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The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011
Echo Problems in Ancient Theatres
1
ECHO PROBLEMS IN ANCIENT THEATRES AND A COMMENT
TO THE ‘SOUNDING VESSELS’ DESCRIBED BY VITRUVIUS
Jens Holger Rindel
Odeon A/S, Scion-DTU, DK 2800 Kgs. Lyngby, Denmark
e-mail: jhr@odeon.dk
Abstract
Ancient Greek and Roman theatres are often considered acoustically perfect. However,
the semicircular shape of the audience area in theatres built from hard and sound
reflective materials may cause acoustic problems, and there is also evidence that the
ancient architects were well aware of this. The Roman architect Vitruvius describes in
his books on architecture four different kinds of sound reflections in a theatre, one of
them called ‘circumsonant’ which is an acoustic phenomenon that we today would
name a focused echo. Computer simulations of some examples of ancient Greek and
Roman theatres confirm that this can be a real problem at some places in the audience
area. For this study is used the echo criterion for speech as suggested by Dietsch &
Kraak; this is implemented in the room acoustics software ODEON, and that makes it
easy to identify positions with echo problems. A possible solution to these echo
problems could be the introduction of sound absorption in the vertical, concave surfaces
in a way similar to that described by Vitruvius for the sounding vessels, i.e. in niches
between the seats arranged in a horizontal range halfway up. Reading the description by
Vitruvius in this light, it makes good sense if the vessels are supposed to act as sound
absorbing resonators. Since they are efficient in a narrow frequency band, it also makes
sense to apply different sizes with resonance frequencies distributed over two octaves,
as described in detail by Vitruvius. Finally, it is noted that the principle of installing the
sounding vessels in the theatre comes from older Greek references; obviously Vitruvius
had no experience with the vessels himself, but he refers to a scheme based on music
theory made by Aristoxenus (4
th
century BC), who was a famous Greek philosopher and
expert in music theory.
Keywords
Ancient theatre, focused reflection, echo, sounding vessel.
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
2
1. Introduction
In his famous books on architecture, the Roman architect Vitruvius has provided de-
tailed information in book V about the design of theatres, in the Greek style as well as
in the Roman style [1, 2]. However, there is no evidence that he himself has been in-
volved in any theatre building; the information seems to be based on older, mainly
Greek writings on architecture.
2. Sound reflections in the theatre
2.1 The knowledge of sound reflections in ancient times
Vitruvius describes four different kinds of sound reflections in a theatre [1, Book
V.viii.1]; the Greek terms are quoted, and in translation they are named ‘dissonant’,
‘circumsonant’, ‘resonant’, and ‘consonant’. He further explains [1, Book V.viii.2]:
“The circumsonant are those in which the voice spreads all round, and then is forced
into the middle, where it dissolves, the case-endings are not heard, and it dies away
there in sounds of indistinct meaning. The resonant are those in which it comes into
contact with some solid substance and recoils, thus producing an echo, and making the
terminations of cases sound double.”
The reflection called ‘circumsonant’ seems to be the focusing effect from concave
surfaces. Although the description is not very clear, it is obvious that the focusing effect
increases the risk of echo problems.
2.2 Echo in the theatre
In order to study the possibility of echoes in a typical Roman theatre, the room
acoustic computer model ODEON version 11 is used. The theatre chosen for this study
is the reconstruction of the Roman theatre in Aspendos [3], see Fig. 1.
Odeon©1985-2011 Licensed to: Odeon A/S
Figure 1 – Computer model of the reconstructed Aspendos theatre.
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
3
With the source near the centre of the stage at a height of 1.5 m above the stage
floor, the early reflections are shown for a receiver position in the orchestra (height 1.2
m) in Fig. 2, and for a receiver in a rear position to one side in Fig. 3. The focusing of
reflections from the concave seating arrangement is clearly seen in Fig. 2, but there are
also reflections from the concave diazoma via the canopy above the stage, and late re-
flections from the colonnade surrounding the theatre. The calculated impulse response
in the latter position shows a clear echo, see Fig. 4.
