The modern use of Ancient Greek and Roman Theatres from an acoustic point of view

Transcription

1 TECHNICAL UNIVERSITY OF DENMARK Acoustic Technology Ørsted DTU The modern use of Ancient Greek and Roman Theatres from an acoustic point of view By Konstantinos Angelakis Supervised by Jens Holger Rindel and Anders Christian Gade October 2006

2 The modern use of Ancient Greek and Roman theaters from an acoustic point of view Acknowledgements At this point I would like to acknowledge the people who contributed in the realization of this project; Jens Holger Rindel, for supervising the project Anders Christian Gade, for supervising the project, as well as providing guiding and assistance during the measurements in Greece Paris Kerketsos, for all the help and support during the measurements, as well as for modeling the theatres in ODEON Lazaridou Varvara (responsible for the performances at the Theatre of Epidauros), for the smooth collaboration and assistance Kazolias Nikos (responsible engineer for both theatres), for the smooth collaboration and assistance Jørgen Rasmussen, for the technical support whenever I needed it, in Denmark Periklis Mathiellis, for the technical support in Greece Torben Poulsen, for his advice on matters related to the listening tests My colleagues who voluntarily participated in the listening tests My colleagues Jorge Alvarez, Konca Saher and Shen Yi, for their advice and friendship My housemates for supporting me through the whole process. Specifically, Mihalis Kampanis for keeping me company during the long nights when I was writing this report, as well as for proofreading the whole document! Candela Torres, for helping in the recordings. This project is the epilogue of a two year effort in specializing in the world of acoustics. Given the opportunity, apart from thanking the professors of the department of Acoustic Technology at DTU, who guided me through the different paths of acoustics, I would like to acknowledge my family for always providing a steady base where I could psychologically rely on. I would like to express my gratitude to: My grandmother Eleftheria for her uncompromised love My sister Olga for sharing her philosophical worries with me, and my brother Minas for his medical advice My mother Violetta for her support and affection My father Thanassis for purifying and strengthening my motivation to study acoustics by being opposite to my decision, at least at the beginning. 2

3 The modern use of Ancient Greek and Roman theaters from an acoustic point of view CONTENTS 1. INTRODUCTION AND OBJECTIVES INFORMATION ON THE THEATRES UNDER INVESTIGATION THE THEATRE OF EPIDAUROS THE THEATRE OF ANCIENT EPIDAUROS CONTEMPORARY USE OF THE THEATRES DESCRIPTION OF ACOUSTIC MEASUREMENTS AND RECORDINGS ACOUSTIC MEASUREMENTS Equipment Calibration Procedure RECORDINGS Equipment Calibration Procedure DESCRIPTION OF THE MODELS MEASUREMENTS AND SIMULATIONS THEATRE OF EPIDAUROS-RESULTS AND DISCUSSION Comparison of source positions Evaluation of the model Addition of a stage THEATRE OF ANCIENT EPIDAUROS-RESULTS AND DISCUSSION Comparison of source positions Evaluation of the model Addition of a stage LISTENING TESTS RESULTS AND DISCUSSION Section Section CONCLUSIONS AND FUTURE WORK CONCLUSIONS FUTURE WORK REFERENCES APPENDIX T30 VERSUS T THE EFFECT OF THE GROUND THEATRE OF EPIDAUROS- GRID RESPONSE ODEON PLOTS THEATRE OF ANCIENT EPIDAUROS-GRID RESPONSE ODEON PLOTS GLOSSARY

4 The modern use of Ancient Greek and Roman theaters from an acoustic point of view LIST OF FIGURES Figure 2.1: A view of the Theatre of Epidauros...11 Figure 2.2: A view of the Theatre of Ancient Epidauros...12 Figure 3.1: The measuring equipment (except from the source and receiver)...14 Figure 3.2: While recording an impulse response at the Theatre of Epidauros. The microphone and the loudspeaker can be seen at the right and upper left of the photograph, respectively...15 Figure 3.3: The setup used for obtaining the data used for calibration of the measuring system Figure 3.4: Plan view of the Theatre of Epidauros. The receiver positions are marked with black dots. The letters and numbers reveal the coding that was chosen for the receiver positions (eg. A5, C15, U15 etc.) Figure 3.5: Plan view of the orchestra and skene of Theatre of Epidauros. The source positions are marked with red dots. The letters and numbers reveal the coding that was chosen for the source positions (S1, S2 and S3) Figure 3.6: Setting up source position S Figure 3.7: Plan view of the Theatre of Ancient Epidauros. The receiver positions are marked with black dots. The letters and numbers reveal the coding that was chosen for the receiver positions (eg. A2, C8, E14 etc.)...19 Figure 3.8: The wooden construction that was built on top of the orchestra and skene of the Theatre of Ancient Epidauros during the time that the measurements were conducted Figure 3.9: Plan view of the orchestra and skene of Theatre of Epidauros. The source positions are marked with red dots. The letters and numbers reveal the coding that was chosen for the source positions (S1, S2 and S3) Figure 3.10: The pair of home-made, binaural microphones that were used for the conduction of the recordings at one of the positions...21 Figure 3.11: The red circles indicate the recording positions at the Theatre of Epidauros Figure 3.12: The red circles indicate the recording positions at the Theatre of Ancient Epidauros...23 Figure 3.13: Two very different stage setups at the Theatre of Epidauros; on the left picture the stage setup for the Persians and on the right picture the stage setup for the Suppliants Figure 4.1: The model of the Theatre of Epidauros. The surrounding box is totally absorbing, in an effort to simulate open-air conditions Figure 4.2: The model of the Theatre of Ancient Epidauros...26 Figure 4.3: Rough sketches and the dimensions of the stage buildings Figure 4.4: The model of the Theatre of Epidauros with the added stage building Figure 4.5: The model of the Theatre of Ancient Epidauros with the added stage building...28 Figure 5.1: Strength (G) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]...30 Figure 5.2: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]...31 Figure 5.3: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]...32 Figure 5.4: Reverberation Time (T30) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]...33 Figure 5.5: Reverberation Time (T30) versus frequency at the Theatre of Epidauros. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The different colors indicate the position of the sound source; blue, pink, green correspond S1, S2 and S3, respectively Figure 5.6: Reverberation Time (T30) versus frequency at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured and simulated values, respectively Figure 5.7: Strength (G) versus frequency for 3 different receiver positions at the Theatre of Epidauros. The source is located in the center of the orchestra. The solid and dotted lines indicate measured and simulated values, respectively Figure 5.8: Reverberation Time (T30) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz 4

5 The modern use of Ancient Greek and Roman theaters from an acoustic point of view and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.9: Strength (G) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.10: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.11: The simulated and integrated decay curves at 1000Hz produced by ODEON, for position A Figure 5.12: The simulated and integrated decay curves at 1000Hz produced by ODEON, for position C Figure 5.13: The direction of reflections responsible for the increase of the energy at 113msec at position A25, according to ODEON...41 Figure 5.14: Clarity (C80) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.15: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively...43 Figure 5.16: Reverberation Time (T30) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.17: Strength (G) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.18: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.19: Clarity (C80) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.20: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively...46 Figure 5.21: Strength (G) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]...48 Figure 5.22: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]...49 Figure 5.23: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]...50 Figure 5.24: Reverberation Time (T30) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]...51 Figure 5.25: Reverberation Time (T30) versus frequency at the Theatre of Ancient Epidauros. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The different colors indicate the position of the sound source; blue, pink, green correspond S1, S2 and S3, respectively

6 The modern use of Ancient Greek and Roman theaters from an acoustic point of view Figure 5.26: Reverberation Time (T30) versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured and simulated values, respectively Figure 5.27: Strength (G) versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. The solid and dotted lines indicate the measured and simulated values, respectively Figure 5.28: Reverberation Time (T30) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively...55 Figure 5.29: Strength (G) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.30: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively...56 Figure 5.31: Early Decay Time (EDT) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. All points indicate measured values Figure 5.32: View of the Theatre of Ancient Epidauros at the time of the measurements...58 Figure 5.33: Early Decay Time (EDT) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The solid and dotted lines indicate the measured and simulated values, respectively Figure 5.34: Clarity (C80) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively Figure 5.35: Clarity (C80) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The solid and dotted lines indicate the measured and simulated values, respectively Figure 5.36: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively...61 Figure 5.37: Reverberation Time (T30) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively...62 Figure 5.38: Strength (G) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.39: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively...63 Figure 5.40: Clarity (C80) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively Figure 5.41: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values 6

7 The modern use of Ancient Greek and Roman theaters from an acoustic point of view at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively...64 Figure 6.1: The recording positions at the Theatre of Epidauros. The red characters indicate the code letters of the positions chosen for the purpose of the listening tests. The black characters indicate the exact position; the letter corresponds to the kerkida and the number to the row. The recording position was chosen to be approximately in the middle of the respective row...67 Figure 6.2: The percentage of the test subjects versus their answers. The performance was not amplified and it took place at the Theatre of Epidauros...68 Figure 6.3: The percentage of the test subjects versus their answers. The performance was amplified and it took place at the Theatre of Epidauros Figure 6.4: The recording positions at the Theatre of Epidauros. The red characters indicate the code letters of the positions chosen for the purpose of the listening tests. The black characters indicate the exact position; the letter corresponds to the kerkida and the number to the row. The recording position was chosen to be approximately in the middle of the respective row...70 Figure 6.5: The percentage of the test subjects versus their answers. The performance was not amplified and it took place at the Theatre of Ancient Epidauros Figure 6.6: The percentage of the test subjects versus their answers. The performance was amplified and it took place at the Theatre of Ancient Epidauros...71 Figure 9.1: Reverberation Time versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue line, indicate the measured values for T20 and T30, respectively Figure 9.2: Reverberation Time versus frequency at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured values for T20 and T30, respectively Figure 9.3: Reverberation Time versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue line, indicate the measured values for T20 and T30, respectively Figure 9.4: Reverberation Time versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured values for T20 and T30, respectively Figure 9.5: The receiver (red dot on black line) receives both the direct sound and the reflection coming from the orchestra floor. The black dot on the solid black line and the black dot on the dashed line indicate the real and the image source, respectively. The notations H S, H R and D stand for Height of Source from the ground, Height of Receiver from the ground and Horizontal Distance between Source and Receiver, respectively...84 Figure 9.6: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 5 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting Figure 9.7: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 15 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting Figure 9.8: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 25 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting Figure 9.9: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 28 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting Figure 9.10: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 38 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting Figure 9.11: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 2 nd row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting...88 Figure 9.12: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 8 th row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting

