---
title: "On Architecture · De architectura"
author: "Vitruvius"
translator: "Morris Hicky Morgan"
languages: [la, en]
shelf: "Classical Latin"
section: 10 of 22
url: https://scriptura.si/works/vitruvius-on-architecture/10/
cite: "Vitruvius, tr. Morris Hicky Morgan, On Architecture · De architectura, section 10. Scriptura (scriptura.si), https://scriptura.si/works/vitruvius-on-architecture/10/"
---

# On Architecture · De architectura

*Vitruvius, tr. Morris Hicky Morgan*

The only architectural treatise to survive from antiquity: firmness, usefulness and beauty, temples and the proportions of the human body, water, sundials and machines.

> Latin: ed. Fritz Krohn, from the Perseus Digital Library (canonical-latinLit, phi1056.phi001, CC BY-SA 4.0).

> English: Morris Hicky Morgan, from the Perseus Digital Library (phi1056.phi001.perseus-eng2). Notes are not included.

> Rows follow the references the two texts share (books, chapters and sections), cut where both reach the end of a sentence.

## 10. Book V · preface, chapters 1–6

Source: https://scriptura.si/works/vitruvius-on-architecture/10/ · cite a paragraph as https://scriptura.si/works/vitruvius-on-architecture/10/#p-N

[¶0] pr.1. 1. THOSE who have filled books of unusually large size, Emperor, in setting forth their intellectual ideas and doctrines, have thus made a very great and remarkable addition to the authority of their writings. I could wish that circumstances made this as permissible in the case of our subject, so that the authority of the present treatise might be increased by amplifications; but this is not so easy as it may be thought. Writing on architecture is not like history or poetry. History is captivating to the reader from its very nature; for it holds out the hope of various novelties. Poetry, with its measures and metrical feet, its refinement in the arrangement of words, and the delivery in verse of the sentiments expressed by the several characters to one another, delights the feelings of the reader, and leads him smoothly on to the very end of the work.

> Latin: pr.1. Qui amplioribus voluminibus, imperator, ingenii cogitationes praeceptaque explicaverunt, maximas et egregias adiecerunt suis scriptis auctoritates. quod etiam velim nostris quoque studiis res pateretur, ut amplificationibus auctoritas et in his praeceptis augeretur; sed id non est, quemadmodum putatur, expeditum. non enim de architectura sic scribitur uti historia aut poemata. historiae per se tenent lectores; habent enim novarum rerum varias expectationes. poematorum vero [carminum] metra et pedes ac verborum elegans dispositio et sententiarum inter personas distinctas [versuum] pronuntiatio prolectando sensus legentium perducit sine offensa ad summam scriptorum terminationem.

[¶1] pr.2. 2. But this cannot be the case with architectural treatises, because those terms which originate in the peculiar needs of the art, give rise to obscurity of ideas from the unusual nature of the language. Hence, while the things themselves are not well known, and their names not in common use, if besides this the principles are described in a very diffuse fashion without any attempt at conciseness and explanation in a few pellucid sentences, such fullness and amplitude of treatment will be only a hindrance, and will give the reader nothing but indefinite notions. Therefore, when I mention obscure terms, and the symmetrical proportions of members of buildings, I shall give brief explanations, so that they may be committed to memory; for thus expressed, the mind will be enabled to understand them the more easily.

> Latin: pr.2. Id autem in architecturae conscriptionibus non potest fieri, quod vocabula ex artis propria necessitate concepta inconsueto sermone obiciunt sensibus obscuritatem. cum ergo ea per se non sint aperta nec pateant eorum in consuetudine nomina, tum etiam praeceptorum late vagantes scripturae, si non contrahentur, ut paucis et perlucidis sententiis explicentur, frequentia multitudineque sermonis inpediente incertas legentium efficient cogitationes. itaque occultas nominationes commensusque e membris operum pronuntians, ut memoriae tradantur, breviter exponam; sic enim expeditius ea recipere poterunt mentes.

[¶2] pr.3. 3. Furthermore, since I have observed that our citizens are distracted with public affairs and private business, I have thought it best to write briefly, so that my readers, whose intervals of leisure are small, may be able to comprehend in a short time. Then again, Pythagoras and those who came after him in his school thought it proper to employ the principles of the cube in composing books on their doctrines, and, having determined that the cube consisted of 216 lines, held that there should be no more than three cubes in any one treatise.

> Latin: pr.3. Non minus cum animadvertissem distentam occupationibus civitatem publicis et privatis negotiis, paucis iudicavi scribendum, uti angusto spatio vacuitatis ea legentes breviter percipere possent. Etiamque Pythagorae quique eius haeresim fuerunt secuti, placuit cybicis rationibus praecepta in voluminibus scribere, constitueruntque cybum CCXVI versus eosque non plus tres in una conscriptione oportere esse putaverunt.

[¶3] pr.4. 4. A cube is a body with sides all of equal breadth and their surfaces perfectly square. When thrown down, it stands firm and steady so long as it is untouched, no matter on which of its sides it has fallen, like the dice which players throw on the board. The Pythagoreans appear to have drawn their analogy from the cube, because the number of lines mentioned will be fixed firmly and steadily in the memory when they have once settled down, like a cube, upon a man's understanding. The Greek comic poets, also, divided their plays into parts by introducing a choral song, and by this partition on the principle of the cubes, they relieve the actor's speeches by such intermissions.

> Latin: pr.4. Cybus autem est corpus ex lateribus aequali latitudine planitiarum perquadratum. is cum est iactus, quam in partem incubuit, dum est intactus, inmotam habet stabilitatem, uti sunt etiam tesserae, quas in alveo ludentes iaciunt. hanc autem similitudinem ex eo sumpsisse videntur, quod is numerus versuum, uti cybus, in quemcumque sensum insederit, inmotam efficiat ibi memoriae stabilitatem. graeci quoque poetae comici interponentes e choro canticum diviserunt spatia fabularum. ita partes cybica ratione facientes intercapedinibus levant actorum pronuntiationes.