Figure 2 – Early reflections from the stage position to a receiver in the orchestra.
Figure 3 – Early reflections from the stage position to a receiver a rear side position.
0 20 40 60 80 100 metres
0
20
40
60 metres
P1
25
P1
Source: 1
Surface: *Receiver*
Refl.: 1
Path <m>: 93,85
Time <ms>: 273
Odeon©1985-2011 Licensed to: Odeon A/S
0 20 40 60 80 100 metres
0
20
40
60 metres
P1
26
P1
Source: 1
Surface: *Receiver*
Refl.: 2
Path <m>: 102,57
Time <ms>: 299
Odeon©1985-2011 Licensed to: Odeon A/S
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
4
Figure 4 – Calculated impulse response in the receiver position from Fig. 3.
In order to make it possible to locate positions with echo problems, the echo crite-
rion suggested by Dietsch & Kraak [4] has been implemented in ODEON version 11.
As an example Fig. 5 shows the echo-curve in the same position as the impulse re-
sponse in Fig. 4. The echo parameter has a value above 1.0, which means that more than
50% would evaluate this as a clearly audible echo when listening to speech.
Figure 5 – Echo criterion curves for the same position as in Figs. 3 and 4.
Fig. 6 shows a calculated grid mapping of the echo parameter at 1 kHz. Echo is
mainly seen in the orchestra close to the stage, but there are also a few places at the
outmost sides of the audience area. However, in general there are only few seats in the
audience area with a risk of echo.
Right ear
time (seconds incl. filter delay)
10,90,80,70,60,50,40,30,20,10
p (%)
100
50
0
-50
-100
Odeon©1985-2011 Licensed to: Odeon A/S
Echo(Dietsch)=1,15 at 63 Hz
gfedc
Echo(Dietsch)=1,15 at 125 Hz
gfedcb
Echo(Dietsch)=1,14 at 250 Hz
gfedcb
Echo(Dietsch)=1,12 at 500 Hz
gfedcb
Echo(Dietsch)=1,12 at 1000 Hz
gfedcb
Echo(Dietsch)=1,11 at 2000 Hz
gfedcb
Echo(Dietsch)=1,10 at 4000 Hz
gfedc
Echo(Dietsch)=0,99 at 8000 Hz
gfedc
Echo time limit
gfedcb
10 % annoyed
gfedcb
50 % annoyed
gfedcb
90 % annoyed
gfedcb
Dietsch echo cur ves
Time (seconds rel. direct sound)
10,80,60,40,20
Echo strength
1,5
1,4
1,3
1,2
1,1
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Odeon©1985-2011 Licensed to: Odeon A/S
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
5
0 20 40 60 80 100 metres
0
20
40
60 metres
P1P1
1,00
0,93
0,86
0,79
0,72
0,65
0,58
0,51
0,44
0,37
0,30
0,23
0,16
Echo(Dietsch) at 1000 Hz >= 1,09
<= 0,11
Odeon©1985-2011 Licensed to: Odeon A/S
Figure 6 – Grid mapping of echo criterion at 1 kHz with the source on the stage.
3. Vitruvius and his books on architecture
3.1 The author and his background
Marcus Vitruvius Pollio was a Roman architect and engineer, known today as the
author of ”The ten books on architecture” [1, 2].
The exact years of his birth and dead are unknown. However, he mentions in the
preface of the books that he had served under Julius Caesar during wars. If he means the
Gallic wars (58-51 BC), Vitruvius cannot have been born much later than 80 BC. He
mentions that he served to supply and repair ballistae, scorpiones, and other artillery [1,
Book I.preface.2].
