© The Author(s), Published by EDP Sciences, 2024

1 Introduction

1.1 Acoustics in the 17th century

Only after Wren’s death, the wave equation was described (d’Alembert, 1743). Moreover, it was not until the late 19th century that the principles of modern room acoustics, useful in architectural acoustic designs, were formulated by W. C. Sabine [1]. However, many concert halls and theatres in the UK from before Sabine, are known for their good acoustics, such as the Sheldonian Theatre (Wren, 1669) and the Royal Institution’s Theatre (Saunders, 1802) [2]. It is therefore interesting to explore how pre-Sabine architects, like Christopher Wren, approached designs for acoustically suitable spaces and what theories they based themselves on. In this section an overview is given of the acoustic design approaches known to be applied in 17th-century Europe, as found through literature study. It is relevant to place and compare Wren’s work in its 17th-century context concerning acoustic knowledge. In Sections 1.2 and 1.3, an in-depth analysis of Wren’s own approach to acoustics is provided.

1.1.1 Marcus Vitruvius Pollio (±85–20 BC) and the wave metaphor

The wave metaphor introduced by Vitruvius in his De Architectura, Libri Decem was used in the Middle Ages and Renaissance to explain sound propagation through the air. In his fifth book, dedicated to the design of Roman theatres, he tackles topics such as sound propagation and reflection, material properties, echoes, and reverberation ([3], 1st cent. BC). Although most of his statements were incorrect given today’s acoustic knowledge, as early as the first century AD, there was an idea of sound as a concentrically expanding ripple through the air that reflects on objects (but however neglects frequency). Furthermore, Vitruvius argues that actors’ voices should meet no obstruction in order to reach the top of the audience and create favourable room acoustic conditions. Therefore, a theatre should be designed in a way that one straight line can be drawn to connect the tops of all the rows of seats ([3], 1st cent. BC).

Since the “rediscovery” of his work in the 15th century, a lot of influential translated editions spread through the Western countries, including England. Reading Vitruvius would be part of every self-respecting architect’s training. Wren’s own writings, studied by L. Soo, prove that he made a close study of Vitruvius [4]. Vitruvius’s approach influenced room acoustic designs as his manuscript was probably one of the sole available set of acoustic guidelines up until the end of the 17th century (2]. His theories led to rounded auditorium shapes and avoidance of obstructions in designs, but however held limitations for indoor spaces [2].

1.1.2 Geometrical acoustics

The 17th century saw the advent of geometrical acoustics, which attempted to mathematically underpin acoustic phenomena [5]. In this approach, the propagation of sound was understood in the same way as light rays travelling through a room and reflecting off surfaces. This way, its propagation could be represented in the same way by direct lines striking all forms of surfaces at a given angle, and Snell’s law of optics (angle of incidence equals angle of reflection) could be applied to them. The geometrical method was mainly used to explain some acoustic phenomena, such as sound reflections (typically referred to as “echoes”), based on particular formal properties of the space and the acoustic focus point(s) in the room. Architects (mainly Italian) employed the guideline by optimally shaping the room to “guide” the sound [2]. The similarity of light and sound was first hypothesised through experiments by Giuseppe Biancani (1566–1624). He was an Italian Jesuit scientist who followed the geometrical approach in his study of echoes in his book Spherae Mundi published in 1620. He named the study of echoes “Echometria”, making it a field of study in its own right [6]. The geometric acoustics approach inspired architects to construct curved or hyperbolical shaped walls as they horizontally spread rays evenly [2]. On the contrary, proscenium ceilings should remain flat in order to avoid sound concentrations [2].

1.1.3 Echo theories

A lot of different echo theories were developed in the 17th, 18th and 19th century. In general, they have in common to quantify (in distance and/or time units) the perception threshold between direct sound and first order reflections [7]. Today, acousticians would describe this as early reflections and would agree that the arrival time between direct and reflected sound should be limited in order to provide satisfactory acoustic environments [7]. The development of the parameters Clarity, Definition, Initial Time Delay Gap (and other) in the 20th century still indicates the importance of designing with early reflections.

Following the example of Biancani in 1620, other scientists such as the French polymath Marin Mersenne (1588–1648) in 1636 and the Jesuit scholar and polymath Athanasius Kircher (1602–1680) in 1673 studied echoes and tried to generalise a theory of sound propagation. Kircher was particularly interested in the study of echoes in rooms with an elliptical, hyperbolic, or parabolic shape that project the voice and function as architectural resonators [8]. Although Biancani, Mersenne and Kircher all attempted to pinpoint the speed of sound, none of their general theories could accurately explain room acoustics effects such as flutter echoes and reverberation. Depending on the assumed speed of sound and research method, different authors found different outcomes, consequently used as guidelines in acoustic design [7]. Postma and Katz found that “echo theory” was used in the design of at least seven venues with both speaking and hearing purposes [7].

1.1.4 Copying and upscaling

Unlike previous approaches that were more physics based, van Royen and Barron respectively discussed practices of “copying” and “upscaling” the dimensions of auditoria that were considered acoustically satisfying [9, 10]. For example the Concertgebouw (1886, NL) small concert hall, copied from the Felix Meritus hall (1788, NL) or the Wiener Musikvereinssaal (1780, AT), which had been upscaled from its predecessor, the Redoutensaal (1748, AT) [9, 10].

1.1.5 Principle based on the propagation of the human voice

Postma et al. also studied an alternate metric guideline, considering the directivity and propagation distance of the human voice [2]. It is based on Vitruvius’s approach of sound circulation and “unobstructed propagation” [2]. A number of studies were carried out to determine the distance at which a human voice is still audible or intelligible. Different experiment conditions lead again to different outcomes.

The design of oval and rectangular shaped auditoria for speech and music, and the limitation of its dimensions were direct results from this approach. Postma et al. discovered it to be used for the design of at least 11 venues both for music and speech in Europe and the USA [2]. Sir Christopher Wren also mentions some minimum intelligibility distances in rooms without describing how that he obtained this data. Postma et al. suggest that Wren’s designs of the Sheldonian Theatre (1669) and the College of Physicians (1675) followed his own guidelines on the minimum intelligibility distance [2].

The literature review showed that until Sabine, no single commonly accepted theory could be of guidance to architects to design spaces with suitable acoustics. On the contrary, architects would apply different approaches and theories or a combination thereof, as we’ll see will also be the case for Wren.