8 The modern use of Ancient Greek and Roman theaters from an acoustic point of view Figure 9.13: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 14 th row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting...89 Figure 9.14: Early Decay Time (EDT) at 1000Hz at the Theatre of Epidauros (without stage)...90 Figure 9.15: Early Decay Time (EDT) at 1000Hz at the Theatre of Epidauros (with stage)...90 Figure 9.16: Reverberation Time (T30) at 1000Hz at the Theatre of Epidauros (without stage) Figure 9.17: Reverberation Time (T30) at 1000Hz at the Theatre of Epidauros (with stage)...91 Figure 9.18: Sound Pressure Level (SPL) at 1000Hz at the Theatre of Epidauros (without stage) Figure 9.19: Sound Pressure Level (SPL) at 1000Hz at the Theatre of Epidauros (with stage) Figure 9.20: Clarity (C80) at 1000Hz at the Theatre of Epidauros (without stage) Figure 9.21: Clarity (C80) at 1000Hz at the Theatre of Epidauros (with stage) Figure 9.22: Speech Transmission Index (STI) at 1000Hz at the Theatre of Epidauros (without stage) Figure 9.23: Speech Transmission Index (STI) at 1000Hz at the Theatre of Epidauros (with stage)...94 Figure 9.24: Early Decay Time (EDT) at 1000Hz at the Theatre of Ancient Epidauros (without stage) Figure 9.25: Early Decay Time (EDT) at 1000Hz at the Theatre of Ancient Epidauros (with stage) Figure 9.26: Reverberation Time (T30) at 1000Hz at the Theatre of Ancient Epidauros (without stage) Figure 9.27: Reverberation Time (T30) at 1000Hz at the Theatre of Ancient Epidauros (with stage)...96 Figure 9.28: Sound Pressure Level (SPL) at 1000Hz at the Theatre of Ancient Epidauros (without stage) Figure 9.29: Sound Pressure Level (SPL) at 1000Hz at the Theatre of Ancient Epidauros (with stage) Figure 9.30: Clarity (C80) at 1000Hz at the Theatre of Ancient Epidauros (without stage)...98 Figure 9.31: Clarity (C80) at 1000Hz at the Theatre of Ancient Epidauros (with stage)...98 Figure 9.32: Speech Transmission Index (STI) at 1000Hz at the Theatre of Ancient Epidauros (without stage) Figure 9.33: Speech Transmission Index (STI) at 1000Hz at the Theatre of Ancient Epidauros (with stage) LIST OF TABLES Table 6.1: General information for the performances...67 Table 6.2: Pairs that were compared in Section 2 of the listening tests. The colors stress whether the performance was amplified (light orange) or not (light yellow). Large = Theatre of Epidauros, Small = Theatre of Ancient Epidauros Table 6.3: The values of the acoustic quantities measured in the receiver positions which are the closest to the recording positions used for this part of the listening tests...75 Table 9.1: Table of values for the Theatre of Epidauros...84 Table 9.2: Table of values for the Theatre of Ancient Epidauros

9 Introduction and objectives 1. Introduction and objectives Greek and Roman theatres have undoubtedly played an important role not only in the society of their times but also today. In fact, many of those theatres are used nowadays, if their present condition allows it. The intensive contemporary use of ancient theatres has given rise to discussions -in national and international level- that range from practical issues (e.g. maintenance and restoration of the theatres) to theoretical aspects regarding their use (e.g. type and content of the performances that take place in those spaces in respect to the protection and preservation of cultural heritage). These topics have been addressed in several international charters ([1], [2], [3]) related to world cultural heritage. The acoustic properties of open-air theatres are also discussed in those charters, since they consist of functional characteristics of those spaces and their investigation is by itself of great importance from a cultural and educational point of view. However, considering the intensive contemporary use of ancient theatres there is a need for directing investigation efforts towards addressing specific issues related to their acoustics; what can be done in order to restore the acoustical properties of the theatres, if and how can they be improved, in which extent can amplification be used in modern performances etc. Part of the objectives of the ERATO 1 project was to process and discuss some of these topics. Under ERATO, acoustic measurements and computer simulations of ancient Greek and Roman theatres were conducted. The theatres that were included were located in Italy, Turkey and Jordan. In the outcomes of ERATO [4], specific recommendations and guidelines have been proposed concerning the modern use of the theatres [5]. For the purpose of evaluating these recommendations and more specifically the ones that suggest restoration of the stage and positioning of the sound sources on the proscenium near the skene wall, it was decided to study two cases of theatres, which this time would be located in Greece. 1 Identification, Evaluation and Revival of the Acoustical heritage of ancient Theatres and Odea : An EU funded program with a duration of 3 years, in which the Department of Acoustic Technology at DTU was involved. 9

10 Introduction and objectives The first theatre that was chosen was the Theater of the Sanctuary of Asklepios at Epidauros (from now on referred to as Theater of Epidauros ) since it is a typical example of an ancient Greek theatre of the Hellenistic period 2 and it is the best preserved of its kind. The second theatre investigated was the, much smaller, Theatre of Ancient Epidauros, the construction of which dates back to the 4 th century BC; however, it took its final form during the Roman era 3 and it is preserved in this form until today. Both theatres are used intensively nowadays and the types of performances that they host vary from modern versions of Ancient Greek tragedies/comedies to musical concerts. In those theatres a set of in situ acoustic measurements were conducted in various source-receiver configurations. The aim was to obtain data that would allow comparisons among different source positions. Furthermore, those measurements were compared to simulations of the theatres created with the use of the ODEON software. After obtaining a satisfactory agreement between the measured and simulated data the models were used in order to investigate the effect of the addition of a stage in the acoustic behavior of the theatres. Finally, in an attempt to approach the effect of amplification on subjective aspects of the acoustical character of the theatres (e.g. the perception of space based only on auditory cues, intimacy) a series of listening tests was conducted. The relation of the observations with objectively measured acoustic parameters (e.g. Sound Pressure Level, Clarity) was also investigated. The material (i.e. the audio tracks) used for the purpose of the tests was obtained from binaural recordings of amplified and non amplified performances in both theatres. The outcomes of the present study are expected to give an insight to the acoustical behavior of the theatres under investigation, as well as to expand the analysis already carried out in the duration of the ERATO project. Last but not least, by combining the use of tools like objective measurements, computer simulations and listening tests, this study s most ambitious goal is to point out a more complete way of approaching the matter of contemporary use. The terms written in italics are Greek (Hellenic) or Latin terms related to the theatres and they are explained in the Glossary. 2 4 th to 1 st century BC 3 Starting around the 2 nd or 1 st century BC 10

11 Information on the theatres under investigation 2. Information on the theatres under investigation 2.1. The Theatre of Epidauros The Theatre of Epidauros is situated at the North-West part of Peloponnesos in Greece. It is a typical example of a theatre of its time, consisting of the basic parts of the ancient Greek theatre; the Koilon, the Orchestra, the Skene. It was built in two stages; the lower part of the koilon (below the diazoma), the orchestra and the skene were built around the 4 th century B.C. The extension of the koilon was made around the middle of the 2 nd century B.C. An idea about the size of the construction can be obtained if we take into account that the longest radius of the koilon is 58m and the diameter of the orchestra is about 20m. The capacity of the theatre is about to14000 spectators The theatre was used for solo singing, chanting, musical/poetical contests (mainly for solo instruments) and theatrical performances of ancient tragedies and comedies. Figure 2.1: A view of the Theatre of Epidauros 11

12 Information on the theatres under investigation 2.2. The Theatre of Ancient Epidauros The Theatre of Ancient Epidauros is situated about 12 km further away from the Theatre of Epidauros, in a small city called Ancient Epidauros. It was discovered rather recently (1970) and the excavations are still in process nowadays. It was constructed in sections and it is speculated that it had a simple initial form. The theatre was built in the middle of the 4th century B.C. and the constructions continued until the Hellenistic times, but later during the Roman period, the orchestra became semi-circular with the erection of a stage nearer to the koilon, of which only the lower part has survived until now. The theatre could host 2000 spectators, although today s capacity is around 500. The Theatre of Ancient Epidauros had been in use for centuries along with the Theatre of Epidauros. Figure 2.2: A view of the Theatre of Ancient Epidauros 2.3. Contemporary use of the theatres Nowadays, during the summer season both theatres host a variety of performances. The performances usually relate in some way with the ancient Greek theatrical heritage, especially in the case of the Theatre of Epidauros. Since, in both theatres under investigation only the ruins of the skene survive until today, the construction of a temporary stage building is often required. In the case of the Theatre of Epidauros it depends on the production and the characteristics of the 12

13 Information on the theatres under investigation construction can vary widely, from a simple wooden panel to a complicated and full size skene. At the Theatre of Ancient Epidauros on the other hand a temporary wooden platform covering the orchestra and the stage is installed every year for the period that the performances take place. Although there are still productions in which no artificial amplification of the voices of the actors (or of musical instruments) is used, the number of productions that experiment with the use artificial amplification is increasing. At the Theatre of Ancient Epidauros most of the presented performances are amplified. 13

14 Description of acoustic measurements and recordings 3. Description of acoustic measurements and recordings 3.1. Acoustic measurements Equipment For the measurements the DIRAC software v3.0 was used, running on a portable computer. The source was a dodecahedron loudspeaker and the receiver was an AKG stereo microphone. A pre-amplifier, an amplifier and the necessary cabling between the devices were used as well. The signal that was used was an exponential sweep with a duration of 10,9 seconds. The signal was produced by the DIRAC software and it was first fed to the preamplifier and amplifier and then directed to the loudspeaker. The microphone was also connected to the laptop and the impulse responses in different positions of the theatres were recorded. Figure 3.1: The measuring equipment (except from the source and receiver). 14

15 Description of acoustic measurements and recordings Figure 3.2: While recording an impulse response at the Theatre of Epidauros. The microphone and the loudspeaker can be seen at the right and upper left of the photograph, respectively. 15

