorganised its administration in 19 BC into three provinces.  Tarraconensis: which was previously Citerior, extended to the northwest. Capital in Tarraco.  Baetica: capital in Corduba, to the south bank of the Guadiana. This was previously a subdivision of the Ulterior.  Lusitania: capital in Emerita Augusta, on the north bank of the Guadiana river. This province included the centre and the south of the future Portugal, and other Spanish regions. In 214 AD, emperor Caracalla created the Gallaecia province by subdivision of the Tarraconensis, and in 298 AD, Diocletian proposed a new administrative division for the Figure 1. Ampuriam wall. Initial entry point of Rome to the Iberian Peninsula. David Mateos Garcia, Creative Commons. 8 entire empire, which would affect Hispania in the creation of two new provinces: the Cartaginensis province and the Gallaecia province (Table 1 and Figure 2). Another effect of the Diocletian reorganisation was the creation of the Hispaniarum, with capital in Hispalis, a diocese dependent on the Prefecture of Gaul and with the province of Mauretania Tingitana, in North Africa, included in this diocese. At the end of the 4th century, the Balearic Islands separated administratively from the Carthaginian region to form a new Roman province, called Balearica. Table 1. Summary of the organisation in provinces in Hispania in the various temporal stages. 197 BC 27/13 BC 214 AD 293/385 AD Hispania Citerior Hispania Ulterior Tarraconensis Baetica Lusitania Gallaecia Tarraconensis Baetica Lusitania Diocesis Hispaniarum capital Hispalis (Seville) Mauretania Tingitana Gallaecia (Bracara Augusta) Tarraconensis (Tarraco) Baetica (Corduba) Lusitania (Emerita Augusta) Carthaginensis (Carthago Nova) ---------------------------------------- Balearica The Romanisation period of Hispania took place between 218 BC (date of the Roman landing in Ampurias) and the beginning of the 5th century (when the Visigoths entered the Peninsula, replacing the authority of Rome). Throughout this extensive period of seven centuries, both the population and the political organisation of the Hispanic territory underwent profound and irreversible changes, and would be forever marked by the unmistakable imprint of Roman culture and customs. In fact, after the period of conquests, Hispania became a fundamental part of the Roman Empire, and provided an enormous wealth of materials and human resources, and for centuries stood as one of the most stable parts of the Roman world and the cradle of several rulers of the empire. 15 three provinces (Gallaecia, Tarraconensis, and Cartaginensis), thereby establishing the capital of the Roman Carthaginensis province in the city of Carthago Nova. 3.1.1 The Roman theatre of Carthago Nova The Roman theatre, built in the time of Emperor Augustus, between the years 5-1 BC, remained in use until the third century. With an original capacity of 7,000 spectators, it remains one of the largest theatres in Roman Hispania. The theatre typology confirms the model proposed by Marco Vitruvius, as in most of the Hispanic theatres, and consists of: scaenae frons (stage front) with double columns; the orchestra, formed by a semicircle in front of the stage in which the authorities sat; the cavea, in which the spectators stood according to their social rank of ima, media, or summa; the proscaenium, which consists of space in front of the stage; and the porticus post scaenam made up of a porticoed courtyard behind the stage. Figure 3 shows a profile of the theatre with the increasing slopes of the cavea to provide good sightlines and soundlines to the spectators. The diameter of the cavea is 87.6 metres; the proscenium has a length of 43.60 m, and was topped by a front articulated by exedrae. In front of the tiers of the stands, the scaenae frons was situated, which can be restored, based on the analysis of the imprints and the architectural elements, with a plan articulated with three curved exedrae, and an elevation of 14.60 m in height with two orders, in which the combination of the reddish tones of the columns, the white of the capitals and bases, and the greys of the podium and entablature provoke a suggestive chromatic framework. In the back, the porticus post scaenam is developed in a terraced manner and articulated with a double-arcaded gallery delimited by a powerful sandstone facing, which also serves as the perimeter wall of the portico onto which semi-circular paths open of 12 m in diameter. The stands are projected by taking advantage of the natural slope of one of the highest hills in the city. The central part of the cavea is excavated into the rock of the hillside 16 itself, while the lateral flanks include vaulted galleries. The theatre is incorporated within the historical centre of the city near emblematic buildings and port facilities (Figure 4(a)). The partial overlapping of the Old Cathedral on top of the Roman theatre is valued as one of the historical singularities of this archaeological site (Figures 4). The traditional construction techniques generally used are opus quadratum, opus vittatum, and opus caementicium. The theatre was built with various materials: limestone, marble, and sandstone from local quarries, of which the columns made of red travertine from Mula stand out, especially all the sculptural ornamentation of the theatre made of white pentelic marble from Greece [31, 32]. Figure 3. Section of the Carthago Nova theatre showing the slopes of the cavea seating areas. 