1.2 Wren’s take on room acoustics

Christopher Wren, the protagonist in this research, although most famous for his work as an architect in London, was above all a scientist. He was educated in Latin and Aristotelian physics at the University of Oxford, and in 1657 appointed Professor of Astronomy at Gresham College, London. His knowledge of mathematics legitimized his architectural profession, as the latter was in the 17th-century generally understood as an applied mathematical science, including material studies, geometry and structural statics, perspective and proportion [11]. Moreover, Wren was a co-founder and president (1680–1682) of the Royal Society, the first British chartered public institution devoted to the corporate pursuit of scientific knowledge founded in London in 1660 [12]. The institution consisted of many well-known British scientists, many of them studying acoustic phenomena: Robert Hooke, George Sinclair, Robert Plot, Walter Charleton, Robert Boyle, and Charles Leigh. They were however primarily occupied studying the motion of strings and pendulums (linked to the Royal Society’s broader study programme of objects in motion) and some specific echo cases, instead of analysing the propagation of sound itself or room acoustics [13]. Robert Hooke formulated Hooke’s law in 1676, describing a linear relationship between the force applied to a spring and its compression or elongation. This insight was not only useful in areas such as mechanics but also in acoustics. The Society’s research was however of no or limited use to architects. They would nevertheless inspire experiments in the field of room acoustics decades later [14]. Furthermore, Robert Hooke, was a good friend of Wren, and was equally appointed by the Commission to collaborate with Wren on the rebuilding of the parish churches after the Great Fire of 1666. While it is plausible that Wren and Hooke discussed the acoustics of the rooms that they designed and built, actual proof of this could not be found. Nevertheless, several excerpts from Wren’s writings offer a clear indication of his conscious approach to sound design in the new churches.

Although no acoustic experiments led by Wren have been recorded in the Society’s transactions, Wren very likely was present during discussions concerning echoes and acoustic experiments carried out by Robert Hooke (and the other above-mentioned scientists) on behalf of the Royal Society [14]. The Society held periodical meetings concerning experiments and their research and had close ties with fellow scientists across Europe [15]. To conclude: One way or another, Wren would probably be up to date with the latest theories and experiments concerning acoustics from the Royal Society but also from the European scientists as discussed above (Sect. 1.1). Therefore, in this study we assumed that Wren’s recommendations about acoustics in parish churches were mainly based on the experience gathered during his 40-year long career as Surveyor General for the church rebuilding Commission and on his exchanges with fellow scientists, mainly in the Royal Society. As we will see in the following section, Vitruvius’ texts, theories of reverberation and human voice propagation and the concept of speech intelligibility were fundamental to Wren’s concept of the “auditorium church” and guided his parish church designs.

1.3 Excerpts from Wren’s writing: “churches fitted for auditories”

Christopher Wren was responsible for rebuilding of 52 parish churches in 17th-century London after the Great Fire of 1666. By 1708, a second act of Parliament for building an additional 50 new parish churches in London passed. Christopher Wren, being in his 70s by that time, was still part of the Rebuilding Commission, but too old to keep his leading role as an architect. Instead, in 1711 he left a memorandum containing recommendations for the building of the new churches based on years of experience (Whinney, 1971). In this text, Wren states that his parish church designs are “fitted for Auditories” (Wren et al. [16]):

“The churches therefore must be large; but still, in our reformed Religion, it should seem vain to make a Parish-church larger, than that all who are present can both hear and see. The Romanists, indeed, may build larger Churches, it is enough if they hear the Murmur of the Mass, and see the Elevation of the Host, but ours are to be fitted for Auditories. I can hardly think it practicable to make a single Room so capacious, with Box pews and Galleries, as to hold above 2000 Persons, and all to hear the Service, and both to hear distinctly, and see the Preacher.” (Wren, 1711).

Apart from gaining insight in the acoustic principles Wren used for his church designs in the 17th century, the value of the letter consequently lies in the fact that it offers insights in the principles Wren applied in his church architecture in response to the liturgical needs of the High Church worship [17]. The Book of Common Prayer set the liturgy of the Church of England since its reintroduction under the Act of Uniformity of 1662. It prescribed that the whole congregation should participate actively in the church service with a clear emphasis on the sermon and the Service of the Word. For Wren, this meant that the congregation could hear and see the service properly when conducted both at the pulpit and the altar [18]. By “hearing”, it is assumed in this study that Wren means “understanding”. “Understanding” was not yet commonly introduced in the 17th century, as can be read in dictionaries from that time. For “hearing”, the definition is: To Hear: To receive a Sound or Voice by the Ear, to examine a Cause as a Judge does [19].

This can only be achieved in a church with limited capacity and dimensions, so the people present would sit at close range from the pulpit and the communion table [18]. Furthermore, in the same letter Wren includes a section dedicated to the placing of the pulpit and the pronunciation of the preacher. Wren prescribes exact distances from which the “voice” of a preacher in his pulpit “may be heard”:

“Concerning the placing of the Pulpit, I shall observe – A moderate Voice may be heard 50 Feet [15.2 m] distant before the Preacher, 30 feet [9.1 m] on each side, and 20 [6.1 m] behind the Pulpit” (Wren, 1711)

The previous two statements can be categorized as the principle based on the propagation of the human voice, as discussed previously (Sect. 1.1). Wren followed his own practical set of distance values to the front, rear and back of the speaker until where his voice was deemed sufficiently audible or intelligible, resulting in limitations for the dimensions of a church. Limitations regarding the height of the church are not mentioned. It is unclear whether Wren understood the impact of the volume of a room on the reverberation in a church.

Wren continues:

“and not this, unless the Pronunciation be distinct and equal, without losing the Voice at the last Word of the Sentence, which is commonly empathical, and if obscur’d spoils the whole Sense. A French Man is heard further than an English Preacher, because he raises his Voice, and not sinks his last Words: I mention this as an insufferable Fault in the Pronunciation of some of our otherwise excellent Preachers; which School-masters might correct in the young, as a vicious Pronunciation, and not as the Roman Orators spoke: For the principal Verb is in Latin usually the last Word; and if that be lost, what becomes of the Sentence?”. (Wren, 1711)

Wren was obviously aware of the fact that the way a sermon was preached affected speech intelligibility, and that the latter differed from one language to another. While the Romans placed more emphasis on the last word of a sentence (since this was the usually the verb in Latin), the intonation in the English language drops off towards the end, arguably to the detriment of intelligibility.

The importance of speech intelligibility also guides Wren in defining principles concerning a church’s dimensions and capacity. While architects building churches in the Classical style had concentrated on recreating “correct” biblical and classical proportions [20], Wren on the contrary clearly deviates from these ideals, proposing a compromise between architectural aesthetic values (a classical ratio of 2:3 is seen as beautiful) and functional requirements [21]. Wren is thus not copying or upscaling acoustically satisfying venues to steer his designs (see Sect. 1.1.4). He mentions that the proportions can be changed, but one must be careful not to increase the size of the church too much, as this reduces the visibility and the speech intelligibility inside:

“By what I have said, it may be thought reasonable, that the new Church should be at least 60 Feet [18.3 m] broad, and 90 Feet [27.4 m] long, (…). These Proportions may be varied; but to build more room, than that every Person may conveniently hear and see, is to create Noise and Confusion.” (Wren, 1711)

By “noise and confusion” Wren most likely means reverberation. Reverberation can be defined as a distorted copy of a signal that can confuse the speaker and/or the audience. Indeed, as is known in modern-day room acoustics, increasing the volume of a room results in an increase in the reverberation time and an overall reduction of the speech intelligibility.

