on the acoustics of ancient greek and roman theaters

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On the acoustics of ancient Greek and Roman theatersAndrea Farnetani,a� Nicola Prodi, and Roberto PompoliDipartimento di Ingegneria, Università degli Studi di Ferrara, via Saragat, 1-44100 Ferrara, Italy

�Received 22 May 2007; revised 4 June 2008; accepted 4 June 2008�

The interplay of architecture and acoustics is remarkable in ancient Greek and Roman theaters.Frequently they are nowadays lively performance spaces and the knowledge of the sound fieldinside them is still an issue of relevant importance. Even if the transition from Greek to Romantheaters can be described with a great architectural detail, a comprehensive and objective approachto the two types of spaces from the acoustical point of view is available at present only as acomputer model study �P. Chourmouziadou and J. Kang, “Acoustic evolution of ancient Greek andRoman theaters,” Appl. Acoust. 69, re �2007��. This work addresses the same topic from theexperimental point of view, and its aim is to provide a basis to the acoustical evolution from Greekto Roman theater design. First, by means of in situ and scale model measurements, the mostimportant features of the sound field in ancient theaters are clarified and discussed. Then it has beenpossible to match quantitatively the role of some remarkable architectural design variables withacoustics, and it is seen how this criterion can be used effectively to define different groups ofancient theaters. Finally some more specific wave phenomena are addressed and discussed.© 2008 Acoustical Society of America. �DOI: 10.1121/1.2951604�

PACS number�s�: 43.55.Gx, 43.55.Ka, 43.55.Mc �NX� Pages: 1557–1567

I. INTRODUCTION

Greek and Roman theaters had a role of paramount im-portance in the history of western culture. Many of suchspaces are still used nowadays for their original scope withminor or no adaptations at all. The outstanding achievementof ancient designers to provide such robust and outstandingspaces of performance has long attracted architects and, inthis framework, acoustics plays a key role. In fact, both fortheir architecture and its related acoustics, the Greek theaterscan be considered the starting point of theater history anddesign.1 The peculiar acoustical character of the ancient the-aters has been the subject of several specific studies in thepast. One of the most important theoretical works in thisrespect is Canac’s book2 where the geometrical room acous-tics approach was applied. In this study a basic energeticequation for the sound level was developed as a function ofthe hearing angle and of the slope of the cavea. Sometimesthe design skill inherited from the past was valorized. This isthe case, for instance, for the design of the cavea and of theGreek technique of increasing its slope toward the farthestpositions, which is regarded as a valid rule also for moderntheater design.3 Furthermore one can find in literature severalreports on acoustical measurements and on computer simu-lations applied to ancient theaters. In Ref. 4, acoustical mea-surements in the Theater of Epidauros are presented. Soundlevel, speech intelligibility, and reverberation time are ana-lyzed, and the conclusion is that the reason for good acous-tics lays on the achievement of Greek designers to optimizetheaters plan and section. Then Shankland,5 on the basis ofspeech articulation score measurements, hypothesized thatthe early scattering from the edge steps plays an importantrole. More recently, measurements in the Aspendos, Perge,

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and Termessos Theaters were presented in Ref. 6 togetherwith acoustical simulations based on computer models. Mea-surements of orthogonal factors were done in Delphi andTaormina.7 Other works used computer simulation to studythe sound field in ancient theaters as Ref. 8 where the acous-tical properties of the Epidauros theater are analyzed andcompared to two other theaters �Dodoni and Patras Odeon�via computer-aided prediction and auralization. Finally, a1:10 scale model of the Delphi theater with 5000 scale-sizedseated figures was built.9 Furthermore a specific issue of thesound field in ancient theaters was recently addressed, that is,the effect of diffraction of the seat rows.10 Although thoseeffects are not specifically studied in the present paper, theywill show up in the obtained results and will be discussed.All in all the review of literature provides a useful outlook onthe main features of either Greek or Roman theaters, butrarely those two types of spaces have been compared directlyin a single work. A notable exception is the recent paper11

where the acoustical evolution from the former to the latterwas investigated by the use of computer modeling. After theuse of such tool was formerly assessed, several models ofideal ancient theaters in their original configuration were de-veloped and systematically studied. The study11 makes verylimited use of acoustical measurements and refers to idealancient theaters, complete in every part. Actually such the-aters are hardly found today due to the consequences of timedegradation or to successive refurbishments with differentstyles.

The aim of the present work is to investigate the changeof the acoustics from Greek to Roman ancient theaters and,in particular, to trace back the acoustical characteristics tospecific design elements introduced during this architecturalevolution. The work is based on in situ acoustical measure-ments in a group of five Greek and Roman ancient theaters
and on scale model measurements. In fact, thanks to a rich
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os, �

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archaeological documentation of the ancient theater of Sira-cusa �Italy�,12 it was possible to focus on the architecturalevolution of this theater across the centuries from Greek toRoman times. Based on the archeological evidences quitespecific historical configurations of the theater of Siracusawere identified and a scale model was built to test themacoustically. Unfortunately this theater is today lacking manyoriginal parts and in situ surveys would not be representativeof historical state. The scale model measurements of the dif-ferent layouts of the Siracusa theater and the in situ measure-ments in the five real theaters were collected into one dataset. By doing so the outstanding role of the several architec-tural elements was isolated. Part of the present work wasdeveloped within the EU Project ERATO �IdentificationEvaluation and Revival of the Acoustical Heritage of AncientTheaters and Odea�13 whose aim was the acoustical and vi-sual reconstruction, in a three dimensional virtual environ-ment, of some outstanding examples of ancient theaters andodea.