[¶4] pr.5. 5. Since these rules, founded on the analogy of nature, were followed by our predecessors, and since I observe that I have to write on unusual subjects which many persons will find obscure, I have thought it best to write in short books, so that they may the more readily strike the understanding of the reader: for they will thus be easy to comprehend. I have also arranged them so that those in search of knowledge on a subject may not have to gather it from different places, but may find it in one complete treatment, with the various classes set forth each in a book by itself. Hence, Caesar, in the third and fourth books I gave the rules for temples; in this book I shall treat of the laying out of public places. I shall speak first of the proper arrangement of the forum, for in it the course of both public and private affairs is directed by the magistrates.

> Latin: pr.5. Cum ergo haec naturali modo sint a maioribus observata animoque advertam inusitatas et obscuras multis res esse mihi scribendas, quo facilius ad sensus legentium pervenire possint, brevibus voluminibus iudicavi scribere; ita enim expedita erunt ad intellegendum. eorumque ordinationes institui, uti non sint quaerentibus separatim colligenda, sed e corpore uno et in singulis voluminibus generum haberent explicationes. itaque, Caesar, tertio et quarto volumine aedium sacrarum rationes exposui, hoc libro publicorum locorum expediam dispositiones. primumque forum uti oporteat constitui, dicam, quod in eo et publicarum et privatarum rerum rationes per magistratus gubernantur.

[¶5] 1.1. 1. THE Greeks lay out their forums in the form of a square surrounded by very spacious double colonnades, adorn them with columns set rather closely together, and with entablatures of stone or marble, and construct walks above in the upper story. But in the cities of Italy the same method cannot be followed, for the reason that it is a custom handed down from our ancestors that gladiatorial shows should be given in the forum.

> Latin: 1.1. Graeci in quadrato amplissimis et duplicibus porticibus fora constituunt crebrisque columnis et lapideis aut marmoreis epistyliis adornant et supra ambulationes in contignationibus faciunt. Italiae vero urbibus non eadem est ratione faciendum, ideo quod a maioribus consuetudo tradita est gladiatoria munera in foro dari.

[¶6] 1.2. 2. Therefore let the intercolumniations round the show place be pretty wide; round about in the colonnades put the bankers' offices; and have balconies on the upper floor properly arranged so as to be convenient, and to bring in some public revenue. The size of a forum should be proportionate to the number of inhabitants, so that it may not be too small a space to be useful, nor look like a desert waste for lack of population. To determine its breadth, divide its length into three parts and assign two of them to the breadth. Its shape will then be oblong, and its ground plan conveniently suited to the conditions of shows.

> Latin: 1.2. Igitur circum spectacula spatiosiora intercolumnia distribuantur circaque in porticibus argentariae tabernae maenianaque superioribus coaxationibus conlocentur, quae et ad usum et ad vectigalia publica recte erunt disposita. Magnitudines autem ad copiam hominum oportet fieri, ne parvum spatium sit ad usum aut ne propter inopiam populi vastum forum videatur. latitudo autem ita finiatur, uti, longitudo in tres partes cum divisa fuerit, ex his duae partes ei dentur; ita enim erit oblonga eius formatio et ad spectaculorum rationem utilis dispositio.

[¶7] 1.3. 3. The columns of the upper tier should be one fourth smaller than those of the lower, because, for the purpose of bearing the load, what is below ought to be stronger than what is above, and also, because we ought to imitate nature as seen in the case of things growing; for example, in round smooth-stemmed trees, like the fir, cypress, and pine, every one of which is rather thick just above the roots and then, as it goes on increasing in height, tapers off naturally and symmetrically in growing up to the top. Hence, if nature requires this in things growing, it is the right arrangement that what is above should be less in height and thickness than what is below.

> Latin: 1.3. Columnae superiores quarta parte minores quam inferiores sunt constituendae, propterea quod oneri ferendo, quae sunt inferiora, firmiora debent esse quam superiora. non minus quod etiam nascentium oportet imitari naturam, ut in arboribus teretibus, abiete, cupresso, pinu, e quibus nulla non crassior est ab radicibus, dein decrescendo progreditur in altitudinem naturali contractura peraequata nascens ad cacumen. ergo si natura nascentium ita postulat, recte est constitutum et altitudinibus et crassitudinibus superiora inferiorum fieri contractiora.

[¶8] 1.4. 4. Basilicas should be constructed on a site adjoining the forum and in the warmest possible quarter, so that in winter business men may gather in them without being troubled by the weather. In breadth they should be not less than one third nor more than one half of their length, unless the site is naturally such as to prevent this and to oblige an alteration in these proportions. If the length of the site is greater than necessary, Chalcidian porches may be constructed at the ends, as in the Julia Aquiliana.

> Latin: 1.4. Basilicarum loca adiuncta foris quam calidissimis partibus oportet constitui, ut per hiemem sine molestia tempestatium se conferre in eas negotiatores possint. earumque latitudines ne minus quam ex tertia, ne plus ex dimidia longitudinis constituantur, nisi si loci natura inpedierit et aliter coegerit symmetriam commutari. sin autem locus erit amplior in longitudine, chalcidica in extremis constituantur, uti sunt in Iulia Aquiliana.

[¶9] 1.5. 5. It is thought that the columns of basilicas ought to be as high as the side-aisles are broad; an aisle should be limited to one third of the breadth which the open space in the middle is to have. Let the columns of the upper tier be smaller than those of the lower, as written above. The screen, to be placed between the upper and the lower tiers of columns, ought to be, it is thought, one fourth lower than the columns of the upper tier, so that people walking in the upper story of the basilica may not be seen by the business men. The architraves, friezes, and cornices should be adjusted to the proportions of the columns, as we have stated in the third book.