35.3º 33.7º 27.9º Figure 4. (a) View of the Roman theatre in Cartagena; (b) View of the stage and a part of the cavea (Source: the authors). (a) (b) 17 3.2 The Roman city of Saguntum The place name of Sagunto, (after the Ibero of Arse) comes from the Roman Sagumtum and refers to a strategic point in the Gulf of Valencia. The Roman presence on this coast, a result of the Carthaginian expulsion, took advantage of a long process of occupation of a lacustrine area largely articulated at the mouths of rivers, such as the Palancia in Saguntum, which also allowed the layout of inland communication routes. In 219 BC, Carthaginian Hannibal besieged, and sacked the pro-Roman city of Arse, prompting a Roman declaration of war on Carthage in spring 218 BC. After the victory of the Republic of Rome, the place name of Saguntum also began to be used, with this name finally prevailing. In the year 214 BC, it received the status of municipum, and the city was equipped with infrastructures and buildings typical of the Roman culture. Figure 5. (a) View of the Roman theatre of Saguntum before its restoration. Source: https://m.forocoches.com/foro/showthread.php?t=5682942. (b) Current view of the Roman theatre of Saguntum (Source: the authors). (a) (b) 18 The Romanisation of the city featured the particularity of its orography, and took place on three terraces and strongly conditioned the canonical configuration of the buildings. On the upper terrace is the old fortified enclosure divided into seven squares. Directly connected to this area is the second level, marked by the theatre construction. The lower part of the city reaching the river banks housed the circus. 3.2.1 The Roman theatre of Saguntum The knowledge of the Saguntum theatre and its representation makes it one of the most widespread pieces of work of Antiquity. Thanks to the restoration work started in 1985 by architects G. Grassi and M. Portaceli and the controversy of the final result (Figure 5), this theatre has become even more well-known. Without entering into legal and convenience considerations, it is necessary to appreciate the irreparable changes that this work has produced [33]. Before describing the canonical characteristics, it is therefore necessary to indicate that the mixed structure, opus quadratum and opus vittatum, of the postscaenium disappeared when a single wall was erected with ashlars similar to the original walls, with the interruption of the scalae in the balteus, and the arbitrary placement of elements on the scaenae frons. On the other hand, the excavations carried out in parallel to the aforementioned work provided important data on the theatrical space. 33.2º 30.4º 34.0º 32.1º Figure 6. Section of the Saguntum theatre showing the slopes of the cavea seating areas. 19 Interventions and adaptations of ancient theatres for their scenic use today are not without their accompanying controversy, both in the specialised scientific community and with the general public (Figures 5). In this respect, Saguntum presents the most complex and controversial example of all, and even involves legal procedures. After a few years of uncertainty regarding its future, including demolitions, the typological invariants can be defined as: The cavea built on the slope of the castle hill, adapts to a difference of approximately 25 m between the highest part and the foundation rock base of the closing wall of the scenic body. Figure 6 shows the longitudinal section of the theatre with the increasing slopes of the cavea. The orography divides the stands into two different parts, of which the lower and middle, facing northeast, are carved out of the rock, while the upper tier is supported by a set of vaulted galleries. This set allows, on the one hand, the stone step to be supported and, at the same time, it enables circulation along internal corridors. Numerous restorations have been carried out on the stands as well as on the rest of the theatre, and for this reason, in order to identify each part of the cavea, it is necessary to refer to topographical studies. By this means, it is deduced that the ima cavea was formed by six seating steps with access to the praecintio. The half cavea comprises eight steps, with four bays opening in its praecintio that provide circulation along radial staircases, which forms the six cunei. The summa cavea consists of nine steps up to the wall of the upper portico, and fourteen in the lateral spaces. The set presents a second ring that has been completely restored, which embraces the cavea from the aditus maximi except in its central part, although it does not