While it was most probably Wren’s own experience as a churchgoer and architect that made him reflect on modern acoustic principles of speech intelligibility and reverberation, as a member of the scientific vanguard he was probably also aware of Vitruvius’ wave metaphor and theories on “unobstructed propagation”. Of all the parish churches that Wren designed, he singled out St James Westminster as the one that was most fitted for an auditorium. He argues this by saying that St James has no internal walls, but that the barrel-vaulted ceiling rests on columns. Indeed, there are no internal walls to block vision or scatter sound.

“I endeavoured to effect this, in building the Parish Church of St. James’s, Westminster, which, I presume, is the most capacious, with these Qualifications, that hath yet been built; and yet at a solemn Time, when the Church was much crowded, I could not discern from a Gallery that 2000 were present. In this Church I mention, though very broad, and the middle Nave arched up, yet as there are no Walls of a second Order, nor Lanterns, nor Buttresses, but the whole Roof rests upon the Pillars, as do also the Galleries; I think it may be found beautiful and convenient, and as such, the cheapest of any Form I could invent.” (Wren, 1711)

Wren continues:

“A Church should not be so fill’d with Pews, but that the Poor may have room enough to stand and sit in the Alleys, for to them equally is the Gospel preach’d. It were to be wish’d there were to be no Pews, but Benches; but there is no stemming the Tide of Profit.” (Wren, 1711)

As previously discussed, Wren prefers openness in a church, which has a favourable impact upon visibility and audibility. Even though his preference for a church without box pews seems to be mainly motivated by “democratic virtues”, the idea does resonate well with his thoughts about openness. Box pews at the time were more comparable to the shape of a modern-day office cubicle. They enclosed a small area in which a few people could sit and could be as high as the height of an average adult male at the time (~170 cm). Wren talks about profit; he refers to the common practice of renting out box pews. This is information gathered from our visit to St Mary Abchurch (see Sect. 2.5).

In Wren’s reports about his recommendations for consolidation of old Saint Paul’s Cathedral (1666), Wren provides arguments for the inclusion of a dome at the cathedral’s crossing (Wren, 1666). Wren mentions that the space under the dome is an ideal place for an auditorium. Could this be based on the theory of geometrical acoustics that provides proof that domes concentrate sound? Whether Wren was not only doing this for visual reasons, but also with improving acoustics in mind, is not known.

“I cannot propose a better Remedy, than by cutting off the inner Corners of the Cross, to reduce this middle Part into a spacious Dome or Rotundo, with a Cupola, or a hemispherical Roof, and upon the Cupola, (for the outward Ornament) a Lantern with a spiring Top (…) By this Means the Deformities of the unequal Intercolumniations will be taken away; the Church, which is much too narrow for the Heighth, render’d spacious in the Middle, which may be a very proper Place for a vast Auditory” (Wren, 1666).

This review shows that, instead of belonging to one of the existing acoustic theories in the 17th century, Wren’s concept of an auditorium church is based on a combination of information provided by these theories, probably moulded by his own lifelong experience as an architect.

1.4 St Stephen Walbrook

The church of St Stephen Walbrook is often mentioned in literature as being the most refined and sophisticated parish church Christopher Wren ever designed [22]. Around 1670, Wren was working on remarkably similar looking (centralised) design plans for St Paul’s Cathedral, of which St Stephen Walbrook is said to be a kind of conceptual rehearsal. In Figure 1 it can be seen how the typologies of the Latin cross and the centralised plan are merged. J. A. Bennett calls the church of St Stephen Walbrook “a clear display of geometrical principles” (Bennet, 2002).

Figure 1 Structural floor plan of St Stephen’s Walbrook as a combination of a Latin Cross typology (blue) and a centralised design plan (pink).

At the crossing, eight Corinthian columns support eight pendentives that carry the hemispherical dome. In the longitudinal direction, the pendentives transition to cross vaults while in the transept the arches open to barrel vaults. The nave is flanked by two side aisles covered by flat ceilings which are supported by 16 Corinthian columns. The flat ceilings are connected to the dome via half cross vaults, fitted with clerestory windows that let in extra light into the dome and church, giving it a spacious feeling. Although the church is rather small (± 18 m × 25 m) with a volume of approximately 5262 m³ only, the large open space under the dome and its slender supporting columns reminds of the church’s “auditorium” character. This is in contrast to the English medieval church, which was conceived as a succession of self-contained compartments, where the church architecture and liturgical furniture (e.g. chancel screen and rood loft), visually and acoustically obstructed the congregation seated in the nave (Addleshaw et al., 1946). Instead, Wren’s church designs were made according to the liturgical considerations of the time about the importance of seeing and hearing the priest. This meant that he favoured large undivided spaces having clear lines of sight with minimal obstructions [23]. The design of St Stephen Walbrook as a combination of two typologies was made with maximum openness and minimum visual obstruction ensuring that the preacher was visible [24], corresponding also to Vitruvius’ obstruction theory.

It is important to note that the Anglican Church kept a close eye on Wren’s designs and ensured that the churches were suitable for Anglican worship [25]. Some of the interior layout choices for St Stephen’s Walbrook indicate that Wren as a commissioner had no say in the furnishing of the parish church(es), as was usually the case [26]. Moreover, those who designed the church fittings did not always understand his architectural intentions. Firstly, the box pews were placed longitudinally, without regard to the dome and central plan, which does not allow for glorious use of the central space under the dome [27]. The box pews were removed in 1888 [27] and have been replaced today by smaller benches (Fig. 2). Secondly, a painting used to cover the main east window from approximately 1776 to 1850 [22]. It certainly cannot have been Wren’s intention to darken an auditorium church, since one of its main guiding concepts is to be able to follow Mass properly and see the preacher.

Figure 2 Picture of the area under the dome of St Stephens Walbrook with the current altar designed by Henry Moore in 1978.

Figure 3 Edmund H. Sedding’s section of St Stephen’s Walbrook (Sedding [29], lithographed print).

The outer walls of the church measure 60 × 82 feet (18.3 × 25 m). As mentioned above, Wren recommends that the dimensions of the parish churches should measure approximately 60 × 90 feet (18.3 × 27.4 m). This ensures that nobody is seated too far away from the preacher [18].

2 Measurements and simulations

2.1 Measurements

Several integrated room impulse response measurements were performed in situ using an exponential sweep signal with a length of 10.9s and 1–2 repetitions. In total, 5 sources and 9 receiver positions were chosen, and measurements were performed with 14 source-receiver combinations of these. Measurement points were determined strategically, avoiding locations near walls or other objects (min 1 m distance), but ensuring a good spread throughout the room (Fig. 4).

Figure 4 Plan view of the reconstructed 3D model (based on 2022 condition) with indication of source positions (S#) and microphone (receiver) positions (M#). On the left side a list of all source-receiver combinations measured on site.

