# The position of Gothic organs in Notre-Dame de Paris: An archeoacoustic simulation study

C. d'Alessandro, E.K. Canfield-Dafilou, S.S. Mullins, Brian F. G. Katz

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## To cite this version:

C. d'Alessandro, E.K. Canfield-Dafilou, S.S. Mullins, Brian F. G. Katz. The position of Gothic organs in Notre-Dame de Paris: An archeoacoustic simulation study. Applied Acoustics, 2025, 231, pp.110506:1-10. 10.1016/j.apacoust.2024.110506. hal-04875418

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# The position of Gothic organs in Notre-Dame de Paris: An archeoacoustic simulation study

C. d'Alessandro<sup>a, ID*</sup>, E.K. Canfield-Dafilou<sup>a,b, ID</sup>, S.S. Mullins<sup>a,c, ID</sup>, B.F.G. Katz<sup>a, ID</sup>

## ARTICLE INFO

### Keywords:

Pipe organ

Room acoustics

Archeoacoustics

Notre-Dame de Paris

## ABSTRACT

This study examines the acoustic effects of Gothic pipe organ placement within the late medieval architecture of the Cathédrale Notre-Dame de Paris. A historically informed geometric acoustic model of the cathedral is used for numerical simulations. The liturgical choir and nave are furnished in a medieval style consistent with the period, including wooden stalls, tapestries, a rood screen, and walls enclosing the chancel. Historical evidence for the positions and dimensions of 14th- and 15th-century organs informs the modelled organ sound source used in the simulations. The acoustic effects of six organ positions (on the western tribune, as a swallow's nest on the south wall, on the rood screen, in the southern transept, and above the northern stalls in the choir), three elevation levels (ground level, triforium, and clerestory), and two occupancy conditions (occupied and unoccupied) are evaluated. Variations in sound pressure level (SPL) and centre time are analysed across the ground level. The results reveal significant effects of organ position on audibility, elevation on clarity, and occupancy on sound intensity and clarity. These findings inform discussions on the musical and political motivations behind organ placement in Gothic cathedrals and their acoustic implications.

## 1. Introduction

Acoustics applied to the sound reconstruction of lost buildings, or archeoacoustics, is becoming an invaluable tool for historical studies [1-4]. The use of archeoacoustics to understand and reconstruct ancient musical practice in historic halls is also a fast-growing field of research, thanks to virtual acoustic simulation [5]. In this interdisciplinary study, we focus on the acoustic conditions of Gothic pipe organs in medieval Cathédrale Notre-Dame de Paris.

Permanently installed pipe organs, and the first written repertoire, began appearing in large Gothic churches and cathedrals in the second half of the 14th century [6] and assumed a growing role in liturgical, devotional, and social activities [7,8]. The position of an instrument was determined by its decorative function, which is subject to its dimensions and visual appearance, but also by its sound and musical functions, which depend on the instrument's acoustic properties and room acoustics.

Our research investigates the audibility and musical intelligibility (in terms of clarity and SPL) of large organs as a function of their position (place, elevation, church occupation) in the acoustic space of medieval

Notre-Dame. The relationship between architecture and organ position [9-11] determines the diffusion of the organ sound in church or cathedral acoustics [12]. The position of the instrument and its audibility/in telligibility in the cathedral are important features for investigating its musical and social role. This important question has not yet been explored to the best of our knowledge with the help of archeoacoustic simulations. The main purpose of this study is the comparison of dif ferences in audibility levels and clarity as a function of different organ positions, elevations, and occupation conditions. These comparisons are then applied to historical discussions regarding the evolution of church organ practice.

To achieve this, a geometric acoustic (GA) model is used to calculate the pipe organ's radiated sound field throughout the medieval building. This involves several steps and different sources of knowledge. A GA model of the contemporary cathedral has been elaborated in earlier works. But the interior architecture and furnishings of the medieval building were different from those of today. For a historically valid simulation, we introduce in the present study medieval architec tural elements, decoration and furnishings into the acoustic model. The sound sources studied are medieval organs. An analysis of historical data

<footnote><sup>a</sup> Institut Jean Le Rond d'Alembert UMR7190, Sorbonne Université/CNRS, Paris, France</footnote>

<footnote><sup>b</sup> Institute of Sacred Music, Yale University, New Haven, United States</footnote>

<footnote><sup>c</sup> Treble Technologies, Reykjavík, Iceland</footnote>

<footnote>* Corresponding author.
E-mail address: christophe.dalessandro@sorbonne-universite.fr (C. d'Alessandro).</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 1. Geometrical acoustic model of Notre-Dame de Paris, highlighting major surfaces with similar material properties, such as wood (brown), stained glass windows (light blue), columns wrapped in fabric (pink), and occupied areas (blue).</figcaption></figure>

and a direct analysis of the building, which we were able to carry out in the framework of the reconstruction work after the 2019 fire, enabled us to better specify the size, position and sound features of the medieval instruments, previously known only from archives. [13]. Pipe organ directivity models are needed for realistic integration of these instruments into the historically informed acoustic model of the medieval building.

