As mentioned in the abstract, during a refurbishment in 1928, the proscenium of the stage was removed in order to open the orchestra pit, which was not considered in the original 1840 design. Acoustic differences between the original design of Alighieri theatre and the present one were studied by using numerical simulations. Two acoustic simulation models were done: the original design and the present one.
The proscenium, as mentioned in the abstract, was the foreground part of the stage, and it was made of wood. The wooden stage is fixed above the air cavity: it works as an acoustic absorber at low frequencies and, at the same time, it shows some re-radiation properties above its coincidence frequency. In order to study the acoustic behaviour of the historic wooden stage, further vibro-acoustic measurements were done. Laboratory tests on specimens helped to evaluate the influence of the aging on fir wood. Then, in situ measurements on the stage of the Alighieri Theatre confirmed the results of specimens, helping the vibro-acoustic behaviour of the historical stage.
After the calibration procedure, two models of the theatre were built: the original and the present one. A virtual sound source was simulated in each model, which was placed in the position used by the soloist during arias, respectively, in the proscenium and on the fore-stage. Room criteria were simulated over the same receivers used in the calibration procedure. Finally, results were compared.
2.1. The Alighieri Theatre in Ravenna
In 1838, Tomaso Meduna (1798–1880) was asked to design the new opera house in Ravenna. Tomaso Meduna, formerly the architect of “La Fenice” Theater in Venice, accepted the job along with his brother Giovanni Battista (1800–1886). The works began in 1840 and the theater was inaugurated in 1853 [
41]. In the 1840 design—in the following cited as the “original” one—the stage was protruded in the cavea (the so-called
proscenium), to a corresponding surface until the line of the first boxes (see
Figure 1). Furthermore, the orchestra was placed at the same level of the listeners in the stalls, corresponding to the second and the third row of chairs. The floor of the stalls, which was entirely made of pine wood, was supported with pine wooden truss holding up larch architraves and brick pillars. A river cobblestone was placed under the floor [
42]. In 1928, the orchestra pit was built, cutting the proscenium. From 1959 to 1967, the theatre remained closed, in order to replace the wooden structures affected by termites: the original wooden structures were replaced by newer ones made by concrete and steel. The theatre reopened in 1967. The wooden stage was replaced a second time in 1970 [
43]. In the summer of 2015, the wooden stage was renewed for a third time. The theatre is now used for opera and symphonic music by the resident “Luigi Cherubini” Young Orchestra, found and conducted by Riccardo Muti.
2.2. Measurements and Simulation Set-Up
On the basis of available plans and sections of the present state of the Alighieri Theatre, a geometrical acoustic model was set up for numerical simulation purposes. This model was calibrated according to the acoustic parameters extracted from the Room Impulse Responses (RIRs), which have been measured during the acoustic measurements in September 2014 and vibro-acoustic measurements on the stage in November 2014.
The workflow of acoustic measurements followed the ISO 3382-1 [
14] recommendations. Three positions of sound sources were used in the stage (two) and inside the orchestra pit (one), following the recommendation of the Ferrara charter [
13]. RIRs were measured for each sound source in each position of stalls, boxes and gallery, for a total amount of about 2500 measurements [
10]. Exponential Sine Sweeps (ESS) were used as excitation signals through a custom high-SPL sound source [
44]. The excitation signal was 128 K length with a sample rate of 48 kHz, allowing for measuring IRs that have enough signal-to-noise ratio in each octave band. A proprietary software was used in order to optimise the time-windowing of the ESS and, consequently, the frequency response of the measured impulse responses [
45].
2.3. Assumptions and Numerical Calibration
In order to understand the acoustic improvements generated by the last renovations and to investigate the acoustic behavior of the original design—the one with the
proscenium—a geometrical model of it was created for numerical simulation aims. In
Table 3, geometrical data of both acoustic models are reported.
