Concert Hall Acoustics: Paper ICA2016-729

Sound energy distribution in Italian opera houses

Massimo Garai(a), Simona De Cesaris(a), Federica Morandi(a), Dario D’Orazio(a)

(a)DIN, University of Bologna. Viale Risorgimento, 2 40136 Bologna (Italy),massimo.garai@unibo.it

Abstract:

A typical Italian opera houses is a complex system of coupled volumes: fly tower, orchestra pit,cavea (the volume where the stalls are), boxes, loggione (gallery). The way of propagation of thesound energy between one volume and the others is still a subject of research. The present workgives a contribution to the discussion by applying the Barron’s revised theory to the analysis ofrecent measurements done in several Italian theatres. The averaged values of sound strengthvs the distance from the sound source is plotted inserting in the Barron’s equation either theclassical reverberation time or the early decay time and different volume values. The significanceof the different choices and their agreement with the experimental values are discussed. It isconcluded that the spatial distribution of sound strength depends on the sound source position.

Keywords: Architectural acoustics, Italian opera houses, coupled volumes, sound strength, earlydecay time

Sound energy distribution in Italian opera houses

1 IntroductionIn Italian opera houses, the acoustics perceived by listeners sitting in the stalls is mainly con-ditioned by the presence of the seats, usually sound absorbing, of a very reflecting surfacesurrounding the stalls at the height of the listeners’ ears (a plaster made of marble powder andslaked lime, called marmorino), of the boxes and of course by the volume. As in a sabinianspace the reverberation time is related to the volume, some authors [1, 2] proposed that thevolume to be taken into account be the one of the main hall, excluding the volumes of the flytower, the boxes and the gallery.

A proposal by Hidaka and Beranek [1], accepted also by Prodi et al. [2], splits the operahouses in two groups, respectively group A and group B. Group A includes theatres with partialdraperies or empty stages, large stage house or hard reflecting surfaces. Group B includes“regular” theatres. Group A and Group B have been defined on the basis of two regressioncurves of the measured values of reverberation time versus the volume of the audience space.It is worth noting that the studies of Hidaka and Beranek [1] and Prodi et al. [2] found differentfitting curves for each group of theatres. The same authors studied the theatres also using thetrend of the ratio EDT/V vs the spatial averaged value of the sound strength G, "according thehypoteses of the diffuse field theory" ([2], Fig. 6).

In this work, relying on the large amount of measurements collected in eleven historical operahouses [3, 4, 5], the Barron’s revised theory, originally conceived for concert halls only, isextended to study the spatial behaviour of the sound energy in Italian theatres.

2 MeasurementsThe eleven theatres were investigated in an unoccupied state. The measurement sessionswere carried out between May 2014 and March 2015. For the purpose of this study, thepositions of the omnidirectional sound source on the stage were chosen similarly in all theatres:the first position (SS1) on the longitudinal axis of the stage at 1 m from the edge (fore stage),the second one (SS2) at the centre of the area closed by the curtains (centre stage). See Fig.1.

In the stalls, impulse response measurements were performed at all seats for the two sourcepositions. In each box, measurements were performed placing the microphone in the frontposition. In the gallery, measurements were taken in correspondence to the seats in the boxes,with some slight differences depending on the setting of the gallery. Over 50,000 IRs wereprocessed [10]. According to ISO 3382-1 the height of the microphone was kept at 1.2 m. Thecurtains were set for a standard performance of a medium-sized orchestra in the large theatresand in the standard configuration for the smaller theatres. For the latter ones, the minimumamount of absorptive material on the stage suggested in the Charter of Ferrara [6] of 500 m2

could not be satisfied. Is important to note that the volume of the fly tower is measured below

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(a) BON (b) ALI (c) MAS (d) ROS

(e) STI (f) GOL (g) DRA (h) RUS

(i) CES (j) CER (k) PET

Figure 1: Plans of the eleven investigated theatres with the source positions on the stage(metric scale).

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Table 1: Architectural features of the eleven investigated Italian historical opera houses.

