Acoustic reconstruction of the Saint Pantaleon church in Cuenca (Spain)

Abstract

The ruins of the church of Saint Pantaleon, located in the historical center of the city of Cuenca (Spain), presents a Romanesque origin related to the Order of the Temple and a Gothic finish. Moreover, the two naves of which it would consist in the 13th century, would become a single one in the 16th century. Through the analysis of the ruins and the investigation of the architectural and stylistic characteristics of the period, as well as the comparison with other temples in Spain, two simulation models have been made for the 13th and the 16th centuries respectively. They have been validated by comparison with studies of temples of similar contexts and dimensions due to the impossibility of validating the model with in-situ measurements. As the observed behaviors are analogous, it indicates that the theorized models are accurate and, therefore, the results are reliable. These models, were simulated in an occupied and empty state for officiant, choir and populus sources. It can be highlighted a more reverberant enclosure in the 16th century, with better values of vocal clarity and definition and better intelligibility than in the case of the 13th century model. Regarding positional differences, it has been observed that there are hardly any differences among the three positions in any of the models. Finally, the inclusion of the audience has a remarkable effect on the acoustics due to the increase of absorption, which leads to a better musical clarity, definition and intelligibility and a shorter reverberation time.

Keywords

acoustic reconstruction acoustic heritage church acoustics archaeoacoustics

Introduction

The ruins of the church of Saint Pantaleon are located in the historical center of the city of Cuenca (Spain), and could probably be considered the oldest church in the city. The building is located in San Pedro Street, very close to the Cathedral of Santa Maria and San Julian, and was declared a historic-artistic monument in 1983 and “Cultural Heritage Asset” with the category of “Monument” in 1992.¹ Figure 1 shows an aerial view obtained using Google-Earth, with the geographical location of the current situation of the ruins of the church of Saint Pantaleon in Cuenca.

The church of Saint Pantaleon brings together a set of unknowns around it, due to the scarcity of documentary references about the origin, history and nature of the building itself, sowing an aura of mystery over how the church came to be. According to such facts, not even in its own denomination there is a consensus throughout its history, since the church will change its name on numerous occasions. “San Juan del Hospital,” “San Juan de Letran” and “San Pantaleón,” gave name to the building in the course of time. This could be due to the origin of the building itself, which could have belonged to the Order of the Temple and, after its dissolution at the beginning of the 14th century, could have been assigned to the property of the Order of the Hospital. This scarcity of information, both in documentary references and in the actual situation of the ruins, sow a wide range of possibilities regarding the possible hypotheses about its origin and construction, which were postulated throughout the research project of the ruins carried out in conjunction with the project of “Musealization of Saint Pantaleon,” carried out by the Consortium of the City of Cuenca.¹

The present ruins after the process of musealization (Figure 2) present a building of reduced dimensions. It is suggested that the plan of the church would have a rectangular and perhaps somewhat trapezoidal shape, since the dimensions of the head and foot of the temple do not correspond exactly. The foot of the temple presents a width of approximately 6.2 m, which includes a doorway of Gothic origin with a pointed arch with archivolts; the lateral walls are not complete, presenting an approximate length of 19.5 m, with colonnades and semicircular arches in the rear part next to the header wall; finally, there is a header wall belonging to the apse of the church with a small opening in its upper part that corresponds to a flared window typical of the Romanesque.

Historical context of the church of Saint Pantaleon

The historical context of the erection of the temple of Saint Pantaleon is set in a town that had recently been conquered in the year 1177 by the Christian King Alfonso VIII together with the Orders of Santiago and Calatrava, after a 9-month siege of the Muslim city.² After the Muslim surrender, the population was reclaimed by the kingdom of Castile and the construction of the first churches and parishes of the new Christian town began.

It is necessary to expose that in the first stages of Cuenca, which would be endowed with the title of city in 1257 by King Alfonso X, the organs of power resided in those who contributed in its conquest, being con-statable this power in the ”Fuero de Cuenca”. This link between the city and the military orders is the root of the construction of the church of Saint Pantaleon. Therefore, the construction of the temple is framed in a population in demographic growth and highlighting the link of the church with the military Orders of Templars and Hospitallers.³

The church would have a Romanesque origin, although its construction could have begun at a later stage, being dated to the second half of the 13th century, according to the stratigraphic study carried out by the Consortium of the City of Cuenca.³ The first mention of the building refers to the donation of a church called “San Juan del Hospital” in 1355.

Another documentary branch dates the beginning of the church at a date much closer to the Christian reconquest of the city (1177), setting the beginning of the works during the last period of the 12th century.¹ This branch of the documentation shows a Templar origin of the church, with denominations of the building as “San Juan de Arce” or “San Juan de Letran.” In this case, the church would house the worship of the knights of the Orders who participated in the military actions of the conquest of the city at the hands of King Alfonso VIII. After the dissolution of the military order at the beginning of the 14th century, the ownership of the church would become vacant, which coincides with the cession of the temple to the Order of the Hospital and the corresponding change in the denomination of the temple.

Being clear the assignment of the church to the cult of military orders, the decadence of the temple would be based on this fact, since with the loss of power of these orders in later stages would leave a church practically in disuse. The temple would undergo architectural interventions over time, changes according to the importance and usefulness that the building may have had throughout its history. In the beginning, a church of larger dimensions could be found, with two or even three naves. Although the three-nave church is a simple hypothesis, since no study supports it, it seems more likely the existence of a second nave, which would be located in the northern part of the church, coinciding with the burials found on Obispo Guerra Campos Street.³ According to the stratigraphic study carried out on the ruins, it is theorized that during the 15th and 16th centuries the church would no longer belong to the Order of the Hospital and would be called “San Juan Bautista,” and the temple would be reduced to a single nave, of dimensions similar to those that we can intuit when observing the ruins of the current site.

