2360

for churches [7, 8]. A special case is represented by baptisteries, rotundae and mosques, which are all basedon a central plan design. The sound field inside such places results in peculiar effects as flutter-echoes and“whispering galleries” due to the high symmetry of the This paper provides the results of a virtual acoustic
restitution of the St. John’s Baptistery in Pisa, which is part of the monumental complex of Piazza del Duomo
included in the UNESCO World Heritage Site [9]. Based on central plan design, the Baptistery is a significant
example of Medieval architecture, composed of the central volume at the ground floor, with the baptismal font,
the Pulpit and the altar; the ambulatory delimitated by arches and cross vaults; and the matroneum at the firstfloor, which is size-comparable to the ambulatory. Due to its long-term construction and the union of styles
coming from different masters, different hypotheses about how the first design should have been, exist [10]. So
that, also the acoustic simulations of such hypotheses were carried out and auralisations of a Gregorian chantinside the Baptistery were done in order to recreate the perceptive atmosphere of its acoustics.

2

RESEARCH METHODOLOGY

In order to deeply investigate the acoustic behaviour of St. John’s Baptistery and virtually reproduce the soundinside such a worship place, the followed methodology was applied. A first step was consisted on analysis
of its current acoustics through in situ measurement campaign carried out according to the ISO standard about
performance spaces [11], then the virtual model was shaped and a rigorous calibration process was completed.
The numerical simulations allowed to obtain reliable Room Impulse Responses (RIR) of the Baptistery as it
was and still is, and as it should had looked following the original design according to some historical studies.
Finally auralisation techniques were used to achieve realistic virtual acoustic restitutions.
2.1 Acoustic mesurements
The acoustic measurement campaign was carried out during closing time of the Baptistery in order to measure
the RIRs in unoccupied conditions. The workflow of measure followed the recommendations of the ISO 3382-1
and the guidelines about acoustic measurements in a worship place [12]. 7 positions of sound sources wereselected spread over the ground floor and the matroneum level at the first floor (2 located on the principal
symmetry axis in the altar, 1 near to the pulpit, 2 in the interior and exterior circular of the ambulatory, and2 placed on the matroneum) and 16 receiver points were identified for the RIRs recordings and two Bruel& Kjaer 4181 and one Schoeps KFM6 stereo microphone were utilized. Exponential Sine Sweeps ESS wereused as excitation signals using high-SPL sound sources [13]. A proprietary software was used for both signal
generation and impulse responses acquisition [14]. All the environmental conditions were monitored during themeasurement session and registered an average temperature and relative humidity of 18 C and 58 % respectively.
In the table 1 the measured values, averaged for each sound sources, inside St. John’s Baptistery are reported.
Table 1. Measured values, spatially and spectrally averaged, of the ISO 3382-1 acoustic parameters.
Altar (S1)
Pulpit (S2)Matroneum (S3)EDTM (s)
12.6
12.8
12.2

T30,M (s)
12.8
12.8
13.0

Ts,M (ms)
909
994
954

GM (dB)
15.9
14.3
12.7

2.2 Acoustic modeling and calibration
A 3D model of the Baptistery was shaped with an approximate interior volume of 24000 m3 and in accordancewith the Geometric Acoustics techniques. In order to avoid the increases of the computational time more thannecessary, the complexity of the geometry was strongly reduced and the final model was composed of about
6300 surfaces. The acoustic simulations were provided by hybrid GA software [15]. A transition order equal
to 2 was used to achieve reliable results for early reflections which are responsible for the perceptual acoustic2361

response of the room (TO=2; number of early rays=23518; IR length=20000 ms). The model of the Baptisteryhas been calibrated according to the acoustic measurements and 3 out of 7 source positions were selected forthe entire process (two at the ground floor - one on the altar (S1) and the second one on the pulpit (S2) - andone placed in the matroneum (S3)). The positions of the receivers were subdivided into three groups according
to their placing compared to the ambulatory or the center volume or the matroneum. The calibration workflow(a) 3D Wireframe(b) Measured positions