II. IN SITU MEASUREMENTS

Within the ERATO project, two well preserved theaterswere chosen for acoustical measurements. The former is lo-cated in Aspendos in the southern part of Turkey and thelatter is the Jerash South Theatre in Jordan. In particular, thetheater of Aspendos is probably the best preserved Romantheater in the world as it is the only one having a completeoriginal stage wall and also an aisle covered by a colonnadein the upper part of the cavea.

Moreover, acoustical measurements were taken in threeother ancient theaters: the Greek theater in Delphi �Greece�,the ancient theater in Taormina, and the ancient theater inSegesta, both located in the South of Italy. In this work thosemeasurements are grouped with the results from the ERATO

FIG. 1. Plans of selected ancient theaters: �a� Aspend

project to have a richer set of data. The plans of the theaters

1558 J. Acoust. Soc. Am., Vol. 124, No. 3, September 2008


measured in situ are shown �not in scale� in Fig. 1. It can benoted that the layout is semicircular for all the theaters ex-cept for Delphi, which shows a lightly pronounced fanshaped cavea. The main architectural characteristics of thetheaters are reported in Table III. The following acronymswill be used to identify the different theatres: Aspendos �AS�,Jerash �JE�, Taormina �TA�, Delphi �DE�, and Segesta �SE�.

The measuring equipment used during the sessions con-sisted of a portable computer and a multichannel sound card.Moreover a dodecahedron sound source and two differenttypes of microphones were used. In fact, acoustical data wereacquired in the binaural and monaural formats as well as inthe B-format one, to have a complete characterization of thesound field and, in addition, to achieve useful primary datafor auralization.

A 20 s long exponential sweep sine signal was generatedfrom 50 Hz to 20 kHz and sent to the source amplifier. Thenthe four channels of a B-format microphone and the twochannels of a dummy head were simultaneously recordedand stored for postprocessing. For each source-receiver po-sition the impulse response was obtained by convolving theacquired signal with the suitable inverse filter. Finally severalacoustical parameters were calculated based on the monauralW signal of the B-format impulse response according to theISO3382-1 standard.14

A different number of sources and receivers were useddepending on theaters size. Two source positions are com-mon to all measured theaters: the former on the front stageand the latter in the central area of the orchestra. The heightof the source was 1.5 m. The microphone probes wereplaced at 0.7 m from each other and all the signals wererecorded simultaneously. Moreover the probes were 1.1 mhigh above their reference floor �the step where the listeners’feet rest�. All the theaters were unoccupied during the mea-

b� Jerash, �c� Taormina, �d� Delphi, and �e� Segesta.

surements.

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III. RESULTS FROM IN SITU MEASUREMENTS

A. Reverberation

The values of reverberation time T30, as defined in Ref.14, obtained averaging all sources and receivers, are reportedin Fig. 2 as a function of frequency in the octave bands from125 Hz to 4 kHz �the overall value is also reported�. Thestandard deviation bars of the spatial distribution of the pa-rameters are included. The bars extend from the top of eachcolumn. AS has the higher T30 �about 1.6 s at middle fre-quencies� because it is the only one that has a complete stagebuilding and the upper colonnade. The theater is laterallyclosed and the sound energy can circulate inside, undergoingmany scattered reflections that cause a longer reverberanttail. The T30 of JE and TA is almost coinciding �1.2 s atmiddle frequencies� even if their dimensions are different. Infact, the cavea in TA is nearly as wide as in AS �inner diam-eter about 100 m� whereas in JE it is only 63 m. Neverthe-less their overall architectural features in the present state aresimilar: both have a partial stage wall and have no uppergallery.

Finally, the lower T30 �about 0.5 s for middle frequen-cies� was found in the DE and SE as they have no stagebuilding. The sound scattered from the tiers of steps does notundergo further reflections and the energy is rapidly lost.

B. Clarity

The C50 parameter, as defined in Ref. 14, is preferred inthis study as the clarity for speech is more suitable in ancienttheaters, where spoken word had a special importance. InFig. 3 the average values of the C50 calculated for all sourceand receiver positions are presented as a function of fre-quency. The spatial standard deviation is also shown for eachfrequency band. First it can be seen that in AS, although thereverberation time is rather high, the values of C50 are alsoremarkably high. This fact is due to the most energetic re-flections which all arrive with limited delay in the very firstpart of the impulse response. Moreover the graphs show agreat variability of the parameter regarding the receiver po-sitions, with a standard deviation of about 2 dB for all thetheaters. Very high clarity values are found in DE and SE

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FIG. 2. Comparison of the average reverberation time for all theaters.

�about 14 and 12 dB for middle frequencies, respectively� in

J. Acoust. Soc. Am., Vol. 124, No. 3, September 2008


accordance with very low measured T30. Finally, JE and TAhave different clarity �4 dB higher in the second theater� al-though they had nearly the same T30. This could be probablyexplained considering the different height of the stage wallwhich is more than double in TA compared to JE.

C. Sound strength

Another interesting analysis can be carried out by con-sidering the sound propagation curves in the five theaters.For this scope the parameter Gmid, which is the average of G,as defined in Ref. 14, for the middle frequencies �500 Hz,1 kHz, and 2 kHz octave bands�, is calculated. All the data,measured for each source-receiver combination, are shown inFig. 4. For ease of comparison in Fig. 5 only the regressionlines obtained with a linear fit of the measured data are re-ported. In Table I the values of the parameters Ai and Bi ofthe equation Gmid=Ai+Bi log10�dist� are reported for eachtheater together with the related regression coefficients. De-spite the different measured T30, the energy levels are fairlysimilar and are comprised within a range of 4 dB. Thisprompts the idea that the sound energy is mainly concen-trated on the first part of the impulse response, including thedirect sound and the two outstanding reflections from the

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FIG. 3. Comparison of the clarity parameter for all theaters.

