THE ENIGMA OF VITRUVIAN RESONATING VASES AND THERELEVANCE OF THE CONCEPT FOR TODAY

Rob GodmanThe Music Centre

Faculty for the Creative andCultural Industries

University of HertfordshireUnited Kingdom

r.godman@herts.ac.uk

ABSTRACTThe clarity of sound within any Greek or Romantheatre (without any form of enhancement) isimpressive to any visitor. The seats arranged incurved rows around the circular orchestra form largehorizontal reflecting surfaces. This ensures that thepath of the sound waves travel from the source (theactor or singer) to each of the listeners in a directpath (i.e. without reflection). Vitruvius, however,claimed further enhancements could be made.

In theatres, also, are copper vases and these areplaced in chambers under the rows of seats inaccordance with mathematical reckoning. TheGreeks call them Echeia. The differences of thesounds which arise are combined into musicalsymphonies... … it becomes fuller, and reaches the audience witha richer and sweeter note.Vitruvius, on Architecture, Book I, – on trainingof architects, Loeb

This paper explores the notion of intent andpurpose behind the Vitruvian concept and alsoaddresses an arguably more complex issue, that of apotential fusion between archaeology, science andmusic.

1. INTRODUCTION1.1 Vitruvius – the person

Marco V. Pollio Vitruvius studied Greek philosophyand science around the 1st Century BC. A practicalexponent of his craft, he gained experience throughhis professional work and was the architect of atleast one complete unit of buildings for Augustus inthe reconstruction of Rome. As an indication of hisdiverse talents, he also oversaw developments in theimperial artillery and military engines – makingVitruvius an important figure in his day.

In modern times, Vitruvius has beenregarded primarily as an architect but hisexplorations of science and art in the widest senseshouldn’t be forgotten. The emphasis of books I-V

is on architecture in the traditional sense of theword. The second five books contain informationrelating to Greek science demonstrating thebackground Vitruvius had during his studies andyounger days. The inspiration of science was at onewith art and literature (although this was not aphilosophy specific to Vitruvius).

The science of the architect depends upon manydisciplines and various apprenticeships which arecarried out in the art.Vitruvius, on Architecture, Book I – on training ofarchitects, Loeb

1.2 The Ten Books on ArchitectureDe Architechura is a collection of ten booksdetailing his practical experience with traditionalGreek theory of the time. Exact dates for thecomposition remain uncertain but it is believed tohave been written around 27 BC (towards the latterperiod of his life).

The complete treatise is detailed as follows:Book 1: Architectural PrinciplesBook 2: Evolution of Building, Use of materialsBook 3: Ionic TemplesBook 4: Doric and Corinthian TemplesBook 5: Public Buildings, Theatres (and music),Baths and HarboursBook 6: Town and Country HousesBook 7: Interior DecorationBook 8: Water SupplyBook 9: Dials and ClocksBook 10: Mechanical and Military Engineering

There are a number of surviving manuscripts thathave been used to create the current publishedtranslations. These date from as early as the 8th

Century (London, British Museum). The text wasrediscovered in the fifteenth century and has beenstudied by renaissance architects to a wider range ofstudent in the current day. A number of translationsof the text exist and are available in print. The threeused for the purpose of this paper (Dover, Loeb,

Cambridge publications) are referenced in thebibliography.

2. THEATRE DESIGNThe design of a Roman theatre has much in commonwith its Greek counterpart. Before discussing thedifferences, it is worthwhile thinking aboutterminology. It is a common mistake to name thesemi-circular Greek and Roman theatres asamphitheatres. They are not! An amphitheatre iscircular (think about the Coliseum in Rome) and atheatre is semi-circular (or at least close to it). Theamphitheatre and theatre have vastly different uses.

The theatre of the Greeks was built on theslope of a hill, securing sufficient elevation for theback row from the naturally occurring landscape.The tiers were either cut directly into rock or if theland was soft an excavation was made in the hillsideand lined with rows of benches. The steps wereoften faced with marble (as in the theatre ofDionysus at Athens). The theatre of the Romans andhence Vitruvius, was potentially a freestandingstructure and therefore a much more complexdesign.