By gathering all these data, informed simulations of the sound fields of medieval organs in their environment are carried out. The Gothic organs' predicted perceived clarity and relative power as a function of their position and the listener's position in the cathedral are studied. These combined results should serve the interests of further archeoaoustics investigations of medieval organ music in Gothic buildings.

The article is organised as follows: In the first part, the geometrical acoustic model of the Cathédrale Notre-Dame de Paris in the late medieval era is introduced. In the second part, medieval organs and their acoustic properties are described. The third part presents and discusses acoustic simulations of the predicted sound field of the medieval organ throughout the cathedral. The final parts discuss some consequences of the pipe organ's position on musical and social practices in medieval Notre-Dame de Paris and summarise the main results of the paper. A glossary of cathedral architectural terms is provided at the end of the manuscript.

## 2. Historically informed Geometric Acoustic model of the late Middle Ages cathedral

The simulations were carried out using a GA model of the cathedral (see Fig. 1), taking into account the geometry and acoustic properties of the building's surfaces. Simulations were carried out using CATT-Acoustic (v9.1e)/TUCT (v2.0e) software.<fnref n="1" /> These simulations are based on ray tracing which approximates the propagation of acoustic waves according to the principles of geometrical optics [14–16]. This approach remains an approximation, as it does not accurately simulate the impact of specific geometrical details [17], the effect of fine texture details of certain materials or other wave phenomena. Despite these limitations, the GA methods provide a good approximation of the effects of the room geometry and the properties of the surfaces that make up the room. The GA approximation cannot simulate certain effects, such as the natural diffraction of acoustic energy at an object's edges, though approximations are included in several solvers. Prior studies have shown that a properly calibrated model and a high-performing numerical solver [18]

can provide results which are comparable to both objective metrics and perceptual evaluations [19]. In the current study, we focus on spatial distributions of acoustic properties. Simulations are used to map several objective metrics throughout the cathedral. This allows for a general comparison of the effect produced at specific positions by changes to the organ's placement.

### 2.1. Architectural model

A historically informed GA model of the cathedral allows for numerical simulation of a virtual instrument positioned within the church. This GA model was created in 2015 before the fire (Fig. 1) and refined since then. It was calibrated from measurements in the cathedral, following the protocol presented in [18]. Historical sources indicate that the organ would have been used primarily on the high feasts of the Christian calendar [20], so the model was further modified to reflect the interior architecture of the cathedral in the late Middle Ages [21,22] and in a high festival state of decoration.

To ensure compliance with the GA method, structural and decorative details were approximated by reducing fine and complex geometric details to simple surfaces which have been assigned high scattering coefficients to simulate their acoustic behaviour (e.g., the precise shapes of columns and statues have been simplified).

The GA model is defined by ≈ 14 680 polygonal planes, representing a total surface area of ≈ 35 200 m<fnref n="2" />, a floor plan area of ≈ 4800 m<fnref n="2" /> and a volume of ≈ 82 700 m³. With over 40 material definitions in the GA model, their reproduction here goes beyond the scope of the paper. The model's mean material property values are provided in Table 1.

The simulation used 100 000 rays for the parameter mapping study on a 0.8 m grid across the main floor of the cathedral. Concerning grid density, one can consider that for 100000 rays equally distributed on a sphere, the ray separation is approximately 0.64 deg. A free-field propagation time of 200 ms is approximately equivalent to a separation of 0.8 m, providing confidence that the early details of the simulated propagation are well represented. Inspection of the resulting parameter mapping contours shows relatively complete contour zones, without mottling due to insufficient ray density for the grid map density, further supporting the configuration settings. Testing empirically the Notre-Dame GA model with a larger number of rays did not change beyond what can be explained by the stochastic processes inherent in the ray tracing model [23].<fnref n="2" />

<footnote n="1">¹ www.catt.se.</footnote>

<footnote n="2">² It is noted that the inclusion of diffraction in a model as complex as that of Cathédrale Notre-Dame de Paris is far more resource-intensive than conven-</footnote>
<table><caption>**Table 1**
Summary of Notre-Dame GA model mean surface properties and specific occupied area material definition (see Section 4.4).</caption><thead><tr><th></th><th>125</th><th>250</th><th>500</th><th>1k</th><th>2k</th><th>4k</th><th>8k</th><th>16k</th></tr></thead><tbody><tr><td>mean abs.</td><td>.060</td><td>.071</td><td>.084</td><td>.114</td><td>.145</td><td>.161</td><td>.170</td><td>.178</td></tr><tr><td>mean scatt. %</td><td>23.9</td><td>24.9</td><td>28.8</td><td>35.0</td><td>42.9</td><td>52.8</td><td>63.7</td><td>77.7</td></tr><tr><td>occupied abs.</td><td>.07</td><td>.19</td><td>.35</td><td>.63</td><td>.86</td><td>.99</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Collection of octave-band mean reverberation times in Cathédrale Notre-Dame de Paris following historically informed simulations (prior to 1987) and measurements (from 1987 onwards), unoccupied conditions (data from [21,22, 24,25]).</figcaption></figure>

To provide acoustic context, Fig. 2 provides a summary of various reverberation times resulting from both GA simulations (typical decorative, unoccupied, prior to 1987) and measurements (from 1987 onwards) of Notre-Dame, as a result of various previous studies [21,22,24,25]. Of note is the *2020 (fire)* condition, representing the post-fire measurements, with holes in the vaulted ceiling, and the *1182 (apse)* condition, when only the Apse end of the cathedral was in open, which both have significantly shorter reverberation times than all other conditions, prior to the consideration of high festive decorations.