A Brüel & Kjaer OmniSource Sound Source Type 4295 was used in combination with a Brüel & Kjaer type 2716 amplifier. The data acquisition was done with a Mac computer running REW (https://www.roomeqwizard.com/).

The temperature and relative humidity were carefully monitored throughout the measurement and averaged (within ISO limits) as well. A 3D LiDAR scan of the floor was made to record the relative positions of source and receiver positions quickly and accurately (approx. 10 cm accuracy is sufficient for these purposes).

Other 3D LiDAR scans were used in combination with manual measurements, laser scanner measurements and historical plan material to allow for a virtual reconstruction of the church.

2.2 3D reconstruction and simulation

To facilitate the investigation into the different virtual scenarios inspired by Wren’s recommendations (see Sect. 3), the 17-century church dimensions and interior configuration were virtually reconstructed in SketchUp Pro 2022. Based on a critical assessment of the accuracy of the available source material, it was chosen to base the reconstruction model on two main historical sources: The historical plan drawings by John [28] and Edmund H. Sedding [29]. Lacunas or uncertainties from these historic sources were completed with manual hand measurements on site with use of digital measuring tools such as a Leica Disto X310 laser meter and an iPad Pro LiDAR scanner. The combination of both historical plan analysis and on-site measurements resulted in a digital reconstruction which was accurate enough for the purpose of the acoustic analysis. Attention was paid to possible material changes during the 20th-century restoration campaign [30, 31], not least to the repairs of the damage incurred in the last World War [32].

All the decisions made for constructing the 3D model of the Church of Walbrook, are recorded in a Metafile [33]. This document keeps record of the source and the degree of hypothesis of each modelled building element and attaches a colour code (Tab. 1). For the model, an accuracy of approximately 20 cm was applied. The result is a coloured 3D reconstruction model indicating a degree of hypothesis for each element (Fig. 5). Most of the surfaces with a significant impact on the room acoustic field could be assigned a degree of hypothesis equal or lower than 1, indicating a high level of reliability in that area.

Figure 5 Isometric section view (north facing).

Furthermore, an analysis of the materials in the church of St Stephen Walbrook was conducted. This included the church’s (interior) construction materials as well the as the interior furnishings. Because the interior furnishings had changed over time, a reconstruction model of the 17-century configuration was made as well as a model for its contemporary state. In order to do this, a comparative study was made of historical interior paintings and drawings of St Stephen Walbrook mostly found in the London Metropolitan Archives and the British Museum. For both models, materials and their acoustic responses were estimated.

2.3 Geometrical acoustic model calibration

The SketchUp model of St Stephen Walbrook in its 2022 configuration was imported in Odeon^® software to which 18 different interior surface materials with differing absorption and scattering coefficients were assigned. The software uses an algorithm that combines the image source method (ISM), the ray tracing method (RT), the early scattering method (ESM) in combination with a ray-radiosity method to compute the impulse response in any chosen location in the model. The impulse response is then analysed in many different standardized (ISO 3382) ways to assess the reverberation, Clarity, and speech intelligibility in a room.

The geometrical details smaller than 20 cm were generally not modelled but compensated for by higher scattering coefficient values (recommended by the Odeon user’s manual and previous experience of authors). These include the plaster mouldings on the dome surface, rough surfaces on the wainscotting, the organ pipes and various other rough surfaces (mainly plaster mouldings).

In an initial phase, only reverberation time (measured in situ) was used for calibration of the model (i.e., to fit simulated and measured values of T₂₀). It was challenging to explain the rather short reverberation time at low frequencies at first. A deeper investigation into the composition of the materials used in the church revealed that significant low frequency absorption was exhibited by the many wooden furnishings and roof constructions in the church. Some of these wooden furnishings, such as the wainscotting on the lower part of the walls, the plastered wooden vaults, the flat wooden ceilings, all have air cavities of different depths situated behind them. These cavities are the likely cause of extra low frequency absorption that was needed to match the simulated reverberation time to the measured values. Also, when analysing historic photographs of the war damage, the dome was found to be made from wooden beams covered by planks subsequently covered in plaster [34]. As a result, some additional low frequency absorption was also attributed to the inside of the dome. Lastly, is important to note that the horizontal ceilings of the church’s side aisles, covering 49% of the church’s surface, strongly reduce the volume (and thus the RT) of the church.

The integrated genetic material optimizer module in Odeon that allows for a multi-parameter automatic optimisation based on a fitness function [35] was used to optimize the absorption coefficients in the room. T₂₀ and C₅₀ were consequently both used as calibration parameters in this study.

The resulting sound absorption coefficients are given in Table 2. Each material was allowed to change to a certain degree (in percentage) by the algorithm, indicated as “Genetic algorithm freedom”. Materials of which the freedom is set to 0 are assumed to be already optimized before running the genetic algorithm, they were not included in the optimization.

The resulting room acoustic parameters fit after optimisation are shown in Figures 6 and 7. The Reverberation Time (T₂₀) and Clarity (C₅₀) were used as optimisation parameters for all the 14 measured source-receiver combinations (Sect. 2.1). The fit for reverberation time was much better than for C_50. No further iterations or actions were taken to improve the fit for Clarity. The main reason is that Reverberation time is more robust parameter, which is quasi position-independent over the room and Clarity is more sensitive to details, which could have played a role due to model simplification. Lower C50 values for simulations in comparison with measurements were found around 250–500 Hz. This can be caused by diffraction of sound from interior elements in the room.

Figure 6 Comparison of mean measured and simulated values of T20 in seconds.

Figure 7 Comparison of mean measured and simulated values of Clarity C50 in dB.

The Just Noticeable Difference between measured and simulated values are given in Figure 8.

Figure 8 Averaged just noticeable differences between measured and simulated values of T20 and C50.

2.4 Comparison of current (2022) and 17th-century interior: box pews

The church as it is today, is well preserved and maintained. The main differences, however, are the interior furnishings. They do not resemble the 17th-century configuration. Box pews used to fill the church but were replaced by curved wooden seats (current configuration as of 2022).

To recreate the 17th-century condition, the original box pews were virtually reconstructed in 3D and then inserted into the calibrated model. The authors consulted several historical iconographic sources (see Figs. 9 and 10) to reconstruct the box pews. The height of the pews was inspired by another one of Wren’s churches, namely St Mary Abchurch (see Sect. 2.5).

Figure 9 John Clayton’s floor plan of St Stephen’s Walbrook (London: Longman) [28].

Figure 10 Left: Pugin, 1809 (London Metropolitan Archive [36]), Right: George François Blondel, 1767 (The British Museum, Print: mezzotint).

Figure 11 Interior view of the virtual model in the SketchUp software. The box pews were modelled in “realistic” fashion using historic architectural plans and sections. The volumes of the box pews were preserved in the model. The audience was modelled by making the inside area of the box pews absorptive.