16 Description of acoustic measurements and recordings Calibration For the calibration of our measuring system the following setup was used. The source (dodecahedron loudspeaker) and receiver (AKG microphone) were positioned at a height of 1,5m and the distance between them was 2m 4. Mineral wool was placed between them (in parallel to the ground plain and covering a surface of about 2m 2 ) at a height of 0,4 m, in order to absorb the reflections coming from the floor. The calibration setup can be seen in Figure 3.3. The signal used for the calibration process was the same exponential sweep which was used for the measurements. The microphone was then rotated in steps of degrees. In every position an impulse response was recorded and the obtained data set was used for the system s calibration. Figure 3.3: The setup used for obtaining the data used for calibration of the measuring system. 4 For calculating Strength, G a correction value of 14dB was added in the results in order to compensate for the fact that the sound source was positioned 2 and not 10m away. 16

17 Description of acoustic measurements and recordings Procedure Theatre of Epidauros For the Theatre of Epidauros, 3 source and 15 receiver positions were chosen. The symmetry of the theatre was taken into account and the receiver positions were chosen in such a way that a grid of measuring points covering only the left half of the koilon, was created; the conclusions that can be derived from those measurements can then be generalized for the whole seating area. The receiver positions were always chosen to be approximately at the center of the respective row and the microphone was positioned at a height of around 60cm from the seat. The kerkides were coded with letters and the rows with numbers; thus, each measuring position is indicated by a capital letter followed by a number (eg. A25, C15 etc.). The positions can be seen on Figure 3.4. U Q C E M A Figure 3.4: Plan view of the Theatre of Epidauros. The receiver positions are marked with black dots. The letters and numbers reveal the coding that was chosen for the receiver positions (eg. A5, C15, U15 etc.). The source positions are marked with a capital S and a number from 1 to 3 (Figure 3.5). To be more specific, source position S1 is exactly at the center of the orchestra of the theatre (thymeli) at a height of 1,5m from the ground. The positions S2 and S3 were chosen in such a way, that they are situated at the vertices of the two equal 17

18 Description of acoustic measurements and recordings angles of an isosceles triangle with its equal sides being around 14,80m and its base being around 10m. The height of the source at positions S2 and S3 was chosen to be 3,80m; according to Vitruvius the height of the logeion in an ancient Greek theatre ought to be not less than ten feet or more than twelve [6]. Thus, by positioning the sources in this way, an effort of recreating the source positions indicated by Vitruvius was made; of course, the absence of a skene could not be compensated. On the other hand, source positions S2 and S3 could give us some useful information about the acoustical behavior of the theatre in case loudspeakers are put in those positions. S1 14,80m 14,80m S2 10m S3 Figure 3.5: Plan view of the orchestra and skene of Theatre of Epidauros. The source positions are marked with red dots. The letters and numbers reveal the coding that was chosen for the source positions (S1, S2 and S3). Figure 3.6: Setting up source position S2. 18

19 Description of acoustic measurements and recordings Theatre of Ancient Epidauros For the Theatre of Ancient Epidauros, 3 source and 12 receiver positions were chosen. The symmetry of the theatre was taken into account in this case as well, and the positions were chosen in such a way that a grid of measuring points covering the left half of the koilon was created. The coding of the positions is based on the principal that was chosen for the Theatre of Epidauros. The positions can be seen on Figure ? G? C? D E 2?? T A B A? Figure 3.7: Plan view of the Theatre of Ancient Epidauros. The receiver positions are marked with black dots. The letters and numbers reveal the coding that was chosen for the receiver positions (eg. A2, C8, E14 etc.). The source positions are marked with a capital S and a number from 1 to 3. In this case, all source positions were at a height of 1,5m from the wooden construction that was covering the ruins of the skene and the whole orchestra at the time of the conduction of the measurements (Figure 3.8). The exact positions of the sources can be seen on Figure 3.9. In this case as well, the source positions S2 and S3 could give 19

20 Description of acoustic measurements and recordings us some useful information about the acoustical behavior of the theatre in case loudspeakers are put in those positions. Figure 3.8: The wooden construction that was built on top of the orchestra and skene of the Theatre of Ancient Epidauros during the time that the measurements were conducted.? 6,14m S1 S2 4,20m 4,20m S3 Figure 3.9: Plan view of the orchestra and skene of Theatre of Epidauros. The source positions are marked with red dots. The letters and numbers reveal the coding that was chosen for the source positions (S1, S2 and S3). 20

21 Description of acoustic measurements and recordings 3.2. Recordings Equipment The equipment that was used for the recordings was 3 hard disc recorders (Sound Devices 722T and 744T) and 3 sets of binaural microphones (2 Sennheiser and 1 made at the Department of Acoustic Technology-DTU). Figure 3.10: The pair of home-made, binaural microphones that were used for the conduction of the recordings at one of the positions Calibration After fixing the gain controls at a specific level (different in each recorder depending on the seating position 5 ) a reference signal was recorded in all three hard disc recorders. The reference signal was white noise MLS noise 6 at 84dB SPL, which was produced by the ODEON software. The sound source was the dodecahedron loudspeaker and each one of the persons carrying the recording equipment recorded consecutively, a short sound sample at a distance of 2m from the source and at 1,5m from the ground. These reference sound files were later used for normalization purposes in order to compensate for the differences in the initial gain setups. The sound files could then be directly compared to each other. For the manipulation of all the recorded files the Adobe Audition software was used. 5 The gain in each recorder was set to be as high as possible in order for the recorded signal to have a high signal-to-noise ratio, but also taking care that no clipping distortion was introduced. 6 A MLS (Maximum Length Sequence) is a periodic pseudo random white noise signal, having the desirable property that its frequency spectrum over one period is as flat as the spectrum of an ideal impulse. Many types of MLS exist. DIRAC uses a subset, with period lengths ranging from 0,34 to 23,8 seconds [7]. 21

22 Description of acoustic measurements and recordings Procedure One amplified and one non-amplified performance was recorded in each theatre. Parts of the performances were recorded simultaneously in 3 different positions in each theatre. The recording positions can be seen in Figure 3.11 and Figure U Q C E M A Figure 3.11: The red circles indicate the recording positions at the Theatre of Epidauros. The performances that were recorded in the Theatre of Epidauros were: Persian by Aeschylos The main type of sound was speech. The performance was not amplified and the scenography was very modest (Figure 3.13). Suppliants by Euripides In this modern version of Euripides s ancient tragedy, the types of sounds were both music and speech. The performance was amplified with a particular amplification system; apart from the array of loudspeakers hanging in either side of the stage, 8 loudspeakers were positioned tilted on the orchestra floor, facing the klimakes (Figure 3.13). 22

23 Description of acoustic measurements and recordings 14 8? G? C? D E 2?? T A B A? Figure 3.12: The red circles indicate the recording positions at the Theatre of Ancient Epidauros. The performances that were recorded in the Theatre of Ancient Epidauros were: Eros Thilikratis The main type of sound was speech and the spoken parts of the performance were not amplified. Chorika This was an amplified musical performance with many persons (musicians, singers) performing on the stage. 23

24 Description of acoustic measurements and recordings Figure 3.13: Two very different stage setups at the Theatre of Epidauros; on the left picture the stage setup for the Persians and on the right picture the stage setup for the Suppliants. 24

25 Description of the models 4. Description of the models Both theatres were modeled in ODEON v8.5. First the geometrical models were made based on plans of the theatres, as well as on photos taken on the sites. In order to simulate open-air conditions, both models were surrounded by a totally absorbing box. Then the absorption coefficients were assigned to the surfaces by assigning different materials, in order to achieve as close match as possible between measured and simulated values in terms of Reverberation Time and Strength. All the materials that were used were found in the Global Material Library of ODEON v.8.5. Finally, for both theatres Marble slabs were used for the area of the koilon, while for the orchestra of the Theatre of Epidauros Glaze plaster and for the orchestra of the Theatre of Ancient Epidauros Floors, Hollow wooden podium. The scattering coefficients were chosen according to the suggestions proposed in the manual of ODEON; thus, very scattering, rigid surfaces that were not modeled in detail (like the koilon of the theatres) were given a high scattering coefficient of 0,4. For the rest of the surfaces (orchestra, stage etc.) a value of 0,05 was assigned. The models can be seen in Figure 4.1 and Figure 4.2. Odeon Figure 4.1: The model of the Theatre of Epidauros. The surrounding box is totally absorbing, in an effort to simulate open-air conditions. 25

26 Description of the models Odeon Figure 4.2: The model of the Theatre of Ancient Epidauros. 26

27 Description of the models For examining the effect of the addition of a stage building on the acoustical behavior of the theatres, both models were modified. In the figures that follow, the modified models are shown. In the Figure 4.3 the dimensions of the stage buildings are given and the models with the added stage buildings are shown in Figure 4.4 and Figure 4.5. a d b e f g c a [m] b [m] c [m] d [m] e [m] f [m] G [m] Theatre of Epidauros 25, ,00 7,00 10,33 8,00 3,00 Theatre of Ancient Epidauros 17,50 6,40 1 4,50 6,18 4,50 0,50 Figure 4.3: Rough sketches and the dimensions of the stage buildings. 27

28 Description of the models Odeon Figure 4.4: The model of the Theatre of Epidauros with the added stage building. Odeon Figure 4.5: The model of the Theatre of Ancient Epidauros with the added stage building. 28

29 Measurements and Simulations 5. Measurements and Simulations In this chapter, the results from the acoustic measurements will be presented, as well as data obtained from simulations in ODEON. The analysis of the data focuses on the comparison of the following acoustic quantities: Sound Strength, G (in db) Reverberation Time, T30 (in sec) 7 Early Decay Time, EDT (in sec) Clarity, C80 (in db) Speech Transmission Index, STI The detailed definitions of the quantities can be found in [8] Theatre of Epidauros-Results and discussion Comparison of source positions In this section the results obtained from measurements with different source positions will be discussed. The analysis will focus on the three receiver positions that were used for the recordings (i.e. E15, C25 and U5). The reason is that by comparing those 9 source-receiver configurations (3 source and 3 receiver positions) it is expected to reach to conclusions that can be related to the listening tests. An important note that it is necessary to point out is that the measurements with the source position S3 were conducted the day after the measurements with S1 and S2 were conducted. The day when the measurements with S3 were conducted the weather conditions were quite different from the previous day; the temperature was lower and the atmosphere was more humid. The level of the background noise was much lower since there was no sound from cicadas (at least not until the measurements had finished). Furthermore, another set of impulse responses meant for creating a calibration data set (as described in 3.1.3) was obtained and used for calibrating the system. In the following figures it is possible to see that S3 has given results quite different from S2, especially in the values for EDT and G. 7 The reason why T30 was chosen and not T20, is explained in paragraph