3. GREEK/ROMAN MUSICBefore exploring the reasoning behind Vitruvius’concept of the resonating vases in Roman theatres itis important to have an understanding behind musicprinciples of the time.

Harmony is an obscure and difficult musicalscience, but most difficult to those who are notacquainted with the Greek language; because it isnecessary to use many Greek words to which thereare none corresponding in Latin. I will thereforeexplain, to the best of my ability, the doctrine ofAristoxenus, and annex his diagram, and will sodesignate the place of each tone, that a person whostudiously applies himself to the subject may veryreadily understand it.Vitruvius, The Ten Books on Architecture, BookV, Dover

The systems as described by Aristoxenusand Pythagoras are different in terms of technicalspecification but particularly in terms of philosophy.Vitruvius (as can be seen from above) follows thetheory of Aristoxenus and it is this that the acousticvases are based upon.

Aristoxenus sets out a theory of scalestructure and a method for analysis. His definition ofinterval is somewhat different to that of thePythagoreans (which is based on ratio andproportion) in that he describes two pitches as beingbounded or marked off by two notes of differentpitch (Landels). A system is a construction ofintervals, the smallest group of which is known as atetrachord.

Figure 1

The groups of four pitches in eachtetrachord are always surrounded by the interval of afourth. Aristoxenus demonstrates three differenttypes (diatonic, chromatic, enharmonic). He uses theterm hemitonion to describe an interval of asemitone and more complex term of diesis for anyinterval smaller than a semitone (Landels). He doesuse mathematical ratios to assist with the concept ofmicrotones but also spoke of them in terms of colourand other descriptive methods.

To make more complex pitch systems it isa simple matter of placing one tetrachord on top ofanother (giving tetrachords based on cycles offourths). This developed into the Greater ComplexSystem giving a two-octave construction and this isthe method that Vitruvius follows for the tunedvases.

4. ACOUSTICS4.1. Problems, vases…A greater understanding of acoustics can beidentified as early as the beginning of the 5thcentury BC (Dionysos at Athens and the theatre atSyracuse). Ironically, the shape of the theatres wasnot based on scientific understanding but rather byaccident. A site on the side of a hill, sloping downat approximately 45 degrees gave a good acousticresult. Other portable solutions also helped theacoustic. Backdrops helped high-frequencyreflections (provided by painted skins). It is believedthe propagation of sound to the audience was aidedby the megaphone effect of the masks worn by theactors.

Further developments in the shape oftheatres are all thought to have been due to attemptsat improving the acoustics. An increased length ofthe seating area (whilst maintaining overallproportion) brought more of the audience close tothe stage and thus improved the acoustics, especiallyas less of the sound could escape at the sides of theorchestra. However, the direction in which theactors were facing became of greater importance,and the height of the stage building was increasedand made of stone to provide more reflection frombehind and improve the distribution of the sound. Afew centuries later, and with the aid of hisknowledge derived from Aristoxenus, Vitruvius was

attempting to solve other acoustical problems stillprevalent in Roman theatres.

The Pythagoreans formulated the modernscience of acoustics in Greece in the 6th centuryBC. Aristoxenus examined the study of musicalsounds further by going beyond the source andpropagation of sound to consider issues ofperception. The work concerning acoustics ofVitruvius is largely based on Aristoxenus’ writings.

In theatres, also, are copper vases and these areplaced in chambers under the rows of seats inaccordance with mathematical reckoning. TheGreeks call them Echeia. The differences of thesounds which arise are combined into musicalsymphonies or concords: the circle of seats beingdivided into fourths and fifths and the octave.Hence, if the delivery of the actor from the stage isadapted to these contrivances, when it reaches them,it becomes fuller, and reaches the audience with aricher and sweeter note.Vitruvius, on Architecture, Book I, – on trainingof architects, Loeb