Entering in detail of the date of abandonment of the building, it is necessary to emphasize that the temple was not included in the famous Disentailment of Mendizabal (1836–1837),⁴ which would indicate that the temple would already be abandoned in that period. This fact is linked to the sad outcome of the church during the third Carlist war, dating the “Taking of Cuenca” (13th–15th July, 1874), where stones from the church were used to form barricades in the failed defense of the city.

Stylistic theorization of the work

Defining the architectural style of a building from roman architecture is a complex process, being necessary to point out that unlike modern times, in ancient times and with greater weight in sacred architecture, the style of a work did not only represent the artistic and cultural concept corresponding to that period and situation, but also exposed a way of building that served as a standard. This is why there is a great homogeneity in the buildings of a given period, since sacred buildings responded to the idiosyncrasy imposed by the ecclesiastical identity and followed construction lines in accordance with the style of the period.

It should be also clarified that the conception that artistic styles correspond to a specific period and location is an erroneous concept, since the diffusion of new artistic and constructive currents is a gradual and slow process. This fact leads to churches that consequently belong to different styles since at the beginning of the work they started from an artistic line and during the building process new artistic trends led to modify the work project, resulting in temples whose style in plan does not correspond to the style of the completion of the construction.

The church of Saint Pantaleon is a case in point. According to the historical context of the work, the building dates from the 13th century with a possible completion toward the end of the same century or even at the beginning of the following century, although certain documentary lines indicate an even earlier construction, which would result in the fact that it is the oldest church in the city.

In any case, this was a church whose architecture corresponded to a Romanesque temple, whose apse was oriented to the east and which would later be finished with Gothic elements, with the arrival of the Gothic influence brought by the Norman cavalry that formed part of the court of King Alfonso VIII, as was the case in the cathedral of the city.

Likewise, we find specific Romanesque elements in the barrel vaulting insinuated in one of the sides of the nave (Figure 3(a)), as well as in the flat masonry apse; an arched window located in the upper part of the chancel (Figure 3(b)), which is typically Romanesque, and semicircular arches on the sides of the church. Also, Romanesque were the construction materials, highlighting the use of ashlar and lightened mortar masonry; due to the unrefined fit of the stone used, smaller stones or binder are required to achieve the necessary solidity and stability. Regarding the link of the church with the order of the Temple, the conservation of certain symbolic elements related to that order can be highlighted: one of the capitals of the flared arch of the entrance (Figure 3(c)), presents a possibly Templar symbolism, showing the representation of a horseman spearing a dragon on an inverted head from whose mouth sprout ropes or vines. Finally, with clear Gothic inspiration, although with precedents in the Burgundian Romanesque, it can be found in the doorway of the temple a pointed arch, which serves as the entrance door to the building (Figure 3(d)).

Simulation of the architectural space

As noted in other reference studies,^5–7 it is possible to evaluate and reconstruct the acoustics of significant historical and religious heritage that has disappeared over time, which can now be partially recovered through modeling and simulation tools and virtual reality technologies.

The starting point for the three-dimensional modeling has been the exhaustive analysis of the existing ruins. These ruins provide a solid and tangible base on which to build the model, allowing a precise approximation of the original dimensions and architectural characteristics of the church and architectural interventions for specific time periods. The archeological remains provide valuable information on the spatial layout and the materials used, elements that have been accurately considered in the modeling for their original dimensions and architectural features.

To ensure that the modeling faithfully reflects its historical context, extensive research has been carried out on the architectural and stylistic characteristics of the period, according to the typical style of the Spanish Romanesque. This historical context has guided key decisions in the design, ensuring that the architectural elements, such as the arches, the vaulting and columns, reflect authenticity and congruence with the Romanesque style.

To complete and enrich the 3D model, a comparison and study with other similar Romanesque buildings in the region and in other parts of Spain from the same period, but with different volumes, has been carried out to analyze their effect on acoustics. These comparisons have provided additional references to architectural elements that may have been present in the church of Saint Pantaleon but are not preserved in the present ruins. This comparative approach has made it possible to fill in some uncertainties about the geometry, materials and degree of occupation, and thus ensure the most complete and accurate reconstruction possible. The influence of temples such as the cathedral of “Santa María y San Julian” in Cuenca, “Santa María de Iguacel” (province of Huesca), “Santo Estevo de Ribas de Miño” (province of Lugo), church of the “Natividad de Nuestra Señora de Arcas” (province of Cuenca), cathedral of “Santiago de Compostela” (province of La Coruña), “San Bartolome del Cañon del Rio Lobos” (province of Soria), church of “Santísima Trinidad” in Pelegrina (province of Guadalajara) and churches of “Santa María del Rey” and “San Gil” in Atienza (province of Guadalajara) should be highlighted at this point.

Taking into account the stylistic characteristics defined above, as well as the historical context of the building, two reconstruction models are proposed for the three-dimensional model, associated with historical landmarks and defined architectural interventions, that in turn derive in hypotheses about the differential acoustic characteristics between the two models:

Original 13th century model, counting on a building articulated in two naves, due to knowledge from the appearance of burials in the rehabilitation of the Ronda de Julian Romero Street. In this model, the lateral arches of the temple, supported on the wall adjacent to the mentioned street, would appear opened and would serve as a passage to the lateral nave. It should be noted that both naves conform only one volume and no two coupled spaces because there is no transition elements between naves.