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FIG. 4. The sound strength measured at different positions in all theaters at
middle frequencies.
Farnetani et al.: On the acoustics of ancient theaters 1559


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floor and the stage building �when present�, and only asmaller amount of energy comes from the tail. For this rea-son the lower levels were registered in DE and SE because ofthe lack of the reflection from the stage wall. The Gmid

propagation curve in JE has actually the same slope as in DEbut it is about 4 dB higher. Moreover, for the shortest dis-tances the sound level in JE is the highest. In fact, havingthis theater the highest cavea slope in the group, for the samesource-receiver distance the stage wall will be closer to theaudience and the reflection from this surface will have moreenergy at the receiver positions. On the contrary, for the far-thest distances, in the AS theater the reflections coming fromthe colonnaded gallery cause the level rise and make thepropagation curve less steep.

IV. SCALE MODELED THEATERS

The ancient theater of Siracusa, situated in the south ofItaly, is one of the biggest theaters of the Magna Grecia. Thetheater had undergone major changes and fortunately the siteexcavations made it possible to trace with great detail threedifferent layouts dating from the fifth century B.C. to thesecond century A.D.,12 that is a Greek, a Hellenistic, and aRoman theater. Consequently, a modular scale model of theSiracusa theater was built to deeply investigate in a singlesite the acoustical changes from the former Greek to thelatter Roman design.

The Siracusa Greek theater �SG�, also called Timoleontetheater, is dated about 335 B.C. It had 37 tiers of steps with

FIG. 5. Comparison of the sound strength regression lines for all theaters atmiddle frequencies.

TABLE I. Linear fit parameters for measured theater sound level decays�Gmid=Ai+Bi log10 �dist� �dB��.

Theater Ai �dB� Bi �dB� R

Free field 20 20 1Aspendos 20.68 −16.43 −0.93

Jerash 25.93 −19.55 −0.92Taormina 15.41 −13.99 −0.93Segesta 23.49 −20.52 −0.94Delphi 22.19 −19.75 −0.93



a slope of 20°. The maximum diameter of the semicircularcavea was about 85 m and its height was 11 m at the laststep. The radius of the orchestra was approximately 12 m.The rows of steps were continuous, without any corridor�diazoma�, and the entrances �parodoi� to the cavea werefrom the upper part of the hill and on the side of the stagebuilding. This was in turn 23 m wide and 8.6 m high, with arow of ten columns on the front supporting a portico 3 mdeep. In front of it, at a distance of 3.5 m, there was thewooden parapet �2.5 m high� which supported a woodenfloor during the public meetings and hid a wagon, having thefunction of a moving support for the set, during the venues.It can be estimated that the SG had space for about 5000. Aview of the model representing SG is shown in Fig. 6�a�.

The Siracusa Hellenistic theater �SH�, also calledGerone II theater, was built from 238 to 214 B.C. basicallyas an expansion of SG. Some 31 tiers of steps were added tothe semicircular cavea which summed up to 68. Thus thecapacity was greatly increased up to nearly 15 000. Despiteits Greek origins, the Hellenistic theater had a covered gal-lery with a colonnade in the upper part of the cavea, asusually found in later Roman theaters. This feature makes theSH theater peculiar with respect to other Hellenistic theaters.As shown later this will imply a closer acoustical similaritywith Roman theaters. A proper diazoma, called diazoma ma-jor, was also added by removing the step rows from 29 to 31and two additional entrances �parodoi� were created at thelateral ends of it. The slope of the cavea was kept at 20° andno changes were made in the orchestra. Now the maximumdiameter of the cavea was 143 m and it was 26 m high,including the columns �whose height was about 5 m�. Thestage building was enlarged up to the lateral piloni �the tworocky bodies flanking the scenic area�. The parodoi, asvaulted corridors, became internal to the building whichgrew up to 28 m wide and 15.4 m high. A stage set 3 m highand 3 m deep was built with stones. Because of the fewremains, it is difficult to know exactly how the facade looked

FIG. 6. Examples of modeled theaters configuration: �a� Greek and �b�Roman.

like, but probably the skene had a monumental appearance.



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In the second century A.D. the theater was again modi-fied to meet the Roman style. Due to an increased need ofspace in the orchestra, the first four seat rows were removed.In order to join the cavea with the orchestra its slope changedfrom 20° to 25°. So the Siracusa Roman theater �SR� had 64tiers of steps and the radius of the orchestra was 15.3 m.Furthermore, row 20 was removed to create the diazomaminor, which was nine tiers of steps under the diazoma ma-jor. Two tunnels �the cryptae� were carved on the sides of thestage building, under the cavea seats, to create two new paro-doi. The stage building was again enlarged. It had a base-ment with a stage front and three storeys with columns onthe facade. It was 41 m wide and about 20 m high. The stageset was 1.5 m high and 7 m deep. The number of seats wasalmost unchanged. Figure 6�b� shows the model of SR: it isnot archeologically proved that the stage building was con-nected to the cavea for the full height.

V. SCALE MODEL ASSEMBLY AND MEASUREMENTSETUP

A. The modular structure

In order to reproduce the historical configurations de-scribed above and derived from the archaeological evidencesthe scale model was designed as a modular structure. Thismeans that by adding or removing some structural parts suchas tiers of steps, the colonnaded gallery, and different stagebuildings, it is possible to assemble each of the above the-aters. Moreover also some hybrid configurations, which werenot historically proved, could be assembled to investigate theacoustical contribution of specific architectural elements.

A 1:20 scale was chosen as the best possible compro-mise between the contrasting requirements of the space tosettle the model on the one hand and the measurable fre-quency range on the other hand.