Vitruvius' understanding of acoustics is extremelyimpressive for its time. He was aware of anacoustical problem caused by the reflection of soundwaves, namely that interference to the originalsource is created by reflections making the originalless clearly audible or defined. Vitruvius called thisreflection of sounds resonantia (which differssomewhat from our modern day meaning of theword resonance which implies a sound beingbounced back and forth repeatedly at a specificpitch). Although such reflections were kept to aminimum by the very design of Roman and Greektheatres, the resonantia would still have been seenas a considerable problem. If any extraneous strongreflections come back to a listener at slightlydifferent times, then speech, for example, wouldhave become difficult to understand. As Vitruviuspointed out, an inflected language such as Latin isdifficult to understand when the final syllables ofwords arrive at slightly different times. Thesetheatres were outdoor venues often built into theside of a hill. The apparent dryness of the resultantacoustic was also a problem for Vitruvius whendealing with music and he went to considerableeffort to invent a system that would counteract it.Resonating bronze vases were his solution to thisproblem.

...let bronze vases be made, proportionate to the sizeof the theatre, and let them be so fashioned that,when touched, they may produce with one anotherthe notes of the fourth, the fifth, and so on up to thedouble octave....the voice, uttered from the stage as from a centre,and spreading and striking against the cavities ofthe different vases, as it comes in contact with them,

will be increased in clearness of sound, and willwake an harmonious note in unison with itself.Vitruvius, The Ten Books on Architecture, BookV, Dover

How well these vases may have worked? Itremains unclear.

4.2 Musical theory within the theatre, placementWhilst there are no known original resonating vasesin existence, a number of sites show evidence ofspaces (niches) where the vases would have beenpositioned.

12 pairs of compartments corresponding to thosedescribed by Vitruvius have been found in thesupporting wall of the uppermost row of seats of theGreek theatre at Aizani in Phrygia, eight in thepodium of the Roman theatre at Nicopolis, andseven in the Greek theatre at Scythopolis in Syria.There are 20 niches in the upper part of the Greektheatre of Gerasa in Jordan; at Ierapetra andGortyn in Crete the theatres have 13 niches each;and at Lyttos, also in Crete, there are three rows of13 niches each.Grove Dictionary (Belli, 1854, Müller, 1886).

Vitruvius clearly states that the vases are tobe placed freestanding.

… so that they touch no walls and all around themhave empty space and place above their heads. Setthem upside down, and on the side facing theplatform put wedges underneath them, no less thanhalf a foot high, and opposite these chambers leaveopenings along the footings for the lower tiers ofseats…Vitruvius, The Ten Books on Architecture, BookV, Cambridge

Different numbers of vases should be useddepending on the size of the theatre.

The method of marking out the positions in whichthe jars are to be placed is as follows. If the theatreis not very large, a horizontal line should be markedout, halfway up the slope [of the auditorium], and13 vaulted cubicles built, with 12 equal intervalsbetween them: then the sounding jars as describedabove are placed in them.So by this arrangement, the voice, radiating fromthe stage as from a centre, spreads itself around[the auditorium]: and, by exciting resonance inparticular vases, produces an increased clarity anda series of notes which harmonize with itself.Vitruvius, The Ten Books on Architecture, BookV, Dover

Figure 2 - vessel pitches for a small theatre

I nëtë hyper bolaiönII nëtë die zeugmenonIII parameseIV nëtë synhemmenönV mesëVI hypatë mesonin media hypatë hypatön

Figure 2 shows the pitches (with Greeknames) of the vases for a small theatre as specifiedby Vitruvius. Vase I (nëtë hyper bolaiön) would beplaced at either side of the theatre with the in mediavase (D 144) placed centrally. All others would beequidistant between.

Larger theatres required a greater numberof vases arranged in three horizontal rows (one forthe harmonia, a second for the chromatic and a thirdfor the diatonic).