Theater, City Seats Vhall (m3) Vstage (m3) Scenic arch (m x m) T30,M (s)BON Bonci, Cesena 798 3130 11634 12 x 7.8 1.39ALI Alighieri, Ravenna 835 3360 8256 12.6 x 9.6 1.12

MAS Masini, Faenza 500 2580 4299 10 x 9.2 1.11ROS Rossini, Lugo 448 1490 3611 9.2 x 8.3 1.00STI Stignani, Imola 550 1750 3895 10 x 8.1 0.96

GOL Goldoni, Bagnacavallo 390 1430 4125 8.2 x 7.9 1.47DRA Dragoni, Meldola 318 1140 1082 6.8 x 7.3 0.83RUS Comunale, Russi 305 900 1372 8 x 7.5 0.97CES Comunale, Cesenatico 271 870 1322 7.4 x 8.6 0.90CER Comunale, Cervia 224 730 1141 8.1 x 7.4 0.84PET Petrella, Longiano 241 630 1392 7.5 x 9.1 1.07

the trellis. In line with the previous literature [1, 2], Tab. 1 shows the main characteristics ofthe theatres under study; the subscript ‘M’ denotes the average over the octave bands centredat 500 Hz and 1,000 Hz.

2.1 Reverberation time and early decay time

The volumes of the main halls of the two biggest theatres, BON and ALI, are comparable (seeTab. 1), but the respective reverberation times are quite different. This is due to the fact that thenumber of seats in the audience is different: 370 seats in ALI, 222 seats in BON. Moreover,while in BON the seats are poorly absorbing (wooden seats with a velvet lining), in ALI theseats are heavily upholstered. This causes a reduction of reverberation time of about 27%.BON is also characterised by a huge stage house, unusually large compared to the main hall.GOL is also highlighted in Fig. 2 as its behaviour does not follow the general trend, due tofinishings and the geometry of the hall.

While the reverberation time T30 is a constant of the hall, due to gaussian properties of theenergy decay curve between -5 and -35 dB, the EDT is more variable, being related to thedeterministic part of the impulse response, and may help in identifying the transition betweenthe early and the late reverberation. In fact, the Italian theatre is a complex system of rever-berating volumes, partially coupled the one with the other. Moreover, in the Italian historicalopera houses, the typical impulse responses are characterised by the presence of strong earlyreflections provided by the proscenium arch, the vault and, for the stalls area, from the smoothside walls. Thus, decays of this kind can be identified as “cliff-type" decays, being the EDT val-ues smaller than the T30 ones. Due to its variability EDT is also useful to qualify the differencebetween the various parts of the audience: stalls, boxes, gallery.

2.2 Sound Strength

The natural amplification of the hall (Sound Strength) is an important factor when the soundsources are mainly singers and the orchestra is often reduced compared to the symphonicones. In the small- or mid-sized theatres under study the measured sound strength values are

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0 1,000 2,000 3,000 4,000

1

1.5

2

B

A

GOLBON

V hall (m3)

T 30,

M(s

)

Figure 2: Plot of the reverberation time T30,M averaged in the octave bands of 500, 1000 Hzversus the volume of the halls V . The dashed gray lines are the regression curves, respec-tively for theatres of group A and B, proposed by Prodi et al. [2].

high enough to assure to the listeners a good intelligibility of the singers’ voice [5].

It has been proved that if the Sabine’s theory is valid, then G is proportional to T30 and inverselyproportional to V [1]. Thus, Fig. 3 shows the plot of the EDT/V ratio vs the G values. Hidakaand Beranek found a high correlation between EDT/V and G for the theatres with highly ab-sorbing stage houses (group B in Ref. [1]); the importance of the draperies is confirmed alsoby the set of data provided in the present work. The linear regressions calculated over theeleven halls with the sound source on the fore stage (proscenium) have an angular coefficientdifferent from the one predicted by the diffuse field theory, with a trend that recalls closely theone found in Ref. [2]; this highlights the greater relative weight of the energy of the directfield to that of the reverberant field when the sound source is placed on the proscenium, i.e.between the coupled volumes of the stage house and the main hall. It should be noted that inthe present study the values measured in the stalls of the theatres of the two groups (A andB) are well fitted by the same curve. This result agrees in some manner with the analogueanalysis in Prodi et al. [2] and differs from the results of Hidaka and Beranek [1] for a set oflarger halls in which the two curves are clearly distinguishable.