> Latin: 1.5. Columnae basilicarum tam altae, quam porticus latae fuerint, faciendae videntur; porticus, quam medium spatium futurum est, ex tertia finiatur. columnae superiores minores quam inferiores, uti supra scriptum est, constituantur. pluteum, quod fuerit inter superiores et inferiores columnas, lumnas, item quarta parte minus, quam superiores columnae fuerint, oportere fieri videtur, uti supra basilicae contignationem ambulantes ab negotiatoribus ne conspiciantur. epistylia, zophora, coronae ex symmetriis columnarum, uti in tertio libro diximus, explicentur.

[¶10] 1.6. 6. But basilicas of the greatest dignity and beauty may also be constructed in the style of that one which I erected, and the building of which I superintended at Fano. Its proportions and symmetrical relations were established as follows. In the middle, the main roof between the columns is 120 feet long and sixty feet wide. Its aisle round the space beneath the main roof and between the walls and the columns is twenty feet broad. The columns, of unbroken height, measuring with their capitals fifty feet, and being each five feet thick, have behind them pilasters, twenty feet high, two and one half feet broad, and one and one half feet thick, which support the beams on which is carried the upper flooring of the aisles. Above them are other pilasters, eighteen feet high, two feet broad, and a foot thick, which carry the beams supporting the principal raftering and the roof of the aisles, which is brought down lower than the main roof.

> Latin: 1.6. [Non minus summam dignitatem et venustatem possunt habere comparationes basilicarum, quo genere Coloniae Iuliae Fanestri conlocavi curavique faciendam, cuius proportiones et symmetriae sic sunt constitutae. mediana testudo inter columnas est longa pedes CXX, lata pedes LX. porticus eius circa testudinem inter parietes et columnas lata pedes XX. columnae altitudinibus perpetuis cum capitulis pedes L, crassitudinibus quinûm, habentes post se parastaticas altas pedes XX, latas pedes II S, crassas I S, quae sustinent trabes, in quibus invehuntur porticuum contignationes. supraque eas aliae parastaticae pedum XVIII, latae binûm, crassae pedem, quae excipiunt item trabes sustinentes cantherium et porticûm, quae sunt summissa infra testudinem, tecta.]

[¶11] 1.7. 7. The spaces remaining between the beams supported by the pilasters and the columns, are left for windows between the intercolumniations. The columns are: on the breadth of the main roof at each end, four, including the corner columns at right and left; on the long side which is next to the forum, eight, including the same corner columns; on the other side, six, including the corner columns. This is because the two middle columns on that side are omitted, in order not to obstruct the view of the pronaos of the temple of Augustus (which is built at the middle of the side wall of the basilica, facing the middle of the forum and the temple of Jupiter) and also the tribunal which is in the former temple, shaped as a hemicycle whose curvature is less than a semicircle.

> Latin: 1.7. [Reliqua spatia inter parastaticarum et columnarum trabes per intercolumnia luminibus sunt relicta. columnae sunt in latitudine testudinis cum angularibus dextra ac sinistra quaternae, in longitudine, quae est foro proxima, cum isdem angularibus octo, ex altera parte cum angularibus VI, ideo quod mediae duae in ea parte non sunt positae, ne inpediant aspectus pronai aedis Augusti, quae est in medio latere parietis basilicae conlocata spectans medium forum et aedem Iovis.]

[¶12] 1.8. 8. The open side of this hemicycle is forty-six feet along the front, and its curvature inwards is fifteen feet, so that those who are standing before the magistrates may not be in the way of the business men in the basilica. Round about, above the columns, are placed the architraves, consisting of three two-foot timbers fastened together. These return from the columns which stand third on the inner side to the antae which project from the pronaos, and which touch the edges of the hemicycle at right and left.

> Latin: 1.8. [Item tribunal, quod est in ea aede, hemicycli schematis minoris curvatura formatum; eius autem hemicycli in fronte est intervallum pedes XLVI, introrsus curvatura pedes XV, uti, qui apud magistratus starent, negotiantes in basilica ne inpedirent. supra columnas ex tribus tignis bipedalibus compactis trabes sunt circa conlocatae, eaeque ab tertiis columnis, quae sunt in interiore parte, revertuntur ad antas, quae a pronao procurrunt, dextraque et sinistra hemicyclium tangunt.]

[¶13] 1.9. 9. Above the architraves and regularly dispersed on supports directly over the capitals, piers are placed, three feet high and four feet broad each way. Above them is placed the projecting cornice round about, made of two two-foot timbers. The tiebeams and struts, being placed above them, and directly over the shafts of the columns and the antae and walls of the pronaos, hold up one gable roof along the entire basilica, and another from the middle of it, over the pronaos of the temple.

> Latin: 1.9. [Supra trabes contra capitula ex fulmentis dispositae pilae sunt conlocatae, altae pedes III, latae quoqueversus quaternis. supra eas ex duobus tignis bipedalibus trabes everganeae circa sunt conlocatae. quibus insuper transtra cum capreolis columnarum contra corpora et antas et parietes pronai conlocata sustinent unum culmen perpetuae basilicae, alterum a medio supra pronaum aedis.]

[¶14] 1.10. 10. Thus the gable tops run in two directions, like the letter T, and give a beautiful effect to the outside and inside of the main roof. Further, by the omission of an ornamental entablature and of a line of screens and a second tier of columns, troublesome labour is saved and the total cost greatly diminished. On the other hand, the carrying of the columns themselves in unbroken height directly up to the beams that support the main roof, seems to add an air of sumptuousness and dignity to the work.