The box pews, being the major difference between the 2022 and 17th century configuration, were given absorption coefficients. These coefficients are given in Table 4. The absorption coefficients are based on various materials in the Odeon library. A distinction was made between the box pew base and other panels. The box pew base, which is slightly elevated, has a cavity. Although the exact construction of these box pew base panels is not known, it is reasonable to assume that the cavity induced some low frequency absorption. Therefore, the panels were given some low frequency absorption in Odeon. The other pew panels were essentially hard wooden panels in mid-air. The absorption of these panels is limited in the low frequency region. Due to their decoration (see Sect. 2.5) the absorption in the high frequency region is slightly higher than a plain smooth surface (absorption is higher upwards of 2 kHz). The scattering coefficient for the pews was left at the default, knowing that Odeon detects edges and applies scattering automatically.

A group of people, or in this case the audience, has a high absorption coefficient. Some concert halls rely on a certain occupancy to reduce the reverberation time. This is no different in the case of St Stephen Walbrook. In its 2022 configuration, there are likely not enough seats in the church to approach the levels of absorption by people (Fig. 4) as in the 17th-century situation. However, full occupancy in the current state was not simulated nor measured; therefore, no definitive statement can be made here. To model the audience, a tightly packed audience was modelled. This is based on the iconographic source in Figure 10 (right). This absorption coefficient was applied to the interior of the box pews (full occupancy was assumed).

To prove that the absorption is largely due to the audience, the configuration with box pews and with and without audience was simulated (Fig. 12). Without any audience, the reverberation times are approximately the same as the current configuration (2022) and the speech clarity is lower by 2–3 dB in the mid frequencies (Figs. 12–13). If the box pews are all occupied by people, the reverberation time does drop significantly. But again, that is mainly due to the presence of the audience.

Figure 12 Comparison of the reverberation times (T20) of different reconstructed configurations (17th century) versus the current simulated configuration of the church (2022).

Figure 13 Comparison of the clarity values of different reconstructed configurations (17th century) versus the current simulated configuration of the church (2022).

Figure 14 Picture of the interior of St Mary Abchurch during impulse response measurements on site. The pews in the middle of the room are visibly lower than the pews at the extremities.

Removing the box pews and filling the entire floor with open benches (a scenario that will be discussed later in more detail) results in an even lower reverberation time and a better speech clarity C₅₀.

2.5 Comparison with St Mary Abchurch (1681–1687)

During the measurement campaign, measurements were performed in another Wren Church using the same procedure. Like St Stephen Walbrook, St Mary Abchurch was rebuilt under the supervision of Sir Christopher Wren after it was partially destroyed in the great fire of 1666. The original 17th-century pews in this church are still standing, although the central ones were “trimmed” in the centuries after to provide more openness. The pews near the walls of the church were, however, left untouched. Their dimensions were used as an extra source to reconstruct the pews in St Stephen Walbrook.

The measured reverberation time in St Mary Abchurch is noticeably shorter than the measured reverberation time in St Stephen Walbrook (Fig. 15). Yet, the volume of both churches is comparable and so are the materials. It could be that the all-round presence of wooden pews or the shape of the flat dome ceiling in Abchurch, which are the main differentiating factors, are responsible for this lower reverberation time. No further action was taken to investigate the differences between both churches.

Figure 15 Comparison of T20 reverberation times in St Stephen Walbrook and St Mary Abchurch. The reverberation time in St Mary is lower than that of St Stephen Walbrook.

3 Scenarios, results, and discussion

Starting from Wren’s own writings, a few scenarios were devised. These scenarios represent hypothetical configurations that serve to “test” Wren’s design recommendations. Scenarios 4 and 5 were added by the authors to further investigate the effect of the dome and of the pulpit’s sounding board respectively on the room acoustics in St Stephen Walbrook. For each scenario, the STI parameter is analysed as well as the Sound Pressure Level (L_p) values. An overview of the scenarios is given in Table 5.

In each scenario the source position that represents the preacher is attributed a standard speech directivity pattern. This sound power level spectrum associated with this source type is given in Figure 16.

Figure 16 Source power level spectrum per octave band of the virtual source associated with the preacher’s voice. It corresponds to a raised voice, assuming that the preacher would put it in a “fair” amount of speech effort.

Figure 17 Interpolation zone of the distances from the pulpit given by Wren to where the preacher (with moderate Voice) can be heard; respectively 20 ft, 30 ft and 50 ft behind, aside, and in front of the pulpit [24].

The background noise (necessary for prediction of STI) was modelled based on the presumed activity in the room (people moving, breathing, etc.). This noise spectrum (included in Fig. 16) was based on auralised sound from Odeon simulations, and the sound was used also for the final auralisations, in which also speech of the priest was included (featured later in the article). It was assumed that under the strict supervision of the preacher, parishioners would mostly remain silent and listen attentively so that the presence of an audience could only be heard though involuntary sounds such as coughing, creaking of pews, shuffling around of people. The background noise level (of this “presence of crowd”) sound is 40 dB (A) in all scenarios. The same noise spectrum was used in all scenarios. More explanation for this can be found in Section 4.

3.1 Scenario 0. 17th-century church configuration

As mentioned before, box pews were originally present in the church, and Wren had no control over their design. It was found that these box pews have a significant effect on the speech intelligibility in the church.

In Figure 18 – left, we can see the speech transmission index (STI, %) simulated for a horizontal plane with a resolution of 0.5 m placed 0.5 m above the box pews to avoid simulation errors. In Figure 18 – right, the distribution of the Sound Pressure Level – L_p (dB) is given. This allows to check whether the values are sufficiently high so that people can hear the person speaking at a reasonable level.

Figure 18 Scenario 0 representing the 17th-century church configuration with box pews. On the left: the STI values. On the right: the SPL values in dB for one speaker in the room. Wren’s zone for good speech intelligibility is indicated in dotted lines.

The diamond-shape (Fig. 17) drawn on the plans in dotted lines corresponds to the distances given by Wren when commenting on the “hearing” range from which the preacher (“with a moderate Voice”) can be understood by the churchgoers (cf. supra). The diamond-shaped zone is an interpretation as it is the result from the researcher’s interpolation of the distances mentioned by Wren (Wren, 1711). It is necessary to note, however, that it is unclear what Wren means by a “moderate Voice”. Due to their experience of preaching in churches, a preacher would adapt his voice to the room he is in. The authors assume that in St Stephen Walbrook, most priests would speak louder, due to lack of sound amplification means and the large church volume. The sound power level spectrum is shown in Figure 16.

As expected, the STI is highest near the speaker. The STI value drops off with distance, to the point where the speech intelligibility is deemed “poor” over the box pews farthest from the speaker. According to these findings, Wren’s diamond-shaped zone corresponds quite well to the transition from “fair” to “poor” STI. As an SPL of 60 dB (A) corresponds to a normal conversation at 1 m distance and an SPL of 50 dB (A) corresponds to a quiet conversation at 1 m distance, one could say that the SPL in the church in this scenario is quite sufficient for the audience to understand the preacher.