The books were written over a long time, dedicated to the emperor Augustus and
probably finished c. 16-13 BC [5, p. 186]. He draws extensively on older, mainly
Greek, writings on architecture and building technology, none of which exists today [1,
Book VII.introduction.1]:
” It was a wise and useful provision of the ancients to transmit their thoughts to pos-
terity by recording them in treatises, so that they should not be lost, but, being devel-
oped in succeeding generations through publication in books, should gradually attain in
later times, to the highest refinement of learning. And so the ancients deserve no ordi-
nary, but unending thanks, because they did not pass on in envious silence, but took
care that their ideas of every kind should be transmitted to the future in their writings.”
[1, Book VII.introduction.14]:
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
6
”... From their commentaries I have gathered what I saw was useful for the present
subject, and formed it into one complete treatise, and this principally, because I saw that
many books in this field had been published by the Greeks, but very few indeed by our
countrymen.”
Concerning his own experience as an architect he mentions, that he superintended
the basilica in Fana, Italy [1, Book V.i.6]. This is the only building that we know Vitru-
vius has actually worked on.
3.2 The development of theatre design in the first century BC
As a background for evaluation of the description of theatre design in the fifth book
of Vitruvius, it is interesting to look at the development of theatre design in the first
century BC.
In Rome it was not allowed to build permanent theatres for political reasons; instead
smaller, temporary theatres were built of wood. The first permanent (masonry) theatre
in Rome was built 61 – 55 BC by Pompejus on his private property and he claimed that
it was a temple, not a theatre - hence the small Venus temple in the top rear of the audi-
ence area. It had room for about 17 000 people. The Marcellus theatre was the second
permanent theatre in Rome, inaugurated in 13 or 11 BC, but it had already been used for
a feast in 17 BC. It seated about 15 000 people. Probably Vitruvius had finished his
books before the Marcellus theatre was inaugurated.
In Pompeii a lot of building activity started after it was made a Colony in 80 BC. In
addition to the older Hellenistic theatre from 3
rd
– 2
nd
century BC, two completely new
types of Roman building were erected in Pompeii: The Odeum (lat. Teatrum tectum) for
song and music (around 75 BC), and the amphitheatre for gladiator fights and enter-
tainment with wild animals (probably around 70 BC) [5, p. 174, 177]. The odeum was
relatively small and surrounded by thick walls to carry the roof covering both audito-
rium and stage. Both new buildings were erected by Quinctius Valgus and Marcus Por-
cius, and both building types became very popular in the following centuries as a sup-
plement to the theatre, the odeum in many Roman cities all over the empire, and the
amphitheatre in the western part of the empire, only.
”While the Romans built amphitheatres side by side with the theatres, the Greeks
built music halls or auditoria even in remote parts of the Greek world during the impe-
rial period.” [5, p. 222]
In Rome the gladiator fights originally took place in the Forum [1, Book V.i.1], but
in 29 BC they were moved to an amphitheatre built from wood. However, this burnt
down in AD 64. Later the Flavian Amphitheatre (Colosseum) was built AD 75 – 80.
Only one odeum was built in Rome by Domitian in AD 86. While the wooden amphi-
theatre existed when Vitruvius wrote his books, both the Colosseum and the odeum
came much later.
But in the provinces outside Rome many theatres were being build. For example the
city of Aosta in Northern Italy was founded by Augustus in 24 BC, and both an odeum
and an amphitheatre were among the public buildings [6].
On this background it is remarkable that the odeum as a building type is not men-
tioned at all by Vitruvius, and the amphitheatre is mentioned only once in connection
with the sites for temples [1, Book I.vii.1]: ”Apollo and Father Bacchus near the theatre;
Hercules at the circus in communities which have no gymnasia nor amphitheatres”.
The question is: Was Vitruvius up-to-date in theatre design? No, obviously not. He
relies heavily on older, mainly Greek descriptions.