Basically, the cavea of the model consists of nine differ-ent circular sectors having an angle of 20.5°, each dividedinto three main parts �Fig. 7�: the lower, the middle, and theupper tiers of steps. Actually two different versions of thelower parts were prepared in order to take into account thedifferent slopes of the steps introduced in SR. Moreover,considering that the lateral parts of the cavea do not have a

Columned gallery

Upper part

Middle part

Diazoma steps

Lower part

FIG. 7. The structure of a “slice” of the model.

perfectly circular shape but end with a straight zone, the two



lateral slices are different from the others. Movable partswere also designed to be able to modify the cavea structureand to introduce the two diazoma added in Hellenistic andRoman theaters, respectively. As it is visible in Fig. 7, theseparts consist in a set of three and a half steps for the diazomamajor and one step only for the diazoma minor. Each of thethree parts, composing all the steps in a circular sector, aresupported by a structure made of beams.

Starting from SG, its cavea is built by joining, for eachslice, the lower and the middle part and adding then togetherthe nine slices. Then, for achieving SH, the upper part of thecavea and the columned gallery are added and three rows ofsteps are removed to create the diazoma major. Finally, theSR is obtained by swapping the first tiers of steps and creat-ing the diazoma minor by removing the 20th step. For eachconfiguration the appropriate stage building was added infront of the respective cavea. The three different configura-tions of the scale model are shown in Fig. 6. The structure ofwooden beams supporting the cavea and the split in nineslices can also be observed in the picture of SG.

B. Scale model approach for open theaters

In order to take acoustical measurements in a scalemodel, it is necessary to use a measurement chain for highfrequency. This can be deduced from a few geometrical andacoustical rules, which define the transformation of full-sizequantities to model quantities.15 Moreover, the sound absorp-tion in the propagation medium has to be taken into accountand two methods have usually been applied.16 Unfortunately,the model of an ancient theater is not a closed room andfurthermore it needs a very big space to be stored. Thus, itwas not possible to dry the air or to fill with nitrogen such abig volume. Another possible method to correct for the airabsorption is the numerical compensation of the acquiredimpulse responses.17 This method was first experienced butlater dropped. Its effectiveness in the present case is, in fact,not as important as in closed spaces. The reason for this isthat the absorption of the missing ceiling is far larger thanany possible correction for the air absorption. This scalemodel approach for open air theaters was validated by meansof both computer simulations18 and real scale measurements.Unfortunately the Siracusa theater today does not correspondto any configuration of the scale model, so that a directacoustical comparison of the real theater with the scalemodel is not possible. Anyway the validation stems from thecomparison of the measurement results in the scale modelwith the data obtained for the respective typology of realtheaters analyzed in this work. In fact, the results showed avery good consistency up to a frequency limit set in the2 kHz band �real scale�. From this band on the discrepanciesdue to the air absorption started to play a not negligible role.Finally, the environmental conditions were very stable duringthe measurement sessions and this improved the reliability ofthe results.

C. Scale model measurement setup

Two different types of sound sources were used in the
measurements. The first one was a spark generator whose


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spinterometer had an omnidirectional emission on a horizon-tal plane. Moreover, the discharge height was 75 mm highcorresponding to 1.5 m in the real scale, which is the sourceheight adopted for the measurements in the real theaters. Thefrequency response, not reported, is not flat, but it rises byabout 9 dB per octave band, almost compensating the airabsorption at high frequencies. Unfortunately the repeatabil-ity of the sparks is not good �level differences within 20%�and this source cannot be employed to measure the soundlevels in the scale model. So this device was primarily usedto analyze the fine structure of the impulse responses becausethe spark is very sharp and clean making it possible to in-vestigate in detail the pattern of reflections.

The second source was a miniaturized dodecahedron,having a diameter of about 70 mm, made of piezoelectrictransducers covered by a layer of paper. The frequency re-sponse of the source, measured at 1 m, is rather flat from2.5 to 50 kHz, which corresponds to 125 Hz–2.5 kHz in thereal scale, considering the scale factor of the model.

For each theater configuration two source positions werechosen. The former is in the orchestra, close but not coincid-ing with the geometrical center, to avoid the focusing effectscaused by the semicircular shape. This position is exactly thesame for all the theaters to allow direct comparisons. Thelatter position was on the stage in the SH and SR. Since SGhas no front stage �the area is occupied by the system formoving the stage set�, the latter position was located in therear part of the orchestra close to the stage. The height fromthe floor to the acoustical center of the source was 7.5 cmtoo.

An eight channel sound card with 192 kHz samplingfrequency was used since this frequency is the highest avail-able within the professional audio standards nowadays. Thus,having a sample rate of 192 kHz, the higher frequency be-comes 96 kHz. This means that passing from the scale modelto the real dimensions the higher working frequency is4.8 kHz. Considering the better combination of size, sensi-tivity, and frequency range, also in relation to the soundsources described above, a 1 /4 in. condenser microphonewas chosen for measurements in the scale model. The micro-phone was pointed toward the source and in each measure-ment position it was placed two steps above so that the dia-phragm was exactly in the position occupied by the head ofa virtual listener sitting on that step.

The measurement positions were distributed in the caveacovering all possible listening positions and were regularlyspaced within each slice of the theater. In SG the measure-ment positions were 36 and in SH 15 more were added for atotal of 51. In the SR, where the first rows changed, thenumber of receivers was 42.

VI. RESULTS FROM SCALE MODEL MEASUREMENTS

In this section the results of the measurements in theunoccupied scale model will be presented. First the modelwas configured as SG, SH, and SR and then some hybrid
configurations were assembled �i.e., removing or adding, for


example, the stage building or the upper gallery� and acous-tically tested. The data are translated into the full scale fre-quencies and distances.