3 MethodThe aim of this work is to prove on an experimental basis that the sound energy inside anItalian opera house is related to the acoustic volume of the hall “seen” by the sound sourceduring the measurements. In other words, the spatial distribution of G depends on the soundsource position. For this purpose the Barron’s “revised theory” and the classical diffuse fieldtheory are compared on the same set of measurements.

The “revised theory” of the semi-reverberant sound field [7] gives a relationship between the

5

0 5 10 15 20

102

103

Prodi et al.

Hidaka

&Ber

anek

GM (dB)

106 E

DT M

/V(1

06s/

m3 )

(a) SS1 (proscenium) V = Vhall

0 5 10 15 20

102

103

Prodi et al.

Hidaka

&Ber

anek

GM (dB)

106 E

DT M

/V(1

06s/

m3 )

(b) SS2 (centre stage) V = Vhall

0 5 10 15 20

102

103

Prodi et al.

Hidaka

&Ber

anek

GM (dB)

106 E

DT M

/V(1

06s/

m3 )

(c) SS2 (centre stage) V = Vhall +Vstage

Figure 3: Plot of EDTM/VM versus GM. The theatres in group A are marked with an emptysquare, the ones in group B are marked with black dots.

expected sound strength value at distance r from the source, G(r) (in dB), the volume of thehall, V (in cubic metres) and the mean of the reverberation time measured in the hall, T (inseconds):

G(r) = 10log[

100r2 +31200

TV

e−0.04r/T]

(dB) (1)

While in a classical concert hall the volume of the hall is unequivocally defined, in an operahouse constituted by several coupled volumes it is more problematic to assess which is theacoustic volume "seen" by the sound source. In other words, it is not clear which volume valuemust be taken into account in Eq. (1). The volume of the cavea only (as proposed by Hidakaand Beranek and Prodi et al.) or both the volumes of the hall and the fly tower? In order toanswer to this question, we tested two formulations of the Barron’s revised theory: in the firstone V = Vhall, in the second one V = Vhall +Vstage.

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Moreover, studying the effect of the balconies, Barron suggested the use of the EDT insteadof T30. Following this suggestion, and taking into account the coupling of the volumes of thestage house and the cavea in Italian opera houses, the original relationship Eq. (1) may beformulated in terms of T30 as well as of EDT . In addition, in order to verify the effectivenessof the coupling effect the Late Decay Time (LDT ) may also be used, being the LDT the rever-beration time calculate from a line fitted over the range -25÷-35 dB of the energy decay curve.This gives rise to six possible combinations, summarized in Tab. 2, which should be repeatedfor each sound source position (SS1 on the fore stage, SS2 at the centre of the stage).

Table 2: Possible combinations of volume and reverberation time values to be used in Eq.(1) for each sound source position and colour code used in Figg. 4 and 5.

EDTM T30,M LDTM

V = Vhall violet red orangeV = Vhall +Vstage cyan green dark blue

4 Results and discussionsThe sound strength values measured in the eleven theatres (see section 2) have been plottedversus the distance r from the sound source. The sound source positions SS1 (fore stage)and SS2 (centre stage) have been used (see section 2). For each theatre the measured soundstrength values (black points) have been compared with the curves of the Barron’s revisedtheory, calculated using in Eq. (1) as volume the volumes of the cavea only or the sum ofthe volumes of the cavea and the fly tower and as reverberation time the measured EDTM,T30,M and LDTM values, averaged over the receivers in the stalls. Fig. 4 shows the results formid-sized theatres, Fig. 5 shows the results for the small-sized theatres.

The behaviour of the Barron’s revised theory curves is quite different for the two sets oftheatres. For the mid-sized theatres the experimental results match the revised theory withV = Vhall. For the small-sized theatres some measured results seem uncorrelated with the the-oretical curves (e.g. see CER in Fig. 5); this may be due to the reduced size of the hallswhere the source-receiver distance and the critical distance of reverberation have comparablevalues. Nevertheless, some examples of small-sized theatres show a general agreement withthe choice V = Vhall when the sound source is in SS1. (e.g. see RUS and PET in fig. 5). Thus,the measurements suggest that, if the sound source is placed on the fore stage (SS1), theBarron’s revised theory holds considering the volume of the cavea, i.e. the volume of the stallsaudience only, according also with the fitting curve of Fig. 3(a). It may be argued that the dif-ferent trend in this figure of the measured value with respect to the fitting curve calculated fromthe classical theory supports the application of the revised theory. Increasing the dimension ofthe theatre the averaged values of the sound strength decrease with respect to the diffuse fieldtheory.