Model with the present floor plan, which could correspond to the church reduced around the 15th–16th centuries. The temple had an approximately rectangular floor plan of 6.2 m at the base, 5.4 m at the chancel and 19.8 m on its east-west longitudinal axis. The sides of the single nave had colonnades that culminated in semicircular arches supported on the lateral wall itself; these walls would have had a flared window of smaller size compared to the window at the chancel. The nave would be finished with a barrel vault and a gabled roof, typical of the Romanesque style. The doorway would have a pointed arch as well as a flat pediment with lateral reliefs, topped with the inclusion of a rose window in the doorway.

Based on the fact that in the current ruins a flared window is preserved in the header wall, and following the same stylistic line, two additional windows have been projected, located in the north and south side walls. The size of both is smaller than that of the chancel, following the Romanesque style of construction. Regarding the existing window in the ruins, the modeling is made following the plans drawn in the musealization project.¹

The inclusion of a rose window in the model refers to its origin as a ecclesiastical military order building, since one of the main symbolisms present in the temples linked to the Templars and Hospitallers is the presence of rose windows. In many of the cases they were initially used to be opened to the outside and did not present glass in the interior drawings, although the popularity of stained glass windows during the 13th century should be widespread in most newly built temples. Having an example so close as the cathedral of Cuenca, of a similar time, it seems logical to presuppose the presence of glass in the rose window located on the main facade, that is, in the front of the temple.

It is a fact that the Romanesque capitals were of very varied aspects and provided didactic functions, representing biblical scenes or specific symbolism. Taking this variety into account, it was decided to model a generic capital that follows the general shape of the Romanesque capital, with a truncated cone-shaped base and a parallelepiped-shaped top. To represent the historical detail of the same, a disk is drawn with circular shapes among other reliefs.

In the current ruins the entrance arch at the front of the temple, despite being in clear deterioration, allows to intuit its original form. As was the case with the flared window, it was decided to represent it in the model following the plans of the musealization project¹ and deducting the remaining part of the pointed arch of the doorway.

The model is architecturally culminated by a barrel vault and a gabled roof, typical of the Romanesque style, and in the case of the lateral nave of the 13th century model, the roof rests on the north wall of the building. It should be noted that apart from the barreled vault other options like a pitched roof were analyzed, choosing the most probable one according to the historical study carried out and taken into account that it will have acoustic differences depending on the solution chosen.^8,9

The church of Saint Pantaleon in the 16th century underwent an architectural change. The plan was reduced to a single nave, suppressing the lateral nave of the north wall. The model designed clearly reflects this change where the semicircular arches of the main nave are transformed into blind arches. In the 16th century model, a half-height partition is preserved to indicate the space occupied by the suppressed nave.

To carry out the simulations, two detailed models were created using the 3D modeling software Sketchup which, once simplified were imported into the acoustic simulation software EASE to carry out the calculations and prediction of the acoustic behavior. In this way, surfaces smaller than 0.5 m were simplified to reduce the total number of surfaces and improve the performance of the AURA-based simulation algorithm, removing decorative elements, whereas selected architectural features such as windows, the crucifix, and access doors/jambs were retained with higher detail to represent the most relevant materials (e.g. wood and glass), prioritizing material characterization over geometric complexity to avoid unnecessary model detail, thus achieving a balance between a greater degree of approximation of the geometries of the enclosure and an efficient and optimized acoustic model in its simulation for the complex analysis of acoustics in three-dimensional space, resulting in the enclosures of Figure 4.

In order to know with certainty the architectural characteristics of the disappeared church, the dilemma arises of choosing the most appropriate materials that could have been found in Saint Pantaleon.¹⁰ It should also be noted that, since measuring or predicting the absorption and scattering properties of surfaces will continue to be a challenge in room acoustic design practice, it is necessary to rely on studies with stylistic or material similarity that can serve as references in order to achieve the best possible approximation.¹¹

Examining the ruins and investigating the available archeological studies, we can find masonry materials where ashlars stand out as a construction element, as well as by the architectural style, it can be deduced that due to its austerity, the building would consist of materials with little complexity of carving. Although there are some techniques to measure the absorption coefficients of the ruins¹² the results would be strongly influenced by material degradation and pathologies caused by aging, climatic exposure, and conservation treatments resulting from the archeological interventions. Moreover, the measurement taken in other historical building could not be appropriate for this church. Consequently, since it was not possible to determine the exact materials used, much less to detail their absorptive (material type) and diffuse (according to geometry and shape) behavior, it was decided to use materials provided directly from the EASE database, specifically from the Global Materials 40 repository, American Base, considering other studies where materials like specific stone or ashlar were taken directly from software databases.^5,13 A choice is then made of the materials that are most similar to those that could have been found in the original temple.

Thus, the main materials used are a stone floor, a brick material that resembles stone masonry, and for the 16th century model, plaster and painted masonry are used to replace ashlar masonry in most of the structure. This change is intended to reflect the modifications in materials that may have occurred during the process of reduction of the temple in the 16th century, using materials in accordance with the period and style. For this reason, certain areas of the ashlar walls are re-covered with plaster and in some surfaces, such as the header wall, masonry painted with evangelical scenes can be found. In addition, different materials are added on specific surfaces such as the door and crucifix, which present a generic wood material; the stained glass of the rose window is assigned a generic glass material; for the openings of the flared windows, an 80% absorbent material is used and for the different stone details such as the arches, columns or capitals, generic lithic materials are used. Table 1 shows the pre-selection and assignment of materials, whose absorption and scattering coefficients can be seen in Figures 5 and 6 respectively.

Table 1.

Description of the materials assigned in the EASE models.

