Investigating the acoustics of ancient theatres by means of a modular scale model

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1 Investigating the acoustics of ancient theatres by means of a modular scale model Andrea Farnetani, Federica Bettarello, Nicola Prodi, Roberto Pompoli Engineering Department, University of Ferrara, Via Saragat 1, Ferrara, Italy, afarnetani@ing.unife.it The study of the sound field inside ancient theatres is one of the targets of the EU project ERATO. Within this project several campaigns of acoustical measurements were done both inside existing ancient theatres and on a scale model of an ancient theatre expressly build for the scope. The scale model was conceived to trace the evolution of theatre acoustics throughout the centuries. The theatre of Siracusa in Italy was selected to build a wooden 1:20 scale model. In fact substantial architectural changes were implemented in this theatre in its passage from to and finally to style. The cavea was enlarged and an ambulacre with columns was added in its upper part. The orchestra was also enlarged and a big stage building was built. The model has a modular structure that can be adjusted to the different periods so that the evolution of acoustics can be investigated. For the acoustical measurements two types of sources were used: a miniaturised dodecahedron made of piezoelectric transducers and a newly made spark consisting of a high voltage generator that drives a spinterometer. The first one was used to calculate the acoustical parameters and the second allows us to analyse the fine structure of the reflection pattern in the impulse responses. The measurements were compared with similar data set from real theatres and the model was thus validated. The main finding of the research was a relationship between the architectural features and the acoustical parameters. 1 Introduction The and theatres are among the most precious and spectacular items of cultural heritage in the Mediterranean countries. The theatres are famous not only for their impressive architecture, but also for their acoustical qualities. Within the European Project ERATO [1] a modular scale model of the ancient theatre of Siracusa was built to investigate the changes in the acoustics from the theatres to the ones. In fact the design of the two types of theatres mostly differs in the amplitude of the cavea, of the stage buildings and in the presence of open or covered aisles. In this work, by means of the modular scale model, the impact of the architectural changes on the acoustics is assessed. 2 The Theatre of Siracusa The theatre of Siracusa is situated in Sicily, south Italy. In fact, as the island was part of Magna Grecia, many theatres were build along its coasts. The first documented theatre in Siracusa had a trapezoidal plan, and for this reason it was not reproduced in the present modular model, which is based upon a semicircular design. The first archaic design was turned in an earlier style (GE) theatre with semicircular plan. Later on it was reshaped to meet the style (HE) and finally it became a theatre (RO). Very interestingly the whole historical process is well documented by archaeologists on the basis of the actual remains [2]. As visible in Fig. 1, the theatre was built on a hill slope facing the sea and the first tiers were directly carved on the rock. Today the theatre hosts a regular summer season and is recognized for having an outstanding tradition in venues of tragedies. Figure 1: The theatre of Siracusa as it is today. 2.1 The Theatre The GE theatre, also called Timoleonte theatre, is dated about 335 B.C. It had 37 tiers of steps with a slope of 20. The maximum diameter of the cavea was about 85 m and its height was 11 m at the last step. The radius of the orchestra was approximately 12 m. The rows of steps were continuous, without any aisle (diazoma), and the accesses (paradoi) to the cavea were from the upper part of the hill and on the side of the stage building. This was in turn 23 m wide and 8.6 m high with a row of columns on the front. It can be estimated that GE had space for around 5500 spectators. In the theatre there was also interesting 2185

2 equipment for moving the stage set. It consisted of two rooms on the sides of the stage building where two stage sets could be stored simultaneously and moved in the centre position by means of a cart running on tracks. 2.2 The Theatre The HE theatre, also called Gerone II theatre, was built from 238 to 214 B.C. basically as an expansion of GE one. Some 31 tiers of steps were added to the cavea that summed up to 68. By doing so the capacity was raised up to nearly Despite its origins the HE theatre had a covered aisle with colonnade in the upper part of the cavea as usually found for later theatres. A proper diazoma, called diazoma major, was also added removing the rows from 29 to 31. The slope of the cavea was kept at 20 and no changes were done in the orchestra. Now the maximum diameter of the cavea was 143 m and it was 26 m high including the columns (whose height was about 5 m). The stage building was enlarged and a second storey was added. It became 28 m wide and 15.4 m high. It is difficult to precisely know how the façade was, but the few remains witness that the first floor had columns. The paradoi on the sides of the stage building were covered with arches and two new ones