represent a significant change in its structure and capacity. The capacity is 4,000 spectators. The proscaenium reaches a maximum dimension with the frons pulpiti of 6.40 metres counted from its wall to the scenic front. The depth of the hyposcaenium is conditioned 20 by the strip of rock that appears at the level of the orchestra and which reaches a difference of 6 metres in the foundation of the stage front. This large gap is bridged with a set of 17 perpendicular walls, which complete 16 trenches. The walls and the cells of the trenches are not equal to each other, but the same construction technique remains, the opus vittatum. To this set, we must add the two drainage areas at the ends, which form part of the water evacuation system. The body of the stage (Figure 5(b)) presents a view of the three exedrae restored from the preserved remains of the valve hospitalarium of the eastern sector and the valve regia. The use of the hillside is the most important feature of the theatrical ensemble. The exposed limestone formed part of the stands, giving a grey totality to the whole. In dissonance with this hue, a white travertine cladding from Teruel was arranged in the new stands. Part of the original elements of the stage has been restored, the blocks with the remains of the architectural decoration are carved in greyish local dolomitic limestone with the exception of the capitals, sculpted in travertine limestone from Viver, which is more porous and warmer in colour. The materials used in the details: railings, windows, drains, gutters, and bars have been strongly criticised, since they are largely difficult to maintain [34]. 21 4. Experimental procedure Measurements were carried out on the theatres without the presence of the public and by following the recommendations of the ISO 3382-1 standard [21]. There was no wind during measuring times (air velocity less than 0.5 m/s) and environmental conditions were monitored by means of measuring the temperature (32°C in Cartagena, and 21.6°C in Sagunto) and relative humidity (49% in Cartagena, and 46.3% in Sagunto). In accordance with the dimensions of the theatres and in order to carry out an exhaustive acoustic characterisation, 3 source positions were chosen, (located in the centre of the stage (S0), on the left-hand side of the stage (S1), and in the centre of the orchestra, (S2)), 20 microphone positions in Carthago Nova and 34 in Saguntum were distributed throughout the audience area, as shown in Figures 7(a) and (b), respectively. The restoration carried out in the latter theatre has enabled greater accessibility for a more detailed acoustic characterisation. In order to carry out the measurements in-situ, the following equipment has been used: The signal generation, acquisition, and analysis process have been carried out with IRIS software [35], and through the MOTU 4PRE HYBRID sound card. The excitation signal Figure 7. Ground plan of the theatres with the positions of the sources (S) and receivers (R) displayed for acoustic measurements. (a) The Roman theatre of Carthago Nova. (b) The Roman theatre of Saguntum. (a) (b) 22 is a sweep of sinusoidal signals with a duration of 5.5 seconds in Carthago Nova theatre and 16 s in Saguntum theatre and a frequency range from 63 Hz to 16,000 Hz. The excitation signal was reproduced in the spaces using an AVM DO-12 omni-directional source located at 1.50 m above the floor, previously amplified with a B&K 2734-type power amplifier. The Room Impulse Responses (RIR) were captured with the Core Sound TetraMic microphone array pointed in the same direction as the seat, which allows temporal and spatial (3D) information to be incorporated. The binaural RIRs were captured with a Head Acoustics HMS III torso simulator (Code 1323) and a B&K 2829 microphone polarisation source. In all cases, microphones were placed at 1.20 m from the floor. The background noise level was recorded with a Svantek SVAN 958 analyser. The B&K 4190 microphone was used with a B&K 2669 preamplifier and the B&K 2829- type 4-channel microphone power supply. For each performance building, a 3D geometric model was created via the SketchUp programme, to import the IRIS plot data for the purpose of visualising plots. 5. Experimental results and discussion This section presents and analyses the parametric results of the impulse responses and the spatial study of the sound field of two perfomance constructions from Roman times in Spain. In the case of the Carthago Nova theatre, certain preliminary results have been published in a conference paper [36]. 5.1 Parametric analysis As described, the two theatres present certain differences in terms of size, in the reconstructions carried out, and in their materials, and less significantly in the placement where the two are located. The theatre in Cartagena is located in the middle of the historic 23 centre surrounded by buildings, while the theatre in Sagunto is on the side of a mountain overlooking the city. The acoustic parameters presented below correspond to the spatial averages carried out in each theatre (20 microphone positions in the case of Carthago Nova and 34 in Saguntum) for each of the three positions of the source in the various octave bands. The local variation is also shown in certain parameters when studying their behaviour as a function of source-receiver distance. 