> Latin: 1.10. ita fastigiorum duplex pectinata dispositio extrinsecus tecti et interioris altae testudinis praestat speciem venustam. item sublata epistyliorum ornamenta et pluteorum columnarumque superiorum distributio operosam detrahit molestiam sumptusque inminuit ex magna parte summam. ipsae vero columnae in altitudine perpetua sub trabes testudinis perductae et magnificentiam inpensae et auctoritatem operi adaugere videntur.

[¶15] 2.1. 1. THE treasury, prison, and senate house ought to adjoin the forum, but in such a way that their dimensions may be proportionate to those of the forum. Particularly, the senate house should be constructed with special regard to the importance of the town or city. If the building is square, let its height be fixed at one and one half times its breadth; but if it is to be oblong, add together its length and breadth and, having got the total, let half of it be devoted to the height up to the coffered ceiling.

> Latin: 2.1. Aerarium, carcer, curia foro sunt coniungenda, sed ita uti magnitudo ⟨ac⟩ symmetriae eorum foro respondeant. maxime quidem curia in primis est facienda ad dignitatem municipii sive civitatis. et si quadrata erit, quantum habuerit latitudinis dimidia addita constituatur altitudo; sin autem oblonga fuerit, longitudo et latitudo componatur, et summae compositae eius dimidia pars sub lacunariis altitudini detur.

[¶16] 2.2. 2. Further, the inside walls should be girdled, at a point halfway up their height, with coronae made of woodwork or of stucco. Without these, the voice of men engaged in discussion there will be carried up to the height above, and so be unintelligible to their listeners. But when the walls are girdled with coronae, the voice from below, being detained before rising and becoming lost in the air, will be intelligible to the ear.

> Latin: 2.2. Praeterea praecingendi sunt parietes medii coronis ex intestino opere aut albario ad dimidiam partem altitudinis. quae si non erunt, vox ibi disputantium elata in altitudinem intellectui non poterit esse audientibus. cum autem coronis praecincti parietes erunt, vox ab imis morata, priusquam in aera elata dissipabitur, auribus erit intellecta.

[¶17] 3.1. 1. AFTER the forum has been arranged, next, for the purpose of seeing plays or festivals of the immortal gods, a site as healthy as possible should be selected for the theatre, in accordance with what has been written in the first book, on the principles of healthfulness in the sites of cities. For when plays are given, the spectators, with their wives and children, sit through them spellbound, and their bodies, motionless from enjoyment, have the pores open, into which blowing winds find their way. If these winds come from marshy districts or from other unwholesome quarters, they will introduce noxious exhalations into the system. Hence, such faults will be avoided if the site of the theatre is somewhat carefully selected.

> Latin: 3.1. Cum forum constitutum fuerit, tum deorum inmortalium diebus festis ludorum spectationibus eligendus est locus theatro quam saluberrimus, uti in primo libro de salubritatibus in moenium conlocationibus est scriptum. per ludos enim cum coniugibus et liberis persedentes delectationibus detinentur et corpora propter voluptatem inmota patentes habent venas, in quas insidunt aurarum flatus, qui, si a regionibus palustribus aut aliis regionibus vitiosis advenient, nocentes spiritus corporibus infundent. itaque si curiosius eligetur locus theatro, vitabuntur vitia.

[¶18] 3.2. 2. We must also beware that it has not a southern exposure. When the sun shines full upon the rounded part of it, the air, being shut up in the curved enclosure and unable to circulate, stays there and becomes heated; and getting glowing hot it burns up, dries out, and impairs the fluids of the human body. For these reasons, sites which are unwholesome in such respects are to be avoided, and healthy sites selected.

> Latin: 3.2. Etiamque providendum est, ne impetus habeat a meridie. sol enim cum implet eius rotunditatem, aer conclusus curvatura neque habens potestatem vagandi versando confervescit et candens adurit excoquitque et inminuit e corporibus umores. ideo maxime vitandae sunt his rebus vitiosae regiones et eligendae salubres.

[¶19] 3.3. 3. The foundation walls will be an easier matter if they are on a hillside; but if they have to be laid on a plain or in a marshy place, solidity must be assured and substructures built in accordance with what has been written in the third book, on the foundations of temples. Above the foundation walls, the ascending rows of seats, from the substructures up, should be built of stone and marble materials.

> Latin: 3.3. Fundamentorum autem, si in montibus fuerint, facilior erit ratio; sed si necessitas coegerit in plano aut palustri loco ea constitui, solidationes substructionesque ita erunt faciendae, quemadmodum de fundationibus aedium sacrarum in tertio libro est scriptum. insuper fundamenta lapideis et marmoreis copiis gradationes ab substructione fieri debent.

[¶20] 3.4. 4. The curved cross-aisles should be constructed in proportionate relation, it is thought, to the height of the theatre, but not higher than the footway of the passage is broad. If they are loftier, they will throw back the voice and drive it away from the upper portion, thus preventing the case-endings of words from reaching with distinct meaning the ears of those who are in the uppermost seats above the cross-aisles. In short, it should be so contrived that a line drawn from the lowest to the highest seat will touch the top edges and angles of all the seats. Thus the voice will meet with no obstruction.

> Latin: 3.4. Praecinctiones ad altitudines theatrorum pro rata parte faciendae videntur, neque altiores quam quanta praecinctionis itineris sit latitudo. si enim excelsiores fuerint, repellent et eicient e superiore parte vocem nec patientur in sedibus suis, quae ⟨sunt⟩ supra praecinctiones, verborum casus certa significatione ad aures pervenire. et ad summam ita est gubernandum, uti, linea cum ad imum gradum et ad summum extenta fuerit, omnia cacumina graduum angulosque tangat: ita vox non inpedietur.