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
7
4. The mystery of the ‘sounding vessels’
4.1 The purpose
The so-called sounding vessels described by Vitruvius have given rise to many
speculations, because it is not very clear what should be the purpose for the acoustics of
the theatre. They were obviously acoustic resonators, but today we know that the effect
can either be sound absorption or sound radiation, depending on the internal losses of
the resonator.
The vessels in the theatre are mentioned several times by Vitruvius, first in book I
[1, Book I.i.9]:
”In theatres, likewise, there are the bronze vessels (in Greek ηχεια) which are placed
in niches under the seats in accordance with the musical intervals on mathematical prin-
ciples. These vessels are arranged with a view to musical concords or harmony, and ap-
portioned in the compass of the fourth, the fifth, and the octave, and so on up to the
double octave, in such a way that when the voice of an actor falls in unison with any of
them its power is increased, and it reaches the ears of the audience with greater clear-
ness and sweetness.”
The explanation of the purpose in book V [2, Book V.v.3] reads in the original
Latin:
”ita hac ratiocinatione vox a scaena uti ab centro profusa se circumagens tactuque
feriens singulorum vasorum cava excitaverit auctam claritatem et concentu conven-
ientem sibi consonantiam.”
- which is, in the translation by Bill Thayer [2]:
”By the adoption of this plan, the voice which issues from the scene, expanding as
from a centre, and striking against the cavity of each vase, will sound with increased
clearness and harmony, from its unison with one or other of them.”
In both quotations it is said that the purpose is to increase the clearness, not the
strength. Thus this is the opposite of creating reflections that might increase the rever-
berance. The description could make some sense if the vessels are meant for sound ab-
sorption. The position of the vessels should be under the seats, i.e. in the concave semi-
circle that can create focusing reflections, and thus the sound absorption by the vessels
will attenuate the reflections that might cause an echo problem.
Today it is well known that sound absorption is possible with Helmholtz resonators.
However, they are only efficient in a narrow frequency bands, and so it also makes
sense to apply different sizes with resonance frequencies distributed over two octaves,
as described in detail by Vitruvius. This may correspond to the frequency range 220 –
880 Hz [7], which reference contains a thorough analysis of the frequencies of the ves-
sels in relation to the ancient Greek musical system developed by Aristoxenus.
Another remark from Vitruvius that is interesting in this connection is in [1, Book
V.v.7], where he says that there is no need for the sounding vessels in the wooden thea-
tres that were built every year in Rome, because the boarding itself is resonant - “But
when theatres are build of solid materials like masonry, stone or marble, which cannot
be resonant, then the principle of the “echea” must be applied.” As we know today, the
low frequency absorption can be obtained with panel absorbers, which may be more ef-
ficient than the rather small number of Helmholtz resonators that has been recom-
mended.
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
8
4.2 The origin of the sounding vessels – Aristoxenus
Concerning the principle behind the sounding vessels and the musical scales used
for the tuning, Vitruvius refers to the ancient Greek music theoretician and philosopher
Aristoxenus [1, Book V.v.6]. He lived in Athens around 350 BC, was a pupil of Aristo-
teles, and wrote a large number of treatises on topics within music, ethics and philoso-
phy. His theory on musical scales was in opposition to the one by Pythagoras based on
mathematical principles. Aristoxenus claimed that the superior evaluation of musical in-
tervals should be made by the human ear. He said that we evaluate the size of the inter-
vals by the ear, and the properties by the brain. In fact he suggested the equally tem-
pered scale more than two thousand years before this scale became generally accepted
in the 18
th
century.
4.3 Where did they exist?
The evidence of the existence of sounding vessels in theatres is very sparse. Obvi-
ously Vitruvius has never seen them himself, but he refers to [1, Book V.v.8] “the dis-
tricts of Italy and in a good many Greek states. We have also the evidence of Lucius
Mummius, who, after destroying the theatre in Corinth, brought its bronze vessels to
Rome”. It is a fact that Lucius Mummius was a Roman general who conquered Corinth
in 146 BC, demolished the city and brought lots of treasures to Rome. The theatre was a
Hellenistic theatre from the 3
rd
century BC [8]. The time and location of this theatre fit
quite well with those of Aristoxenus, see above.