Figure 3 - vase pitches for a large theatre

Vitruvius discusses why acoustic vaseswere not used in the theatres of Rome. Owing totheir wooden construction, singers who wished toincrease the projection of their sound could directtheir voices towards the scene doors (valvae). Whena theatre is made of solid materials (such as stone)then it should be equipped with the vases asspecified. Vitruvius states that there are manyexamples in Greek cities (Corinth). The expense ofthe bronze vases is also considered by Vitruvius:

‘many clever architects who have built theatres insmall cities, from the want of others have made useof earthen vases, yielding the proper tones, andhave introduced them with considerable advantage’.Vitruvius, The Ten Books on Architecture, BookV, Dover

4.3 How did the vases sound?It is likely that the function of the vases would havebeen to make some sounds louder than others byallowing them (or the air within them) tosympathetically vibrate when certain harmonics ‘hit’them. So, when a singer performs a perfectly in-tune scale, a number of vases would ring creating aharmonic chord. An artificial reverberation (RT60time estimated as 0·2–0·5 seconds, Landels)containing only those harmonics listed in the vasespitches would be produced in an open-air theatrethat would otherwise have none.

There may be another purpose for the vasesother than those already mentioned. Some believethe acoustic jars helped singers and those relying onear for maintaining pitch to keep to proper pitch. Asindicated, the resonance of the vases would havegiven emphasis to important pitches leaving theothers silent. If the artificial reverberation conceptis difficult to accept, the assisted resonance idea isperhaps a little more attractive.

No definitive answer has been found to thequestion of authenticity and intent with regardsVitruvian resonating vases. It is known that manyof the original bronze vases were later used for otherpurposes and even melted down. The earthenwarevases are obviously more prone to damage makingthem more unlikely to survive the ravages of time.

We have only limited information as tohow large and what shape they were and thisinformation varies depending on which translationyou use of the Vitruvian text. As a result, a lot ofreasoning and occasional down right guesswork isrequired in order to begin piecing together theenigma of function and intent. However, we dohave much greater knowledge of Helmholtzresonators and bass-traps and a comparison is usefulwhen attempting to predict the shape and size of theVitruvian vases.

Various suggestions for shape and designare cited in Grove, Dictionary of Music (Acoustics)2002. Particular attention should be paid to neckshaping and proportion.

4.4 Helmholtz resonators and bass-traps

There is a clear relationship in terms of functionbetween the Vitruvian vases and Helmholtzresonators and bass-traps. Helmholtz resonancedeals with air resonance in a cavity with the namebeing taken from Hermann von Helmholtz (the 19th

Century Physicist). The sound created when air isblown across the top of an empty bottle is a muchcited example of Helmholtz resonance. In acousticstring instruments, the resonance curve has theHelmholtz resonance as one of its peaks (furtherpeaks can be found from resonances within thephysical body of the instrument).

There are two principle types of bass traps(resonating and porous). Resonating absorbers

generally absorb a narrow range of frequencies andporous absorbers absorb sound all the way acrossaudible frequencies. Clearly, examples of theresonating type of bass trap include Helmholtzresonators. Many examples of Helmholtz resonatorscan be found throughout the world but a particularlyfine set of spherical resonators can be seen in theDepartment of Physics, University of Toronto,Canada.

Whilst a detailed account of Helmholtzresonators and bass-traps is outside the scope of thispaper, it is clear many similarities exist betweenthem and Vitruvian vases.

5. VIRTUAL RECONSTRUCTIONS5.1 Touching the vases…We can assume that the word ‘touch’ as used byVitruvius means to make the vases (or the air insidethem) ring sympathetically when the vibration of asound source with a particular frequency in itsharmonic series comes into contact.

A number of methods for experimentationwere attempted including building banks of resonantfilters within Max/MSP. Detailed below aremethods of using impulse responses and a more‘creative’ use of additive synthesis.

5.2 Impulse response methodBy clapping your hands in a church, you arelistening to the church’s response to the impulseyour palms have made. Commercially availableconvolution reverb software is available to emulatesuch responses. What this means is that it ispossible to ‘sample’ an acoustic and use it as a plug-in of your choice. Audioease have developedAltiverb™, software that allows the user theopportunity of combining a dry input sound with animpulse response created in a real acousticenvironment.

From conversations with Stephen Morris(Department of Physics, University of Toronto,Canada) at the Subtle Technologies Conference,Toronto, May 2005, we believe that the material ofthe vase itself is relatively unimportant. It is the airinside the vase that would resonate and not thephysical material of the vase (Vitruvius does statethat bronze or ‘earthenware’ options would workand also suggests that the use of different material islargely down to economic practicalities). Helmholtzhad used a variety of materials as resonators,including glass cylinders and tubes. He later askedKoenig to make metal resonators.