30 Measurements and Simulations E15_S1-2,00 Strength, G [db] -4,00-6,00-8,00-1 E15_S3 C25_S1 C25_S2 E15_S2 C25_S3 U5_S1 U5_S2 U5_S3 E15_S1 E15_S2 E15_S3 U5_S1 U5_S2 U5_S3 C25_S1 C25_S2 C25_S3-12, Distance from source [m] Figure 5.1: Strength (G) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]. For the source positions S1 and S2, the Strength of sound is inversely proportional to distance and with increasing distance strength seems to decrease with an almost constant slope. In free-field conditions the sound pressure level drops 6dB per doubling of distance. Due to the fact that the sound field in the space of the theatre is not free at all a less steep drop would be expected. Nevertheless, by comparing E15_S1 and U5_S1 it seems that this is not the case here. Concerning S3, the values of G in all receiver positions are even higher than S1 (Figure 5.1); which is strange since S1 is almost 15m closer to the receiver points than S3 (Figure 3.5). It could be argued that it is the different set of data that has been used for calibration that creates this difference. If that was the case then particular data would only be expected for the G values since among the quantities presented and compared in this study, they are the only ones which are affected by the calibration of the system. However, some seemingly irregular results are observed in Figure 5.2 for EDT, as well. The values obtained with the source positioned at S3 are much higher than the ones measured for either S1 (around 0,09) or S2 (around 0,15). Unlike G, the calculation of EDT is not affected by the calibration procedure since it is calculated 30

31 Measurements and Simulations directly from the slope of the integrated impulse response curves. Thus, the explanation of a calibration error does not cover this case. 0,80 Early Decay Time, EDT [db] 0,70 C25_S3 0,60 E15_S3 0,50 0,40 U5_S3 0,30 0,20 E15_S2 U5_S2 0,10 E15_S1 C25_S1 U5_S Distance from source [m] E15_S1 E15_S2 E15_S3 U5_S1 U5_S2 U5_S3 C25_S1 C25_S3 Figure 5.2: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]. An alternate explanation could attribute these results to the effect of the weather conditions on the acoustic properties of the theatre. Taking into account that the measurements were conducted early in the morning under the conditions described previously, it could be possible that the temperature gradient in the different layers of air was such that could cause a downward bending of the sound rays. This is a complicated phenomenon and its explanation is out of the scope of this investigation but the occurrence of this phenomenon would mean that a bigger amount of sound rays (comparing to the previous day) would reach the receiver positions. This could explain the higher G values but also the higher EDT values. Nevertheless, this assumption cannot be proven from the analysis undergone so far; in previous investigations of this phenomenon at the Theatre of Epidauros no pronounced effect on the acoustical properties of the theatre had been observed [9]. 31

32 Measurements and Simulations 1,00 STI 0,90 E15_S1 E15_S2 0,80 0,70 C25_S1 C25_S2 E15_S3 U5_S1 U5_S2 C25_S3 U5_S3 0,60 0,50 0,40 0,30 0,20 0, Distance from source [m] E15_S1 E15_S2 E15_S3 U5_S1 U5_S2 U5_S3 C25_S1 C25_S2 C25_S3 Figure 5.3: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]. A safe observation that it is possible to point out is that STI (as shown in Figure 5.3) is not affected by the source position and it is over 0,7 for every source-receiver configuration. This observation justifies the fame of this theatre that a performance is intelligible even at the most remote seats. As far as Reverberation time is concerned, looking at Figure 5.4 it is possible to see that there is no obvious dependency of T30 from the source-receiver distance. Furthermore in Figure 5.5 it is shown that when the source is positioned on the orchestra the values of T30 are higher comparing to the other source positions. This could be explained by the fact that in the absence of a skene, when the source is positioned in the back (where the skene used to be), more sound rays escape from the space of the theatre. In Figure 5.5 the value that T30 takes at 4000Hz for S3 can be seen. As said before, the day that measurements with source position S3 were conducted was the only day where there was no background noise from cicadas; thus it was possible to obtain reliable results for T30 at this octave band. 32

33 Measurements and Simulations 1,40 Reverberation Time, T30 [sec] 1,20 1,00 0,80 0,60 0,40 0,20 E15_S1 C25_S1 E15_S2 C25_S2 E15_S3 C25_S3 U5_S1 U5_S2 U5_S3 E15_S1 E15_S2 E15_S3 U5_S1 U5_S2 U5_S3 C25_S1 C25_S2 C25_S Distance from source [m] Figure 5.4: Reverberation Time (T30) versus distance at the Theatre of Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]. 1,40 Reverberation Time, T30 [sec] 1,20 1,00 0,80 0,60 0,40 0,20 S1 S2 S Frequency [Hz] Figure 5.5: Reverberation Time (T30) versus frequency at the Theatre of Epidauros. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The different colors indicate the position of the sound source; blue, pink, green correspond S1, S2 and S3, respectively. 33

34 Measurements and Simulations The source positions S2 and S3 were chosen to be placed at the positions where (according to Vitruvius) the actors were performing in the ancient times. It was attempted to investigate whether by positioning the sound sources at the specific positions would have a positive effect in the acoustical behavior of the theatre. Under the present conditions of the theatre (absence of skene) this does not seem to be the case. According to our data the source position does not affect the acoustical properties of the Theatre of Epidauros, except from an increase in T30 values when the source is positioned on the orchestra. However, this could be an improvement for performing music (since T30 is already too low for musical performance) but as far as speech is concerned any source position would be just as good in terms of intelligibility. Last but not least, taking into consideration the results obtained from source position S3 it is clear that outdoor measurements depend on factors that apart from the fact that they are frequently impossible to either predict or control, their effects are difficult to be investigated. 34

35 Measurements and Simulations Evaluation of the model Based on the previous analysis on the effect of source positions it was decided to position the source on the orchestra, in the model of the Theatre of Epidauros. Thus, in the analysis that follows the measured data that were obtained from this specific source position will be presented and compared with the simulated results. In order to evaluate the model, the receiver positions were chosen to be the same as in the measurements. In the following graphs, it possible to compare the values given by the ODEON model and the values obtained by the measurements. Reverberation Time, T30 [sec] 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0, Frequency [Hz] Figure 5.6: Reverberation Time (T30) versus frequency at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured and simulated values, respectively. According to the measurements, the Reverberation time of the theatre is around 1,3 seconds in all frequencies from 125Hz to 2000kHz. Background noise from cicadas affected the measurements at 4000kHz, giving extremely high values (around 5-6 sec) at this specific frequency band. Thus, those values where omitted from the presented results. The results from the model are in accordance to the ones of the measurements especially in the frequency range from 500 to 2000Hz. 35

36 Measurements and Simulations C5_measured C5_simulated C25_measured C25_simulated Q15_measured Q15_simulated 5 0 Strength, G [db] Frequency [Hz] Figure 5.7: Strength (G) versus frequency for 3 different receiver positions at the Theatre of Epidauros. The source is located in the center of the orchestra. The solid and dotted lines indicate measured and simulated values, respectively. In Figure 5.7 it possible to observe that the measured values for G at the 125Hz octave band drop as the receiver moves to the upper rows. This could be due to the fact that the phase shift between the direct sound and the orchestra floor reflections is such that they interfere destructively when reaching the receiver positions. The sound pressure level at those points (in the specific octave band) takes lower values than it does in the other octave bands. A more detailed explanation of this phenomenon is given in section 9.2 of the Appendix. Above 500Hz, strength does not seem to depend strongly on frequency. According to the measurements, in this frequency interval, strength is almost constant for a specific receiver position. The values obtained from the simulation -with the exception of the row which is closer to the source- are in general lower in the same interval. It is possible to see that for C25 the computer simulation results and the measured data are in quite good agreement. 36

37 Measurements and Simulations Reverberation Time, T30 [sec] 1,80 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0, Distance from source [m] Figure 5.8: Reverberation Time (T30) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. In Figure 5.8 it can be seen that, according to the measurements, Reverberation Time (T30) ranges from 0,97 to 1,54 seconds. It can also be seen that as the distance from the source increases, the dispersion of the T30 values becomes smaller; T30 in the most remote positions is around 1,35 seconds. The model gives values of T30 which have a larger dispersion, ranging from 0,62 to 1,67 seconds. 37

38 Measurements and Simulations 4,00 2,00 Strength, G [db] -2,00-4,00-6,00-8, ,00-14, Distance from source [m] Figure 5.9: Strength (G) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. The Strength according to the measurements drops from 1,30dB for the places close to the source to -8,21dB for the most remote ones. The results from the model indicate a similar behavior, with the Sound Pressure Level decreasing from 2,9 to -12,15dB. 38

39 Measurements and Simulations 1,80 1,60 Early Decay Time, EDT [sec] 1,40 1,20 1,00 0,80 0,60 0,40 0, Distance from source [m] Figure 5.10: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. Early Decay Time decreases with increasing distance from 0,26 seconds at the positions which are closer to the source to 0,05 seconds for the positions which are further away. The values obtained from the simulation follow a similar pattern, ranging from 0,14 to 0,04 seconds. It is easy to identify 5 points on Figure 5.10 where EDT takes very high values. This particularity of the theatre is also verified by the model. Those points correspond to receiver positions situated on the first kerkida and more specifically to the positions A5, A15, A25, M5 and M15. The explanation of this phenomenon is that the specific positions receive quite strong reflections coming from the seating area opposite to them. In Figure 5.11 and Figure 5.12, it is possible to compare the decay curves between the positions A25 and C25, which are positioned in the same row but different kerkida. 39

40 Measurements and Simulations Decay curves at 1000 Hz, T30=1,15 (s) gfedcb gfedcb gfedc gfedc gfedc E, Simulated E, Integrated E, Corrected I, Simulated I, Integrated SPL (db) ,05 Odeon ,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 Time (seconds rel. direct sound) 0,7 0,75 0,8 0,85 0,9 0,95 1 Figure 5.11: The simulated and integrated decay curves at 1000Hz produced by ODEON, for position A25. Decay curves at 1000 Hz, T30=1,52 (s) gfedcb gfedcb gfedc gfedc gfedc E, Simulated E, Integrated E, Corrected I, Simulated I, Integrated SPL (db) Odeon ,1 0,2 0,3 0,4 0,5 0,6 0,7 Time (seconds rel. direct sound) 0,8 0,9 1 1,1 Figure 5.12: The simulated and integrated decay curves at 1000Hz produced by ODEON, for position C25. For this example, it is possible to see that in position A25 the SPL of the direct sound decreases until 113msec where an increase of SPL is observed. This is not observed in position C25. This fact indicates that A25 receives strong reflections from a surface being about 39 meters away (Figure 5.13). 40