The acoustic simulations were provided by hybrid ray tracing software Odeon v.12 (Lyngby, Denmark). The software uses two different calculation methods for early and late reflections and it switches from one to the other according to the transition order (TO) that the user indicates. The early reflections calculation is carried out with the deterministic image source method, while the late reflections calculation is driven by the statistical ray tracing method. A transition order equal to 2 was used. The number of late rays used in the calculations was enough to allow an adequate accuracy, according to the investigation of the reflection density parameter that should be higher than at least 25 reflections/ms for reliable results [
46]. A length of the simulated impulse response of 2500 ms was selected to be greater than the estimated reverberation time. The virtual sound source was placed on the fore-stage, at 1 m from the edge; in the original design model, the sound source was placed on the proscenium, at 1 m from the edge. Twelve virtual receivers were placed in the stalls, eight on two column boxes—two in each tier—and two in the gallery, as suggested by a Ferrara-charter [
13].
The model of the theatre (see
Figure 2) was calibrated according to the acoustic measurements and the reliability of the calibration process was evaluated following simulation procedures based on the previous studies [
29,
47]. The calibration workflow mainly consisted of an iterative process which involved the acoustic material proprieties, as absorption and scattering coefficients, and thus the selection of these values is responsible for the reliability of the simulations. A data collection for credible values of absorption coefficients was carried out based on the scientific literature on this matter, according to both the material typologies and historical context [
48,
49]. Some values were slightly adapted according to the specific case and conditions, e.g., elements which were simplified or even not modeled as the technical equipments in the fly tower. In fact, some values of absorption coefficients have been slightly modified in order to adapt them to the specific case of the theatre, while remaining within reasonable ranges considering comparable materials in the literature. Values of plaster inside the fly tower and hall results higher than the referenced ones due to the presence of furniture—as scenography furniture for the stage and general furniture for the hall—during the measurement session. The most significant adaption of values of absorption coefficients was done for the case of the boxes where the geometrical details as seats and objects inside were not modeled in order to avoid the increase of number of surfaces, which are not necessary for the simulation process [
46]. In particular, the absorption and scattering coefficients assigned to the boxes are significantly high due to the lack of interior modeled surfaces. Considering the lack of complex small details in comparison to the main volumes, particular scattering proprieties were assigned to fix it. The scattering and absorption coefficients of all the materials involved in the geometric acoustic (GA) simulations are reported in
Table 4.
The following acoustic parameters were considered in the calibration process: Early Decay Time
, Reverberation Time
, Center Time
and Clarity
[
50]. Giving the couples of sound sources/receivers used in the calibration process, the work was completed once the difference between the measured values and the simulated one was less than twice Just Noticeable Differences (JNDs). For sake of brevity, the calibration results are reported in
Figure 3, where
and
values were plotted—for each octave band—showing for sound source the averaged values over three groups of receivers—respectively, stalls, boxes, and gallery.
2.4. Vibroacoustic Measurements of the Historical Wooden Stage
A crucial aspect of the work concerns the stage. In an HOH, the stage was typically made of light wooden fir, in order to fix the scenes during operas. Any acoustic reason was taken into account by pre-Sabinian scholars regarding the stage design [
18]. Previous works related to wooden stage-air cavity are purely numerical [
51,
52], or related to the fork-effect of cellos and double-bass only [
53] or the early work of Beranek, which showed an increment of radiation in the 125 Hz octave band [
54]. Instead, the present work needed vibro-acustic measurements for archeo-acoustical reasons. The question was: “Are the historical stage properties similar to the present ones?”.
In 2014, the direction of the Alighieri Theatre stated the renovation of the wood of the stage and the authors were asked to study the effects of wood aging on stage acoustics. The original stage was made of fir boards, arranged in square blocks, measuring 17.30 m by 17.30 m and sloping “nel rapporto di vent’uno di base per uno di altezza” (the ratio is 21/1 in height, corresponding to a slope of 2.6 degrees). Samples of not-aged and two-year aged firs were analyzed in a laboratory and compared with a historical sample of the stage.