First of all the reflection pattern of a typical impulseresponse measured in the modeled theaters has to be consid-ered. An example of the first 250 ms of an IR recorded in SR�source in the orchestra, receiver on the fifth step� is shownin Fig. 8. From the analysis of the pattern of reflections itappears that after the direct sound �a� there are only twomajor reflections: the former comes from the orchestra floor�b� and the latter, less loud and delayed too, is from the stagebuilding �d�. Some reflections are also recognized betweenthe floor and the stage building reflections �c�. A geometricalverification of the delay times of these reflections showedthat the peaks correspond exactly to seven step edges behindthe microphone position. The reflection of the closer seatriser and those of the steps in front of the microphone arecompletely masked by the direct sound and by the floor re-flection. After the stage building �d�, in the impulse responseone can recognize a group of distributed reflections withmuch smaller amplitude �e�. They make up the reverberanttail and are mainly caused by the multiple scattered reflec-tions of sound on the tiers of steps in the cavea. Keeping thisfigure in mind, the results of the measured acoustical param-eters can be presented.

A. Reverberation

For the scale model the reverberation time T20 is used asin some cases there was not enough dynamics to measure T30

in a reliable way. A comparison of T20 measured in SG, SH,and SR is shown in Fig. 9. The data are the average of thetwo sources and all the receivers and the bars correspond tothe spatial standard deviation. For SR and SH the values ofthe parameter are the same, within the standard deviation,and they are as high as 1.8 s at 500 Hz and 1.7 s at 1 kHz.Although these band values are comparable with the respec-tive results in AS, the value at 2 kHz is now lower probablydue to air absorption as discussed above. For this reason the“midaverage” �500 Hz, 1 kHz, and 2 kHz� is a little less thanin AS and close 1.6 s. When SG is considered, the values of

db

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FIG. 8. Example of IR from SR: source in the orchestra, receiver on the fifthstep �first 250 ms�. �a� Direct sound, �b� orchestra floor, �c� upper steps, �d�stage building, and �e� reverberant tail.

T20 are much lower and close to 1 s.



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The early decay time �EDT� parameter, not shown, pre-sents lower mean values and with a very marked variability.In fact, the reflection coming in the very first part of theimpulse response from the stage building arrives with differ-ent delays depending on the source position and this affectsEDT rather than T20. Thus in the present context T20 is moresuited than EDT to achieve a robust qualification of the mea-sured theaters according to the design typology. In otherwords the intrinsic EDT variability with position could maskthe effect of architectural elements.

A further investigation was done exploiting the possibil-ity of adding and removing the model parts. The results arereported in Fig. 10. The base model was SH �whose caveahas a constant slope� and the diazoma was suppressed withfurther tiers of steps. The base stage was also that of SH andfour configurations of the model were fixed by combiningthe presence or the absence of the stage building and of theupper columned gallery.

From Fig. 10 it is evident that longer reverberation timesare due to the presence of the upper gallery. In fact, theresults show that removing the upper gallery causes the T20

at middle frequencies to decrease by about 25% whereaswithout the stage building the reverberation decreases by15% at the same frequencies. In addition, while the removalof the stage does not affect the frequency trend of the rever-beration time, when the gallery is removed one can find a

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FIG. 9. The reverberation time in the three configurations of the Siracusatheater.

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FIG. 10. Reverberation time measured in the scale model for four “hybrid”
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more marked decrease in T20 in the lower frequency range.The upper gallery is thus mostly effective in this frequencyrange. Finally, the cavea alone, that is the theater withoutstage and gallery, has a T20 lower than the complete theaterby 50%.

B. Clarity

The parameter clarity for speech C50 is reported in Fig.11. It can be easily seen that, as for T20, the values are verysimilar for SR and SH and are different for SG. Interestingly,the clarity in SR and SH is high although the T20 is alsorather high. The frequency trend of C50 shows a dip in the250 Hz octave band for all theaters which is actually moremarked in SG.

To investigate what was producing the gap in the energyparameters, proper measurements were taken in the simplestconfiguration of the theater: SG without the stage building.The spark source was placed near the center of the orchestraand the microphone in a central sector in the middle of thecavea. In Fig. 12 the frequency analysis results of four dif-ferent measures are plotted. The first �black dotted� is the

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FIG. 11. Clarity for speech measured in the three configurations of the scalemodel.

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1 2 3 4 5 6 7 8 9 10-95

-90

-85

-80

-75

-70

-65

-60

-55

Dip due toscattering Dip due to

comb filtering

Leve

l[dB

]

Frequency [kHz]

Zoomwindow

FIG. 12. Frequency analysis at the receiver position, in the model scale,showing the effect of comb filtering and a zoom of the curves from1 to 10 kHz. �a� Greek theater configuration, �b� sound absorbing materialclose to the microphone, and �c� sound absorbing material covering the
orchestra.


Redistrib

frequency response of the spark source in a free field; thiscurve is reported only for comparison and its level is notrelated to the other curves. Curve �a� �black solid� is thereference configuration described above. It appears that thereason for the dip at 250 Hz �real scale� in the clarity graphsis due to the comb filtering generated by the interferencebetween the direct sound and the reflection from the orches-tra floor, which has a remarkable dip at 5 kHz �model scale�.Then to exclude other effects generated very close to themicrophone, the capsule was surrounded by sound absorbingmaterial. Curve �b� �gray dashed� shows the result of thismeasurement: it can be seen that this curve is very similar tocurve �a� representing the reference configuration. Only thefrequency gaps caused by comb filtering are a bit more pro-nounced. Finally, as a check, the absorption around the mi-crophone was removed and a layer of the same sound ab-sorbing material was laid to cover the whole orchestra. Theresult is described by curve �c� �gray solid�, which shows acourse similar to the free field condition for most of thefrequency range. Actually the dip at 5 kHz �250 Hz realscale� is removed but, very interestingly, curve �c� showsanother dip in the frequency region close to 4 kHz �200 Hzreal scale�. This second dip is not removed neither by placingsound absorbing material on the orchestra nor very close tothe microphone. A further inspection on the geometry of thecavea revealed that the half wavelength of this frequencycorresponds exactly to the diagonal period of the steps.