41 Measurements and Simulations 9 P1 Odeon Surface: 1531 Path <m>: 38,93 Time <ms>: 113 Figure 5.13: The direction of reflections responsible for the increase of the energy at 113msec at position A25, according to ODEON. Due to the fact that these reflections are relatively loud (comparing to the direct sound) and arrive rather late after the direct sound, they will be perceived as distinct echo [10]; however, it must be stressed that the measurements were made when the theatre was unoccupied. In the case of the occupied theatre the absorption added by the audience would effectively reduce the amount of energy reflected to those positions. 41

42 Measurements and Simulations Clarity, C80 [db] 2 18,00 16,00 14,00 12,00 1 8,00 6,00 4,00 2, Distance from source [m] Figure 5.14: Clarity (C80) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. As it can be seen in Figure 5.14, in the same 5 positions discussed before, Clarity takes low values; this result was expected since Clarity is an early-to-late arriving sound energy ratio and there are more late-arriving reflections in those positions. In general, Clarity is high and even at the seats which are further away from the source it is more than 14dB. [8] 42

43 Measurements and Simulations 1 0,9 0,8 0,7 0,6 STI 0,5 0,4 0,3 0,2 0, Distance from source [m] Figure 5.15: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. Finally, the values of the Speech Transmission Index are in all positions higher than 0,68 according to the measurements. The simulation gives in general very high values for STI (more than 0,9), while the receiver positions situated in the first kerkida can be identified at the points where the values of STI are around 0,7. However, it should be mentioned that during the ODEON calculations the background noise was not defined. Therefore, ODEON results for STI represent an ideal situation, where there is no background noise at all. The calibration of the model and the good match between measured and simulated values gives the opportunity to use the computer model to check the impact of the addition of the stage to the acoustic properties of the theatre. 43

44 Measurements and Simulations Addition of a stage The effect of the construction of a simple stage on the acoustic properties of the Theatre of Epidauros will be discussed here. As shown on Figure 5.16, the addition of the stage building does not affect much T30. It could be said that it reduces the dispersion of the values around a mean value of around 1,4 seconds, while Strength is increased in most positions by 1-2dB (Figure 5.17). Early Decay Time increases in all positions and the increase is more obvious as the receiver moves towards the positions which are further away from the source (Figure 5.18). As expected, the increase of EDT is followed by a drop of Clarity in most positions by more than 7dB (Figure 5.19). According to these last two figures, it could be stated that the echo phenomenon appearing in the first kerkida (discussed previously) seems to be smoothened. Moreover, STI remains between 0,6 and 0,7 even for the most remote positions (Figure 5.20). This result was expected since STI depends on reverberation time and background noise; background noise is not taken into account and T30 does not change too much, so STI should be at the same levels as before. 2,50 Reverberation Time, T30 [sec] 2,00 1,50 1,00 0,50 wo/ stage w/ stage Distance from source [m] Figure 5.16: Reverberation Time (T30) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 44

45 Measurements and Simulations Strength, G [db] 6,00 4,00 2,00-2,00-4,00-6,00-8, ,00 wo/ stage w/ stage -14, Distance from source [m] Figure 5.17: Strength (G) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 4,50 Early Decay Time, EDT [sec] 4,00 3,50 3,00 2,50 2,00 1,50 1,00 0,50 wo/ stage w/ stage Distance from source [m] Figure 5.18: Early Decay Time (EDT) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 45

46 Measurements and Simulations 2 15,00 Clarity, C80 [db] 1 5,00 wo/ stage w/ stage -5, Distance from source [m] Figure 5.19: Clarity (C80) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 1,20 Speech Transmission Index, STI 1,00 0,80 0,60 0,40 0,20 wo/ stage w/ stage Distance from source [m] Figure 5.20: Speech Transmission Index (STI) versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 46

47 Measurements and Simulations Summarizing, by adding the stage building it is possible to compliment the reverberance of the theatre but not without paying the price of the sound becoming less clear. Thus, judging only from the above presented parameters, a musical performance could benefit more from the presence of a stage building, than a performance were the dominant type of sound is speech. Graphical illustrations of the effect of the addition of a stage at the Theatre of Epidauros can be found in section 9.3 of the Appendix. 47

48 Measurements and Simulations 5.2. Theatre of Ancient Epidauros-Results and discussion Comparison of source positions Similar to the case of the Theatre of Epidauros, in this section the results obtained from measurements with different source positions will be discussed. Since it was not possible to obtain recordings at the exact measured receiver positions, data obtained from the positions which are the closest to the recording positions will be examined (i.e. C2, C8, C14 and D8). Taking into consideration the much smaller size of the Theatre of Ancient Epidauros this approximation is not expected to introduce an error when comparing acoustic quantities like T30, G, EDT and STI. The expectation of reaching to conclusions that could be related to the listening tests dictated the choice of the specific 12 source-receiver configurations (3 source and 4 receiver positions). In the case of this theatre all measurements were conducted during the same day and only one data set was used for the calibration of the measuring system. Thus an error in the calibration cannot explain the fact that when the source is positioned at S3 Strength at the receiver points is, in general, higher than Strength measured for the other configurations with almost the same distance between source and receiver (Figure 5.21). 1 Strength, G [db] 9,00 C2_S1 8,00 7,00 C2_S3 6,00 C2_S2 D8_S1 5,00 C8_S1 4,00 D8_S2 C8_S2 C8_S3 3,00 C14_S1 D8_S3 C14_S3 2,00 C14_S2 1, Distance from source [m] C2_S1 C2_S2 C2_S3 C8_S1 C8_S2 C8_S3 D8_S1 D8_S2 D8_S3 C14_S1 C14_S2 C14_S3 Figure 5.21: Strength (G) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific sourcereceiver setup [8]. 48

49 Measurements and Simulations The downward bending of sound rays cannot be responsible for this result either, because the S3 was measured in the middle of the day when the gradient of temperature in the air layers would cause the opposite phenomenon (i.e. upward bending of sound rays), thus lower G values would be expected. So far, no satisfying explanation for this result can be given about this fact. However, judging by the results obtained from the source positions S1 and S2 it is possible to see that in general G depends rather on the distance from the source, than the specific source position. Similar to the case of the Theatre of Epidauros, G seems to drop more than 6dB per doubling of distance which would be the case in free-field conditions (C2_S1 and C14_S1). 0,60 Early Decay Time, EDT [sec] 0,50 0,40 0,30 0,20 0,10 C2_S1 C2_S2 D8_S1 C8_S1 C8_S2 C14_S2 C14_S1 C2_S3 D8_S3 D8_S2 C8_S3 C14_S3 C2_S1 C2_S2 C2_S3 C8_S1 C8_S2 C8_S3 D8_S1 D8_S2 D8_S3 C14_S1 C14_S2 C14_S Distance from source [m] Figure 5.22: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]. Concerning, Early Decay Time (shown in Figure 5.22) source position S3 in general seems to give the lowest results, while for S1 and S2 the values are around 0,3 (with the exception of D8_S1 and D8_S2). 49

50 Measurements and Simulations 0,90 STI 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 C2_S1 C2_S2 C8_S1 D8_S1 C2_S3 C8_S3 C8_S2 D8_S2 C14_S2 D8_S3 C14_S1 C14_S3 C2_S1 C2_S2 C2_S3 C8_S1 C8_S2 C8_S3 D8_S1 D8_S2 D8_S3 C14_S1 C14_S2 C14_S Distance from source [m] Figure 5.23: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]. Speech intelligibility in the Theatre of Ancient Epidauros is very high (Figure 5.23) and independent both from source-receiver distance and source position. This result was expected since the background noise was constant during the measurements and furthermore (as it can be seen in Figure 5.24 and Figure 5.25) reverberation time is nearly independent of either source-receiver distance or frequency. 50

51 Measurements and Simulations 0,70 Reverberation Time, T30 [sec] 0,60 0,50 0,40 0,30 0,20 0,10 C2_S1 C2_S2 D8_S1 C8_S1 C8_S2 C2_S3 C14_S2 D8_S2 D8_S3 C14_S1 C8_S3 C14_S3 C2_S1 C2_S2 C2_S3 C8_S1 C8_S2 C8_S3 D8_S1 D8_S2 D8_S3 C14_S1 C14_S2 C14_S Distance from source [m] Figure 5.24: Reverberation Time (T30) versus distance at the Theatre of Ancient Epidauros. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific source-receiver setup [8]. 0,70 Reverberation time, T30 [sec] 0,60 0,50 0,40 0,30 0,20 0,10 S1 S2 S Frequency [Hz] Figure 5.25: Reverberation Time (T30) versus frequency at the Theatre of Ancient Epidauros. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The different colors indicate the position of the sound source; blue, pink, green correspond S1, S2 and S3, respectively. 51

52 Measurements and Simulations In this section it was attempted to investigate whether the source position could have an effect in the acoustical behavior of the Theatre of Ancient Epidauros. Under the present conditions of the theatre (absence of skene) this does not seem to be the case. The Theatre of Ancient Epidauros is dry, in terms of reverberance, and taking into account that both Strength and STI are high in all receiver positions, it is (in its present conditions) more suitable for performances where the main type of sound is speech. 52

53 Measurements and Simulations Evaluation of the model For evaluating the model of the Theatre of Ancient Epidauros, the source under consideration is the one located on the orchestra and the receiver positions were chosen to be the same as in the measurements. In the following graphs, it possible to compare the values given by the ODEON model and the values obtained by the measurements. 0,70 Reverberation Time, T30 [sec] 0,60 0,50 0,40 0,30 0,20 0, Frequency [Hz] Figure 5.26: Reverberation Time (T30) versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured and simulated values, respectively. In Figure 5.26 it is possible to see that the Reverberation Time (T30) is quite flat in the frequency spectrum from 500 to 2000Hz, as indicated by both the measured and the simulated values. Nevertheless, the simulated values are around 0,1 second lower in most frequency bands. It is important to mention that the results of the measurements at 4000Hz were omitted in this case as well; the increased background noise floor at this frequency band created by cicadas made it impossible to conduct a reliable measurement. 53