3.2 Scenario 1. Central pulpit

The floor plan of St Stephen’s is a combination of the basilica typology with nave and lower aisles, and a centralized floor plan centred upon a domed crossing (Fig. 1). It is not known whether Wren intended the pulpit to be located right under the centre of the dome. He might have preferred this configuration, as it provides a better view of the pulpit and allows the preacher’s voice to be spread more equally throughout the church. Moreover, it was not uncommon for this to happen in centrally planned churches of that time. Churches in the Dutch Republic, promoted as specifically built for Protestant worship, were often designed as centralised churches with a dome or crossing vault and a more centrally located pulpit underneath; one instance of this can be found in the Noorderkerk in Amsterdam. As mentioned in Section 1.3, in his report on Old St Paul’s, Wren states that he conceives of the space under the dome as the “proper” place for an auditory.

Placing the pulpit in a central position in the church, however, would have important liturgical consequences, which was much debated in the Anglican Church in the 18th century [18]. This article does not elaborate on this aspect. Figure 19 shows the results for a configuration with the speaker (pulpit) in the middle, and Wren’s ideal hearing zone (diamond) as overlay. They demonstrate that this area fits well within the church space and covers more occupied box pews than in scenario 0. It was found that, compared with scenario 0, there is a greater contrast in terms of speech intelligibility in the church. The central placement allows for a better STI value for churchgoers seated towards the west. Towards the east end of the church (altar), however, speech intelligibility is rather poor/bad if the preacher is strictly facing west. This can be expected knowing that the speech directivity that was used is biased towards the front. A likely result is that the preacher would have had to turn around more often to obtain the same Speech intelligibility to the west of the pulpit, if possible.

Figure 19 Scenario 1 with pulpit centrally located directly under the dome. On the left: the STI values. On the right: SPL values in dB.

3.3 Scenario 2. The pulpit of St James Piccadilly church

Wren designed and built three parish churches on private commission, meaning that they were not built with income from the coal tax [37]. One of them, St James Piccadilly (1676–1684), is mentioned by Wren himself in his Letter to a Friend on the Commission as being most suited as an auditorium church (Wren, 1711). A scenario has thus been created in which the liturgical furniture of St James Piccadilly is mimicked in the church model of St Stephen Walbrook, which amounts to changing the layout and position of the Walbrook pulpit.

Exceptionally, Wren was involved in designing the interior furniture for St James Piccadilly. In this church’s original interior design, as assumed from historical plans (Hulsbergh, c.1724–29), there used to be a triple-decker type of pulpit placed in front of the altar. In St Clement Dane’s (1680–1682), another church built by Wren on private commission, the same triple-decker type of pulpit can be found positioned in the same location in front of the altar on historical plans (Sir. Christopher Wren, c. 1680). At least two other churches are suspected to originally have had the same pulpit configuration (Christ Church in Newgate and St. Nicholas Cole Abbey), but there is no conclusive evidence for these latter two [26]. Placing the pulpit in front of the altar, meaning that the church minister would have his back towards the altar, would have religious and liturgical consequences; it could be considered as a religious statement about the importance of preaching relative to the Eucharist performed at the altar in church services [26]_.

Therefore, for this hypothetical scenario, a triple-decker pulpit based on the dimensions of the pulpit with the reading desk and clerk’s desk used in the previous scenarios, was included in the virtual model at the position in front of the altar. The simulated STI and SPL values are visualised in Figure 20. By moving the pulpit closer to the altar, the STI values do not reach the low levels observed in scenario 1. This placement probably also enabled a greater number of people to see the officiating church minister in the pulpit clearly.

Figure 20 Scenario 2 with pulpit located in front of the altar of the church. On the left: the STI values. On the right: SPL values in dB.

3.4 Scenario 3. Box pews versus benches

From his own writings it is known that Wren was in favour of replacing box pews with “benches” in general (Wren, 1711). By benches, Wren most likely meant open wooden benches, consisting of a seating surface and an open backrest.¹ This improves the visibility in the church and makes the church more accessible to lower classes that could not afford to rent a box pew. In this scenario, the box pews (see Fig. 11) are replaced by the mentioned type of benches for a depiction of the box pews as modelled in the Odeon model).

In terms of room acoustics, the removal of the box pews allows for more people to be seated in the same area, replacing free-standing wooden panels from the box pews that barely absorb sound by people with a much higher absorption coefficient. In the 3D model, the audience was modelled as a box volume of 1 m high. This is a common approach in geometrical room acoustics simulation to simulate a tightly packed audience. The measurement plane was again placed at 0.5 m above the modelled audience to avoid simulation artefacts.

Wren’s open benches fit perfectly into the concept for an auditorium church: they cause less visual obstruction, and as can be seen in Figure 21, they also improve the speech intelligibility inside the church. Due to the increased absorption by the more tightly packed audience on open benches, STI generally improves, and SPL levels decrease to be generally lower than in the other scenarios. If the background noise would be higher for some reason, listeners in the back rows would be experience bad SNR.

Figure 21 Scenario 3 with box pews removed and replaced with benches. In the simulation this is approximated by introducing a box of 1 m high. Left: the STI values. Right: the SPL values in dB. The diamond shape, an interpretation of the rule of thumb set forth by Wren, is overlaid on the figures for reference.

In Figure 12, we can also see that the speech clarity values are also higher by about 3dB with this simple intervention.

3.5 Scenario 4. No dome

Wren himself states that “to build more room, (…), is to create Noise and Confusion” (Wren, 1711), referring to “reverberation”. The volume of St Stephen Walbrook is relatively small (5262 m³) but could be made smaller by omitting the large dome, which represents 10% of the church’s total interior volume. In this scenario the researchers want to test if the dome’s volume influences the overall speech intelligibility in the church. The scenario is strictly hypothetical as it is not directly connected to a specific design intention presented by Wren.

In Figure 22, we can see that the difference with scenario 0 (original configuration) is negligible. This is largely due to the presence of the sounding board above the pulpit which greatly affects the directivity of the source (preacher). The sounding board redirects a lot of upward sound energy downwards, reducing the contribution of the volume above the speaker to the overall clarity/speech intelligibility.

Figure 22 Scenario 4 with the dome removed. Upper row: scenario 0 results: Lower row: scenario 4 results. Left: the STI values. Right: the SPL values in dB.

3.6 Scenario 5. No sounding board

The results from scenario 4 raise the question how much the sounding board contributes to the speech intelligibility. Again, this scenario is strictly hypothetical as it is not directly connected to a quote or an idea of Christopher Wren.

As illustrated in Figure 23, the absence of the sounding board does have a significant effect on the STI values obtained through simulation. Due to the limited size of the sounding board, the effect is the greatest a few meters in front and to the sides of the pulpit. In other words, the sounding board offers little to no improvement to the speech intelligibility for listeners seated three or more pew rows removed from it. The size of the pulpit should be larger for more effect. This result is expected, as a larger surface close to the sources is able to reflect more early energy towards the audience for a better speech intelligibility.