Moreover the first dip at 5 kHz is presented here for asingle position and moving the microphone in the caveawould cause just a minor frequency shift. For this reason thiseffect is also visible in the average value of the energy pa-rameters in the 250 Hz band real scale. Finally, this combfiltering effect is less marked in SH and SR since more re-flections coming from the bigger stage buildings and fromthe upper gallery reach the receiver and add in an uncorre-lated way.

C. Sound strength

10 20 30 40 50 60 70-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

GreekHellenisticRomanFree field

Gm

id(li

near

regr

essi

on)[

dB]

Distance [m]

FIG. 13. Strength measured in the three configurations of the scale modelcompared with the free field.

In Fig. 13 the strength Gmid propagation curves are re-



ported. As above they are expressed with the regression linesfor each data set to make the graph more intelligible and, fora better comparison, only the values measured with thesource in the orchestra are shown. The receivers were placedon a line along a central sector of the theater. The propaga-tion curve for the source in the free field is also reported forreference.

It is to be noted that, different from the case of in situmeasurements, it is impossible to neglect the air absorptionwhen calculating the free field propagation curve. Conse-quently, a MATLAB code was written to calculate the level ofa source in a free field at a certain distance by introducing thecorrection for the air absorption given in the standardISO9613-1.19 This modified free field is taken as the refer-ence propagation curve for the evaluations. The measure-ments relative to the G parameters in the three theaters weretaken under the same temperature and humidity which were,respectively, 15 °C and 35%. Using these data the G param-eter was calculated first for single frequencies in steps of0.5 Hz, then for the 10 kHz, 20 kHz, and 40 kHz octavebands and finally averaged to obtain Gmid. The distanceswere then rescaled by 20 times. The linear fit Y =Ai+BiX,where Y =Gmid and X=log�distance�, was calculated for allthe data sets. For the free field the results are Afree

=22.41 dB and Bfree=−22.10 dB with a regression coeffi-cient R=−0.99. All the parameters calculated with the linearfits are summarized in Table II. In general the Gmid values arequite low compared to closed theaters and the trend con-stantly decreases with a slope very close to the free field.

With no surprise, since SR and SH are very similar, theirsound strength propagation curves are quite close to eachother and are about 5 dB higher than the free field values inthe considered range of distances. Moreover, the 1 dB lowervalues found in SG are probably due to a less efficient re-flection from the stage building caused by the presence of theportico.

VII. THE ACOUSTIC EVOLUTION OF ANCIENTTHEATERS

The main characteristics of the theaters included in thiswork are summarized in Table III. The above set of scalemodel measurements can be compared with the data mea-sured in situ reported in Sec. III. As is evident from theacoustical measurement results, derived from real theaters�Figs. 2, 3, and 5� and from the scale model configurations�Figs. 9, 11, and 13�, the sound field in the ancient theatershas a unique character. The contributions of the specific ar-chitectural parts can be traced back in the impulse response

TABLE II. Linear fit parameters for measured theater sound level decays�Gmid=Ai+Bi log10 �dist� �dB��.

Theater Ai �dB� Bi �dB� R

Free field 22.41 −22.10 −0.99Roman 30.54 −24.02 −0.99

Hellenistic 28.52 −22.49 −0.99Greek 28.46 −23.72 −0.99

�Fig. 8�. In particular, the orchestra floor and the stage build-



Redistrib

ing provide very strong early reflections and the cavea con-tributes with the scattered sound that makes up the reverber-ant tail. Anyway, even if the theaters have no ceiling, whichcan be replaced by an ideal surface of unit absorption, thereverberation time in Roman theaters is similar to closedtheaters, but in this case the clarity is higher and the soundstrength is very low.

The nature of the scattering in the tail deserves furtherspecific investigations. In fact, for a correct interpretation ofthe phenomenon it is necessary to resort to an advancedwave scattering theory as reported in Ref. 10 but the presentmeasurements cannot be directly matched to what theoreti-cally predicted in Ref. 10. A new dedicated set of measure-ments in the scale model is required to exactly correlate thewave theory of scattering with the experimental results. Atpresent, scattering measurements on a sample of steps of thescale model have been accomplished using advancedtechniques.20 It was found that the typical “knee” of the re-sulting scattering curve for the step layout lies around200 Hz. This frequency region coincides with the frequen-cies where, as evidenced by curve �c� of the zoom window inFig. 12, the deep was originated by the cavea steps.

The effect of the architectural elements can be initiallytested through examination of the measured RTmid, the aver-age of the reverberation time �T30 for the real theaters andT20 for the scale model� in the 500 Hz, 1 kHz, and 2 kHzoctave frequency bands, also reported in Table III. The re-sults of such procedure are shown in Fig. 14 where differentgrays correspond to the presence of the various architectural

TABLE III. Main characteristics of all the theaters i

Theater GalleryCavea

diameter �m�Cs

Siracusa Roman Yes 143 20Siracusa Hellenistic Yes 143

Aspendos Yes 98Taormina No 109

Siracusa Greek No 85Jerash No 63

Siracusa Greek–No stage No 85Segesta No 63Delphi No 50

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

SiracusaRoman

SiracusaHellenistic

Aspendos Taormina SiracusaGreek

Jerash SiracusaGreek NO

stage

Segesta Delphi

RT m

id[s

]

Stage Building, Gallery

Stage Building, NO Gallery

NO Stage Building, NO Gallery

FIG. 14. Comparison between the RTmid measured in all the analyzed the-
aters. Full bars: real theaters, slashed bars: scale model.


parts, the full bars refer to real theaters, and the slashed barsto the scale model configurations. Three groups can be iden-tified: the first including SR, SH, and AS, the second withTA, SG, and JE, and the last with SG without stage, SE, andDE.