54 Measurements and Simulations D2_measured D2_simulated D14_measured D14_simulated Strength, G [db] Frequency [Hz] Figure 5.27: Strength (G) versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. The solid and dotted lines indicate the measured and simulated values, respectively. According to the measurements, the Theatre of Ancient Epidauros has a particular acoustical behavior in terms of Strength (G). Apart from the fact that it is possible to observe an attenuation of the sound pressure level with increasing frequency (starting from 250Hz), a dip is observed at the 1000Hz octave band. This could be related to the so-called seat-dip effect, where in some concert halls similar dips are observed, which depend on the distance between the rows of seats and the height of the seats. However, in this case it is not possible to make a secure assumption for this phenomenon. Similar to the Theatre of Epidauros, a strong attenuation of the lower frequencies is observed. In this case as well, probably the phase shift between the direct sound and the floor reflections is such that they interfere destructively when reaching the receiver positions; thus the sound pressure level at these point (in the specific octave band) takes lower values than it does in the other octave bands. A more detailed explanation of the phenomenon can be found in section

55 Measurements and Simulations 0,70 Reverberation Time, T30 [sec] 0,60 0,50 0,40 0,30 0,20 0,10 5, , ,00 3 Distance from source [m] Figure 5.28: Reverberation Time (T30) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. Figure 5.28 shows that the model calculated, in general, lower values (around 0,45 seconds) for the Reverberation Time (T30) comparing to the measurements (around 0,55 seconds). However, in both the simulated and the real theatre, Reverberation Time (T30) does not depend on the distance from the source. This is, most likely, related to the size of the theatre and by looking at Figure 5.8 it is possible to see that in the case of the much larger Theatre of Epidauros, T30 is more affected by the distance from the source. In terms of Strength (G), the model estimated values of approximately 2dB lower than the real data. It must be noted though that the slope of the decrease of the strength with increasing distance is similar in the real and the virtual theatre (Figure 5.29). Concerning Early Decay Time (EDT) it is possible to observe a large dispersion of the values for both the simulated and measured values. By looking at this graph it is not possible to identify the pattern that the values of Early Decay Time follow. On the other hand, it is interesting to observe the results plotted versus the specific kerkida that the receiver positions are situated (Figure 5.31). 55

56 Measurements and Simulations 1 8,00 Strength, G [db] 6,00 4,00 2,00-2,00 5, , ,00 3 Distance from source [m] Figure 5.29: Strength (G) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. 0,60 Early Decay Time, EDT [sec] 0,50 0,40 0,30 0,20 0,10 5, , ,00 3 Distance from source [m] Figure 5.30: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. 56

57 Measurements and Simulations In Figure 5.31 it is possible to observe that according to the measurements Early Decay Time increases as we approach to the axis of symmetry of the theatre (kerkida E). In the kerkides D and E Early Decay Time ranges from 0,44 to 0,51 seconds depending on the row. It seems that for some reason there is a focusing of reflections towards kerkida E. This phenomenon is probably due to the reflections coming from the wooden panel that is shown in Figure This panel was installed on a wooden platform which was built on the ruins of the skene, perpendicular to the theatre s axis of symmetry at the time that the measurements took place. Nevertheless, it must be stated that even though this panel was included in the ODEON model the results did not show a similar behavior Figure ,60 Early Decay Time, EDT [sec] 0,50 0,40 0,30 0,20 0,10 Row2 measured Row8 measured Row14 measured Number of Kerkida Figure 5.31: Early Decay Time (EDT) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. All points indicate measured values. 57

58 Measurements and Simulations Figure 5.32: View of the Theatre of Ancient Epidauros at the time of the measurements. 0,60 Early Decay Time, EDT [sec] 0,50 0,40 0,30 0,20 0,10 Row2 measured Row8 measured Row14 measured Row2 simulated Row8 simulated Row14 simulated Number of Kerkida Figure 5.33: Early Decay Time (EDT) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The solid and dotted lines indicate the measured and simulated values, respectively. 58

59 Measurements and Simulations 18,00 16,00 14,00 Clarity, C80 [db] 12,00 1 8,00 6,00 4,00 2,00 5, , ,00 3 Distance from source [m] Figure 5.34: Clarity (C80) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. In terms of Clarity (C80) the measured values range from 12,40 to 16,39 db, while the simulation gave values from 8,75 to 13,20 db (Figure 5.34). According to the model, Clarity seems to increase with increasing distance, although this phenomenon is not observed in the measurements. The trend that it is possible to observe in the measured data is that the dispersion of the results reduces as the receiver is further away from the source. 59

60 Measurements and Simulations 18,00 16,00 14,00 Clarity, C80 [db] 12,00 1 8,00 6,00 4,00 2,00 Row2 measured Row8 measured Row14 measured Row2 simulated Row8 simulated Row14 simulated Number of Kerkida Figure 5.35: Clarity (C80) versus the number of the kerkida at the Theatre of Ancient Epidauros (1 to 5 corresponds from A to E respectively). The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The solid and dotted lines indicate the measured and simulated values, respectively. By plotting C80 versus the kerkida that the receiver is positioned, it is possible to see that Clarity seems to take its lower values, when approaching the central kerkida E (no. 5). This phenomenon was expected since Early Decay Time shows an opposite behavior as seen in Figure However, this is not observed in the simulated values, which follow a trend that basically verifies the observation made in the previous paragraph; there is a dependency between C80 and the row that the receiver is seating; Clarity tends to be higher in the upper rows. 60

61 Measurements and Simulations 1,00 0,90 0,80 0,70 0,60 STI 0,50 0,40 0,30 0,20 0,10 5, , ,00 3 Distance from source [m] Figure 5.36: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate the measured and simulated values, respectively. According to the measurements, the Speech Transmission Index is in general higher than 0,65 and the positions which are closer to the source show the highest values (around 0,80). On the other hand, according to the simulations the values of STI are higher than the measured data, although the difference reduces when approaching the source. This can be explained by the fact that -as in the case of the Theatre of Epidauros- ODEON does not take into account background noise, if not defined by the user. Thus, the simulation gives higher values for STI. The fact that STI decreases with increasing distance in the real data reflects the fact that not only the receiver is moving away from the source, but is also approaching the source of the background noise, which in this case is mainly cicadas on the surrounding pine trees. In the case of the Theatre of Ancient Epidauros the match between measured and simulated values was not as good as in the case of the Theatre of Epidauros. The reason is mainly the difficulty of defining the absorption and diffusion characteristics of the materials used in the model. Nevertheless, keeping in mind its limitations it will be attempted to use the model for examining the effects of the addition of a stage to the acoustical behavior of the theatre. 61

62 Measurements and Simulations Addition of a stage The effect of the addition of a stage building on the acoustic parameters of the Theatre of Ancient Epidauros is similar to the case of the Theatre of Epidauros. Looking at Figure 5.37 it is possible to see that the addition of a stage building increases the Reverberation Time (T30) by almost 0,2 seconds in most of the positions, while the values for Strength (G) are increased around 2dB Figure In terms of Early Decay Time (EDT), Figure 5.39 indicates that the addition of the stage has drastic effects; EDT increases in general and as the receiver moves away from the source this increase becomes larger, exceeding 100% in the back rows of the theatre. As expected, Clarity (Figure 5.40) is decreasing and at the most remote seats it drops more than 6dB. However, also in the case of this theatre STI remains at levels between 0,66 and 0,72 which signifies Good intelligibility (Figure 5.41). 1,20 Reverberation Time, T30 [sec] 1,00 0,80 0,60 0,40 0,20 wo/ stage w/ stage 5, , ,00 3 Distance from source [m] Figure 5.37: Reverberation Time (T30) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 62

63 Measurements and Simulations Strength, G [db] 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 wo/ stage w/ stage -1,00 5, , ,00 3 Distance from source [m] Figure 5.38: Strength (G) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. Early Decay Time, EDT [sec] 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 wo/ stage w/ stage 5, , ,00 3 Distance from source [m] Figure 5.39: Early Decay Time (EDT) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 63

64 Measurements and Simulations Clarity, C80 [db] 14,00 12,00 1 8,00 6,00 4,00 2,00 wo/ stage w/ stage 5, , ,00 3 Distance from source [m] Figure 5.40: Clarity (C80) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. Speech Transmission Index, STI 1,00 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 wo/ stage w/ stage 5, , ,00 3 Distance from source [m] Figure 5.41: Speech Transmission Index (STI) versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue dots indicate values obtained from the model of the theatre with and without stage, respectively. 64

65 Measurements and Simulations From the results presented in this section it seems that the addition of a stage will have more evident effects to the Theatre of Ancient Epidauros than in the case of the Theatre of Epidauros. However, taking into account that T30 and EDT are quite low even after adding the stage, the theatre is still too dry for hosting a non amplified musical performance. Graphical illustrations of the effect of the addition of a stage at the Theatre of Ancient Epidauros can be found in section 9.4 of the Appendix. 65

66 Listening Tests 6. Listening Tests A series of listening tests consisting of 2 sections was conducted in an attempt to indirectly investigate the effect of the loudspeaker systems, which were used in some of the performances, on subjective aspects of the acoustical character of the theatres. The observations were related with objectively measured acoustical quantities whenever it was possible. In the first section the test subjects were asked to listen to 3 audio tracks recorded at the same time in 3 different seating positions at each theatre; the task was to choose among those 3 positions, the one that seemed closer to the source for them and also to state the one that they would prefer to be seating. In the second section, the test subjects were asked to choose between 2 short presentations of different performances, which one was more intimate for them, as well as to indicate in which of the 2 audio tracks the theatre seemed larger to them. The test group consisted of 11 persons with ages between 20 and 30 years old. All test subjects at the time of the tests, were working or studying at the Acoustic Technology Department of the Technical University of Denmark. All of them had undergone various kinds of listening tests, as well as several audiometric analyses in the past; thus, there was no training previous to the listening tests. All test subjects had normal hearing at mid-frequencies. The test subjects had to give their answers on a paper form that was presented to them at the beginning of the listening tests. 66

67 Listening Tests 6.1. Results and discussion Section 1 Theatre of Epidauros General information related to the performance and the presentation of the recording positions at the Theatre of Epidauros is shown in Table 6.1 and Figure 6.1, respectively. LOCATION Theatre of Epidauros Theatre of Ancient Epidauros PERFORMANCE Perses Iketides Eros Thilikratis Chorika AMPLIFICATION No Yes No Yes Table 6.1: General information for the performances B U5 C C25 A E15 Figure 6.1: The recording positions at the Theatre of Epidauros. The red characters indicate the code letters of the positions chosen for the purpose of the listening tests. The black characters indicate the exact position; the letter corresponds to the kerkida and the number to the row. The recording position was chosen to be approximately in the middle of the respective row. 67