Assigned materials
Material	Nomenclature	Model	Layout
Ashlar	Clay brick	Both	Walls and general 13th century; non-plastered areas 16th century.
Plaster	Masonry-PT	16th	Walls and general structure; generic painted masonry.
Stone floor	Concrete rough	Both	Floor of the building.
Vault	Clay brick-vault	13th	Barrel vault.
Plastered vault	Masonry-PT-vault	16th	Barrel vault with plaster cover.
Stone reliefs	Stone reliefs	Both	Elements with details and reliefs in stone.
Pointed arch	Stone arch	Both	Pointed arch of the doorway and its jambs.
Rose window	Rose window	Both	Glass material assigned to the front rose window.
Wood	Generic wood	Both	Wood material assigned to the crucifix and the door.
Absorber 80%	Absorption at 80%	Both	80% absorption material assigned to the opening of the flared windows.
Public standing	Public standing	Both	Simulates the absorption in the audience areas (approx. 2.7 pers/m²).

With the aim of assessing and quantifying the general acoustic differences that were caused in the temple due to the presence of attendees to the ceremonies in extreme conditions of occupation (church with and without audience), it is proposed to incorporate surfaces at 1 m from the ground that simulate the effect of the presence of audience in the models of the enclosures.¹⁴

In this type of heritage spaces, where reflective materials (stone, plaster, and wood) combine with relatively medium-to-low volumes (500–2000 $m^{3}$ ), it is important to consider the high sensitivity of receivers located in audience areas to variations in sound absorption in the virtual acoustic reconstruction.⁶ Thus, in order to represent the absorbing effect of the audience in a representative way, the material is assigned at a height of 1 m above the floor in each of the zones with possible occupation. The area near the altar corresponds to the officiant’s area; the choir area is located between the center of the enclosure (assembly) and the presbytery or altar. Finally, the public areas (populus) are distributed in three zones: the part closest to the altar or central audience area; the side area, which in the case of the model of the 13th century is the area that would house a large part of the coupled volume of the side nave; and the entrance audience area located close to the front of the church and farther away from the altar.

As for the acoustic characteristics of the material used as an audience to simulate occupation, they reflect the absorbent effect of an audience that would be arranged standing and with a density of 2.7 people per square meter. Obtaining the absorption coefficients of such material and its incorporation into the EASE database has been carried out on the basis of the results presented in.¹⁴

As for the assignment of diffusion to certain surfaces (only to those with complex geometries such as the “Vault,” “Stone reliefs,” “Pointed arch” and “Rose window”), diffusion coefficients are calculated and assigned as a function of frequency; the rest of the surfaces will be considered as flat surfaces. The diffusion coefficients of the barrel vault (“Vault”) have been obtained from the results presented in^11,15,16; the rest have been calculated from the tool Calculate Scattering of the Base Material module of the EASE 4.4 software, basing the calculations on approximations to 1D and 2D figures according to their dimensions.¹⁷

As for the background noise, it is proposed to use the NC-40 curve for the simulations. The decision to use this noise curve is based on two bases: the location of the church in the historic center of the city of Cuenca and the historical context, being in a process of repopulation and reconstruction of the city. In any case, the noise would be higher than that stipulated for the conditions of measurement and simulation in the acoustic characterization of enclosures, that for the case of churches is usually taken as the NC-30 curve. Considering this noise as lower than the noise hypothesis, a somewhat higher curve is taken as the NC-40 for all the models and that in any case will only affect the intelligibility results.

As for the sound source selection, the human male voice source type is chosen from the EASE Speaker Base database. Global Speakers 40. human, specifically the MAN LOUD source. The choice of this type of source seems obvious, since the people involved in the medieval liturgy would be clerics and therefore male in the case of both the officiant and the choir.

With the aim of seeking a representational balance of liturgical participation together with the interest of studying the acoustics of the enclosure more exhaustively, it is decided to place three different source configurations in the temple, as established in similar works in which the positional influence of three specific liturgical zones is analyzed and synthesized in the position of the officiant, choir zone and zone of the assembly/populus.¹⁸ In this way, by individually activating each source configuration, the results and conclusions that show the positional acoustic differences inside the enclosure for each of the models (13th and 16th centuries) and in two different occupancy situations (with and without public) can be drawn.

Officiant configuration. This is an individual source located next to the altar in the typical arrangement of the period. This means that he would be directing the liturgy with his back to the faithful, facing the altar, crucifix and the apse wall.

Choir configuration. This is a group source located between the chancel and the altar. The grouping consists of five individual sources located in a “U” shape. The choice of form and number is based on sonological and phonetic studies of the interpretative practice of Hispanic chant, which supports the position of the clerical choral groups during the medieval liturgy, depending on whether it was antiphonal or responsorial chant.¹⁹

Populus configuration. This is a group source located in the center of the area assigned to the audience, farthest from the altar and arranged in the same ”U” choir configuration. Although the faithful would have had little or no participation in the liturgy of the time, this populus configuration has been included in order to obtain greater representability in the simulations and because it is possible that in certain praises or chants, they could collaborate with the choral group. The arrangement is identical to the choir configuration (five sources arranged in a ”U” shape), and is based on the fact that the objective of the study, in this case, is to verify the acoustic differences that occur in the audience areas depending on whether the three emission configurations (officiant, choir and populus) are activated. Therefore, by moving the choir to the indicated position of the populus, effective comparisons can be established between both simulations, since the results come from the same type of source, varying only the spatial position of emission.