## 2.2. Furnishings

The lateral chapels in Notre-Dame were completed in 1350 [26], signifying the last major architectural change to date. With the cathedral now in a position of architectural stasis, most subsequent alterations relative to earlier modelled states are in the form of interior decorations. At this time, the choir was furnished with wooden choir stalls in a horseshoe shape with carpets laid on the ground at significant positions (underneath the Archbishop's feet, for instance) and tapestries hung from the back of the stalls facing inwards towards the canons. Additionally, the choir and high altar were physically separated from the ambulatory of the chancel by a highly decorated stone clôture depicting Biblical scenes [27]. A rood screen, or *jubé*, further buttressed the transitional space between the choir stalls and the transept crossing, a large gate between the two areas that served as one of the stations in reli-

gious processions and a platform from which music and scriptures were declaimed [28,29].

An exemplary depiction of the choir in this state can be found in Fig. 3a (see [31]), by architect Daniel Marot at the end of the 17th century. While this depiction postdates the focus of this article by approximately 200 years, it was drawn before a series of significant renovations to this area and served as a useful visualisation of the more decorative approach common to the pre-Baroque era. The medieval rood screen and the high backs of the westernmost choir stalls have been omitted in this engraving to reveal the interior of the choir [30]. The tapestries on the interior side of the choir stalls are clearly visible, as is the clôture at the easternmost end of the sanctuary. Other decorations, including the overhanging canopies above the choir stalls, the high altar and its surrounding tapestries, and the *feretory* containing the most precious relics behind the high altar, can be seen in the background.

Historical records indicate that the lateral chapels were individually furnished by patrons and confraternities of the cathedral, with a wide range of decorative states possible depending on the tastes of the chapel's sponsors [33,34]. These chapels were physically separated from the main volume of the cathedral using ornamental screens and walls and were typically furnished with altars, votive or funerary statues, textiles, and other art objects. Fig. 3b (see [32]) depicts the inside of one of these chapels circa 1448, located in the chancel, clearly showing the separating screen and internal decorations of the family chapel in the foreground. Meanwhile, the background shows votive statues standing within the ambulatory of the cathedral.

It was common to wrap the cathedral's columns with decorative cloths for high feasts and hang banners from the triforium level of the nave [20]. The acoustic model was revised to reflect the decorations of the liturgical choir and lateral chapels, furnishings in the ambulatory, and the addition of fabric wrapping the columns on each side of the nave's central aisle.

Fig. 4 shows the resulting reverberation time averaged across receiver positions throughout the cathedral, comparing the previous normal decorative condition (1350 (lateral chapels) in Fig. 2) with a 15th century *festive decoration* condition incorporating hypothetical festival textiles in both unoccupied and occupied states. Note that reverberation time in the late Middle Ages appears significantly shorter than today and somewhat comparable to the situation of the *2020 post-fire* measurements in Notre-Dame de Paris. This can be interpreted as the effect of the rood screen, furnishing and decoration.

# 3. Locations and acoustics of late Middle Ages Gothic organs

## 3.1. *Gothic organ position in cathedrals*

The location and size of organs in large Gothic buildings varied widely [6,9,10]. These locations are, of course, not random. They correspond to the consideration of several (possibly conflicting) constraints. Among the most noticeable constraints one can mention are visibility, audibility, circulation, size, and weight of the instrument. One of the most complex machines at the time, the pipe organ was a monument and an object of admiration, like monumental clocks (which appeared in the same period). Visibility was then a prominent issue. The place where the organ is sounding attracts the attention of the audience. The two privileged spaces are the liturgical choir (the centre of liturgical ceremonies) and the cathedral's entrance. Entrances are many: the western portal (open to the city) and transept portals (open to the canon's cloister). Other constraints are circulation (i.e. leave the floor free for the audience and procession circulation), and the size and weight of large instruments that require sufficient space and structural solidity. These constraints explain why medieval pipe organs were placed at the tribune or atop of rood screens.