68 Listening Tests In Figure 6.2 and Figure 6.3 it is possible to see that in both performances the test subjects could identify that position B was the furthest. In the case of the non amplified performance (Figure 6.2) it would be expected that the test subjects could identify that position A was closer to the source; according to the measurements presented in 5.1.1, Strength in A is almost 3dB higher than in B, when the source is positioned on the orchestra (which was actually the case in this performance). The Just Noticeable Difference according to the ISO standards [8] for Strength is 1dB, so this result is probably affected by the fact that the microphones used at position A introduced noise to the recordings. For the amplified performance (Figure 6.3) it is easier to explain why most test subjects chose seat C to be the closest to the sound source since this position was closer to one out of the two columns of loudspeakers used in the performance. Percentage of test subjects Which seat seems closer to the source? Where would you prefer to seat? 100,0 90,0 80,0 70,0 60,0 50,0 40,0 30,0 20,0 10,0 0,0 A B C NO PREF. Answers Figure 6.2: The percentage of the test subjects versus their answers. The performance was not amplified and it took place at the Theatre of Epidauros. 68

69 Listening Tests Percentage of test subjects Which seat seems closer to the source? Where would you prefer to seat? 100,0 90,0 80,0 70,0 60,0 50,0 40,0 30,0 20,0 10,0 0,0 A B C NO PREF. Answers Figure 6.3: The percentage of the test subjects versus their answers. The performance was amplified and it took place at the Theatre of Epidauros. In any case, from both figures presented above, it is clear that in both performances the test subjects preference of seat is based on the perceived level of the sound source. This conclusion was verified also by the test subjects when asked to explain the reason or their choice. There was also a part of the test group that chose seat B for the amplified performance for the reason that they perceived a better balance of the sound sources, according to their later comments. 69

70 Listening Tests Theatre of Ancient Epidauros The recording positions chosen for the Theater of Ancient Epidauros can be seen in Figure 6.4. C C10 GA C5 B? D6???? T A? Figure 6.4: The recording positions at the Theatre of Epidauros. The red characters indicate the code letters of the positions chosen for the purpose of the listening tests. The black characters indicate the exact position; the letter corresponds to the kerkida and the number to the row. The recording position was chosen to be approximately in the middle of the respective row. At the Theatre of Ancient Epidauros it was more difficult for the test subjects to indicate the position that was closest to the source in both amplified and nonamplified performances. This could be explained by the fact that the difference in the distance from the source, between the positions A, B and C was not more than a few meters. Furthermore, by examining the measured positions C8_S1 and D8_S1, which are close to the recording positions, according to the results presented in Figure 5.21, G is around 5dB in both cases; however, this observation could only be related with the non amplified performance. 70

71 Listening Tests Percentage of test subjects Which seat seems closer to the source? Where would you prefer to seat? 100,0 90,0 80,0 70,0 60,0 50,0 40,0 30,0 20,0 10,0 0,0 A B C NO PREF. Answers Figure 6.5: The percentage of the test subjects versus their answers. The performance was not amplified and it took place at the Theatre of Ancient Epidauros. Percentage of test subjects Which seat seems closer to the source? Where would you prefer to seat? 100,0 90,0 80,0 70,0 60,0 50,0 40,0 30,0 20,0 10,0 0,0 A B C NO PREF. Answers Figure 6.6: The percentage of the test subjects versus their answers. The performance was amplified and it took place at the Theatre of Ancient Epidauros. The fact that the test subjects cannot identify the seat closest to the source is also reflected in the fact that their seat preference for the non-amplified performance (Figure 6.5) does not follow any trend; although it must be pointed out in this case as 71

72 Listening Tests well, the problematic microphones of the person recording at position A could the reason why this position was not preferred by any test subject. For the amplified performance though (Figure 6.6), the seat that is closer to the axis of symmetry of the theatre seems to be preferred, for the reason of more equal balance of the sound sources, as in the case of the large theatre. 72

73 Listening Tests Section 2 The results and discussions on the second section of the listening tests, where the test subjects had to indicate the performance that was more intimate for them, as well as to indicate which theatre seems larger for them are presented in the following paragraphs. When choosing which recording would be used for this part of the listening tests there were a number of factors to consider; first the recorded signal had to have a high signal-to-noise ratio, thus recordings from position A were excluded. Furthermore, Position B at the Theatre of Epidauros was too far to be compared to any of the recordings in the Theatre of Ancient Epidauros. Eventually, the recordings from position C in both theatres were used for this part of the listening tests. As it can be seen in Table 6.2 when an amplified (light orange) and a non-amplified (light yellow) performance were presented to the test subjects, they would indicate the amplified performance as more intimate. Taking into account that in the amplified performances the level of the sound was much higher than in the non amplified ones, apparently the intimacy criterion that this test group of people had was strongly related to the level of the sound 8. It also has to be stated that a small part of the test group noted that a female voice is always more intimate for them than a male one, which is worth to report as a note but does not change the initial remark that intimacy is related with the level of the source ( at least for this test group). Another interesting observation is that when the test subjects had to comment on the size of the theatres by listening to an amplified and a non-amplified performance, they -in all cases- indicated the one where the non-amplified performance was taking place to be bigger. This fact might imply that the presence of a sound amplification system alters the sound field in a great extent by effectively defining the auditory space; but of course, it could also be that again the perception of level is the cue that people tend to follow. 8 It was considered to try to relate the results of the listening tests with objective parameters that are more known to be related to Intimacy like the Late Lateral Sound Level (LG, in db). Due to the fact that no measurements during the performances were conducted and also because LG cannot be obtained directly from DIRAC but indirectly from ODEON, it was decided to focus on Strength and/or Reverberance. 73

74 Listening Tests Pair 1 Large / Non Amplified Large / Amplified No difference Which is more "intimate" for you? 9,1% 81,8% 9,1% Which theatre seems larger to you? 90,9% 9,1% 0,0% Pair 2 Small / Non Amplified Small / Amplified No difference Which is more "intimate" for you? 0,0% 100,0% 0,0% Which theatre seems larger to you? 81,8% 9,1% 9,1% Pair 3 Small / Non Amplified Large / Amplified No difference Which is more "intimate" for you? 18,2% 72,7% 9,1% Which theatre seems larger to you? 63,6% 27,3% 9,1% Pair 4 Large / Non Amplified Small / Amplified No difference Which is more "intimate" for you? 18,2% 81,8% 0,0% Which theatre seems larger to you? 100,0% 0,0% 0,0% Pair 5 Large / Non Amplified Small / Non Amplified No difference Which is more "intimate" for you? 27,3% 63,6% 9,1% Which theatre seems larger to you? 36,4% 27,3% 36,4% Pair 6 Large / Amplified Small / Amplified No difference Which is more "intimate" for you? 0,0% 90,9% 9,1% Which theatre seems larger to you? 63,6% 9,1% 27,3% Table 6.2: Pairs that were compared in Section 2 of the listening tests. The colors stress whether the performance was amplified (light orange) or not (light yellow). Large = Theatre of Epidauros, Small = Theatre of Ancient Epidauros. From the comparison of the last two pairs (Pair 5 and 6) it possible to see that the majority of the test subjects chose in both cases the performances at the Theatre of Ancient Epidauros to be more intimate. As said before, this could be related to the fact that the perceived level at the Theatre of Ancient Epidauros is higher. However, by taking a closer look at the results given for Pair 5 and by comparing the measured quantities at those positions (Table 6.3) it can be seen that Intimacy cannot be related only to perceived level; if that was the case, the 9dB difference in strength between the 2 recording positions would most probably be sufficient to provide a very strong cue on Intimacy for the non amplified performance, which is not the case as shown in Table 6.2. Furthermore, looking at the same pair it can be seen that the test subjects could not definitely decide on the size of the theatre. In Table 6.3 it is possible to see that the acoustic quantities at the 2 positions have large differences. Nevertheless, this could be explained by the fact that the criterion on how to evaluate the pairs had been 74

75 Listening Tests defined by the previous paired comparisons between the amplified and non-amplified performances in which the answers given are very consistent. This is an indication that a deeper investigation of non amplified performances should be conducted in order to come up with relations between objective measurements and subjective evaluations. C8_S1 (Theatre of Ancient Epidauros) C25_S1 (Theatre of Epidauros) G (in db) 5 db -4 db T30 (in sec) <0,6 sec 1,2 sec EDT (in sec) <0,3 sec 0,1 sec Table 6.3: The values of the acoustic quantities measured in the receiver positions which are the closest to the recording positions used for this part of the listening tests. 75

76 Conclusions and future work 7. Conclusions and future work 7.1. Conclusions In the present study, it has been attempted to approach the matter of investigating the acoustics of Ancient Greek and Roman theatres under the light of their modern use. By combining results from objective acoustic measurements, computer simulations and listening tests a holistic way of studying the issue has been proposed. With the help of the in situ measurements it has been possible to observe that in the present conditions of the theatres the source position does not have an influence on the acoustic properties of the theatre which in terms of strength are mainly affected by the distance between source and receiver. Specifically for the Theatre of Epidauros by positioning the sound source where the logeion used to be when the skene of the theatre was intact, no positive effect on the acoustic characteristics was observed. On the contrary, an increase in T30 values was observed when the source was positioned on the orchestra. However, as stated before this could be an improvement for performing music (since T30 is already too low for musical performances) but as far as speech is concerned any source position would be just as good in terms of intelligibility. Another interesting result that was evident in both measurements and simulations is that when the theatre is not occupied, the reflections arriving to the first kerkida from the surfaces that are in opposite side (and vice versa) could be experienced as a distinct echo. The computer simulation showed that this effect could be smoothened by the addition of a stage. Although after adding the stage T30 and G do not increase much, the effect is obvious on EDT and consequently on C80. However, even if C80 decreases STI still remains at quite high values around 0,65. In the Theatre of Ancient Epidauros the wooden panel positioned at the back of the stage seemed to create an increase in the EDT when the receiver was approaching to the axis of symmetry of the theatre. This fact causes C80 to drop to low values in the middle kerkida although for the specific theatre this is not so important because its size is quite small and the values of C80 and STI are high in most positions. This phenomenon was not observed at the simulations. The agreement of the measured and 76