Trying to find a representative balance of liturgical participation, four audience areas are located covering most of the surface of the enclosure. These areas could be separated into two groups depending on the liturgical participation, finding an audience area for the religious officiant, which is located in the area corresponding to the main altar and three audience areas that would be occupied by the assistants.²⁰

These three areas are distinguished according to the social stratum to which they could belong. The audience of the assembly is located in the central area; and in the area farthest from the altar, the one corresponding to the entrance, the royal or high society people. A last audience area is located in a lateral zone, because having two models that differ in shape, it is very interesting for the acoustic study to know the behavior in the lateral nave in the case of the 13th century church. On the other hand, for the reduced 16th century model, that zone would correspond to the area located between the side of the central zone and the side wall facing north, that is, the wall lowered in the reduction of the church. In the 13th century church of Saint Pantaleon, this side aisle could have different uses: it could have been used for royal use because it was a more reserved space, although it could also have been assigned to part of the faithful (populus) or not even used during the course of the liturgy. Figure 7(a) and (b) show the location of the sound sources and audience areas in the models designed for the 13th and 16th centuries respectively; in these images it can be seen that the difference in audience areas between the two models lies in the area of the lateral nave facing north.

Model validation

Due to the current state of the ruins of the church of Saint Pantaleon, it is impossible to carry out acoustic measurements to validate the model as usual.²¹ Therefore, a search for reference studies carried out in churches in contexts similar to that of Saint Pantaleon was carried out, from which four different studies of Spanish churches were selected: the church of Santa Cristina de Lena (Asturias),²² the church of La Vera Cruz (Segovia),²³ the church of Santa Maria de Melque (Toledo)²⁴ and the church of San Cebrian de Mazote (Valladolid),²⁴ which are churches with a style and articulation of space similar to the church that is the objective of this study (Saint Pantaleon) and of which there are also acoustic references with “in-situ” measurements of parameters, which allow us to propose different hypotheses. The choice of these studies and in particular the selection of these churches is due to the fact that they share similarity in volume (all have a volume around 2000 $m^{3}$ ), except the smallest in Lena (Asturias), and the construction period and architectural approach is mostly similar,²⁵ being built in the 9th and 10th centuries for the pre-Romanesque churches and in the 13th century for the Romanesque church of La Vera Cruz. Within this selection of churches, the comparative exception is Santa Cristina de Lena, which differs from the previous ones, being of a significantly smaller volume (370 $m^{3}$ ). The purpose of introducing it into the comparison is to observe the notable differences in the volumes and articulation of the space and its acoustic dependence on building materials of comparable characteristics. Table 2 shows a summary of the characteristics of each church and Figure 8 shows the external appearance of each one, being possible to find more information about their characteristics, plans and inside photos of these churches in the reference studies^22–24 and links provided in Figure 8.

Table 2.

Characteristics of the compared churches.^22–24

Church	Period	Style	Volume (m³)
Santa Cristina de Lena (Lena, Asturias)	9th cent.	Pre-Romanesque // Asturian	370
Santa Maria de Melque (San Martin de Montalban, Toledo)	7th–8th cent.	Pre-Romanesque	1220
San Cebrian (San Cebrian de Mazote, Valladolid)	10th cent.	Pre-Romanesque // Mozarabic	2700
Vera-Cruz (Segovia)	13th cent.	Romanesque	2178
Saint Pantaleon (Cuenca)	13th cent.	Romanesque	2190
Saint Pantaleon (Cuenca)	16th cent.	Romanesque-Gothic	1819

Color cells shown the color that will have each church in the results figures.

In order to contrast the results of the reverberation time $T_{30}$ obtained in the reference studies,^22–24 with the results of the simulation models proposed for the 13th and 16th century for the church of Saint Pantaleon, a simulation was carried out using the AURA module (Aura Mapping based on CESAR algorithms developed by Aachen University-RWTH) implemented by EASE software, which is used to obtain results contrasted with the ISO-3382 (1) standard.²⁶ For each of the models a maximum quality configuration has been performed, that is: particles with very high resolution, length extended, scattering with default S-curve, and orientation point to sound configuration for Lateral Fraction.

The results of the acoustic characterization parameters presented in this article for the Saint Pantaleon models are obtained as an average value of the set of all the audience areas except the one corresponding to the emission area (officiant, choir or populus), with the aim of associating an acoustic perception representative of the areas where the sound emission does not occur and therefore more molded/colored by the enclosure.

Comparing the reverberation time $T_{30}$ shown in Figure 9, a great similarity of the Saint Pantaleon models with the measurement of La Vera Cruz (Segovia) is obtained, which is explained by the similarity in dimensions and materials (both enclosures were originally built in the 13th century). Going deeper into this similarity, the low frequency behavior of the La Vera Cruz church is strikingly similar to that of the Saint Pantaleon model; that could be due to the great similarity in materials, since the Segovian church has ashlar as construction materials (covered at certain points with plaster and paint), which is in exact agreement with the materials assigned in the 16th century model of Saint Pantaleon. This fact can give great credit to the design and the theorization of the materials used, since the Segovian church presents a historical context parallel to that of Saint Pantaleon, with a Romanesque origin of Templar inspiration and transitioning toward a Gothic style in the completion of the work.²⁷

Contrasting the results of the reverberation time with the other pre-Romanesque churches, we found that the church of Saint Pantaleon presents a more reverberant acoustic behavior than Santa Maria de Melque and San Cebrian de Mazote, highlighting that the 13th century model behaves similarly to the church of San Cebrian de Mazote at low frequency, although at mid-frequency there are differences of half a second between the two churches. It is evident that the church with the drastically lower volume, Santa Cristina de Lena, presents drastically lower reverberation times than the rest and therefore, any similar value in the rest of the parameters between the designed models and Santa Cristina de Lena should be unexpected and consequently reanalyzed.

Therefore, the values obtained in the simulation, although they could potentially be adjusted by knowing in depth the sound absorption of the materials originally used in the finishes of the 13th and 16th century, show consistent and contrastable results against enclosures of a similar historical context, period, style and volume.