From this graph �Fig. 14� it can be seen that the RTmid

values can be grouped together according to their architec-tural layout. In fact, the measured RTmid in the AS theateralmost matches those measured in SR and SH, having boththe complete stage building and the upper gallery. Further-more, it can be noted that, despite the slight slope differencesand the spread of overall dimensions, the measured RTmid issimilar. Finally, as already noted, the RTmid in SH and SR issimilar even if they have very different stage buildings.

Moving to the second group of data, the theaters withoutthe upper columned gallery, the JE and TA theaters have aRTmid very similar to those measured in SG, even if they haddifferent dimensions of the cavea and of the stage building.Theaters in the last group show almost identical RTmid.

Similar considerations come out from the analysis ofclarity parameter averaged for the middle frequencies,C50mid. In Fig. 15 the average value measured for the threegroups is shown. Even though the clarity has a much highervariability with respect to the receiver positions, the threegroups of theaters can be still identified. Analyzing in detailFig. 15 it can be seen that the differences between the the-aters with and without the gallery are very small while, whenremoving the skene wall, C50mid becomes very high.

gated in this work.

Stage buildingStage building

height �m�RTmid

�s�Seatingcapacity

° Yes 20.0 1.63 15 000Yes 15.4 1.61 15 000Yes 26.0 1.68 15 000

Yes �part.� 20.0 1.16 5 500 �today�Yes 8.6 1.03 5 000

Yes �part.� 8.5 1.19 3 000 �today�No ¯ 0.40 5 000No ¯ 0.45 4 000No ¯ 0.50 5 000

0

2

4

6

8

10

12

14

16

18

20

22

24

26

SiracusaRoman

SiracusaHellenistic



stage

Segesta Delphi

C50

mid[dB]


Stage Building, No Gallery

No Stage Building, No Gallery

FIG. 15. Comparison between the C50mid measured in all the analyzed

nvesti

avealope

°–2520°33°39°20°43°20°26°28°

theaters. Full bars: real theaters, slashed bars: scale model.



Redistrib

Finally, the averaged difference �Gfree between the lin-ear fit curve of the Gmid and the free field can be analyzed.

The differences calculated for all the theaters are re-ported in Fig. 16. The bars represent the standard deviationfrom the mean value and in this case they take into accountalso the slope difference between the sound propagationcurves in the theater and in the free field.

The strength depends on the stage wall providing a firstreflection and on the upper gallery providing a more delayedsound but also on the slope of the cavea as the case of thesteep JE clearly indicates. The interplay and ranking of thesefactors are not straightforward. For instance, one can arguethat the stage wall reflection is surely more valuable for mostlisteners than a delayed reflection coming from the gallerybehind. In this respect, it can be safely stated that the in-creased stage building dimensions in Roman theaters helpedthe listeners with the sound strength more than the uppergalleries. Moreover if JE is compared to the first group �SR,SH, and AS� it is found that a steep slope is able to increasethe strength at the listeners at least as does a complete stagewall. This is consistent with the cited strategy used by an-cient designers to optimize the listening conditions at farthestseats by increasing the final slope. Regarding the comparisonof the first and the second group it is also to be noted that,should JE be taken out of its group, a clear decreasing trendcould be reported from group one to the next. This meansthat in many cases, at least in theaters where the slope doesnot exceed 25°–30°, the contribution of the upper gallerycould be precisely isolated. Finally the complete removal ofthe stage wall reflection which characterizes the third group�SG without stage, SE, and DE� causes the G to decreasesignificantly. These theaters can be regarded as a sort of basic

0

1

2

3

4

5

6

7

8

9

SiracusaRoman

SiracusaHellenistic



stage

Segesta Delphi

�Gfree[dB]


Stage Building, No Gallery

No Stage Building, No Gallery

FIG. 16. Comparison between the �Gfree �average difference between Gmid

in the theaters and in a free field� measured in all the analyzed theaters. Fullbars: real theaters, slashed bars: scale model.

TABLE IV. Values of the main acoustical parameter

Type Real

Complete Roman Aspendos Siran

Roman or Greek without galleryand incomplete stage building

TaorminaJerash

Sir

Greek without stage building DelphiSegesta

Sirwithou



acoustical spaces, since the sound strength profits of just onesingle floor reflection, and the �Gfree is consistently assessedat values very close to 3 dB. It is to be stressed here that asimilar result could never be obtained without an appropriatesloping of the audience because of the screening effect of therows in front.

VIII. CONCLUSIONS

The above comparisons are a confirmation that the evo-lution of acoustics in ancient theaters can be qualified byarchitectural details and can be quantified by acoustical mea-surements. In this respect a few elements were isolated,namely, the stage wall, the upper columned gallery, and theslope of the cavea. Their interplay seems capable of describ-ing the overall acoustical properties of several types of an-cient theaters even if their design does not strictly match themodel configurations. For this reason a summary of architec-tural features and the related RTmid for measured theaters isreported in Table III. Moreover the findings allow to proposea set of expected values for the main acoustical parameters oftheaters falling in the three groups identified above based ontheir design elements. The proposed values are summarizedin Table IV.

The reverberation time has a limited variability so theestimate of this parameter in other theaters with similar de-sign should be rather accurate. In this respect it was alsopossible to rank the different elements considering how theyaffect the reverberation in an ancient theater. In fact, it wasfound that the overall space dimensions seem to have lessimportance than the completeness of the theater itself in itsdifferent parts. This behavior differs from the classical theoryof reverberation in closed spaces, where the reverberation isdirectly proportional to the room volume. Moreover, the up-per gallery seems to be the chief element to keep the soundenergy circulation inside the cavea prolonging the reverber-ant tail, whereas the slope of the cavea is not important forthe reverberation time. Unfortunately, the role of occupancystill remains unexplored and shall be possibly considered inthe future.