Figure 1. 3D wireframe of the calibrated model and the positions of the sources and microphones selected forthe acoustic measurements.
mainly consists of an iterative process which involves the acoustic material proprieties, as absorption and scattering coefficients, and thus the selection of these values is responsible of the reliability of the simulations. A
data collection for credible values of absorption coefficients was carried out basing on the scientific literatureon this matter, according to both the material typologies and historical context [6, 16, 17]. Where necessary
some values were slightly adapted according to the specific case and conditions (e.g. elements which were
simplified or even not modeled), according to similar procedures [20]. About the lacking of complex small details in comparison to the main volumes was fixed by assigning particular scattering proprieties. The occupied
condition was simulated and analyzed basing on previous researches on this topic [16, 21]. Considering that theapplied sound absorption coefficients depend on the occupancy density, it was decided to adopt a condition with
1 person per square meter and a scattering coefficient of 0.7 as well. The numerical models were calibrated
taking into account the measured values of Early Decay Time EDT , reverberation time T30 and center time Ts .
The calibration process was considered completed once the simulated values were inside the JND values.
Table 2. Absorption (a) and scattering (s) coefficients for all the materials involved in the simulation.

2362

a

s

Materials

Surface%

125 Hz250 Hz500 Hz1000 Hz2000 Hz

4000 Hz

MarblePlaster
Furniture
Windows
Wood
Faithfuls

71
20
6
2
1
1.5

0.01
0.07
0.12
0.35
0.10
0.16

0.01
0.07
0.12
0.25
0.15
0.29

0.01
0.05
0.10
0.18
0.18
0.55

0.02
0.03
0.04
0.12
0.20
0.80

0.02
0.04
0.02
0.07
0.20
0.92

0.02
0.05
0.02
0.04
0.20
0.90

0.30
0.05
0.70
0.10
0.15
0.70

Ref.
[18]
adapted [18]adapted [17]
[19]
[18]
[16]

2.3 Numerical simulations of the historical models
The perceptible difference between the Baptistery and the external context gave rise to a long debate on what
was the form originally thought by the designer Diotisalvi. Three significant historical studies have been selected
for this paper proposes: De Fleury’s proposal (DF), Boeck’s proposal (BO) and Manenti Valli’s one (MV) [10].
The first two studies were focused on the figure of a cusped dome open on the top with heights corresponding
to the current building. DF’s model was also composed of a lower matroneum than BO’s model and the actualone. MV model appears considerably reduced compared to the current aspect due to the reduction of thematroneum height and the hemispherical dome placed on the inner ring.

(a) DF (V=23600 m3 ; H=50 m)(b) BO (V=23000 m3 ; H=50 m)(c) MV (V=18500 m3 ; H=31 m)

Figure 2. 3D Wireframes of the historical hypotheses about the early design of the Baptistery.
Considering these different hypotheses about the early design of St. John’s Baptistery, the same methodology,
described above, was adopted in order to reproduce the acoustics atmosphere inside. Three different GA models
were shaped according to the historical studies and the materials properties (see fig. 3) used in the simulations
were taken from the calibration of the actual model [22]. At the same manner the computational calculation
was set up, taking into account the volume differences between the models, which involve the calculated effectof the air absorption and the number of rays used. The numerical simulations were ran using the same sourcereceivers configurations of the actual model based on the in situ acoustic measurements.

% A (m2 Sabine)

100
80
60
40
20
0

100

100

80

80

60

60

40

40

20

20

0
125

250

500

1000

Octave bands (Hz)(a) Calibrated Model

2000

4000

MRB
PLS
Others
AIR

0
125

250

500

1000

2000

4000

Octave bands (Hz)(b) BO and DF Restistution

125

250

500

1000

2000

4000

Octave bands (Hz)(c) MV Restitution

Figure 3. Percentage of equivalent absorption area of main materials for each octave band (MRB = Marble,
PLS = Plaster, AIR = Air absorption, Others = all the remaining materials listed in table 2.