For this study, we have selected six positions where organs are most typically found in Gothic cathedrals (see Fig. 5 and Table 2). These positions were not all actually used in Cathédrale Notre-Dame de Paris,

<footnote>tional ray tracing. Preliminary comparisons showed that including diffraction introduced only negligible differences in the mapped parameter results. The decision was, therefore, made to exclude diffraction from simulations for visual analysis. If one desired to carry out detailed auralizations (e.g. listening to the simulation through headphones or loudspeakers), taking into account diffraction and a larger number of rays would certainly be needed.</footnote>
<figure><img src="image_6.png" /><figcaption>(a) *Le Te Deum chanté dans nostre Dame*, engraving by Daniel Marot. Musée Carnavalet CC0 public domain [31].</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) *Le Prévôt des marchands Jouvenel des Ursins et sa famille*, anonymous. Musée du Louvre, Département des Peintures [32].</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. Simulated reverberation time ($T_{30}$) of Notre-Dame, comparing the typical decorations of the 1350 architectural condition (Fig. 2), the modified 15th century festive decorative condition, and the subsequent addition of the occupied configuration.</figcaption></figure>

but have been identified in other Gothic cathedrals, providing interesting and relevant comparisons. Medieval organs were often placed in the choir, such as in Sens Cathedral, Saint Agricol in Avignon or San Petronio in Bologna (still in place). It is a position that has remained common to this day in Italy and Spain, and is the position of the 19th century choir organ at Notre-Dame de Paris (labelled position (F)). Small Medieval organs were also found at the entrance to the choir, situated atop the rood screen in the Middle Ages in the cathedrals of Chartres or Reims. It is a position that remains common to this day in England, corresponding to position (E). Position (D) is in the transept. The transept organ, placed above a lateral portal, is found, for example, in the cathedrals of Le Mans and Tours. The most common position for the organ in the Middle Ages was on one of the nave walls, with the case suspended on a wall (swallow's nest). The case may be hung on the south or north wall, with varying proximity to the choir. This was the position of the 14th century Notre-Dame de Paris's organ, close to the transept crossing (position (C), with hypotheses H1 and H2 for its elevation, see next Section). The great medieval organs of the cathedrals of Strasbourg and Metz were on the north wall nearer to the entrance (reflected in position (B) but on the south wall). Finally, the most common modern position in France is above the western portal, position (A).

The organ's mounting height in the cathedral certainly has an important effect on the diffusion and perception of sound. Singers are

<figure><img src="image_9.png" /><figcaption>Fig. 5. Elevation and plan of Notre-Dame showing organ positions under study: (A) the 15th century organ, (B) and (C) possible positions of the 14th century organ, (D) south transept, (E) on the rood screen, (F) 19th century choir organ.</figcaption></figure>

at ground level, as is the main audience. In contrast, rood screen instruments can be positioned on the order of 5 m to 10 m above the floor. Most known examples of extant medieval organs are placed at a medium height within the building, usually at the tribune or triforium level [9,11]. In classical Gothic architecture, this architectural level is generally one-third of the total elevation. As the organ is a tall instrument, it occupies the second third of the elevation, visually situating its centre halfway between ground level and the vaulted ceiling.

## 3.2. Gothic organs in Notre-Dame de Paris

Evidence of a large pipe organ in the Cathédrale Notre-Dame de Paris appears in the 14th century [20,35]. According to traces in the masonry we recently found [13], the instrument was placed in a swallow's nest (a wooden gallery protruding from a wall of the building) at or above the triforium level in the nave, in the second bay of the south wall in the transept, counting from the transept crossing. Replaced stones in the second bay (and in this bay only) give rise to two hypotheses for elevation. Hypothesis H1 corresponds to an instrument placed at the triforium level (labelled C in Table 2), if replaced stones were placed at the top of the case. Hypothesis H2 corresponds to an instrument placed in a higher position (labelled C+ in Table 2). Replaced stones in this case correspond to the corbels that support the organ gallery. H2 is the more likely hypothesis [13], because a medieval citation indicates that the instrument was occluding a clerestory. This is the position represented in an artist's view of the organ case in Fig. 6.
<table><caption>**Table 2**
Summary of organ positions and conditions studied.</caption><thead><tr><td>position</td><td>location</td><td>elevation</td><td>Notre-Dame de Paris</td></tr></thead><tbody><tr><td>A</td><td>western tribune</td><td>tribune level</td><td>15<sup>th</sup> c. organ</td></tr><tr><td>B</td><td>fifth bay south wall</td><td>triforium</td><td></td></tr><tr><td>C</td><td>second bay south wall</td><td>triforium</td><td>14<sup>th</sup> c. organ (H1)</td></tr><tr><td>C –</td><td>second bay south wall</td><td>ground (lowered 5.5 m)</td><td></td></tr><tr><td>C +</td><td>second bay south wall</td><td>clerestory (elevated 8 m)</td><td>14<sup>th</sup> c. organ (H2)</td></tr><tr><td>D</td><td>south transept</td><td>under the triforium</td><td></td></tr><tr><td>E</td><td>rood screen,</td><td>top of rood screen</td><td></td></tr><tr><td>F</td><td>wall in the choir</td><td>under the triforium</td><td>19<sup>th</sup> c. choir organ</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Gothic organ cases in the Cathédrale Notre-Dame de Paris represented at the same scale. (a) Artist's view of the 14th century swallow's nest organ in the second bay of the nave (elevation H2, organ case of San Pedro de los Francos, Calatayud anamorphosed to the proportion of the 14th organ in Notre-Dame, see text); (b) View of the 15th century organ in the western tribune, central part of a drawing by Silvestre [37].</figcaption></figure>