Regarding the parameters of musical clarity $C_{80}$ and vocal definition $D_{50}$ , shown in Figures 10 and 11, two radically different behaviors are observed. The first corresponds to Santa Cristina de Lena, providing results of great musical clarity and definition that are explained mainly by the great volumetric difference, and smaller relative source-receiver distances derived from a greater articulation in height of the space.

Regarding the second behavior, it could be established that they are similar, increasing in frequency and within a range of values of less than 4 dB for musical clarity and around 10% for vocal definition. Regarding the contrast of the recreated models, the Saint Pantaleon models exhibit coherent behaviors in terms of these two parameters. Entering into the evaluation of the musical clarity parameter and following the range defined by Michael Barron,²⁸ the musical clarity of the church would be poor, taking into account the usual use of this type of places of worship where the importance of the liturgy is more important than other musical aspects.

As for the objective parameters of intelligibility, shown in Table 3, it is difficult to make a strict comparison because the different studies do not provide the same intelligibility parameters. The study of Santa Cristina de Lena is the only one that presents intelligibility values for both ALCons and RASTI; the rest of the studies do not provide the same intelligibility parameters; the other studies only count with the RASTI values. On the other hand, with respect to the speech transmission index (STI) there is the problem that it is available for the simulated models, but the selected studies only have the RASTI available; as both parameters present a great analogy, a comparison can be carried out on the enclosures using the STI values in the case of the simulated ones and RASTI in the studies with measurements.²⁹ This method has been evaluated multiple times, having been validated for several languages and in comparison with other speech transmission rates.³⁰

Table 3.

Comparison of intelligibility with similar churches.

Church	STI/RASTI	ALCons (%)
S.P. 13th (STI)	0.4	16.4
S.P. 16th (STI)	0.5	13.0
S.C. Lena (RASTI)	0.5	11.2
S.M. Melque (RASTI)	0.6	-
S. Cebrian (RASTI)	0.4	-
Vera-Cruz (STI)^a	0.5	-

Simulation results.

The color shown for each church is the same than in results figures.

The results show that all the enclosures present very similar values³¹ about STI-RASTI, which indicates that the simulated models seem to behave coherently, highlighting a better result in Santa Cristina de Lena as expected due to its size, although none of the churches achieves a high intelligibility due to a high reverberation time.

Comparing the models of Saint Pantaleon, it can be concluded that the reduced model with a single nave (16th century) presents better intelligibility for both STI and ALCons. It can therefore be concluded that with respect to the designed models, in terms of intelligibility, the reduced volume of the 16th century enclosure makes the difference despite the fact that it presents less absorbent materials such as plaster or painted masonry. The intelligibility is more conditioned by the acoustic behavior in the bands close to 2 kHz, in fact, between the bands of 1, 2 and 4 kHz most of the speech intelligibility is defined.

Considering this fact and studying the behavior of the reverberation time in these bands, shown in Figure 9, it is explained that because the reverberation is very similar in that bandwidth, the difference lies in the reduction of the total volume of the room that consequently brings an “approach” of the source to the receiver, leading to a slight improvement in intelligibility.

In conclusion, comparing the two models of Saint Pantaleon with the results of measurements made in rigorous studies in places of worship in similar contexts and dimensions, it is possible to affirm that the acoustic model designed is a close approximation to what has been theorized in this project about the disappeared church; the results are coherent and provide sufficiently accurate and contrasted information to give it reliability given the conditions of the simulation.

Results

The simulation approach in each of the four models (13th and 16th centuries in occupied and empty states) follows the same method, where three sets of simulations corresponding to each of the sound source configurations (officiant, choir and populus) are run. In each simulation, the audience areas that do not correspond to the position of the sound source are enabled, therefore, three simulations are performed for each of the models:

Officiant configuration: the vocal source located at the altar is used and the results in the entrance, center and side audience areas are simulated.

Choir configuration: the group configuration of vocal sources placed in a “U” shape at a certain distance in front of the altar is used and the results are simulated at the entrance, side and officiant audience areas.

Populus configuration: the same configuration of vocal sources as for the choir case is used, but now they are moved to the entrance of the enclosure and the results are simulated in the rest of the audience areas (center, side and officiant).

Subsequently, the average value of each simulation is obtained and, from them, an overall average is calculated for each sound source configuration, with spatial representativeness of the acoustics of the church. These average parameters allow comparisons to be made between the different sound emission positions considered. In addition, the results of the three types of simulation are averaged to obtain a global characterization for each model (13th and 16th centuries in occupied and empty states).

In order to synthesize the most relevant results presented regarding the positional differences that occur due to the three possible emission configurations (officiant, choir and populus), the simulation results for the subjective aspects of reverberation (EDT), early lateral energy fraction ( $J_{L F}$ ) and vocal clarity ( $C_{50}$ ) will be presented for each model (13th and 16th centuries), being in these aspects where the most interesting conclusions and significant differences could be found according to.³²

Saint Pantaleon 13th century

The positional differences in terms of initial reverberation time, shown in Figure 12, show practically equal results, parallel behavior and minimal differences between the different positions of sound emission. This is because the volume of the church of Saint Pantaleon is relatively small, which together with low absorbent materials results in a reverberant field with little influence of the position of the sound source. Moreover, in a high reverberation enclosure like this one, with EDT values above 2.5 s below 2 kHz, the acoustic field has a sufficiently diffuse behavior so that the critical distance is very close to the source and therefore, the positional differences are not noticeable according to the initial reverberation time.