As regards �Gfree it can be seen that when passing fromgroup one to group three the strength is halved since one ofthe two reflections �that on the skene wall� is lost. Anyway,as discussed above, the parameter is more affected by thestate of conservation of the stage building, and the steepnessof the cavea plays an important role too. For this reason theintermediate type of theaters �second row of Table IV� car-ries most of the variability for this parameter.

ected in ancient theaters.

del RTmid �s� C50mid �dB� �Gfree �dB�

Romanlenistic

1.64�0.13 5.4�2.3 5.7�1.0

Greek 1.13�0.10 6.4�2.0 4.9�1.2

Greekge building

0.45�0.12 16.5�2.1 2.9�1.0

s exp

Mo

acusad Helacusa

acusat sta



Redistrib

Moreover, the values of clarity are mostly governed bythe reflection of the skene. The parameter slightly changeswhen removing the gallery but, when the stage wall is re-moved, its values more than double.

The acoustical measurements also showed that in an-cient theaters the wave effects cannot be neglected. In par-ticular, comb filtering effects have been discussed due to theorchestra floor reflection but more subtle wave phenomenaare caused by the scattering of the cavea. For their full un-derstanding further experimental and theoretical researchesare required.

Finally, as discussed above, the work has adopted thestandard in Ref. 14, whose objective acoustical parameterswith their related optimal ranges were developed for closedspaces. Here some unusual behavior was outlined when em-ploying the same concepts in open air theaters. Thus thesubjective significance of the present findings and the even-tual adoption of peculiar objective parameters are still a mat-ter of research which will be addressed in the near future.

ACKNOWLEDGMENTS

The authors would like to acknowledge Dr. T. Hidaka ofTakenaka Corporation, Chiba, Japan for kindly lending theminiaturized dodecahedron source. Dr. Shin-ichi Sato ofHangyang University, Korea and Dr. Hiroyuki Sakai are alsoacknowledged for support during acoustical measurements inTaormina and Delphi. The measurements in Segesta weretaken within the Italian National Research Project “PRINanno 2005-prot. 2005081870.”

1G. Izenour, Theater Design, 2nd ed. �Yale University Press, New Haven,CT, 1996�.

2F. Canac, L’Acoustique des Theatres Antiques: Ses Enseignements (TheAcoustics of Ancient Theatres: Their Teaching) �CNRS, Paris, 1967�.

3L. Cremer and H. Muller, Principles and Applications of Room Acoustics�Applied Science, London, 1982�.

4B. Papathanasopoulos, “Acoustiche messungen in theater von Epidauros



�Acoustical measurements in the theatre of Epidauro�,” Proceedings ofFifth ICA, Liege, 1965.

5R. Shankland, “Acoustics of Greek theatres,” Phys. Today 26�10�, 30–35�1973�.

6D. Irkli, “Acoustical properties of ancient theatres: Computer simulationand measurements,” Ph.D. thesis, Middle East Technical University, An-kara, Turkey �1995�.

7S. Sato, H. Sakai, and N. Prodi, “Acoustical measurements in ancientGreek and Roman theatres,” Proceedings of Forum Acusticum, Sevilla,2002.

8S. Vassilantonopoulos and J. Mourjopoulos, “A study of ancient Greek andRoman theater acoustics,” Acta. Acust. Acust. 89, 123–136 �2003�.

9D. Noson, T. Bosworth, and N. Folk, “Private communication on the 1:10scale model of delphi theatre at the college of architecture and urbanplanning, University of Washington” �2000�, URL: http://www.caup.wahsington.edu/support/ newsletter/2000_winter.pdf �lastviewed 7/11/08�.

10N. Declercq and C. Dekeyser, “Acoustic diffraction effects at the hellenis-tic amphitheater of epidaurus: Seat rows responsible for the marvelousacoustics,” J. Acoust. Soc. Am. 121, 2011–2022 �2007�.

11P. Chourmouziadou and J. Kang, “Acoustic evolution of ancient Greekand Roman theatres,” Appl. Acoust. 69, 514–529 �2007�.

12L. Polacco, Il Teatro Antico di Siracusa (The Ancient Theatre of Siracusa)�Maggioli, Rimini, 1981�.

13“Erato project �identification evaluation and revival of the acoustical heri-tage of ancient theatres and odea�, ica3-ct-2002-10031. Part of the Euro-pean Commission Fifth Framework Incomed Programme,” URL: http://server.oersted.dtu.dk/www/oldat/erato/ �last viewed 7/11/08�.

14“ISO/dis 3382-1:2004. Acoustics—Measurement of room acousticparameters—Part 1: Performance rooms,” Technical Report, ISO, 2004.

15H. Kuttruff, Room Acoustics, 4th ed. �E&FN SPON, London, 2000�.16N. Xiang and J. Blauert, “Binaural Scale Modelling for Auralization and

Prediction of Acoustics in Auditoria,” Appl. Acoust. 38, 267–290 �1993�.17K. Lorenz, “Auralisation of a scale model of the Royal Albert Hall,” J.

Acoust. Soc. of the Netherlands 158 �2001�.18A. Farnetani, “Investigation on the acoustics of ancient theatres by means

of modern technologies,” Ph.D. thesis, Università degli Studi di Ferrara,Ferrara, Italy �2006�.

19“ISO 9613-1:1993. Acoustics—Attenuation of sound during propagationoutdoors—Part 1: Calculation of the absorption of sound by the atmo-sphere,” Technical Report, ISO, 1993.

20A. Farnetani, N. Prodi, and R. Pompoli, “Measurements of sound scatter-ing of the steps of the cavea in ancient open air theatres,” Proceedings ofthe International Symposium on Room Acoustics, Sevilla, 2007.



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