In Book V, Vitruvius applied Pythagorean principles of harmonic ratios in the design of theatres. He implemented a “room equalization system” based on bronze or earthen vessels – called “echea” – placed under the seats of theatres, to assist, by their resonance, the voices of the performers.

This is one of the first examples of an enclosed space conceived as a musical instrument where its design features are intended to enhance specific sounds that take place within it. The Vitruvian theaters interact with the performers, amplifying and “equalizing” the sounds of their on-stage performances. In figure 2-2 we can clearly appreciate that the tuning of the room is not indifferent to its design; small and large theaters were tuned differently.

“The harmonies that human nature can measure out are called symphoniae in Greek, and number six: diastesseron (fourth), diapente (fifth), diapason (octave), and disdiatesseron (octave + fourth), disdiapente  (octave + fifth) and disdiapason (double octave).“In theaters, likewise, the bronze vessels – the ones the Greeks call echea – which are enclosed underneath the seats, are placed according to mathematical principle based on their pitch. The vessels are grouped in sections around the circle of the theater to create intervals of a fourth, a fifth and so on up to a double octave. As a result, the speaker, as it occurs onstage, should be so located in the theater’s overall design that when it strikes the echea it will be amplified on impact, reaching the ears of the spectators as a clearer and more pleasant sound.”

Tuning system for the vessels.

The vessel tuning suggested by Vitruvius follows the progression of the first four partials after a fundamental tone, which are also separated by a fifth, a fourth and the resulting double octave. By reinforcing the first partials of an implied fundamental he provided the space with a characteristic resonance. Like in brass instruments, that “theoretical fundamental” is the lowest possible resonance that can be obtained from an instrument – in this case an enclosed space – related to its size and length of the sound waves. That resonance is not aurally present but it is the basis for the harmonic series. Vitruvius’ design follows that same principle, using the vessels tuned to the first partials of a harmonic series to provide the space with a particular formant. However that approach depends almost exclusively on the richness of the spectrum of the sound performed on-stage. The pure tone of a lyre would rarely provide enough spectral energy to stimulate the vibration of the vessels and – on the other hand – a strong baritone voice would take true advantage of them.  Following a basic acoustical principle, the Vitruvian vessels can reinforce properties already existing in a sound source but they are unable to generate them as there is no acoustical design capable of filling frequency “holes”. “Indeed, we can observe this from performers who sing to the lyre, who, when they want to sing in a higher key, turn toward the stage doors and thus avail themselves of the harmonic support that these can provide for their voices. When, however, theaters are constructed of more solid material, that is, of masonry, stone, or marble, which can not resonate, then they should be outfitted with echea for just that reason.”

Theater ceiling and audience area suggested by Vitruvius.

It is clear that the Roman master was foreseeing two core acoustical issues of theater design: reinforcement of sounds events happening on-stage and the frequency response of the space. His solution came from a combination between the steep angle of the audience seats and the design of the ceiling (sound reinforcement) and the resonating vessels system (frequency response). “By this contrivance the voice onstage, poured forth from stage – as it were, from the center of the theater – and circling outward, strikes the hollows of the individual vessels on contact, stirring up an increased clarity and a harmonic complement to its own tone.”

Vitruvius was already considering in his designs the quality of the sound perceived by the audience in a theater. He sought for a “clear and pleasant sound” with the desire to provide every member of the audience with the same aural experience. Those concerns are very much current today when la­rge audiences are the norm. In the design of theaters, aural architects have to simultaneously deal with the general acoustic properties of the space and their perception, reassuring that they propagate evenly throughout the audience area.  Parameters of balance, warmth, brightness and clarity are of standard use by architects in order to measure the desirable qualities of a space designed for performance. The aural pleasure of the audience was Vitruvius’s ultimate desire. Sound was his main concern in theatre design, and he strived to achieve an “ideal sound” that would please the audience members. Vitruvius translated the general harmonic proportions of sound into theater design. In other words, he made a theater a “tuned resonant body”.