were added laterally at the diazoma level. multilayer wood having different thickness depending on the part of the theatre. For example the steps are 1.8 cm thick to avoid vibration in the measured frequency range. Moreover, the model was varnished to make the acoustical properties of the material more similar to the stone found in the real theatres. The cavea of the model consists of nine different slices each divided in three different parts: the lower, the middle and the upper tiers of steps. Actually two different versions of the lower parts were prepared in order to take into account the different slopes of the steps introduced in RO. Movable parts were also designed to be able to modify the cavea structure and introducing the two diazoma added in HE and RO respectively. Therefore, the cavea of GE is built by joining the lower and the middle part of the nine slices. Then, in the HE configuration, the upper part of the cavea and the columns are added and three rows of steps are removed to create the diazoma major. Finally, the RO theatre is obtained by swapping the first tiers of steps and creating the diazoma minor. For each configuration the appropriate stage building was added in front of the respective cavea. The three different configurations of the scale model are showed in Figure 2. The structure of wooden beams supporting the cavea and the split in nine slices can also be observed. 2.3 The Theatre In the II century A.D. the theatre was again modified to meet the style. Due to an increased need of space in the orchestra the first four rows were removed. To join the cavea with the orchestra the rise of the first twelve tiers was increase and, consequently, the slope of the very first part of the cavea changed from 20 to 25. The RO theatre had 64 steps and the radius of the orchestra was 15.3 m. Furthermore row 20 was removed to create the diazoma minor nine tiers of steps under the diazoma major. Two tunnels were carved on the sides of the stage building to create two new paradoi. The stage building was again enlarged. It had a basement with a stage front and three storeys with columns on the facade. It was 41 m wide and about 20 m high. The number of seats was almost unchanged. a b 3 The scale model A modular scale model of the Siracusa theatre was built to reproduce the above historical configurations derived from the archaeological evidences. The 1:20 scale was chosen as the best possible compromise between the contrasting requirements of the space to settle the model on the one hand, and of the measurable frequency range on the other. The model is made of c Figure 2: The scale model: a) theatre - GE, b) theatre - HE, c) Theatre - RO. 2186

3 4 Measurement setup A high frequency measurement chain is necessary to take acoustical measurements in a scale model. Considering the 1:20 scale factor, a 192 khz A/D converter was chosen to get a frequency response up to 4.8 khz in the real scale. Moreover two types of sound sources and two different microphones were tested in the measurements. This was done in order to optimize the measurement chain both for the acoustical parameters and for the study of the reflection patterns. 4.1 Sources Two different sound sources were used for the measurements: a piezoelectric miniaturized dodecahedron and a spark source. The first one is a dodecahedron with a diameter of 8 cm where the loudspeakers are replaced with piezoelectric transducers. Its frequency response is rather flat up to 90 khz. The second source is a newly made spark consisting of a high voltage generator that drives a spinterometer. The shape of the spinterometer was optimised to obtain an omnidirectional emission in the horizontal plane. The spark emission rises with a slope of 9 db per octave. This type of source produces a very sharp and powerful impulse which was very useful to analyze the reflection patterns in the impulse responses. The spark was also used for auralizations and the results sounded quite realistic probably due to peculiar frequency response of the spark, which compensates for the air absorption at very high frequencies. The two sources are showed in Figure 3 a) and b) respectively. Only the spinterometer is showed for the spark source. a b the 1/4 microphone has a much higher sensitivity but the frequency response is flat only up to 80 khz in a free field. All possible source-microphone combinations were tested to find the best results in term of S/N ratio and good extension in frequency. The optimum choice for the measurement of the acoustical parameter was the 1/4 microphone together with the piezoelectric source. 4.3 Signal generation and acquisition The measurements chain included a desktop PC with an audio card with a sampling rate of 192 khz. The 1:20 scale of the model gave acoustical parameters up to almost the complete 4 khz third octave band in the real scale. To measure the impulse responses a sine sweep from 500 Hz to 95 khz was used and the software for generation, recording and processing was the Aurora plug-in for Adobe Audition. 