Ironically, the closest modern day vases tomatch the patterns suggested by archaeologists,historians and acousticians (Brüel 2002) were foundrecently in a farm shop close to the author’s home!A Greek farmer is importing a variety of vases from

Crete and selling them as garden ornaments, water-features…

By spending some time singing into thevases, it soon became clear that these objectsresonated quite effectively at certain frequencies,and that these frequencies could be changed byplacing material (sand, water etc.) into the vase tochange its’ volume. The shape and depth of neckalso proved important as can be seen frommeasurements on Helmholtz resonators.

Figures 4a and 4bModern earthenware vase (manufactured in Crete).Approximate dimension are 60cm high with a neck18cm wide. The close-up of the neck shows aloudspeaker with a 5-inch driver suspended withinthe vase.

5.3 Physical Modelling methodDr. Richard Polfreman (Music Centre, University ofHertfordshire) has investigated the potential forphysical modelling of the Vitruvian vases. UsingModalys , he has created an aural and visualrepresentation of a vase that will also provide animpulse response. Initial findings from this researchhave given strong indications of the effectiveness offunctionality. Currently, these are based on a modelof a single vase. Potentially, an entire theatre withvases could be modelled to test the relationship

between these vases themselves. This research is inan early stage of development.

Figure 5

5.4 Additive synthesis method

The author began designing software based upon theconcepts of Vitruvius in 1999. The experimentsbegan by building a synthesizer using the ratiosspecified by Vitruvius to explore the types of soundto be generated. A number of assumptions weremade as to how the vases would have sounded - aprinciple assumption being that the harmonicswould be largely sinusoidal.

Presets

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195.776031146.83 347.992737261.035248 391.543243293.664764 440.497131522.708618 220.24866330.211517Frequency of���� Vessels or Harmonics (Hz)

1.333331. 2.371.777777 2.66662. 3.3.5599 1.5000012.248901Fine Tune (as a ratio of Fundamental)

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© Rob Godman February 2004

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23

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Figure 6 – additive synthesis patch

No attempt was made at modelling theamplitude envelope of the vessel, although it wouldhave been relatively simple to do. This proved to bea very enlightening way to proceed as it made theauthor address issues of authenticity in themodelling process. Clearly this was an artisticreconstruction based upon the Vitruvian principlewhere many of the physical constraints (decay timeand other naturally occurring acoustic phenomenacould be largely ignored as a result of being in thedigital domain).

The patch shown is an early additivesynthesis patch consisting of sixteen oscillators (ten

shown here). The programme can be used to triggerthe oscillators via external sound (using percussiveor pitch detection objects, [bonk~] or [fiddle~] forexample), which would be close to the originalfunction of the Vitruvian vases. Video input viaSoftVNS or Jitter, other sensor input or via a quasi-random process for automatically ‘sounding’ theoscillators are also possible.

Ironically, what began as an experimentproduced some very interesting musical results. Thequasi-assisted resonance approach has featured inmost of the author’s work over the past six years.

6. ANALYSISA variety of impulse responses were created usingthe Altiverb™ Impulse Response Pre-Processorsoftware. Sinusoidal sweeps gave the best resultswhen a good quality loudspeaker was placed around150cm from the neck of the vase (attempts weremade at placing sound sources directly inside thevase as indicated in the images). The microphoneused to record the sweep was also placed in avariety of positions - the most dramatic result beingproduced when placed several centimeters into theneck of the vase.

The analysis took place within the anechoicchamber at the University of Hertfordshire.

Figure 7 - The sweep used to create the impulse response.

Figure 8A waveform of a recording of the impulse (sweep).A number of resonant peaks can be seen. Thefrequencies of these peaks for this vase are asfollows (the vase can be ‘transposed’ by changingits volume by placing sand or other solid objectswithin it):

(Hz)683 31303913 32111070 35181407 49561790 50352150 562724652759

It is likely that there will be many higher harmonics,but these gave an accurate rendition of theresonance of this vase. Interestingly, it is far fromobvious what the fundamental of the vase is!