Figure 23 Scenario 5 with the sounding board removed. Upper row: scenario 0 results. Lower row: scenario 5 results. Left: the STI values. Right: the SPL values in dB.

4 Auralisations

To go beyond quantifiable parameters, auralisations were made based on recordings in the laboratory of acoustics at KU Leuven. An English native speaker was invited to perform in the semi anechoic chamber. An original 17th-century sermon that was once delivered by William Beveridge at the consecration of the parish church of St Peter’s Cornhill (also designed by Wren) in 1681 was recorded. The researchers asked the narrator to read the text in multiple ways: fast and “normal” or “natural”. He was asked to perform as if he was in the 17th century, preaching in the original pulpit of St Stephen Walbrook for a fully packed church. The narrator had the freedom to decide himself how to interpret these instructions (speed, sound level, rhythm) as this was crucial to keep the speech from sounding too unnatural. The recording was made using a dBX (brand) omni-directional microphone in conjunction with a Roland 12-channel soundcard, using the Audacity software (https://www.audacityteam.org). No reverberation feedback was available to the speaker to aid in the narration. Despite the lack of reverberation, the recordings sound natural. A selection of the auralisations can be played by clicking the play buttons in Table 6.

The built-in auralisation tool of Odeon was used to auralise different sounds including the recorded speech. A standard HRTF profile (Subject_021Res5deg_M3, 0_SRate44100_Apass0, 50_Astop40, 00_BovrLap100%_PPrHRTF256) was used and .wav files were exported. Background noise sources were added in three realistic dispersed positions throughout the church to resemble the 17th-century conditions in a parish church service. The noise sources include a man coughing, chair shuffling and creaking wooden planks. The result of the auralised background noise spectrum was used to calculate the STI parameter. The level of these background noises was adjusted to 40 dB (A); this was achieved by assuming a level of 65 dB (A) for the speech (approximate average level during recording). Three receiver positions were chosen: at point A, B and C in the church (Fig. 24). Position A is where the privileged parish mayor could follow the service. It is interesting to compare the acoustics of this position with point B, in the unprivileged back of the church, behind pillars, located under the flat ceilings and outside Wren’s hearing zone. Lastly, position C is subject to a lot of change between the different scenarios, often away from the speaker’s main speaking direction, and located under the dome. It is important to keep in mind that the auralisations were done for positions that were 0.5 m above the box pews (instead of inside the box pews/audience) to avoid simulation artefacts. Therefore, the effect of the box pews is more limited than expected. Additionally, no matter what the position of the speaker or receiver, the receiver is always facing the speaker head on.

Figure 24 Perspective view of horizontal cut (plan view) of St Stephen Walbrook model with box pews. Positions of auralisation speaker and listening positions are indicated according to the legend.

The positions of speaker, receiver and noise source are indicated in Figure 24.

In this project, the listening part was limited to a subjective impression by the researchers. The samples were listened to in a controlled environment (low background noise) with Sennheiser HD650 headphones and desktop soundcard. Some differences between the samples can be perceived clearly:

• 0: Regarding the original 17th-century condition, the speech intelligibility is acceptable both close to the speaker (A) and farther away from him (B) despite the low STI values obtained for the latter (Fig. 18). If the speaker does not speak too fast, the speech is comfortable to listen to. The farther from the speaker and the faster the speech, the worse the intelligibility and listener comfort.

• 0 vs. 1: No difference in reverberation is heard closer to the speaker in any of the positions. A slight difference in position can be heard, but it does not seem to affect speech intelligibility.

• 0 vs. 2: The clarity of the speech is diminished slightly for position (A) since the pulpit is moved farther away from this position in this scenario (more towards the altar). At position (B), no perceivable difference could be heard comparing to scenario 0.

• 0 vs. 3: A slight difference in reverberation is noticeable between both scenarios closer to the speaker (A). Scenario 3 is clearly more comfortable to listen to due to less reverberation farther away from the speaker (B). When comparing the fast spoken versions, scenario 3 in position (B) is a much clearer improvement. The pace of the speech is certainly a determining factor, a factor which is merely considered as an average in the STI calculation (by way of many repeated empirical tests [38].

• 0 vs. 4: The dome, as the STI parameter results suggest, does not contribute to better or worse speech intelligibility. Only at position (B) there seems to be a slightly higher clarity for scenario 4. This is understandable, as is previously established that the sounding board has more effect for positions near the pulpit. So, position (B), located outside the zone affected by the sounding board, will be more affected by a change in volume due to higher significance of late reflections to the impulse response in that position.

• 0 vs. 5: This comparison reveals that clarity at position (A) is partly provided by the sounding board, which increases the number of early reflections that arrive at a listener’s ear located below in front of the pulpit. Without the sounding board the clarity and speech intelligibility are reduced in position (A) but remains similar for position (B).

5 Conclusion

Room acoustics in 17th-century Europe were not developed well enough as a discipline to equip an architect with accurate quantitative measuring and design tools. Fellow scientists of the day were indeed interested in sonic phenomena, but a general theory on the propagation of sound had not been developed in 17th century. The first working theoretical approach to sound propagation in rooms would only be described by Sabine some 200 years later. Despite that, Sir Christopher Wren seemed to have at least a few principles and rules of thumb at his disposal to achieve his room acoustic design goals, the origins of which seem to lie in his own experiences. He most definitely understood the importance of speech intelligibility in church services, even discussing the topic to some extent in his writings. He related room size/volume to speech intelligibility and consequently promoted the idea of building relatively compact spaces to achieve that goal, a design rule that still applies today. To test Christopher Wren’s own recommendations about acoustic performance of church designs and interior layouts, a case study of St Stephen Walbrook, a London parish church designed and build by Wren in 1672–1679, was conducted. To assess the acoustics of the church the following steps were taken: first an acoustic simulation model of St Stephen Walbrook’s 17th-century layout was created using Odeon software. This was accomplished by investigating the materials that were present in the room during that era and using the results of initial RIR (room impulse response) measurements. It was found that given the 17th-century conditions in the church (Scenario 0), the reverberation time dropped significantly at full occupancy (which can be assumed for that period) when compared to the current situation. However, due to the geometry of the original box pews, the speech clarity did not improve. Despite the much higher absorption in the church (with full occupancy), speech was not anymore intelligible than it is today.

The investigation continued with different configurations, some of which were suggested by Wren himself in his writings about his parish church designs and in his report on restoring St Paul’s Cathedral; others focused on exploring and illustrating the essential acoustic design elements of St Stephen Walbrook. Changing the location of the pulpit from the centre of the church to a position near the altar has a predictable outcome, but without changing the absorption characteristics the impact of this remains limited (scenario 1 and 2). Churchgoers sitting behind the pulpit will mostly receive late reflections, so for them speech intelligibility will naturally suffer, considering that the preacher faces away from them, looking towards the largest part of the audience. Scenario 1 is consequently better for people seated at the west side of the church, and scenario 2 for the people sitting east, near the altar. Unless the preacher would have been inclined to move around his head during the sermon to provide a better SNR to churchgoers in the west. Scenario 3, replacing the box pews with benches, a direct inspiration from Wren’s own writings, did result in a better STI overall and a higher clarity as well. Wren’s suggestion, meant to make a church more accessible to those who cannot afford to rent box pews, would have led to a better speech intelligibility according to our simulations. His motivations for this recommendation seemed to be rooted in his democratic and practical thinking; we cannot confirm whether he was aware that the change would affect the room acoustics, too.