2363

20
DF Restitution (Unocc.)
DF Restitution (Occ.)
BO Restitution (Unocc.)
BO Restitution (Occ.)
MV Restitution (Unocc.)
MV Restitution (Occ.)
Calibrated Model (Unocc.)
Calibrated Model (Occ.)

T30 (s)

15
10
5
0

125

250

500 1000 2000 4000
Octave band (Hz)Figure 4. Values of T30 averaged over the receivers positions, in unoccupied and occupied conditions, for the
Calibrated and Restitution models.

2.4 Auralisation
The first step on the MIMO (Multiple-Input-Multiple-Output) auralisation workflow was to put in the Baptisterythe sound sources corresponding to each singer, so that a whole choir could be simulated. A virtual choir offour singers, which may be considered a reference for Gregorian Chant, was simulated. The choir configuration
has been chosen following two displacements: the choir was placed in the ambulatory, directed orthogonallyto the radius of the Baptistery; in the other configuration the choir was near the baptismal font. Such two
positions correspond to different acoustic excitation of the Baptistery, considering the possible effects of soundfocusing. In order to reproduce as close as possible the listening conditions achieved during the performances,
several binaural receivers (multiple-output) are placed on the floor of the Baptistery and Binaural Room Impulse
Responses (BRIRs) were calculated and filtrated with Head Related Transfer Functions (HRTF) for each virtual
receiver. Indeed a set of BRIRs were extracted in occupied conditions in order to reproduce the effect ofthe presence of the faithfuls at the ground floor and the layer of the floor was replaced with the layer of
the audience. For the aim of the present work an anechoic motif was recorded [23], which was La missa deNotre Dame di Guillaume de Machaut (1300–1377), a typical example of musical composition basing on cantus
firmus. Four professional singers of Gregorian Choir, were selected and each singer at time played his part one
after another, following a reference video of the conductor. The recording room was the listening room of the
University of Bologna, treated with high density fiberform (80 kg/m3 ). The porous materials and box-in-a-box
structure made by gypsum board allow a negligible reverberation in a wide range of frequency. The microphone
was placed at about 1.1 m from the soloist, within the critical radius of reverberation, allowing more than 10 dBof direct-to-reverberant ratio. Audio-Technica AT4050 microphone have been used thanks to the good recording
capability and low noise characteristics. The microphone has been set in cardioid configuration and has been
pre-amplified and A/D converted by a RME Micstasy.

3

DISCUSSION

In order to analyze the spatial distribution of sound energy inside the Baptistery, the Calibrated and MV Restitution models were selected leaving aside the other two hypotheses of restitution (see above). Such a selection
was done considering which features would have resulted much more interesting to investigate. Indeed MV
Restitution was opted for according to the significant differences in term of volumes (the matroneum volume
is halved compared to the actual one) and shapes (i.e. hemispherical shaped vs tend shaped dome). So thatthe investigation was based on the comparison of the spatial distribution of sound energy with the analytical2364

prediction curves of Martellotta’s model [7] and generalised µ model [8], elaborated for churches. For sake ofbrevity, detailed descriptions of models are not reported here. Seeing that inside the Baptistery the early reflections still remain after the typical value of 80 ms as limit between the early and late energy part, a time limitof 800 ms was assumed, according to the measurements and particular characteristics of sound field conditions.
Consequently, the coefficient values introduced by the double-rate decay model [7] were chosen taking into
account such a time limit and the geometric complexity of the space, as well as the absorption and scattering
proprieties of the materials. The same considerations were made in order to fit the simulated values of soundstrength in each measured position to the generalised µ model. A value of 0.4 was taken from [8] for the mean
µ given the high complexity of the geometry of the Baptistery. In Figures 5 and 6, the simulated values of GM
and Ts,3 in unoccupied state are reported and compared to the prediction curves above mentioned.
20