[¶21] 3.5. 5. The different entrances ought to be numerous and spacious, the upper not connected with the lower, but built in a continuous straight line from all parts of the house, without turnings, so that the people may not be crowded together when let out from shows, but may have separate exits from all parts without obstructions. Particular pains must also be taken that the site be not a “deaf” one, but one through which the voice can range with the greatest clearness. This can be brought about if a site is selected where there is no obstruction due to echo.

> Latin: 3.5. Aditus complures et spatiosos oportet disponere, nec coniunctos superiores inferioribus, sed ex omnibus locis perpetuos et directos sine inversuris faciendos, uti, cum populus dimittatur de spectaculis, ne comprimatur, sed habeat ex omnibus locis exitus separatos sine inpeditione. Etiam diligenter est animadvertendum, ne sit locus surdus, sed ut in eo vox quam clarissime vagari possit. hoc vero fieri ita poterit, si locus electus fuerit, ubi non inpediatur resonantia.

[¶22] 3.6. 6. Voice is a flowing breath of air, perceptible to the hearing by contact. It moves in an endless number of circular rounds, like the innumerably increasing circular waves which appear when a stone is thrown into smooth water, and which keep on spreading indefinitely from the centre unless interrupted by narrow limits, or by some obstruction which prevents such waves from reaching their end in due formation. When they are interrupted by obstructions, the first waves, flowing back, break up the formation of those which follow.

> Latin: 3.6. Vox autem est spiritus fluens aeris, e tactu sensibilis auditu. ea movetur circulorum rotundationibus infinitis, uti si in stantem aquam lapide inmisso nascantur innumerabiles undarum circuli crescentes a centro, quam latissime possint, et vagantes, nisi angustia loci interpellaverit aut aliqua offensio, quae non patitur designationes earum undarum ad exitus pervenire. itaque cum interpellentur offensionibus, primae redundantes insequentium disturbant designationes.

[¶23] 3.7. 7. In the same manner the voice executes its movements in concentric circles; but while in the case of water the circles move horizontally on a plane surface, the voice not only proceeds horizontally, but also ascends vertically by regular stages. Therefore, as in the case of the waves formed in the water, so it is in the case of the voice: the first wave, when there is no obstruction to interrupt it, does not break up the second or the following waves, but they all reach the ears of the lowest and highest spectators without an echo.

> Latin: 3.7. Eadem ratione vox item ad circinum efficit motiones; sed in aqua circuli planitiae in latitudine moventur, vox et in latitudine progreditur et altitudinem gradatim scandit. igitur ut in aqua undarum designationibus, item in voce cum offensio nulla primam undam interpellaverit, non disturbat secundam nec insequentes, sed omnes sine resonantia perveniunt ad imorum et ad summorum aures.

[¶24] 3.8. 8. Hence the ancient architects, following in the footsteps of nature, perfected the ascending rows of seats in theatres from their investigations of the ascending voice, and, by means of the canonical theory of the mathematicians and that of the musicians, endeavoured to make every voice uttered on the stage come with greater clearness and sweetness to the ears of the audience. For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn so the ancients devised methods of increasing the power of the voice in theatres through the application of harmonics.

> Latin: 3.8. Ergo veteres architecti naturae vestigia persecuti indagationibus vocis scandentis theatrorum perfecerunt gradationes, et quaesierunt per canonicam mathematicorum et musicam rationem, ut, quaecumque vox esset in scaena, clarior et suavior ad spectatorum perveniret aures. uti enim organa aeneis lamminis aut corneis ἠχεῖα ad chordarum sonitûm claritatem perficiuntur, sic theatrorum per harmonicen ad augendam vocem ratiocinationes ab antiquis sunt constitutae.

[¶25] 4.1. 1. HARMONICS is an obscure and difficult branch of musical science, especially for those who do not know Greek. If we desire to treat of it, we must use Greek words, because some of them have no Latin equivalents. Hence, I will explain it as clearly as I can from the writings of Aristoxenus, append his scheme, and define the boundaries of the notes, so that with somewhat careful attention anybody may be able to understand it pretty easily.

> Latin: 4.1. Harmonice autem est musica litteratura obscura et difficilis, maxime quidem quibus graecae litterae non sunt notae. quam si volumus explicare, necesse est etiam graecis verbis uti, quod nonnulla eorum latinas non habent appellationes. itaque ut potuero quam apertissime ex Aristoxeni scripturis interpretabor et eius diagramma subscribam finitionesque sonituum designabo, uti, qui diligentius attenderit, facilius percipere possit.

[¶26] 4.2. 2. The voice, in its changes of position when shifting pitch, becomes sometimes high, sometimes low, and its movements are of two kinds, in one of which its progress is continuous, in the other by intervals. The continuous voice does not become stationary at the “boundaries” or at any definite place, and so the extremities of its progress are not apparent, but the fact that there are differences of pitch is apparent, as in our ordinary speech in sol, lux, flos, vox for in these cases we cannot tell at what pitch the voice begins, nor at what pitch it leaves off, but the fact that it becomes low from high and high from low is apparent to the ear. In its progress by intervals the opposite is the case. For here, when the pitch shifts, the voice, by change of position, stations itself on one pitch, then on another, and, as it frequently repeats this alternating process, it appears to the senses to become stationary, as happens in singing when we produce a variation of the mode by changing the pitch of the voice. And so, since it moves by intervals, the points at which it begins and where it leaves off are obviously apparent in the boundaries of the notes, but the intermediate points escape notice and are obscure, owing to the intervals.