The impulse responses within Altiverbgave interesting results when different sounds wereplayed through them. Speech gave strong resonantresults (male voice). Some of my existingsynthesized drones were also played back.Obviously, those that contained a high number offrequencies close to those listed above gave strongresonant results.

6.1 Physical reconstructionsEarly in his career, Per Brüel attempted to duplicatethe resonating vase concept by physically building aseries of vases to experiment with. None ofVitruvius’ original diagrams illustrating the size andshape of the bronze vases survive so Brüel’sexperimental vases were made of clay in a wine-beaker shape. The depth and diameter of the neck issignificant. In depth readings on Helmholtzresonators demonstrates the mathematical reasoningbehind these findings. Brüel claims his experimentsshowed that they enhanced reverberation at theresonant frequency (although the vases were nottested in a real theatre or in an anechoic chamber).

Ideally, a complete set of vases needs to bemade. However, the sheer cost of a minimum of tenbronze vases has presumably prevented mostresearchers from pursuing the project. Acombination of all available methods (physical anddigital) may provide a truer picture that is realizablecommercially, scientifically and artistically.

7. THE CONCEPT AS COMPOSITION

7.1 Halo for piano and responsive electronicsReceiving its US premiere at the ICMC, NewOrleans, 2006, Halo uses an additive synthesiser to‘emulate’ the Vitruvian resonances, triggered by amicrophone detecting transient dynamic changes([bonk~]). Halo was recorded by Philip Mead andthe author for the UH Record Label.

7.2 inside the eye of silence - a collaboration with Vivienne SpiteriThe following is a programme note by VivienneSpiteri for inside the eye of silence. It demonstratestheir preoccupation with the Vitruvian concept andhow they pushed the principle away from a purelypractical ‘problem-solving’ idea. By focusing on theresonance of the harpsichord, the piece explores theinner most world of the instrument, removing theeffect of time and physical barriers through the useof granular synthesis.

Figure 8 - image from the documentary DVD version of insidethe eye of silence.

where does sound stop and silence begin, end,sound, begin?

one of the harpsichord's best kept secrets lies hidden within herchambered spaces between the notes, between those plucked

strings (the sound of a harpsichord is like two skeletons makinglove on a corrugated iron roof) whose piercing sting obliterates

all potential revelation of the secret : her resonance jiuces.

to isolate a single sound, to let the time-life of a solitary pluckedstring linger, live and rise through to its natural end, is to reveal

all : birth, breath, life, death and rebirth. all swell withsong. skeletons no more this full-bodied dancing sound,

laughing and rejoicing, these rich spectra liberated, escapedfrom their string prison, these wingéd frequencies, free as air.

airah, airspace

air-spaceand time

where do air, space and time unite?"and time is te space your mind movs through" (gwendolyn macewen :

"vacuum genesis" from afterworlds 1987-88)

sound. sound becoming silence through air-travel, through openair, through air within a space. an enclosed space? of time?

time, ah time. sound's phantom vessel.where does it wander? what is its voyage?

what is its voyage, never lowering anchor?

to step inside the eye of silence is to listen deeply, to feel it atyour ear. for as long as air and time give it wing, sound-in-

silence-in-sound births and breathes itself, expanding,contracting, like the lungs of a whale, huge and light as air.

enter vitruvius, ah vitruvius. he who knew the secret of thewingéd. his siren-song, embodied in resonating bronze inside

semi-circular spaces of another place, an other time, drew forth,beguiled and captured the wild and wandering waves, colouring

them lively : live, alive, life. long life. longer still. unending.

enter the spider, weaver of webs, silent siren temptress, vitruvius-collaborator inside the eye, along her radii.

toronto. chemistry building. hanlan's point. harpsichord assiren temptress inside the eye, weaving through space,

resonanting her chambers.

listen, dive, fly, let the air wing youaroundspace

is timeis sound is

silenceis

infnity's music© Vivienne Spiteri August 2002

Commissioned by New Adventures in Sound Art forSign-Waves, inside the eye of silence was firstshown in a multi-room environment using anoctaphonic system at The Chemistry Building,Toronto Island, Canada in August 2002.