20
S1
S2
Generalised µ model [8]Martellotta’s model [7]1816

GM (dB)

GM (dB)

18

14
12
10

S1
S2
Generalised µ model [8]Martellotta’s model [7]

16
14
12

0

4

8

12

16

20

Source–receiver distance r (m)(a) Calibrated: V = 24000 m3 , T30,M = 13 s

24

10

0

4

8

12

16

20

24

Source–receiver distance r (m)(b) MV Restitution: V = 18500 m3 , T30,M = 11.9 s

Figure 5. Simulated GM values in unoccupied state, considering the actual layout (a) and the MV model (b) forS1 and S2 sound sources positions. “M” subscript identifies mean values over the central octave bands 500 1000 Hz. Simulated values are compared with analytical prediction curves: Martellotta’s model (solid lines) [7]and Berardi et al.’s generalised µ model (dashed lines) [8].
Looking at the distribution of GM along all the receivers (see fig. 5), both the analytical prediction curves give
acceptable fitting, even if they have been applied to churches, which may not geometrically link to central
base spaces as in the Baptistery. This works for both the Calibrated and MV Restitution models. In orderto ensure the applying of such analysis, the distribution of Ts,3 , similarly plotted as function of the sourcereceiver distance, was compared with the prediction curve of Martellotta’s model (see fig. 6). In both the cases,
the fittings are not achieved and the regression curves associated with the simulated values are shifted down.
Moreover the change of the slope between early and late reflections may move down. According to these
considerations, future efforts have to be made in order to verify the accuracy of the limit time between earlyand late reflections, which was approximated to 800 ms in the present work, and the applicability of the methodof investigation used.

4

CONCLUSION

Throughout virtual acoustics techniques, the present paper investigates the sound of St. John’s Baptistery in
Pisa, which is included in a site of UNESCO World Heritage. The measurements inside the Baptistery enabled
an accurate calibration of the virtual model corresponding to its actual status, which provided support to theanalysis of spatial distribution of the sound energy inside the Baptistery compared to analytical prediction curves
adapted for churches. Furthermore the calibrated model ensured numerical simulations of the three different

2365

1,200

1,000

1,000

800

800
Ts,3 (ms)Ts,3 (ms)

1,200

600
400

0

400

S1
S2
Martellotta’s model [7]fitting from sim. data

200
0

4

8

12

16

20

Source–receiver distance r (m)(a) Calibrated: V = 24000 m3 , T30,M = 13 s

600
S1
S2
Martellotta’s model [7]fitting from sim. data

200
24

0

0

4

8

12

16

20

24

Source–receiver distance r (m)(b) MV Restitution: V = 18500 m3 , T30,M = 11.9 s

Figure 6. Simulated Ts,3 values in unoccupied state, considering the actual layout (a) and the MV model (b)for S1 and S2 sound sources positions. “3” subscript identifies mean values over the central octave bands 500- 2000 Hz. Simulated values are compared with analytical prediction curve of Martellotta’s model (solid lines)[7] and fitting from simulated values (dashed line)

hypotheses about the original design, giving support to the historical research. Finally, the developing of MIMO
auralisations of a Gregorian Choir placed into two potential configurations gives back the acoustic render ofsuch a place, which is significant in terms of both intangible and tangible Cultural Heritage.

ACKNOWLEDGEMENTS
The authors have to acknowledge Opera Primaziale Pisana for the availibility. The work needed several interdisciplinary contributions: Architects Franca Manenti Valli and Giulia Oleari provided CAD models; Davide
Bonsi provided technical informations about the previous measurement campaign; Francesco Martellotta discussed about the acoustics of the Baptistery; Luigi Bartolomei teached about the Medieval rituals and Cesarino
Ruini the Gregorian Chant, Giacomo COntro and the professional singers of Schola gregoriano-polifonica bolognese.

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