Comparing the behavior of the three positions in terms of laterality and spatial effect³³ (Figure 13), it can be seen that if the source is located in the area farthest from the altar, in the so-called populus position, the lateral efficiency is clearly lower than the other two positions. The lower laterality of the populus position may be due to the fact that it is further away from the rest of the simulated positions and in a spatial situation close to the entrance of the church, where the projection of the populus vocal configuration is not efficient in terms of spatial effect on the rest of the audience areas. However, the choir and officiant sources, which following the ecclesiastical tradition of the time, were focused toward the altar, leaving the audience and most of the volume of the room behind them, are the ones that obtain a greater spatial effect, which is reflected in higher frequency behavior than that obtained for the populus, and greater for the choir configuration, possibly due to a greater centrality on the articulation of space.

Specifically, the highest laterality coefficients are located in the side nave when the choir and officiant sources are activated, which can be explained by the fact of having an added volume and the pointing of the sources toward the altar, further enhancing the fact that there is a greater spatiality behavior in the side nave.

Analyzing the positional differences related to vocal clarity in the 13th century model, shown in Figure 14, it can be observed that in low and medium frequency the positions of choir and populus present a similar result. The performance in this bandwidth of both positions improves by 1 dB the results provided by the officiant’s position. At high frequency, the two curves that were similar are separated, establishing a range of differences of 1 dB between the three positions. Thus, the best result is obtained when the populus source is emitting, followed by the choir source and the worst result is obtained for the officiant position. If attention is paid to the just noticeable differences (JND) related to vocal clarity, the differential threshold is set at 1 dB and therefore, there should be differences in the perception of vocal clarity in the different positions of the temple.

Apart from the average value of each energetic parameter shown above, it could be interesting to show and analyze the spatial distribution of these parameters. In that way, their spatial behavior shows some dependence on the distance to the source and the development of the reverberant field, with high values near the source, and becoming more homogeneous as the reverberant field dominates in areas farther away.

Thus, and taken into account the amount of graphics for each parameter, sound source and frequency band, only a map has been included as an example for the vocal clarity at the frequency of 1 kHz (Figure 15) when the officiant and choir sources are active to simulate a typical liturgical situation derived from the Hispanic rite, in which there is a “dialog” between the officiant and the choir, the officiant recites a verse and the choir responds.

Regarding the STI and ALCons parameters shown in Table 4, the simulations show a better result in the position of the choir. Consistently, the sources located in central positions of the temple present better intelligibility and the worst value is located in the officiant position, mainly due to higher position gradients of source-receiver. Therefore, the choir source located in the center of the room presents the smallest distances with respect to the rest of the audience areas, and it is the one that shows a notably more intelligible result. Regarding the results of the simulation in relation to intelligibility, it should be noted that the officiant’s source is individual, while the choir and the populus are formed by a ”U” configuration of five sources, which has a significant effect on the sound energy emitted and therefore also on the ratio of sound pressure levels received in the audience areas.

Table 4.

Intelligibility for the 13th century model.

Source configuration	STI	ALCons (%)
Officiant	0.4	23.6
Choir	0.6	7.3
Populus	0.4	18.3

The color shown for each source is the same than in results figures.

Saint Pantaleon 16th century

As in the case of the 13th century model, the differences in initial reverberation time, shown in Figure 16, determine that the responses in initial reverberation time have a similar behavior. In fact, since the room is more reverberant than its predecessor, the positional differences relative to the reverberation time are hardly noticeable.

The laterality behavior shown in Figure 17 is very similar to that developed in the positional analysis of the 13th century. It can be seen that the populus position has a laterality around 10% lower than the rest. The source position with the highest laterality is located in the officiant’s, which in medium and high frequency presents a $J_{L F}$ that exceeds 32%. The three positions present a great similarity in their spectral behavior, since despite the numerical differences, the behavior of the graphs follows the same pattern, finding a stable value at low frequency (25% for the populus position and over 29% for choir and officiant) that grows at medium frequency and stabilizes toward high frequency (values close to 32% for choir and officiant) except for the populus position. While the other two positions stabilize at high frequency or show a very slight decrease, the populus position is characterized by a clear decrease in high frequency, going from values above 29% in the third octave of 1 kHz to drop to 23% at 10 kHz.

Regarding the positional differences in the calculation of the vocal clarity of the enclosure, shown in Figure 18, all the sources present a behavior coherent with the studies taken as reference and similar in frequency behavior for all the emission positions (officiant, choir and populus), although with quantifiable differences. The officiant position is the one with the worst results, due to the fact that it is an individual source oriented with its back to the audience areas and therefore with less vocal projection due to the characteristic directivity pattern. The next position in terms of vocal clarity is the choir position, with a difference of 2 dB above the officiant result, while the difference with the populus source is 1 dB at mid-frequency and up to 2 dB at high frequency. Finally, the populus position shows the best performance; the reason for this better result is due to the fact that this source configuration is grouped and, being located in the closest part to the entrance of the church, pointing to the head of the church, it has the rear surface of the entrance and nearby side surfaces that allow the sound to be projected toward the head of the church, which allows a greater amount of direct energy than for the other emission zones (choir and officiant).

As for the 13th century, in Figure 19 the distribution of the vocal clarity parameter is shown for the 16th century model when officiant and choir sources are active, being possible to observe the same results of a higher value near the sound source and more homogeneous values as the reverberant field dominates.

Studying the positional differences of the 16th century regarding intelligibility, a better intelligibility response is obtained when the emitting source is the choir, due to the centered position of this source and to the fact that it is a group source, as shown in Table 5. Among the sources farther away from the center of the enclosure (populus and officiant), similar results are obtained despite the fact that the populus source is a group source.

Table 5.

Intelligibility for the 16th century model.

Source configuration	STI	ALCons (%)
Officiant	0.5	13.6
Choir	0.5	8.7
Populus	0.4	16.5

The color shown for each source is the same than in results figures.