The organ case was inscribed in an approximately 5.33 m square (about 18 foot in ancient measurement units<fnref n="3" />). The largest pipe in the facade was about 10 foot (2.96 m) long (sounding length 9 foot (2.66 m)), the pipework of tin weighing 800 pounds (or 391.2 kg<fnref n="4" />). With a keyboard of 35–38 keys, this weight is corresponding to a principal rank of 35–38 pipes in the facade and 200–300 mixture pipes for the inner pipework inside the case behind the facade. Considered an acoustic source, this instrument can be seen as a set of approximately 300 pipes with fundamental frequencies of 60 Hz to 1000 Hz radiating through a facade inscribed in a 18 feet × 9 feet (5.33 m × 2.66 m) rectangle. The first Gothic instrument required repairs in 1394, and the chapter decided to build a larger organ between 1401 and 1403.

The second medieval organ was located in a different place, on the stone gallery (the same place as the current great organ) at the cathe-

dral's west end (position (A) in Fig. 5). To the best of our knowledge, this was the first time in France and Europe that a pipe organ was placed at the west entrance of a church or cathedral. A small sketch of the organ case is visible in a drawing of the interior of the Cathédrale Notre-Dame de Paris by Israël Silvestre [37] from around 1690. The width of the case is 24 feet (7.10 m), and the total height of the case, with the spire, is 50 feet (14.80 m). The keyboard had a compass of 46 notes starting at H0 (18 foot, 5.32 m sounding length), with the facade and inner pipework totalling approximately 600 pipes. Considered an acoustic source, this instrument can be seen as a set of 600 pipes with fundamental frequencies from 30 Hz to 1000 Hz radiating through a facade inscribed in a 24 feet × 18 feet (7.10 m × 5.33 m) rectangle.

The two instruments are represented in Fig. 6. Only the proportions are known for the first organ. To give an artist's view of the first organ, the organ case of the medieval instrument of San Pedro de los Francos, in Calatayud [38], anamorphosed to the proportion of the 14th organ in Notre-Dame is used for figuration. This instrument was chosen as the best representation for the lost instrument in Notre-Dame because it is an authentic example of a typical of 14th or early 15th medieval instrument. It is placed at the position and with the proportions we hypothesize for the first medieval organ in Notre-Dame in order to visualize the effect of this instrument in the cathedral. The drawing by Israël Silvestre [37] is the only known representation of the second 15th organ in Notre-Dame.

### 3.3. Organ source

In addition to modelling the geometry and acoustic properties of the building's materials, the organ's approximate acoustic directivity was also considered. Although there has been a great deal of research into the acoustics of organ pipes, very few studies have been conducted on the directivity properties (or “acoustic radiation”) of the collective set of pipes found in large organ or choir organ cases. In situ measurements of organ directivity are highly limited due to the acoustic conditions available, often a highly reverberant church where one must obtain the non-reverberated direct sound, and the limited access 360° around the instrument, limiting the ability to obtain the spherical directivity patterns required for use in GA simulations.

For all simulated organ positions except the one on the rood screen (E), the directivity of a small proxy organ, representing an organ buffet, measured in anechoic conditions was used [39,40]. This laboratory instrument comprised a plywood box (134 cm × 98 cm × 58 cm) with 136 foam-filled PVC tubes and a cylindrical loudspeaker representing pipe organ excitation employed to examine the diffraction and scattering effects of pipes within an organ case on the radiated sound pressure (see Fig. 7a).

The proxy organ was about half the width of the 14th century choir organ. Consequently, the associated frequency-dependent directivity measurements were scaled by a factor of 2 to represent that organ. An example of the directivity measurements is shown in Figs. 7b and 7c, illustrating the radiation from the organ case for a front opening.

For the position on the rood screen, an omnidirectional directivity was used to approximate the organ, given that such a location would likely have two façades (one facing the choir and the other the nave) or more, generally radiating equally in all directions.

<footnote n="3">³ The Roman foot of 0.296 m is used here according to medieval metrology [36].</footnote>

<footnote n="4">⁴ The pound or “livre de Troyes” corresponding to 0.489 kg in medieval metrology [36].</footnote>
<figure><img src="image_11.png" /><figcaption>(a) Proxy organ.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(b) Measured directivity, horizontal plane.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(c) Measured directivity, vertical plane.</figcaption></figure>

<caption>Fig. 7. Proxy organ used to evaluate general directivity pattern of radiated sound for including in acoustic simulations, in the condition with side and rear panels of the buffet enclosure in place.</caption>

For all simulations, the organ source was set to an output level of 100 dB at 1 m with a pink noise spectrum, a value typical of a close-field level for a pipe organ [41]. This fixed reference level allows for cross-comparisons between organ position variations. It is, however, noted that this setting, of course, does not represent the actual SPL for each historical organ that would likely have varied between designs as they evolved over the centuries.