5.1.1 Decay-time parameters Impulse responses recorded by the IRIS system show a sufficient range in the impulseresponse-to-noise ratio (INR > 45 dB in each octave band) for the decay ranges in each band of interest in the Carthago Nova and Saguntum theatres. Regarding the study of linearity of the decay curves in the Carthago Nova theatre, the results show that the criteria established in the ISO standard [37] are verified above all in the receptors of the upper part of the ima cavea and in those of the media cavea with the source at position S0. For S1 and S2 source positions, the linearity criteria fail in all octave bands in receivers at the lower part of the cavea, while in receivers placed in the upper part of the cavea criteria are not fulfilled in certain bands. In the Saguntum theatre, on the other hand, the linearity criteria are widely verified in all source-receiver combinations and octave bands. The temporal description of the sound field in the theatres and the variations between them are studied through the reverberation time (T30) for a physical description of reverberation, and through the early decay time (EDT) as a descriptor of the perceived reverberation. Since the IRIS platform also provides T20 reverberation time, the results of these three parameters have been compared in each theatre. In the Cartagena theatre, the longest values in all receivers and sources correspond to T30, and to decreasing T20, and 24 finally to EDT. The non-linearity in the decay curves is the cause of these discrepancies, especially in the receivers of the scaena and the orchestra for the three positions of the source. Likewise, the comparison of the results of T30m and T20m (the subscript m refers to the spectral average suggested by the ISO standard [21]) has revealed that there are differences in the receivers of the scaena and the orchestra with variations of up to 0.5 s for source S0 and up to 0.54 s for S2; the smallest differences between the two parameters are presented at source S1. In the Saguntum theatre, the aforementioned linearity gives rise to major coincidence in the results of T30, T20, and EDT, particularly regarding the proximity of the results of the EDT with T30, which is described in greater detail below. The comparative study of the results of T20m and T30m has shown that there is agreement in both parameters in practically all source-receiver combinations and that at most the differences in the values do not exceed 0.1 s; their similarity and/or agreement is extensible to all octave bands. Figure 8. Time parameters in the theatres versus frequency (a) Reverberation time, T30; (b) Early decay time, EDT. Frequency (Hz) 125 250 500 1000 2000 4000 Reverberation Time T 30 (s) 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Frequency (Hz) 125 250 500 1000 2000 4000 Early Decay Time EDT (s) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 (a) (b) S0 Saguntum S1 Saguntum S2 Saguntum S0 Carthago S1 Carthago S2 Carthago 31 reflections in many measurement receivers. As a reference, in the Sagunto theatre, in the middle of the space, the Gm reaches 2 dB for all sources [41]. In both theatres, the slopes of the regression lines from the experimental results are similar when comparing positions of the sound source, but slightly higher in the case of Sagunto. The values for Cartagena for sources S0, S1, and S2 are -0.30, -0.24 and -0.40 dB/m respectively, while for Sagunto they correspond to -0.32, -0.28 and -0.42 dB/m. Therefore, the greatest drops with distance appear when the source is located in the orchestra, followed by the central location in the scaena, and lastly in the lateral location. The levels for the two performance venues at mid-frequencies are around 4-5 dB as in other Roman theatres [18]. However, the situation changes at 4000 Hz, where a great colouration of the sound field is present in the Sagunto theatre, as stated before, with differences between the two theatres of up to 13 dB. 5.1.3 Speech intelligibility and spatial impression parameters Figure 11. (a) Speech Transmission Index, STI, versus source-receiver distance for all sources in both theatres; (b) Early Interaural Cross-Correlation coefficient, IACCE, and its standard errors versus the frequency octave band for the three sources in both theatres. Distance (m) 0 10 20 30 40 50 STI 0.0 0.15 0.30 0.45 0.60 0.75 0.90 Bad Good Excellent Poor Fair Frequency (Hz) 125 250 500 1000 2000 4000 Interaural Cross-Correlation IACC E 0.0 0.2 0.4 0.6 0.8 1.0 (a) (b) S0 Saguntum S1 Saguntum S2 Saguntum S0 Carthago S1 Carthago S2 Carthago S0 Saguntum S1 Saguntum S2 Saguntum S0 Carthago S1 Carthago S2 Carthago 32 These differences in the theatres pointed out through the Definition parameter can also