Comparison among Saint Pantaleon models

A comparison is stated in this subsection about the behavior of the models in two different occupancy states: occupied and empty. As can be seen, the absorbing effect of the audience is clear, radically reducing the reverberation time shown in Figure 20. At low and high frequencies, the difference is more than 1 s, while at medium frequency the models without audience present a reverberation time of more than 2 s difference. Regarding the reverberant maximum in the 250 Hz octave, for the 16th century model with full occupancy, it is practically aligned with the trend of the rest of the curve, although it is possible to intuit an incidence in that band since, despite being quite flattened, it still conserves the absolute maximum of the curve.

These higher EDT values observed in the low-frequency range, centered around the 250 Hz band, may be attributed to strong interactions between the barrel vault geometry and the flat floor surface, an effect further reinforced when the enclosure exhibits clear symmetry along the east–west longitudinal axis, as in the 16th century model. Moreover, the reference studies used for result comparison also show increased low-frequency reverberation, closely matching the behavior of the Vera-Cruz church and, to a lesser extent, that of San Cebrián de Mazote.

Due to the presence of more absorbent enclosures in the occupied state, the parameters of musical clarity (Figure 21) and definition (Figure 22) improve their results in both cases. The biggest difference between occupied and unoccupied modes is again in the mid-frequency, where a higher absorption due to the audience is stated; in addition, at high frequency, the frequency response of the models tends to converge due to the effects derived from air absorption. As for the intelligibility of the models, shown in Table 6, worse results are obtained in those that present an unoccupied state, associated with a higher reverberation time with values above 1.5 s practically for the entire frequency range of simulation.

Table 6.

Comparison of intelligibility results for the two models (13th and 16th centuries) in occupied conditions and empty church.

Model	STI	ALCons (%)
S.P. 13th	0.4	16.4
S.P. 16th	0.5	13.0
S.P. 13th Full	0.6	7.6
S.P. 16th Full	0.6	8.4

The color shown for each model is the same than in results figures.

Comparing the unoccupied 13th and 16th century models, there appears to be better musical clarity and definition in the 250 and 500 Hz bands for the 13th century model. This difference is as much as 2 dB in musical clarity ( $C_{80}$ ) and of 5% in vocal definition ( $D_{50}$ ); in the mentioned bands and from the 1 kHz band onward, they show similar values in both parameters. For intelligibility values, they are very similar in the STI, although the 16th century model presents a slightly better result, with a loss percentage of 3% less.

Definitely, it can be stated that the 13th century model presents a slightly less reverberant behavior compared to the 16th century model at low frequency. Therefore, the difference in most parameters between the two models is centered in this bandwidth. As a key aspect of this comparison, it should be noted that the intelligibility is better for the more reverberant church (16th century model), especially in the ALCons parameter, which indicates that the reduction of the volume of the church predominates over the somewhat more reverberant effect of the materials used, in terms of intelligibility. Evaluating the models in the occupied state, it should be noted that the increase in the acoustic absorption of the church leads to significant differences in the parameters, resulting in a less reverberant room with greater musical clarity, definition and intelligibility. On the other hand, the inclusion of the public in the enclosures does not alter to a great extent the parameters related to the laterality of the acoustics inside the church.

Conclusions

This paper shows the documentation process of the disappeared church of Saint Pantaleon, in Cuenca (Spain), with the aim of extracting relevant information from the perspective of acoustics. This technical information on the possible structure of the enclosure, as well as on the materials that could make up the building, has made it possible to generate detailed models that were subsequently analyzed acoustically by means of simulation.

In this process it has been possible to verify that the models, although they present a high degree of hypothesis about how the temple could have been, provide highly reliable results in the simulation.

Since in-situ measurements cannot be made, the validation of the model has been carried out by checking if the generated models present acoustic behavior coherent with reality by means of a comparative contrast. This comparative test aims to contrast the designed models with worship enclosures of similar contexts, being able to establish great similarities between the behavior of the models of Saint Pantaleon with the churches of La Vera Cruz (Segovia), Santa Maria de Melque (Toledo) and San Cebrian de Mazote (Valladolid). The comparative contrast provides very positive results on the designed models, which show similar behaviors to the rest of the enclosures.

Comparing the two models of Saint Pantaleon, corresponding to two different periods: 13th century and 16th century, it is observed that after the reduction of the temple and the inclusion of new materials during the 16th century, a more reverberant enclosure is obtained in low frequency, presenting worse values of vocal clarity and definition. On the other hand, the 13th century temple results in a worse intelligibility due to its higher volume and, therefore, greater relative distances between the source and the listening position.

Regarding the positional differences, it is verified that there are no great differences in the reverberation time among the different source positions in both models. The magnitudes that present more differences among the different locations of the sound source are those related to vocal clarity and laterality of the enclosure. As for vocal clarity, it is observed that at high frequency the populus position stands out among the others. And about the $J_{L F}$ parameter, the same position presents a laterality behavior of about 10% lower than when the source is placed in the choir and officiant positions.

Comparing the states of occupation, it is found that the inclusion of the public inside the church has a significant effect on the acoustics of the room. In this way, a much more absorbent room is obtained in the occupied models and, as a consequence, the acoustic parameters present greater musical clarity, definition and intelligibility and shorter reverberation time.

Eventually, this paper reflects the achievement of characterizing the acoustics of the disappeared church of Saint Pantaleon in Cuenca (Spain), by means of simulation and recreation of its acoustic space, using for the validation of the model a method by comparison with other churches due to the impossibility of performing in-situ measurements.

Footnotes

Acknowledgements

The authors would like to thank the Consortium of the City of Cuenca for making available the documentation necessary to carry out this research.

ORCID iDs

Samuel Quintana

José A. Ballesteros

Marcos D. Fernandez

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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