> Latin: 4.2. Vox enim mutationibus cum flectitur, alias fit acuta, alias gravis; duobusque modis movetur, e quibus unus effectus habet continuatos, alter distantes. continuata vox neque in finitionibus consistit neque in loco ullo, efficitque terminationes non apparentes, intervalla autem media apparentia, uti sermone cum dicamus: sol lux flos vox. nunc enim nec unde incipit nec ubi desinit, intellegitur, †sed quod ex acuta facta est gravis et ex gravi acuta, apparet auribus. per distantiam autem e contrario. namque cum flectitur inmutatione, vox statuit se in alicuius sonitus finitione, deinde in alterius, et id ultro citro crebre faciendo ⟨non⟩ constans apparet sensibus, uti in cantionibus cum flectentes vocem varietatem facimus. modulationis itaque intervallis ea cum versatur, et unde initium fecit et ubi desiit, apparet in sonorum patentibus finitionibus, medianis autem patentia intervallis obscurantur.

[¶27] 4.3. 3. There are three classes of modes: first, that which the Greeks term the enharmonic; second, the chromatic; third, the diatonic. The enharmonic mode is an artistic conception, and therefore execution in it has a specially severe dignity and distinction. The chromatic, with its delicate subtlety and with the “crowding” of its notes, gives a sweeter kind of pleasure. In the diatonic, the distance between the intervals is easier to understand, because it is natural. These three classes differ in their arrangement of the tetrachord. In the enharmonic, the tetrachord consists of two tones and two “dieses.” A diesis is a quarter tone; hence in a semitone there are included two dieses. In the chromatic there are two semitones arranged in succession, and the third interval is a tone and a half. In the diatonic, there are two consecutive tones, and the third interval of a semitone completes the tetrachord. Hence, in the three classes, the tetrachords are equally composed of two tones and a semitone, but when they are regarded separately according to the terms of each class, they differ in the arrangement of their intervals.

> Latin: 4.3. Genera vero sunt modulationum tria: primum quod Graeci nominant ἁρμονίην, secundum χρῶμα, tertium διάτονον. est autem harmoniae modulatio ab arte concepta, et ea re cantio eius maxime gravem et egregiam habet auctoritatem. chroma subtili sollertia ac crebritate modulorum suaviorem habet delectationem. diatoni vero, quod naturalis est, facilior est intervallorum distantia. in his tribus generibus dissimiles sunt tetrachordorum dispositiones, quod harmonia [tetrachordorum] et tonos et dihesis habet binas (dihesis autem est toni pars quarta; ita in hemitonio duae diheses sunt conlocatae); chromati duo hemitonia in ordine sunt composita, tertium trium hemitoniorum est intervallum; dia⟨tono⟩ toni duo sunt continuati, tertium hemitonium finit tetrachordi magnitudinem. ita in tribus generibus tetrachorda ex duobus tonis et hemitonio sunt peraequata, sed ipsa cum separatim uniuscuiusque generis finibus considerantur, dissimilem habent intervallorum designationem.

[¶28] 4.4. 4. Now then, these intervals of tones and semitones of the tetrachord are a division introduced by nature in the case of the voice, and she has defined their limits by measures according to the magnitude of the intervals, and determined their characteristics in certain different ways. These natural laws are followed by the skilled workmen who fashion musical instruments, in bringing them to the perfection of their proper concords.

> Latin: 4.4. Igitur intervalla tonorum et hemitoniorum et ⟨diheseon⟩ tetrachordorum in voce divisit natura finîtque terminationes eorum mensuris intervallorum quantitate, modisque certis distantibus constituit qualitates, quibus etiam artifices, qui organa fabricant, ex natura constitutis utendo comparant ad concentus convenientes eorum perfectiones.

[¶29] 4.5. 5. In each class there are eighteen notes, termed in Greek of which eight in all the three classes are constant and fixed, while the other ten, not being tuned to the same pitch, are variable. The fixed notes are those which, being placed between the moveable, make up the unity of the tetrachord, and remain unaltered in their boundaries according to the different classes. Their names are proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. The moveable notes are those which, being arranged in the tetrachord between the immoveable, change from place to place according to the different classes. They are called parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, paranete synhemmenon, trite diezeugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

> Latin: 4.5. Sonitus, qui graece φθόγγοι dicuntur, in unoquoque genere sunt X et VIII, e quibus VIII sunt in tribus generibus perpetui et stantes, reliqui X, cum communiter modulantur, sunt vagantes. stantes autem sunt, qui inter mobiles [sunt] interpositi continent tetrachordi coniunctionem et e generum discriminibus suis finibus sunt permanentes; appellantur autem sic: proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. mobiles autem sunt, qui in tetrachordo inter inmotos dispositi in generibus ex locis loca mutant; vocabula autem habent haec: parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, ⟨paranete synhemmenon,⟩ trite diezeugmenon, paranete diezeugmenon, trite hyperbolaeon, paranete hyperbolaeon.

[¶30] 4.6. 6. These notes, from being moveable, take on different qualities; for they may stand at different intervals and increasing distances. Thus, parhypate, which in the enharmonic is at the interval of half a semitone from hypate, has a semitone interval when transferred to the chromatic. What is called lichanos in the enharmonic is at the interval of a semitone from hypate; but when shifted to the chromatic, it goes two semitones away; and in the diatonic it is at an interval of three semitones from hypate. Hence the ten notes produce three different kinds of modes on account of their changes of position in the classes.

> Latin: 4.6. Ei autem qua moventur, recipiunt virtutes alias; intervalla enim et distantias habent crescentes. itaque parhypate, quae in harmonia distat ab hypate ⟨dimidium⟩ hemitonium, in chroma transmutata habet hemitonium. quae lichanos in harmonia dicitur, ab hypate distat hemitonium, in chroma translata progreditur duo hemitonia, in diatono distat ab hypate tria hemitonia. ita X sonitus propter translationes in generibus efficiunt triplicem modulationum varietatem.