8. CONCLUSIONSVitruvius understands and addresses problems facedby performers and audiences in Roman Theatres.Vase placement is derived from an understanding ofacoustics and musical theory of the day.Authenticity and intent are still arguable and weshould at some point be brave enough to ask (andpotentially answer) a simple question – did the vasesas specified by Vitruvius actually do their intendedjob? There is now a large amount of evidence tosupport the concept. Other resonating vases havebeen found throughout history and some are still inuse. There is no doubt that Vitruvius was the sourcefor vases used in medieval churches. In Europethere are examples found in St. Clements,Sandwich, Kent, St. Peter Mancroft, Norwich,Fountains Abbey, York, UK and St. Martin, Angers,Bjeresjoe, Sweden. Most of these jars are between20 cm and 30 cm in length with fundamentalfrequencies of between 90 to 350 Hz (not far awayfrom the pitches specified by Vitruvius). However,some of these examples of vases used in churchesmay have been used to reduce reverberation andechoes by absorbing resonance (Landels). Manywere cemented into place and not placed loose aswith the Vitruvian examples. So, with these manycontradictions, it is hardly surprising thatarchaeologists are wary of the function of the vases.

9. BIBLIOGRAPHY-Vitruvius. The Ten Books on Architecture, Loeb1960, Dover 1960 and Cambridge University Press2002-Helmholtz, On the Sensations of Tone, Dover1877/1954-Peacock, Thomas Love, Gryll Grange, Macmillan1896-Rossing, Moore and Wheeler, The Science ofSound, Addison Wesley 2002-Grove, Dictionary of Music (various) 2002-Landels, John G. Assisted Resonance in AncientTheatres - Greece & Rome XIV, Routledge 1967

-Landels, John G. Music in Ancient Greece andRome, Routledge 2000-Robert G. Jahn, Paul Devereux, and MichaelIbison, Acoustic Resonances of Assorted AncientStructures (J. Acoust. Soc. Am. 99(2): 649-658.February 1996)-Harrison, Kenneth. Vitruvius and Acoustic Jars inEngland during the Middle Ages, AncientMonuments Society 1967-68-Vassilantopopoulos, Mourjopoulos, A study ofAncient Greek and Roman Theather Acoustics, ActaAcoustica, vol 89 (2003), 123-136.-Levin, F. R. The Manual of Harmonics ofNicomachus the Pythagorean (translation), Phanes1994-James, J. The Music of the Spheres, Abacus, 1993-Roads, Curtis, The Computer Music Tutorial (forGranular Synthesis, 168-184, MIT 2001-Roads, Curtis, MicroSound, MIT 2004

10. WEBLIOGRAPHY

http://www.soundtravels.cahttp://www.philophony.com/pageshttp://www.audioease.comhttp://www.phys.unsw.edu.au/jw/Helmholtz.htmlhttp://www.psych.utoronto.ca/museum/helmholtz.htmhttp://perseus.herts.ac.uk/uhinfo/staff/?id=719376http://perseus.herts.ac.uk/uhinfo/staff/?uuid=D9F1E18F-B9B7-C828-8A8BFDADFCC70827http://www.dream.unipa.it/dream/11/documenti/ICA%202007%20-%20Ianniello.pdfhttp://www.sea-acustica.es/Sevilla02/rba01007.pdf

11. ACKNOWLEDGEMENTSI am very grateful to Stephen Morris (University ofToronto) and Lydia Sharman (Concordia) forinspiring me to pursue the physical characteristics ofthese vases.

I would also like to thank Per Brüel fordiscussions in-person at the First Pan-American/Iberian Meeting on Acoustics in Cancun,Mexico, 2002; Aaron Watson for equallyilluminating conversations at Reading University2002 and private communication with John Landelsand Sam Moorhead (British Museum).

During the Summer of 2007, this researchprovided the focal point for a Wild Dream Filmsproduction in the series 'Ancient Discoveries' for theUS history channel, a popular documentary showfocusing on ancient technological innovation anddiscovery.