# 4. Simulated sound field due to the organ and perceived acoustic effects

## 4.1. Room acoustic metrics

To assess the audibility and suitability of various hypothetical organ positions in Notre-Dame, sound pressure level (SPL) and centre time ($T_s$) were computed across the ground floor of the cathedral. Mapping SPL as a function of listening position in the cathedral allows us to visualise the areas where the organ will be the loudest and quietest. Comparing the various hypothetical organ positions, employing the same source SPL reference, demonstrates how various zones of the cathedral (e.g., stall in the choir, position in the apse-end of the nave, or a side chapel) are affected by the position of the organ, ignoring potential details in individual organ construction. The general consensus is that just a noticeable difference (JND) for changes in SPL is approximately 1 dB for expert listeners, while 3 dB is considered a clearly noticeable difference. To focus analysis on significant differences, SPL contour maps use 3 dB delineations.

Centre time is selected as a proxy metric for assessing musical intelligibility. $T_s$ is expressed in ms and equates to the time when the cumulative early and late arriving energy are equal [42], calculated as per Eq. (1). Thus, positions close to a source typically exhibit low $T_s$ as the energy of the direct sound and early reflections will be significantly greater than that of late reverberation. In contrast, positions far from a

source typically exhibit a greater $T_s$ as the direct sound will be quieter (or absent when the source is occluded) relative to late arriving energy.

$$T_s = \frac{\int_{0}^{\infty} t \cdot h^2(t) dt}{\int_{0}^{\infty} h^2(t) dt} \qquad T_s = \frac{\sum_{n=0}^{N} n \cdot \Delta t \cdot h^2[n]}{\sum_{n=0}^{N} h^2[n]} \qquad (1)$$

$T_s$ is preferred over clarity metrics such as $C_{50}$ and $C_{80}$, which are fundamentally based on time limits for analysing common speech phonemes and average note lengths for classical music, respectively. Centre time does not impose context-dependent time integration limits [43], favouring a more generalised description of early-to-late energy balance without musical or other source material-specific limitations.

As a point of reference for metric familiarity, a $C_{80} = 0$ dB equates to $T_s = 80$ ms. For clarity parameters, which decrease as reverberant energy increases, centre time will increase as the barycentre of energy moves later in the Room Impulse Response $h$. As the reverberation time of a cathedral is significantly longer than that of a concert or lecture hall, and the structure of medieval music is extremely different from symphonic classical music or speech, centre time seems like a more suitable metric for evaluating musical clarity in the context of organ music in Notre-Dame. As [44] showed that the JND for $T_s$ in spaces with long reverberation times is related to a percentage of the nominal $T_s$ time, the $T_s$ contour maps use a logarithmic time scale.

## 4.2. Acoustic effect of organ position

Figs. 8 and 9 show contour maps of SPL and $T_s$ comparing the six organ positions evaluated in the cathedral (Fig. 5) in unoccupied conditions. Overall, it is apparent that the modern choir organ position (F) on the clôture of the choir provides the highest SPL and lowest $T_s$ in the portions of the cathedral where liturgical actions take place, while organ positions in the nave provide higher SPL and lower $T_s$ in the central nave, where the audience is found.
<figure><img src="image_14.png" /><figcaption>**Fig. 8.** Simulation results of SPL (A-weighted) for unoccupied condition. Organ positions from left to right: (A) in the tribune, (B) in the 5th bay, (C) in the 2nd bay, (D) in the transept, (E) on the rood screen, (F) position of the contemporary choir organ.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 9.** Center time ($T_s$) for unoccupied condition. Organ positions from left to right: (A) in the tribune, (B) in the 5th bay, (C) in the 2nd bay, (D) in the transept, (E) on the rood screen, (F) position of the contemporary choir organ.</figcaption></figure>

As the 14th century organ was likely along the triforium level in the nave, comparing positions (B) and (C) is interesting. The SPL is relatively high and uniform throughout the nave for both positions. Due to its proximity to the apse, an organ positioned in the 2nd bay from the transept would be louder within the choir than the more distant organ in the 5th bay.

The 15th century organ, located below the western Rose window (A), has a very similar SPL to that of an organ positioned in the 5th bay (B) both in the central nave and in the chancel. However, since it faces east towards the transept, $T_s$ remains lower at greater distances along the main axis of the cathedral. The distance to the choir is significant. Such a position is well suited for events such as solemn entrances, processions, and *alternatim* (call/response) with singers in the choir. However, the accompaniment of polyphonic music in the choir would be difficult, if not impossible, because of the acoustic propagation delays due to the large distance (propagation time of ≈ 175 ms from the organ (A) to the rood screen), far exceeding acceptable delays for ensemble playing [45].

Positioning the organ in the transept (D) does not seem particularly effective in Notre-Dame. As discussed in [28], the large volume of the transept and deep triforium level impedes sound transmission between the nave and apse of the cathedral. As the transept of Notre-Dame is rather deep, an organ there would not have a visual line-of-sight with most of the nave, with sound diffraction effects likely playing a substantial role in the sound reaching the public. Further details regarding the diffracting effects around complex columns is beyond the scope of the

current study, but has been discussed in [17]. Consequently, an organ in the transept would likely only be effective for those in the first few bays in the nave.