be appreciated when observing the values of the Speech Transmission Index (STI) in Figure 11(a). For the calculation of this parameter, the background noise spectrum measured in the two theatres has been taken into account, which corresponds to a global sound pressure level of 53 dBA in Cartagena and 35.7 dBA in Sagunto, respectively. In the Roman theatre of Cartagena, the STI values present a variation range from 0.60 to 0.75, and hence the intelligibility of speech in this performance space can be described as good. However, the STI values for the Roman theatre of Sagunto vary from 0.46 to 0.62, thereby qualifying the intelligibility of speech as fair. This is due to the fact that, in this Roman theatre, as explained in the previous section, the entire stage front has been reconstructed, which causes a greater number of late reflections to occur, thereby increasing reverberation, sound strength, and centre time and decreasing clarity and the intelligibility of speech. The early interaural cross-correlation coefficient (IACCE), which provides the correlation between the sounds that reach each ear, that is, it indicates the degree of similarity Figure 12. (a) Early Lateral Energy Fraction, JLF; (b) Late Lateral Sound Level, LJ, versus the frequency octave band for the three sources in both theatres. Frequency (Hz) 125 250 500 1000 2000 4000 Early Lateral Energy Fraction J LF -0.1 0.0 0.1 0.2 0.3 0.4 Frequency (Hz) 125 250 500 1000 2000 4000 Late Lateral Sound Level L J (dB) -20 -15 -10 -5 0 (a) (b) S0 Saguntum S1 Saguntum S2 Saguntum S0 Carthago S1 Carthago S2 Carthago 33 between the two signals in the early interval 80 ms after direct sound, is shown in Figure 11(b). This parameter is very similar in the two Roman theatres: each has similar decrements across the whole frequency ranges except for source S1 in Sagunto, which decays more than the remaining sources at medium and high frequencies. The (1-IACCE) values correlated with the apparent source width are therefore moderately low. In Sagunto, the apparent source width is independent of the source location when it is centred either on the stage or in the orchestra, and, as expected, significantly improves when the source moves onto the stage. In Cartagena, this improvement also holds true but, in contrast, a better behaviour is presented when the source is centred in the scaena instead of in the orchestra due to the greater proximity to the remains of the stage front. According to Hidaka et al. [42], the IACCE averaged values at 500, 1000, and 2000 Hz fall into the category of poor acoustics as proposed for an empty concert hall. Only in the case of the displaced source in the Sagunto stage would a very good rating be obtained. The analysis of the spatial impression of the performance spaces completes the spectral study of the early lateral energy fraction parameter, JLF, which is correlated with the apparent source width and the late lateral sound level LJ parameter. For the JLF parameter (Figure 12 (a)), the results from the IACCE parameter are corroborated. In all cases, the parameter lies within a very low range, with values of less than 0.2 for the two theatres in the range of frequencies of interest for the parameter (125-1000 Hz), although within the typical range [21]. Finally in the evaluation of the sound attribute of listener envelopment, the value of the LJ parameter is lower in the case of the Carthago Nova theatre, and for most of the frequencies lies outside the preferred range for concert halls; in the case of the Sagunto theatre the results of the parameter are more favourable [41]. Logically, local variations in the results are more pronounced in the early directional parameter than in the late directional parameter. Again the increase of late lateral energy 34 at 4000 Hz is attributable to the acoustic behaviour of the marble used in the restoration of almost the entire cavea in this theatre, which replaced the original stone (Figure 5(b)). 5.2. Tridimensional description of the sound fields IRIS software [35] provides a plot of 3D impulse responses that shows sound energy arriving at a receiver position as a series of vectors: the length of each vector indicates the level, the angle indicates the incoming direction, and the colour corresponds to the time of arrival (Figure 13). The four tetrahedral cardioid signals from the TetraMic are converted into another 3D system called the first-order B-format. B-format encodes the pressure (omni-directional) and three particle-velocity (figure-of-8) signals in the X, Y, and Z directions. IRIS software identifies the relevant part of the recording for analysis: this runs from the onset Figure 13. Energy diagram of vectors in broadband for the S2-R3 combination of the Roman theatre of Cartagena for the speech time intervals. 35 (a) (b) Figure 14. Energy diagram of extended rays in broadband in the 3D model of the Roman theatre of Cartagena for the S2-R3 combination in the 0-inf. ms time interval: (a) view of the stage; (b) perspective towards the cavea . 