4.4 Measurement positions For each theatre configuration two source positions were chosen. The former is in the orchestra, close but not coinciding with the geometrical centre to avoid the focusing effects caused by the semicircular shape. This position is exactly the same for all the theatres to allow direct comparisons. The latter position was on the stage for HE and RO. Since GE has no front stage (the area is occupied by the system for moving the stage set), the latter source in this case was located in the rear part of the orchestra, near the back wall. The height from the floor to the acoustical centre of the source was 7.5 cm that corresponds to 1.5 m in the real scale. The measurement positions were distributed in the cavea covering all possible listening positions, and were regularly spaced within each slice of the theatre. In GE the measurements positions were 36 and in HE other 15 were added for a total of 51. In RO, where the first rows of steps changed, the number of receivers was 42. The microphone was pointed toward the source and the capsule was in the same position of the head of a listener. 5 Results Figure 3: The sources: a) piezoelectric, b) spark 4.2 Microphones For the signal acquisition two different microphones were tested: a 1/4 and a 1/8 measurement microphones. The 1/8 microphone has a flat response up to 140 khz but a very low sensitivity (1 mv/pa) and Some measurements results will be presented and discussed in what follows. The data are translated into the full scale frequency equivalent. If not specified, the results refer to an average value of both sources and of all the receivers. The standard deviation bars are also included. 2187

4 5.1 Reverberation time A comparison of the reverberation times measured in the three theatres is showed in Figure 4. For RO and HE the values of the parameter are as high as 1.8 s at middle frequencies, a figure which is comparable with closed theatres. The frequency trend is rather flat for all the theatres and the values for GE are much lower than the others and close to 1 s. The EDT, not shown, has a course similar to RT, but it is almost 0.5 s lower. Moreover, the variability for EDT from position to position is remarkable. T20 [s] Figure 4: RT vs frequency for the three theatres Thanks to the modularity of the model it was possible to test other interesting configurations of the theatres, even if not specifically based on archaeological evidences. For example in Figure 5 the RTs measured in GE with and without the stage building are compared. It is evident that removing the stage building causes the RT to decrease below 0.5 s in almost all the frequency range. The discrepancies between the two conditions are more limited in the lower frequency range. T30 [s] w/o stage Figure 5: RT comparison between theatres with and without stage building Then also a modified RO was prepared by removing the aisle and the colonnade in the upper part of the cavea. This RO setup is also interesting for comparison with other preserved theatres having similar dimensions but without colonnade. The results show that there are noticeable variations only in the lower frequency region where the RT decreases by 30% to 40%. The medium and higher frequencies seem much less affected. T30 [s] w/o columns Figure 6: RT comparison between theatres with and without columns on the upper part of the cavea 5.2 Energy parameters The parameter Clarity for speech C50 is reported in Figure 7. It can be easily seen that, as for RT, the values are very similar for RO and HE and are different for GE. Interestingly the Clarity is high although the RT is also rather high. The frequency trend of C50 shows a gap in the 250 Hz octave band for all theatres. The close inspection of the impulse responses showed a marked comb filtering effect whose strongest component was exactly at 250 Hz. A further investigation on the main reflections proved that an interference of the direct sound with the orchestra floor reflection was causing the comb filtering. The values of the Clarity parameter for music C80, not reported, are higher than C50 of about 2 db in all the frequency bands. If this finding is compared with closed theatres with a similar reverberation time, it is seen that a 2 db difference is typically found at distances between one and two critical distances. C50 [db] Figure 7: Clarity vs frequency for the three theatres 2188

5 5.3 The sound level In Figure 8 the strength parameter G is reported vs distance as an average of the middle frequency bands (500 Hz, 1 khz and 2 khz). The graphic is in a semilogarithmic scale for the distances and the regression lines are reported together with the free field values. For a better comparison only the values measured with the source in the orchestra are showed. In general the G mid values are quite low compared to closed theatres and the trend is constantly decreasing with a slope close to the free field. In particular RO and HE have a very similar trend, and are about 5 db higher than the free field values. The small differences visible at the single positions are imputable to the different dimensions of the front stage in the two theatres. GE has lower values probably due to a less efficient reflection from the stage building caused by the presence of the porch. Gmid [db] Free FIeld Log. () Log. () Log. () Distance [m] 10 Figure 8: Strength vs distance for the three theatres 6 Discussion All the results reported above point to the close investigation of the reflection pattern of a typical impulse response measured in the modelled theatres. An example of the first 200 ms of an IR recorded in RO (source in the orchestra, receiver at the diazoma minor) is shown in Figure 