77 Conclusions and future work simulated values was not as good as in the Theatre of Epidauros, basically due to difficulties in defining successfully diffusion and scattering coefficients in the surfaces of the modeled theatre. However, from the relative results between the model with and without the stage it was possible to observe that the addition of the stage in the Theatre of Ancient Epidauros has similar results as in the Theatre of Epidauros. It has to be stressed that the comparison between measured and simulated data is focused in the case where the sound source is situated on the orchestra. According to the results of the listening tests, the use of amplification systems in both theatres has to be treated with extra care since the characteristics and settings of the system, define in a great extent the sound field, and in a way they denude the theatre from its natural acoustically perceived spatial properties, which they are only underlined by the visual cues. It is also important to be stated that the existence of a common sound amplification system (normally comprised of 2 columns of loudspeakers positioned in the left and right side of the stage) increases the danger of a shifted auditory image for the people seating close to the loudspeakers. As shown in the first part of the listening tests, the danger is higher in the Theatre of Ancient Epidauros because it is smaller and the loudspeakers are usually positioned closer to the seating area. However, the loudspeaker system increases greatly the level in all positions, allowing the spectators which are seating at the most remote positions to be able to follow with no effort the performance. This is not so important in the Theatre of Ancient Epidauros since its size is much smaller. Finally, according to the results of the listening tests the use of a loudspeaker system also improves the feeling of acoustical intimacy for the spectators, which seems to be related to the level of the sound. Many obstacles appeared all along the way of this project and in all the different stages. Some of them have been discussed in this study. For example: The effect of the weather conditions in the outdoor measurements (observed in the measurements from source position S3, at the Theatre of Epidauros) 77

78 Conclusions and future work The difficulty of assigning absorption and scattering characteristics to the surfaces in the models of the theatres in order to obtain a good agreement between measured and simulated results The difficulty of designing/conducting listening tests and interpreting the results Some other problems related to the organization of a project like this, the realization of which depends on many individuals and authorities cannot be shown or evaluated. However, planning has been an important part of this project and it deserves to be mentioned. The interaction with people from different disciplines (public servants from different related authorities - archaeologists, engineers, artists, producers, philologists) that is needed to organize and conduct a project like this is part of the learning process; moreover, it is necessary in order to be able to perceive the issue of the modern use of Ancient Greek and Roman Theatres from all the different points of view Future work First of all, the models of the theatres should be further improved in order to give results that are in better agreement with the measured data. As far as the effect of the source position on the acoustical behavior of the theatres under consideration, further investigation of the measured data is required. Furthermore, comparison of the measured data, with simulations of other sourcereceiver configurations, is needed. For investigating specifically the positions of the sound sources proposed by Vitruvius [6] for the Theatre of Epidauros, the theatre should be modeled in its initial form. In terms of relating objective parameters with measured data, more listening tests should be conducted; as far as Intimacy is concerned the relation with parameters like LG or LEF (which are known to be related with subjective parameters as Listener Envelopment and Apparent Source Width, respectively) could be studied. There is a necessity for acoustical measurements in the occupied theatres. Those data could help in retuning the models and approach the modern use of the theatres from a more realistic point of view. 78

79 References 8. References [1]: ICOMOS, Principle for the analysis, conservation and structural restoration of Architectural Heritage, [2]: Burra Charter, Ar.18, [3]: The Australia ICOMOS Charter, For the Conservation of places of Cultural significance, [4]: ERATO: Final Report: covering period from 1 February 2003 to 31 January [5]: Michel Vallet, Bruno Vincent, Martin Lisa Nielsen, Report on the Assessment of the Virtual Environments, ERATO: Deliverable 9.4. November [6]: Vitruvius, The Ten Books on Architecture, Translated by Morris Hicky Morgan, Ph.D., LL.D., Dover Publications, Inc., New York. [7]: Technical Note 001, Measuring Impulse Responses using DIRAC, Acoustics Engineering, February [8]: ISO 2005, Annex A (informative), Auditorium measures derived from impulse responses, ISO/CD , [9]: L. Cremer, Different Distributions of the Audience, Auditorium Acoustics, Applied Science Publishers LTD, London [10]: H. Kuttruff, Room Acoustics, Fourth Edition, Spon, London, [11]: Finn Jacobsen, Lecture notes for course 31260, Advanced Acoustics, Ex9. Outdoor Sound Propagation, Acoustic Technology, Oersted DTU,

80 Appendix 9. Appendix 9.1. T30 versus T20 For concert halls, T20 is considered to be a more reliable descriptor of the reverberation time in concert halls/auditoriums, since T30 is more vulnerable to background noise. However, on the Figures that follow below it is possible to observe how close the values for T20 agree with the ones for T30, when plotted versus distance, but versus frequency as well. As expected, the values for T20 are generally somewhat lower than the values for T30. Furthermore, with the current version of ODEON it is easier to obtain results and graphs for T30, rather than T20. Considering that a large part of the analysis presented in this report is based on results obtained from ODEON simulations, and keeping in mind that the real measurements showed a close agreement between T20 and T30, it was decided to use the parameter T30 for evaluating reverberation time in both theatres. Reverberation Time [sec] 1,80 1,60 1,40 1,20 1,00 0,80 0,60 0,40 0,20 S1_T20 S1_T Distance [m] Figure 9.1: Reverberation Time versus distance at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue line, indicate the measured values for T20 and T30, respectively. 80

81 Appendix 1,40 Reverberation Time [sec] 1,20 1,00 0,80 0,60 0,40 0,20 S1_T20 S1_T Frequency [Hz] Figure 9.2: Reverberation Time versus frequency at the Theatre of Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured values for T20 and T30, respectively. 0,70 0,60 Reverberation Time [sec] 0,50 0,40 0,30 0,20 0,10 S1_T20 S1_T30 5, , ,00 3 Distance [m] Figure 9.3: Reverberation Time versus distance at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values at 500Hz and 1000Hz octave bands, for the specific receiver position [8]. The pink and blue line, indicate the measured values for T20 and T30, respectively. 81

82 Appendix 0,70 Reverberation time [sec] 0,60 0,50 0,40 0,30 0,20 0,10 S1_T20 S1_T Frequency [Hz] Figure 9.4: Reverberation Time versus frequency at the Theatre of Ancient Epidauros. The source is positioned in the center of the orchestra. Each point represents the average of the values measured in all receiver positions, for the specific octave band. The pink and blue line, indicate the measured values for T20 and T30, respectively. 82

83 Appendix 9.2. The effect of the ground 9 The sound pressure produced by a monopole in free field conditions at a distance r, is given by: j( ωt kr) jωρqe pˆ = (9.1) 4πr Where ρ is the density of the air (in kg/m 3 ), ω is the angular frequency (in rad/sec), Q is the volume velocity of the source (in m 3 /sec), κ is the wave number (in m -1 ). When the source is located above a rigid plane surface an additional term should be added which represents the contribution of the image source symmetrical about the surface. pˆ = jωρqe 4πR j( ωt kr ) d d j( jωρqe + R 4πR ωt kr ) r r = jωρqe 4πR j( ωt kr ) d d R 1 + R( R d r e jk ( R R ) R d ) (9.2) Where R is the plain wave reflection coefficient of the image source, R d is the direct path length (in m), R r is the reflected path length (in m). If the floor of the orchestra is assumed to be a totally reflecting surface then the plain wave reflection coefficient R can be assumed to be equal to unity and the first equation can be simplified to: j( ωt krd ) j( ωt krr ) j( ωt krd ) jωρqe jωρqe jωρqe R = + = + d jk ( Rr pˆ 1 e 4πR d 4πR r 4πR d Rr R ) d (9.3) Taking as reference the sound pressure produced by the monopole in free field conditions, it is possible to express the last equation in db. 2 pˆ = R + d jk ( R 10log 10log 1 r Rd e pˆ ref R r ) 2 (9.4) Plotting the equation given above for different receiver points, it is possible to see in which frequencies the pressure reaches its minima for each receiver position. 9 The theoretical analysis concerning the effect of a rigid plane surface in the sound field of a monopole can be found in [11]. 83

84 Appendix In the case of this analysis, for low frequencies it is possible to assume that the sound source behaves as a monopole, the floor of the orchestra is totally reflecting and the seating area can be approximated by a tilted surface (Figure 9.5). In the Table 9.1, the positions of the receivers for the Theatre of Epidauros can be found. With simple geometrical calculations the direct (R d ) and the reflected (R r ) path length can be calculated and in Figure 9.6 to Figure 9.10 the effect of the ground reflection can be seen for the different receiver positions. H R H S D Figure 9.5: The receiver (red dot on black line) receives both the direct sound and the reflection coming from the orchestra floor. The black dot on the solid black line and the black dot on the dashed line indicate the real and the image source, respectively. The notations H S, H R and D stand for Height of Source from the ground, Height of Receiver from the ground and Horizontal Distance between Source and Receiver, respectively. Row H S [m] H R [m] D [m] 5 1,50 2,50 17, ,50 6,00 23, ,50 9,60 29, ,50 16,20 41, , ,50 Table 9.1: Table of values for the Theatre of Epidauros. 84

85 Appendix For the receiver points at the Theatre of Epidauros the first minimum in the pressure occurs around 400Hz for the receivers which are closer to the source, while for the ones which are further away it occurs between 100 and 200Hz. In the real case, where the floor of the orchestra is not totally reflecting, the minima shown above will shift towards even lower frequencies. This phenomenon most likely explains why in the measured data at the Theatre of Epidauros, Strength takes relatively low values in frequencies below 500Hz. Figure 9.6: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 5 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting. 85

86 Appendix Figure 9.7: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 15 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting. Figure 9.8: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 25 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting. 86

87 Appendix Figure 9.9: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 28 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting. Figure 9.10: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 38 th row of the Theatre of Epidauros. The floor of the orchestra is considered totally reflecting. 87

88 Appendix Following the same way of thinking it is possible to reach to similar conclusions concerning the drop in Strength for frequencies lower than 500Hz for the Theatre of Ancient Epidauros, as well (Table 9.2 and Figure 9.11 to Figure 9.13). Row H S [m] H R [m] D [m] 2 1,50 1,00 8,70 8 1,50 3,50 14, ,50 5,70 18,90 Table 9.2: Table of values for the Theatre of Ancient Epidauros. Figure 9.11: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 2 nd row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting. 88

89 Appendix Figure 9.12: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 8 th row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting. Figure 9.13: The effect of the interference of the direct sound and the reflection coming from the floor of the orchestra, on the sound pressure measured at the 14 th row of the Theatre of Ancient Epidauros. The floor of the orchestra is considered totally reflecting. 89