36 of the direct sound to when the impulse response decays into noise. The octave–bandfiltered B-format impulse response is then divided into a series of non-overlapping rectangular windows. The length of these windows is determined by the speech time intervals which give rise to 4 time intervals: 0-2, 2-50, 50-80, and 80-Infinite ms. The recommended resolution is 2 ms, which introduces a low frequency limitation, and Figure 15. Energy diagram of extended rays in broadband in the 3D model of the Roman theatre of Sagunto for the S0-R14 combination in the 80-inf. ms time interval: (a) general view towards the stage; (b) lateral perspective towards the stage. (a) (b) 37 therefore the plot only shows frequencies of 500 Hz and higher. Thus, the first vector, with a higher level and red colour, corresponds to the arrival of the direct sound. IRIS plots can be exported for the purpose of both visualising plots in SketchUp software and also extending the plot vectors to the boundaries of the room. When an extended vector hits a surface, a cross appears on the intersection thereof. To this end, a 3D geometrical model of each Roman theatre has been created, where broadband results from IRIS software for all source-receiver combination in each theatre have been imported to the geometrical models (see Figures 14 and 15). The analysis of each theatre therefore implies the visual inspection of each receiver in four time intervals and for 4 octave bands (500-4000 Hz) for each source. This represents 960 cases in Cartagena and 1632 in Sagunto, where the origin of the reflections (lateral or frontal), the level of the first reflections, the positon of the receiver in the theatre, and the surfaces upon which they strike are studied. The results of the overall spatial and temporal energy analysis confirm the results expected by geometrical acoustics at a global level and enable the energy distribution over time to be shown in detail and the acoustic importance of certain parts of the theatre to be ascertained. These aspects are presented for each theatre and for the receivers located in the various areas: scaena, orchestra, ima cavea, media cavea, and summa cavea (the latter is present only in the Roman theatre of Sagunto). Overall, for both theatres, the main energy contributions from the three cavea areas, regardless of the location of the source and time, come from the area itself. In each cavea area, the energy reinforcements obtain their particular contribution from one of the other areas. In the same way, as expected, the early lateral energy that reaches the receivers is scarce when the sources are centered, and increases when the source is moved onto the scaena, 38 whereby late lateral reflections increase but with less energy input. Nevertheless, except for particular cases (receivers on the stage in the Sagunto theatre or close to the old church in the case of Cartagena, for example), in most receivers the early energy presents a frontal-rear spatial origin. The late energy, with the lowest energy contribution, is that which provides the lateral energy. This fact is in line with the results obtained that judge the spatial impression of listeners, Figure 11(b). The possible symmetric distribution of energy at equivalent points has been estimated. It has been verified only for the late energy. 5.2.1 Carthago Nova theatre On the scaena, the receivers are dominated by the energy contributions from the scaena floor and the stage front throughout the entire time interval and for the three source positions, Figure 14(a). When the source is displaced on the stage, the late energy presents energy reinforcements from the ima cavea. When the source is in the orchestra, the reflections that arrive after the first 50 ms come from the ima cavea. In the orchestra, for the three sources, the same pattern is followed: in the first 80 ms the greatest energy contributions come from the orchestra for the most centred receptors, while those located in the poedria present a reinforcement of the first rows of the ima cavea, due to its proximity. The ima cavea plays a major role for late energy. There are no energy contributions from the media cavea in the entire time interval. For the receptors located in the ima cavea, when the sources are located on the scaena, the main early energy reinforcements to the energy coming from the area itself originate from the orchestra. When the source is located in the orchestra, the lower receivers have a greater energy contribution from the orchestra compared to that from the ima cavea. For the late energy, in all three sources, the reinforcement principally comes from the 39 orchestra, followed by that from the stage. There are no significant contributions from the media cavea, Figure 14(b). For the media cavea, with the sources located on the scaena, in the first 50 ms there are energy reinforcements of the scaena and, from 80 ms onwards, the ima cavea, the scaena floor, and the orchestra all contribute with equal importance. If the source is located in the orchestra, then in the first 50 ms, the energy reinforcements come from the orchestra and the ima cavea contributes significantly to sound energy from 80 ms onwards. 