In the last two scenarios, the contribution of the dome and the pulpit’s sounding board have been investigated. The dome, being located high enough above the ground floor, acts as a scattering surface, with its focus point too high above the audience to cause audible focus effects. However, most of the direct sound does not reach the dome because it is reflected by the sounding board of the pulpit (located right above the speaker). Dome or no dome, the sounding board seems to make this volume change irrelevant, except for the listening positions further away from the speaker.

The auralisations tell the same story as the numerical parameter results. Subjectively speaking, however, even for positions further away from the speaker, speech was found to be understandable (given the used background noise). The best speech intelligibility is achieved without box pews (scenario 3). The difference mostly comes down to comfort if the speaker succeeds in maintaining the right pace (rather slow) and adequate intonation.

In the end, can St Stephen Walbrook be considered as an auditorium church? Yes, thanks to the presence of a significant amount of wood panelling (wainscotting, flat ceilings, dome), the reverberation time at low frequencies stays reasonably low, therefore not creating long low frequency reverberation tails that could be disturbing [39, 40]. The volume is rather small, and the sounding board helps to direct early reflections towards the churchgoers. It should be noted that for less subjective interpretations, more controlled and large-scale listening tests should be conducted. Regardless, by moving away from English medieval church designs and adhering to the then liturgical preferences for active participation in the church service, Wren’s design, through its more open layout and composition, in itself improved the visual and acoustic qualities of the London parish churches.

Finally, reflecting on the methodology and epistemology of this research, it can be said that close collaboration between acousticians, historians and architects was necessary. This research followed by no means a linear process where interdisciplinary cooperation was key. The research was more cyclical in nature, iterating back and forth between historical, architectural and room acoustic expertise. The historic data needs to be viewed through a different lens (that of the sonic experience), and it often requires going back to original letters or archives to be able to ask the right questions. The collaboration between the different disciplines provides new insights that can help us better understand our heritage and design an appropriate future for it.

Acknowledgments

The authors would like to thank Rolf Hughes for recording a sermon in the anechoic chamber. The authors would also like to thank Elizabeth Maragh and Revd Stephen Baxter for allowing the measurements to take place in the St Stephen Walbrook church. Lastly, the authors would like to thank Dr. Mark Kirby for providing invaluable information for the research.

Conflicts of interest

The authors declare that they have no conflicts of interest in relation to this article.

Data availability statement

The sound files associated with this article are available in on Zenodo, under the reference [45].

References

All Tables

All Figures

	Figure 1 Structural floor plan of St Stephen’s Walbrook as a combination of a Latin Cross typology (blue) and a centralised design plan (pink).
In the text

	Figure 2 Picture of the area under the dome of St Stephens Walbrook with the current altar designed by Henry Moore in 1978.
In the text

	Figure 3 Edmund H. Sedding’s section of St Stephen’s Walbrook (Sedding [29], lithographed print).
In the text

	Figure 4 Plan view of the reconstructed 3D model (based on 2022 condition) with indication of source positions (S#) and microphone (receiver) positions (M#). On the left side a list of all source-receiver combinations measured on site.
In the text

	Figure 5 Isometric section view (north facing).
In the text

	Figure 6 Comparison of mean measured and simulated values of T20 in seconds.
In the text

	Figure 7 Comparison of mean measured and simulated values of Clarity C50 in dB.
In the text

	Figure 8 Averaged just noticeable differences between measured and simulated values of T20 and C50.
In the text

	Figure 9 John Clayton’s floor plan of St Stephen’s Walbrook (London: Longman) [28].
In the text

	Figure 10 Left: Pugin, 1809 (London Metropolitan Archive [36]), Right: George François Blondel, 1767 (The British Museum, Print: mezzotint).
In the text

	Figure 11 Interior view of the virtual model in the SketchUp software. The box pews were modelled in “realistic” fashion using historic architectural plans and sections. The volumes of the box pews were preserved in the model. The audience was modelled by making the inside area of the box pews absorptive.
In the text

	Figure 12 Comparison of the reverberation times (T20) of different reconstructed configurations (17th century) versus the current simulated configuration of the church (2022).
In the text

	Figure 13 Comparison of the clarity values of different reconstructed configurations (17th century) versus the current simulated configuration of the church (2022).
In the text

	Figure 14 Picture of the interior of St Mary Abchurch during impulse response measurements on site. The pews in the middle of the room are visibly lower than the pews at the extremities.
In the text

	Figure 15 Comparison of T20 reverberation times in St Stephen Walbrook and St Mary Abchurch. The reverberation time in St Mary is lower than that of St Stephen Walbrook.
In the text

	Figure 16 Source power level spectrum per octave band of the virtual source associated with the preacher’s voice. It corresponds to a raised voice, assuming that the preacher would put it in a “fair” amount of speech effort.
In the text

	Figure 17 Interpolation zone of the distances from the pulpit given by Wren to where the preacher (with moderate Voice) can be heard; respectively 20 ft, 30 ft and 50 ft behind, aside, and in front of the pulpit [24].
In the text

	Figure 18 Scenario 0 representing the 17th-century church configuration with box pews. On the left: the STI values. On the right: the SPL values in dB for one speaker in the room. Wren’s zone for good speech intelligibility is indicated in dotted lines.
In the text

	Figure 19 Scenario 1 with pulpit centrally located directly under the dome. On the left: the STI values. On the right: SPL values in dB.
In the text

	Figure 20 Scenario 2 with pulpit located in front of the altar of the church. On the left: the STI values. On the right: SPL values in dB.
In the text

	Figure 21 Scenario 3 with box pews removed and replaced with benches. In the simulation this is approximated by introducing a box of 1 m high. Left: the STI values. Right: the SPL values in dB. The diamond shape, an interpretation of the rule of thumb set forth by Wren, is overlaid on the figures for reference.
In the text

	Figure 22 Scenario 4 with the dome removed. Upper row: scenario 0 results: Lower row: scenario 4 results. Left: the STI values. Right: the SPL values in dB.
In the text

	Figure 23 Scenario 5 with the sounding board removed. Upper row: scenario 0 results. Lower row: scenario 5 results. Left: the STI values. Right: the SPL values in dB.
In the text

	Figure 24 Perspective view of horizontal cut (plan view) of St Stephen Walbrook model with box pews. Positions of auralisation speaker and listening positions are indicated according to the legend.
In the text