While the organ was not located on the rood screen (E) in Notre-Dame, this position seems musically desirable. Its proximity to the chancel means the SPL is high and the $T_s$ low within the choir stalls. Its location also privileges the easternmost portion of the central nave. Finally, like the organ positioned below the western rose window (A), its position on the central axis of the cathedral provides a uniform gradient of SPL and $T_s$ down the cathedral's central aisle.

### 4.3. Acoustic effect of elevation

Fig. 10 shows SPL and $T_s$ for an organ positioned in the 2nd bay of the nave (C) at three different heights: at the level of the triforium, elevated 8 m (covering the window one level higher), and lowered 5.5 m (at the height of 19th century choir organ).

The elevated position does not significantly change the SPL in the cathedral except in the portion of the nave directly opposite the organ's location. However, raising the height of the organ significantly decreases $T_s$ throughout the cathedral. From an elevated position, the direct sound path will be longer from all listening locations on the ground, and diffuse late energy will arrive earlier.
<figure><img src="image_16.png" /><figcaption>**Fig. 10.** Simulation results for SPL (A-weighted) and Center time, unoccupied condition, organ position in the 2^nd^ bay (C): organ height: (C+) elevated, (C) triforium position, and (C−) lowered.</figcaption></figure>

The lowered position, below the triforium, increases SPL in the east-
ern half of the nave. Likewise, closer proximity decreases T_s in this nave
area, equating to increased clarity.

4.4. Acoustic effect of occupation

In addition to the 51 canons, the Cathédrale Notre-Dame de Paris
was staffed by over a hundred chaplains, dozens of altar boys and sev-
eral churchwardens. Notre-Dame was rarely empty of people, even when
it was closed to the public. In addition to these almost 200 permanent
staff, large crowds of visitors were expected on such solemn days as
Christmas, Easter, important holidays, and venues of royal or important
persons. The cathedral can welcome several thousand people on those
festive occasions. Around the start of the 15th century, Paris was the
largest city in Europe, with some 200 000 inhabitants. Therefore, the in-
fluence of such crowds on the perception of organs merits investigation.
A density of 2 people per 3 m², drawn from laboratory measurements
of worshippers reported in [46] under condition *Standing in Rows on
Concrete* was used in simulations (see Table 1 for values).

Fig. 11 shows SPL and T_s for the organ positioned at the triforium level of Notre-Dame in the 2^nd^ bay (C) for the unoccupied and occupied states, both reflecting the festival state decorations (see Section 2.2). The SPL maps show a very similar pattern in both conditions, with

the occupied condition ≈ 3 dB quieter, due to the additional absorp-
tion. Likewise, T_s decreases significantly with the reduced reverberation
time.

5. Discussion and conclusion

5.1. Discussion

The different positions studied correspond to different relationships
between the two main acoustic sources for music and speech in a cathe-
dral: the liturgical choir and the pipe organ. For organs on the rood
screen or in the choir, the organ's contribution merges with that of the
choir, concentrating the sound sources and attention to sound in the
centre of the cathedral. For the swallow's nest position, the instrument
is outside the choir visually while remaining fairly close to the centre of
the cathedral acoustically.

At the Cathédrale Notre-Dame de Paris, the organ has been relocated
to the west portal gallery since the 15th century. This significant change
in position maximises the distance between the two sound sources and,
therefore, results in a bi-polarisation of the soundscape. Acoustic simu-
lations clearly show that the displacement of the large organ from the
southern wall to the western tribune offers the maximal contrast be-
tween music performed at the cathedral's eastern (choir) and western
(organ) sides. The dimension of this second instrument greatly expanded
compared to that of the first. The lowest notes are an octave deeper in
pitch, and the larger pipe is twice as high, displaying considerably more
grandeur power and solemnity. Its move to the west portal may have
accentuated its musical function for displaying the power of the secu-
lar and the transition from the profane (outside Notre-Dame) to sacred
spaces, as it lent itself well to the pomp of a solemn entrance [47].

Although the position of the 14th century organ in Notre-Dame is still
hypothetical, acoustic simulations indicate that the differences between
all the simulated positions have significant impact on the cathedral's
soundscape. The position of the instrument and its associated area of
optimal audibility suggests that the function of the pipe organ in Cathé-
drale Notre-Dame de Paris evolved between the 14th and 15th centuries.
The first instrument was likely closer to the liturgical choir, both in its
position and in its musical function of choir accompaniment, even if its
exact position has not yet been confirmed. By its displacement to its cur-
rent position at the western portal, it became rather an instrument of
wonder (quoted “the wondrous machine” in [20]), accompanying the
entrance of high-rank persons or procession in the cathedral and re-
sponding to singing in the choir. In addition, the distance between the
organ and the choir, and the associated acoustic difficulty in ensemble
playing, may have contributed to the differentiation between vocal and
instrumental music, which became increasingly important at the turn of
the 15th century.