When the sound source is placed at centre stage (SS2) the Barron’s theory seems no moreapplicable, as shown by the comparison with measurements. In fact the experimental sound

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(a) BON

(b) ALI

(c) MAS

(d) ROS

(e) STI

(f) GOL

Figure 4: Averaged G values for the mid-sized theatres under study. Left side: soundsource in SS1. Right side: sound source in SS2. Colour code in Tab. 2.

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(a) RUS

(b) DRA

(c) CER

(d) CES

(e) PET

Figure 5: Averaged G values for the small-sized theatres under study. Left side: soundsource in SS1. Right side: sound source in SS2. Colour code in Tab. 2.

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strength values do not show any decreasing trend increasing the distance from the soundsource. In this conditions the sound field found in the stalls seems to match the diffuse fieldtheory, if both the volumes of the hall and the fly tower are taken into account (see Fig. 3(c)),as suggested also by the offsets of the curves in Fig.4, right side. Remarkably, the generaltrend of the experimental sound strength vs. distance shows a different behaviour for the twotheatres of the A group (BON, GOL). The effective volume ’seen’ by SS2, according to themeasurements, seems to be an intermediate value between Vhall and Vhall +Vstage. Furthercomparisons between the equivalent absorption area of the fly tower and of the stalls mayallow to better understand the behaviour of group A theatres.

It is worth noting that, on the contrary of the concert halls studied by Barron, in the Italianopera houses the sound strength increases for the receivers near the backside of the cavea(and, more in general, at the edges of the stalls). This is due to the peculiar shape of thesetheatres, being more evident when they are elliptical in plan (e.g. see the measured soundstrength of ROS and STI in Fig.4 and their plans in Fig. 1).

5 ConclusionsThe energy distribution of the sound field in eleven Italian historical theatres has been investi-gated, comparing the measured values of sound strength with the predictions of the Barron’srevised theory.

When the sound source is on the fore stage (proscenium) the revised theory is confirmed.When the sound source is placed at centre stage the revised theory seems not applicable:indeed the sound strength does not show any significant dependence on the distance from thesource. This may be due to the fact that some of the hypotheses (on the behaviour of thereflections) underlying the Barron’s revised theory are not applicable when the sound sourceis not inside the same volume of the audience, but inside a second volume (the stage house)coupled to the first. Moreover, an interesting relationship has been found between the G valuesand the volume of the opera house: when the sound source is on the fore stage, only thevolume of the hall contributes to the reverberation; when the sound source is at centre stageboth the volume of the stage house and the volume of the hall must be taken into account.This fact has been proved in two ways: first by using some results of the Barron’s revisedtheory, and secondly by comparing the measured values of EDT/V vs G with the diffuse fieldtheory. This findings extend some proposals of the previous literature in which only the volumeof the hall has been considered.

The categorization of opera houses in group A and group B, proposed in the previous literature,seems relevant also for the sound energy distribution. While group B includes “normal” operahouses, in group A theatres the acoustic volume ’seen’ by the sound source at centre stageis about Vhall +Vstage/2. Further studies may be able to correlate this behaviour with the ratiobetween the equivalent absorption areas of the stage and of the hall.

Finally, the method proposed in this study allows to identify as “small theatres” the ones smallerthan a threshold, below which the proposed method seems to be meaningless. This happens

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when the theatre dimensions are comparable to the critical distance of reverberation: in thiscase the sound field is dominated by the direct sound field and the first reflections, thus notfulfilling the hypoteses underlying the Barron’s revised theory.

Acknowledgements

This research project was supported by CIRI - Edilizia e Costruzioni (POR-FESR 2007-2013).The authors gratefully acknowledge the directions of the studied theatres and the students whocontributed to the measurement sessions.

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