5.2.2 Saguntum theatre Receivers located on the scaena receive the highest energy inputs from the stage front followed by those from the stage floor for sources located on the scaena. When the source is placed in the scaena, the order is reversed. Receivers located in the cavea receive most of the energy from the vicinity of the tiers, to which that from the stage front is added in all energy intervals and for all sources. Only when the source is located in the orchestra does it contribute significantly in the interval within the first 50 ms. When considering possible energy contributions between the three parts of the cavea, it is observed that the summa cavea works independently, without energy contributions from the ima and media cavea. These two in turn have no significant energy influence on each other on a general level (Figure 15(a)). Finally, it should be borne in mind that the roof of the stage front contributes no energy to the receivers (see Figure 15(b)). Although the audience can observe a sloping wooden ceiling, it lacks acoustic value since it is composed of widely spaced wooden sheets and the sound energy falls on the rear ceiling, which is completely closed, and made from the same material as the stage front. 40 The study of symmetry in both theatres has shown that at equivalent points, although there may be symmetry in terms of the density of energy inputs in the different time intervals, there is none in terms of the origin of the surfaces involved. 6. Conclusions The detailed spatial and temporal analysis of the acoustic energy together with the measurements of the impulse responses in the Roman theatres of Cartagena and Sagunto have enabled the acoustic behaviour of both venues to be explained. The comprehensive analysis of the energy reveals that specific areas of the theatre (scaena, scaenae frons, orchestra, and cavea) are involved in sound perception for the intervals corresponding to early and late energy. In addition, is shown that the three zones of the cavea (ima, media, and summa) function independently without supplying energy between them. Only in the Cartagena theatre does the media cavea show late energy contributions from the ima cavea. In the case of the Sagunto theatre, it has been shown that the ceiling of the stage front does not contribute acoustically to the sound perception of the spectators. On the other hand, the RIR analysis shows that, although suitable conditions for the measurement of reliable room impulse responses are achieved, the energy decay curves manifest a lack of linearity in the Cartagena theatre, leading to a large decrease in the early reverberation time, EDT, with respect to the T30 reverberation time in all octave bands, and to a great variability in the pattern of the initial reflections in the various receivers in the theatre. In the Sagunto theatre, on the other hand, the energy decay curves are linear and there is a coincidence between the two parameters EDT and T30: the spatial dispersion is very low. The reverberation time is notably higher in the Sagunto theatre (average at medium frequencies, 2.25 s) than that of Cartagena (1.85 s). This increase in reverberation and excess amplification of sound in the first theatre is due to the thorough reconstruction of its scaenae frons and results in a decrease in clarity, sharpness of sound 47 [34] S. Lara, El Teatro Romano de Sagunto: avatares de una década, Loggia, 13 (2002) 32- 37. [35] Iris Software, http://www.iris.co.nz/ (archived 10/04/2020). [36]J.A. Romero-Odero, J. Alayón, M. Galindo, F.J. Nieves, L. Burridge, S. Girón, Acoustic characterisation of the Roman theatre of Carthago Nova, in: Proceedings of Acustica, 2020 Faro, Portugal 21-23 October, pp. 371-382. [37] ISO 3382-2:2008(E), Acoustics-Measurement of room acoustic parameters-Part 2: Reverberation time in ordinary rooms. International Organisation for Standardisation, Geneva, Switzerland, 2008. [38] A. Álvarez-Corbacho, T. Zamarreño, M. Galindo, S. Girón, Virtual acoustics of the Roman theatre of Regina Turdulorum, in: Proceedings of Tecniacustica, 2015, Valencia, Spain, 21-23 October, pp. 1515-1522. [39] A. Álvarez-Corbacho, P. Bustamante, M. Galindo, S. Girón, T. Zamarreño, Measurement and analysis of the acoustics of the Roman theatre of Segobriga (Spain), in: Proceedings, of InterNoise19, 2019, Madrid, Spain, 16-19 June, paper1833. [40] H. Arau Puchades, ABC de la Acústica Arquitectónica, CEAC, Barcelona, 1999. [41] J.S. Bradley, Review of objective room acoustics measures and future needs, Appl. Acoust. 72 (2011) 713-720. https://doi.org/10.1016/j.apacoust.2011.04.004. [42] T. Hidaka, T. Okano, L.L. Beranek, Studies of Inter‐Aural Cross Correlation (IACC) and its relation to subjective evaluation of the acoustics of concert halls. In: Proceedings of the 122nd Meeting of the Acoustical Society of America, Houston, Texas, USA, 4-8 November 1991.