The simulations in this study are based on several approximations
of real-world conditions, including the precise acoustic characteristics
of the organ's radiation pattern, its positioning, variations in spectral
content across different organ evolutions, and the general constraints
of geometrical acoustic simulations. Despite these limitations, the re-
sults reveal clear and consistent trends that support the validity of the
conclusions. These trends indicate that the findings are likely generaliz-
able to similar contexts, providing valuable insights despite the inherent
constraints of the modelling approach.

5.2. Conclusion

In this archeoacoustic study, the effect of large Gothic pipe organs
in the late Middle Ages Cathédrale Notre-Dame de Paris is investigated.
The architectural state of the cathedral in the 14th and 15th centuries is
reconstituted and taken as a model for geometrical acoustic simulations.

The architecture differed from today's, mainly due to the presence
of a rood screen, which bisects the nave with a high wall across its en-
tire width, and to high festival decorations. The effect of this interior
architecture is significant.
<figure><img src="image_17.png" /><figcaption>**Fig. 11.** Simulation results for SPL (A-weighted) and Centre time for unoccupied and occupied conditions. Organ position (C) in the 2nd bay.</figcaption></figure>

Simulation results show that changes in the organ's position would considerably modify its perception on the ground floor. An organ is generally audible anywhere in the building, but its loudness and definition (or musical intelligibility) vary greatly according to different positions. The organ's location is clearly audibly identified, drawing attention to its position in the cathedral.

The instrument's height also has a noticeable audible effect. Its position at the tribune level, approximately in the centre elevation of the building, compromises audibility and visibility. It would be more powerful on the ground, but the organ case and its façade of glittering silvery pipes are an object of beauty and prestige that must be seen by all as much (and more often) than they are heard.

When a large audience gathers in the cathedral during major celebrations, the acoustics is significantly altered. Reverberation time decreases, the clarity of the organ increases, and its perceived power diminishes. This effect, well known to organists, is, of course, still perceptible today. Acoustic simulations make it possible to quantify it.

The results of this archeoacoustic study will nurture musicological investigations on the sound and music of pipe organs in the Gothic era.

**Nomenclature (see Fig. 12)**

**Ambulatory:** The side aisles of the apse surrounding the choir, but separated from the choir by the clôture. This area was unconsecrated and not used by the chapter during services.

**Apse:** The semicircular termination of the cathedral to the east of the transept. In this paper, it is sometimes used interchangeably with chancel.

**Chancel:** The portion of the eastern end of the cathedral contains straight bays, including the liturgical choir and portions of the ambulatory.

**Choir/liturgical choir:** The central portion of the apse contains the choir stalls and seats for high church officials.

**Clerestory:** The uppermost walls of the central aisle are just below the ceiling, where the large stained glass is located.

**Clôture:** The highly decorated stone wall enclosing the choir and the sanctuary, separating them from the ambulatory.

**Facade:** Or organ facade, the visible pipes in an organ case, as opposed to inner, invisible pipes.

**Sanctuary:** The portion of the apse where the high altar is, separated by a low wall and some stairs from the choir.

**Transept/transept crossing:** The rectangular aisle dividing the main axis of Notre-Dame into nave and apse. The transept is responsible for the cruciform shape of the cathedral.

<figure><img src="image_18.png" /><figcaption>**Fig. 12.** Plan of Notre-Dame with key architectural terms marked. The rood screen is indicated in orange, and the clôture is indicated in red.</figcaption></figure>

**Triforium:** The interior galleries along the perimeter of the cathedral, above the arcades of the ground floor and below the clerestory windows. The triforium includes both wide galleries (tribunes) along the perimeter of the nave and apse and narrow service passages in the transept.

**CRediT authorship contribution statement**

**C. d'Alessandro:** Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Conceptualization.
**E.K. Canfield-Dafilou:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation, Conceptualization.
**S.S. Mullins:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Data curation, Conceptualization.
**B.F.G. Katz:** Writing – original draft, Visualization, Validation, Supervision, Software, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization.

**Funding**

Funding has been provided by the European Union's Joint Programming Initiative on Cultural Heritage project PHE (The Past Has Ears, Grant No. 20-JPIC-0002-FS, [phe.pasthasears.eu](http://phe.pasthasears.eu)), the French project PHEND (The Past Has Ears at Notre-Dame, Grant No. ANR-20-CE38-0014, [phend.pasthasears.eu](http://phend.pasthasears.eu)), and the *Chantier scientifique CNRS/Ministère de la Culture/Notre-Dame* ([notre-dame-de-paris.culture.gouv.fr/fr](http://notre-dame-de-paris.culture.gouv.fr/fr)). Special thanks to Cathédrale Notre-Dame de Paris personnel for their
assistance and patience during measurements before the fire. Access for researchers to the cathedral's restoration worksite has been made possible thanks to the public administrative establishment responsible for the conservation and restoration of Notre-Dame de Paris.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

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