9. From the analysis of the reflections it appears that after the direct sound there are only two major reflections: the former comes from the orchestra floor and the latter, less loud and delayed too, is from the stage building. Some edge scattering is also recognised in the small peaks following the floor and the stage building reflections. Then in the IR one can see a group of distributed reflections with much smaller amplitude which are mainly caused by the scattering of sound on the tiers of steps in the cavea. Keeping this figure in mind, the relation between the measured acoustical parameters can be explained. Time (s) Figure 9: Example of an Impulse Response recorded in theatre (first 200 ms) At each position the energy it is concentrated in the very first part of the IR, including the direct sound and the two outstanding reflections, and just a very small amount of energy comes from the tail. Therefore the clarity it is very high and the sound level strongly depends on the distance of the receiver mostly from the source but also from the stage building. This reasoning can explain the trend of the G parameter, which, though similar in the three cases, shows some biases at a fixed distance according primarily to the stage characteristics. On the contrary the tail is very important for the reverberation time and therefore the visible differences are given by the dimension of the cavea and the presence or absence of architectural features like the upper colonnade. Finally a compensation for the air absorption in the IR was experienced but later dropped. Its effectiveness in the present case is surely not as important as in closed spaces; in fact the absorption of the missing ceiling is far larger then any possible correction for the air absorption. 7 Concluding remarks As it is evident from the acoustical measurement results, the sound field in the ancient theatres has a unique character. The contributions of the specific architectural parts can be traced back in the impulse response. In particular the orchestra floor and the stage building provide very strong early reflections and the cavea contributes with the scattered sound that makes up the reverberant tail. Even if the theatres have no ceiling, which is replaced by an ideal surface of unit absorption, the reverberation time in theatres is similar to closed theatres: but in this case the clarity it is higher and the sound level is very low. The above set of scale model measurements can be compared with the measured data taken in several real scale well preserved ancient theatres [3], [4]. Amplitude (db) 2189

6 Columns and stage Different stage buildings No columns No stage building No columns 1.4 T30 [s] (mid freq) Aspendos Jerash w/o columns Figure 10: Comparison between RTs measured in real theatres and different configurations of the scale model Taormina Delphi w/o stage By doing so the effect of the architectural elements can be further tested through examination of the measured RT at middle frequencies. The results of such procedure are shown in Figure 10. The Aspendos theatre (Turkey) it is a very well preserved theatre with the colonnade and the complete stage wall. Despite the differences in tiers slope and overall dimensions, the measured RT almost matches with RO and HE scale models. Moreover the Jerash theatre (Jordan) is a theatre without the colonnade and with a stage wall where just one storey is preserved, and Taormina theatre (Italy) is a theatre without colonnade where the stage wall as a very wide opening making it less effective as a reflector. On an architectural basis these theatres could therefore be approximately compared respectively with RO without columns and with GE models. The match of GE and Taormina is quite interesting and rather unexpected while, since RO is effectively bigger than Jerash and has a wider and much higher stage building; their RTs are only roughly similar. Finally the Delphi theatre (Greece) is a theatre without stage building whose dimensions are very similar to GE. As a result the average RTs of Delphi and GE without stage are almost identical. The above comparisons are a confirmation that the evolution of acoustics in ancient theatres can be qualified by architectural details and can be quantified by means of the scale model. In this respect a few elements were isolated, namely the stage wall or stage building, the upper colonnade and the extension of the cavea. Their interplay seems capable of describing the overall acoustical properties for several types of ancient theatres even if their design is not strictly matching with the model preparations. 8 Acknowledgements Dr. T. Hidaka is kindly acknowledged for providing the miniaturized dodecahedra for this research. The authors wish to thank also Dr. S. Sato for contributing in the measurements. References [1] ERATO project (identification Evaluation and Revival of the Acoustical heritage of ancient Theatres and Odea), Contract Number ICA3-CT , [2] L. Polacco, Il teatro antico di Siracusa, Maggioli, Rimini, Bibliografia Nazionale (1981) [3] A. Farnetani, N. Prodi, P. Fausti, R. Pompoli, Acoustical measurements in ancient theatres, J. Acoust. Soc. Am. 115, 2477 (2004) [4] S. Sato, S. Sakai and N. Prodi, Acoustical measurements in ancient greek and roman theatres Proc.of Forum Acusticum 2002, Sevilla, September, Revista de Acustica, Vol. XXXIII,