[¶31] 4.7. 7. There are five tetrachords: first, the lowest, termed in Greek ὕπατον; second, the middle, called μέσον; third, the conjunct, termed fourth, the disjunct, named διεζευγμένον; the fifth, which Greek ὑπερβόλαιον. The concords, termed in Greek συμφωνίαι, of which human modulation will naturally admit, are six in number: the fourth, the fifth, the octave, the octave and fourth, the octave and fifth, and the double octave.

> Latin: 4.7. Tetrachorda autem sunt quinque: primum gravissimum, quod graece dicitur ὕπατον, secundum medianum, quod appellatur μέσον, tertium coniunctum, quod συνημμένον dicitur, quartum disiunctum, quod διεζευγμένον nominatur, quintum, quod est acutissimum, graece ὑπερβόλαιον dicitur. concentus, quos natura hominis modulari potest, graece quae συμφωνίαι dicuntur, sunt sex: diatessaron, diapente, diapason, et disdiatessaron, et disdiapente, et disdiapason.

[¶32] 4.8. 8. Their names are therefore due to numerical value; for when the voice becomes stationary on some one note, and then, shifting its pitch, changes its position and passes to the limit of the fourth note from that one, we use the term “fourth”; when it passes to the fifth, the term is “fifth.”

> Latin: 4.8. Ideoque et a numero nomina ceperunt, quod, cum vox constiterit in una sonorum finitione ab eaque se flectens mutaverit et pervenerit in quartam terminationem, appellatur diatessaron, in quintam diapente [in sextam diapason, in octavam et dimidiam diapason et diatessaron, in nonam et dimidiam diapason diapente, in XII disdiapason].

[¶33] 4.9. 9. For there can be no consonancies either in the case of the notes of stringed instruments or of the singing voice, between two intervals or between three or six or seven; but, as written above, it is only the harmonies of the fourth, the fifth, and so on up to the double octave, that have boundaries naturally corresponding to those of the voice: and these concords are produced by the union of the notes.

> Latin: 4.9. Non enim inter duo intervalla, cum chordarum sonitus aut vocis cantus factus fuerit, nec inter tria aut sex aut septem possunt consonantiae fieri, sed, uti supra scriptum est, diatessaron et diapente et ex ordine ad disdiapason convenientiae ex natura vocis congruentis habent finitiones. [et ei concentus procreantur ex coniunctione sonituum, qui graece φθόγγοι dicuntur.]

[¶34] 5.1. 1. IN accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up to the double octave. Then, having constructed niches in between the seats of the theatre, let the vessels be arranged in them, in accordance with musical laws, in such a way that they nowhere touch the wall, but have a clear space all round them and room over their tops. They should be set upside down, and be supported on the side facing the stage by wedges not less than half a foot high. Opposite each niche, apertures should be left in the surface of the seat next below, two feet long and half a foot deep.

> Latin: 5.1. Ita ex his indagationibus mathematicis rationibus fiant vasa aerea pro ratione magnitudinis theatri, eaque ita fabricentur, ut, cum tangantur, sonitum facere possint inter se diatessaron, diapente ⟨et⟩ ex ordine ad disdiapason. postea inter sedes theatri constitutis cellis ratione musica ibi conlocentur ita, uti nullum parietem tangant circaque habeant locum vacuum et ab summo capite spatium, ponanturque inversa et habeant in parte, quae spectat ad scaenam, suppositos cuneos ne minus altos semipede; contraque eas cellas relinquantur aperturae inferiorum graduum cubilibus longae pedes duo, altae semipede.

[¶35] 5.2. 2. The arrangement of these vessels, with reference to the situations in which they should be placed, may be described as follows. If the theatre be of no great size, mark out a horizontal range halfway up, and in it construct thirteen arched niches with twelve equal spaces between them, so that of the above mentioned “echea” those which give the note nete hyperbolaeon may be placed first on each side, in the niches which are at the extreme ends; next to the ends and a fourth below in pitch, the note nete diezeugmenon; third, paramese, a fourth below; fourth, nete synhemmenon; fifth, mese, a fourth below; sixth, hypate meson, a fourth below; and in the middle and another fourth below, one vessel giving the note hypate hypaton.

> Latin: 5.2. Designationes autem eorum, quibus in locis constituantur, sic explicentur. si non erit ampla magnitudine theatrum, media altitudinis transversa regio designetur et in ea tredecim cellae duodecim aequalibus intervallis distantes confornicentur, uti ea echea, quae supra scripta sunt, ad neten hyperbolaeon sonantia in cellis, quae sunt in cornibus extremis, utraque parte prima conlocentur, secunda ab extremis diatessaron ad neten diezeugmenon, tertia diatessaron ad paramesen, quarta ad neten synhemmenon, quinta diatessaron ad mesen, sexta diatessaron ad hypaten meson, in medio unum diatessaron ad hypaten hypaton.

[¶36] 5.3. 3. On this principle of arrangement, the voice, uttered from the stage as from a centre, and spreading and striking against the cavities of the different vessels, as it comes in contact with them, will be increased in clearness of sound, and will wake an harmonious note in unison with itself. But if the theatre be rather large, let its height be divided into four parts, so that three horizontal ranges of niches may be marked out and constructed: one for the enharmonic, another for the chromatic, and the third for the diatonic system. Beginning with the bottom range, let the arrangement be as described above in the case of a smaller theatre, but on the enharmonic system.