Izenour has described the existence of nine equally spaced cavities located behind
the diazoma in the ruins of a Roman theatre in Beth Shean, Israel [9, p. 39-40]. Al-
though the number should have been 13 according to Vitruvius, and not only nine, Ize-
nour has shown in sketches how the vessels might have been installed in the cavities.
In 1958 some clay vessels were found when a theatre was excavated in Nora, Sar-
dinia. The site was visited by Dr. Brüel, who made a photo of the vessels together with
other observations [10, p. 18]. However, he concludes that from the findings there is
nothing making it likely that the vessels have improved the acoustics of the theatre in
any way.
So, the sounding vessels have actually existed in some theatres, but only very few
and seldom cases. In the vast majority of Greek and Roman theatres the sounding ves-
sels were not used.
5. Conclusion
Echo problems can occur in certain places in the ancient theatres, particularly in the
orchestra area due to the focusing effect of the concave shaped steps of seats. In this re-
spect the diazoma is particularly important because of the higher wall, and this is pre-
cisely where the sounding vessels described by Vitruvius should be installed.
From careful reading of the description given by Vitruvius, and collection of infor-
mation from excavated theatres, the following is concluded:
- The idea and the guidelines for the sounding vessels goes back to Aristoxinus in
the 4
th
century BC, in those days an outstanding capacity in music theory,
- The purpose might have been to attenuate sound reflections from a concave sur-
face that could create a focused echo,
- The sounding vessels could not possible make any improvement to the acoustics
in practice,
The Acoustics of Ancient Theatres Conference
Patras, September 18-21, 2011 J.H. Rindel
Echo Problems in Ancient Theatres
9
- Only very few theatres had the sounding vessels installed; in general they were
not used, neither in Greek nor in Roman theatres.
References
[1] M. Vitruvius, “The ten books on architecture”, 1
st
century BC, translated by Mor-
ris Hicky Morgan (Harvard University Press, 1914), reprint by (Dover Publica-
tions, New York, 1960).
[2] http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/home.html, Vitru-
vius, “The ten books on architecture”, 1
st
century BC, Original text in Latin and
English translation by Bill Thayer.
[3] J.H. Rindel, “The ERATO project and its contribution to our understanding of the
acoustics of ancient theatres”, Proceedings of the Acoustics of Ancient Theatres
Conference, Patras, Greece, 2011.
[4] L. Dietsch, & W. Kraak, “Ein objektives Kriterium zur Erfassung von
Echostörungen bei Musik- und Sprachdarbietungen” (in German). Acustica 60 ,
205-216 (1986).
[5] Margarete Bieber, “The history of the Greek and Roman theater”, Second Edition
(Princeton University Press, 1961, 1971).
[6] F. Corni, “Aosta Antica – Aoste Antique, La città romana – La cite romaine” (In
Italian, French translation by A. Perrin), (Tipigrafia Valdostana, Aosta, Italy,
2004).
[7] A. Barba Sevillano, R. Lacatis, A. Giménez, J. Romero, “Acoustics vases in an-
cient theatres: disposition, analysis from the ancient tetracordal musical system”,
Proc. of Acoustics’08, Paris, 2008, 4155-4160.
[8] R. Frederiksen, “Typology of the Greek Theatre Building in Late Classical and
Hellenistic Times.” Proceedings of the Danish Institute at Athens - III, S. Isager &
I. Nielsen (ed.). Athens, 2000, 135-175.
[9] G.C. Izenour, “Theater Design”, (McGraw-Hill, New York, 1977).
[10] P.V. Brüel, “Episodes and Achievements within Acoustics before 1954” (In Dan-
ish). Danish Acoustical Society, 2005.
