5On the foregoing principles, the brazen vases are to be made with mathematical proportions, depending on the size of the theatre. They are formed so, as when struck, to have sounds, whose intervals are a fourth, fifth, and so on consecutively to a fifteenth. Then, between the seats of the theatre, cavities having been prepared, they are disposed therein in musical order, but so as not to touch the wall in any part, but to have a clear space round them and over their top: they are fixed in an inverted position, and on the side towards the scene are supported by wedges not less than half a foot high: and openings are left towards the cavities on the lower beds of the steps, each two feet long, and a half a foot wide.
2The following is the rule for determining the situations of these vases. If the theatre be of moderate size they must be ranged round at half its height. Thirteen cavities are prepared at twelve equal distances from each other, so that those tones above-named, producing netè hyperbolæon, are to be placed in the cavities at the extreme ends; second, from the ends, the vessels are to be of the pitch of netè diezeugmenon, bearing an interval of one fourth from the last mentioned. The third netè paramesôn, an interval of another fourth. The fourth, netè synemmenôn, another fourth. The fifth, mesè, a fourth. The sixth, hypatè mesôn, a fourth: in the centre of the range, hypatè hypatôn, a fourth.
3By 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. If, however, the theatre be on a larger scale, the height is to be divided into four parts, so that three ranges of cavities may be provided, one for harmonic, the second for chromatic, and the third for diatonic vases. That nearest the bottom is for the harmonic genus as above described, for a lesser theatre.
4In the middle range on the extremities, vases producing the chromatic hyperbolæon are placed: in the second cavities the chromatic diezeugmenon, a fourth from the last: in the third, at another interval of a fourth, the chromatic synèmmenon: in the fourth, the chromatic meson, another fourth: in the fifth, the chromatic hypaton, another fourth: in the sixth, the paramesè, which is a fifth to the chromatic hyperbolæon, and a fourth to the chromatic meson.
5In the centre none are to be placed, because no other sound in the chromatic genus can be in consonance therewith. In the upper division and range of the cavities, the vases on the extremities are constructed to produce the tones of the diatonic hyperbolæon: in the next cavities, those of the diatonic diezeugmenon, a fourth: in the third, of the diatonic synèmmenon, a fourth: in the fourth, of the diatonic meson, a fourth: in the fifth, of the diatonic hypaton, a fourth: in the sixth, proslambanomenos, a fourth: in the centre, mesè, between which and proslambanomenos is an octave, and a fifth between it and the diatonic hypaton.
6He who is desirous of more fully understanding these matters, must refer to the musical diagram at the end of the book, which is that left to us by Aristoxenes, who with much intelligence and labour, formed a general scale of the tones. Hence, he who carefully attends to these rules, to the nature of the voice, and to the taste of the audience, will easily learn the method of designing theatres with the greatest perfection.
7Some one may perchance urge, that many theatres are yearly built in Rome, without any regard to these matters. But let him not be herein mistaken, inasmuch as all public theatres which are constructed of wood, have many floors, which are necessarily conductors of sound. This circumstance may be illustrated, by consideration of the practice of those that sing to the harp, who when they wish to produce a loud effect, turn themselves to the doors of the scene, by the aid of which their voice is thrown out. But when theatres are constructed of solid materials, that is of rubble, squared stones or marble, which are not conductors of sound, it is necessary to build them according to the rules in question.
8If it be asked what theatre in Rome can be referred to as an example of their utility, we cannot produce one, but such may be seen in some of the provinces of Italy, and many in the Grecian States. We moreover know that L. Mummius on the destruction of the theatre at Corinth, brought to Rome some of its brazen vases, and dedicated them as spoils at the temple of Luna. Many clever architects who have built theatres in small cities, from the want of other, have made use of earthen vessels, yielding the proper tones, and have introduced them with considerable advantage.