A set of measurements was carried out in the laboratory to determine several relevant parameters related to the acoustical quality of the wood. In particular, density, wave propagation speed and elastic modulus have been measured and calculated. Furthermore, considering these characteristics, it is possible to define other quantities useful to compare the acoustical properties of different materials: the quasi-longitudinal wave speed in beams, the characteristic impedance, the sound radiation coefficient and the loss factor were determined for three specimens. In order to compare the measured and the predicted data, propagation velocities and elastic modulus were measured in all of the directions, by using mechanical impulses and accelerometers: the equipment included a signal conditioner Brüel and Kjær NEXUS, two Piezoelectric charge accelerometer Brüel and Kjær 4371V, an instrumented impact hammer APTech AU02 (Bombay, India) and a calibrator Brüel and Kjær 4294.
Figure 4 shows how the measurements were performed on the samples: two accelerometers were fixed at a reference distance
d and impulses were generated with an impact hammer along the longitudinal axis (
), the tangential axis (
) and the radial axis (
). The signal acquired from the accelerometers and the impact hammer were therefore analyzed in order to calculate the wave propagation speed considering the time delay from the two signals. A Matlab code (The MathWorks, Boston, MA, USA) was then created to calculate the wave speed
in the longitudinal direction with the impulse generated in the longitudinal direction. Similarly, the quasi-longitudinal wave speed
in the tangential direction with the impulse generated in the tangential direction was determined. The values of the different wave speeds obtained with the method described are summarized in
Table 5.
The wave propagation speed along different axes was measured in order to compare the three samples’ characteristics. With the obtained values, it was possible to determine the dynamic elastic modulus
E from Equation (
1), the characteristic impedance
z and the sound radiation coefficient
R from Equations (
2) and (
3), respectively. The sound velocity is defined as the root square of the ratio between elastic modulus
E and density
:
The characteristic impedance is defined as a product of sound velocity
c and density
:
and, finally, the radiation coefficient
R is defined as the square root of ration between the elastic modulus
E and cubic density
:
These quantities allowed for analyzing the acoustic properties of the different samples and comparing them with the ones found in other studies. From these values, it is possible to calculate the elastic modulus in longitudinal and tangential directions, respectively
and
[
55]:
See
Table 5 for the values measured in the specimens. The main result is that the radiation properties of the two-year aged specimen were quite similar to the historical one, in the first approximation of the used model.
Moreover, vibration measurements were carried out on the stage of the Alighieri Theatre in November 2014, see
Figure 5. Using the instrumented hammer as the source, impulse responses were recorded by accelerometers. Then, the measured impulse responses were evaluated two at a time, taking into account the disposition and the distance. The velocities extracted were statistically analyzed through histograms of occurrences: only the measurements with the receivers aligned are plotted in
Figure 5c. The mean value of the measured velocities on the stage is about 770 m/s and this value is comparable with the laboratory measurement value of 800 m/s, done for historical fir in
Table 5.
The in situ measured vibro-acoustic impulse responses were also analysed in frequency.
Figure 6 shows the amplitude of the modulus of the Fourier Transform of the measured velocities, which were normalised, with each curve plot a source–receiver couple. The maxima are in the range 70–100 Hz and this aspect was considered in the calibration process, by increasing the absorption of the wooden stage in the octave band of 125 Hz. Since the voice of a soloist shows a negligible contribution in this frequency range, the vibro-acoustic behaviour of the stage/proscenium may be considered negligible in all other aspects of the present study.
Finally, it is interesting to note that the acoustic properties of the two-year aged specimen are close to the ones of the historical specimen. It follows that only aged wooden boards should be used in the stage refurbishment; at the same time, the renewed stage can ’play’ like the former one, from a vibro-acoustic point of view. It should be noted that the present works concerned fir wood only, which is the most used wood essence for the stage.