> Latin: 5.3. Ita hac ratiocinatione vox a scaena uti ab centro profusa se circumagens tactuque feriens singulorum vasorum cava excitaverit auctam claritatem et concentu convenientem sibi consonantiam. sin autem amplior erit magnitudo theatri, tunc altitudo dividatur in partes IIII, uti tres efficiantur regiones cellarum transverse designatae, una harmoniae, altera chromatos, tertia diatoni. et ab imo quae erit prima, ea ex harmonia conlocetur, Ita uti in minore theatro supra scriptum est.

[¶37] 5.4. 4. In the middle range, place first at the extreme ends the vessels which give the note of the chromatic hyperbolaeon; next to them, those which give the chromatic diezeugmenon, a fourth below; third, the chromatic synhemmenon; fourth, the chromatic meson, a fourth below; fifth, the chromatic hypaton, a fourth below; sixth, the paramese, for this is both the concord of the fifth to the chromatic hyperbolaeon, and the concord of the chromatic synhemmenon.

> Latin: 5.4. in mediana autem prima in extremis cornibus ad chromaticen hyperbolaeon habentia sonitum ponantur, in secundis ab his diatessaron ad chromaticen diezeugmenon, in tertiis ad chromaticen synhemmenon, quartis diatessaron ad chromaticen meson, quintis diatessaron ad chromaticen hypaton, sextis ad paramesen, quod et ad chromaticen hyperbolaeon diapente et ad chromaticen synhemmenon diatessaron habet consonantiae communitatem.

[¶38] 5.5. 5. No vessel is to be placed in the middle, for the reason that there is no other note in the chromatic system that forms à natural concord of sound. In the highest division and range of niches, place at the extreme ends vessels fashioned so as to give the note of the diatonic hyperbolaeon; next, the diatonic diezeugmenon, a fourth below; third, the diatonic synhemmenon; fourth, the diatonic meson, a fourth below; fifth, the diatonic hypaton, a fourth below; sixth, the proslambanomenos, a fourth below; in the middle, the note mese, for this is both the octave to proslambanomenos, and the concord of the fifth to the diatonic hypaton.

> Latin: 5.5. In medio nihil est conlocandum, ideo quod sonitûm nulla alia qualitas in chromatico genere symphoniae consonantiam potest habere. in summa vero divisione et regione cellarum in cornibus primis ad diatonon hyperbolaeon fabricata vasa sonitu ponantur, in secundis diatessaron ad diatonon ⟨diezeugmenon⟩, tertiis ad diatonon synhemmenon, quartis diatessaron ad diatonon meson, quintis diatessaron ad diatonon hypaton, sextis diatessaron ad proslambanomenon, in medio ad mesen, quod ea et ad proslambanomenon diapason et ad diatonon hypaton diapente habet symphoniarum communitates.

[¶39] 5.6. 6. Whoever wishes to carry out these principles with ease, has only to consult the scheme at the end of this book, drawn up in accordance with the laws of music. It was left by Aristoxenus, who with great ability and labour classified and arranged in it the different modes. In accordance with it, and by giving heed to these theories, one can easily bring a theatre to perfection, from the point of view of the nature of the voice, so as to give pleasure to the audience.

> Latin: 5.6. Haec autem si qui voluerit ad perfectum facile perducere, animadvertat in extremo libro diagramma musica ratione designatum, quod Aristoxenus magno vigore et industria generatim divisis modulationibus constitutum reliquit, de quo, si qui ratiocinationibus his attenderit, ad [naturas vocis et] audientium delectationes facilius valuerit theatrorum efficere perfectiones.

[¶40] 5.7. 7. Somebody will perhaps say that many theatres are built every year in Rome, and that in them no attention at all is paid to these principles; but he will be in error, from the fact that all our public theatres made of wood contain a great deal of boarding, which must be resonant. This may be observed from the behaviour of those who sing to the lyre, who, when they wish to sing in a higher key, turn towards the folding doors on the stage, and thus by their aid are reinforced with a sound in harmony with the voice. But when theatres are built of solid materials like masonry, stone, or marble, which cannot be resonant, then the principles of the “echea” must be applied.

> Latin: 5.7. Dicet aliquis forte multa theatra quotannis Romae facta esse neque ullam rationem harum rerum in his fuisse; sed errabit in eo, quod omnia publica lignea theatra tabulationes habent complures, quas necesse est sonare. hoc vero licet animadvertere etiam ab citharoedis, qui, superiore tono cum volunt canere, avertunt se ad scaenae valvas et ita recipiunt ab earum auxilio consonantiam vocis. cum autem ex solidis rebus theatra constituuntur, id est ex structura caementorum, lapide, marmore, quae sonare non possunt, tunc echeis hae rationes sunt explicandae.

[¶41] 5.8. 8. If, however, it is asked in what theatre these vessels have been employed, we cannot point to any in Rome itself, but only to those in the districts 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, and made a dedicatory offering at the temple of Luna with the money obtained from the sale of them. Besides, many skilful architects, in constructing theatres in small towns, have, for lack of means, taken large jars made of clay, but similarly resonant, and have produced very advantageous results by arranging them on the principles described.

> Latin: 5.8. Sin autem quaeritur, in quo theatro ea sint facta, Romae non possumus ostendere, sed in Italiae regionibus et in pluribus Graecorum civitatibus. etiamque auctorem habemus Lucium Mummium, qui diruto theatro Corinthiorum ea aenea Romam deportavit et de manubiis ad aedem Lunae dedicavit. multi etiam sollertes architecti, qui in oppidis non magnis theatra constituerunt, propter inopiam fictilibus doliis ita sonantibus electis hac ratiocinatione compositis perfecerunt utilissimos effectus.

[¶42] 6.1. 1. THE plan of the theatre itself is to be constructed as follows. Having fixed upon the principal centre, draw a line of circumference equivalent to what is to be the perimeter at the bottom, and in it inscribe four equilateral triangles, at equal distances apart and touching the boundary line of the circle, as the astrologers do in a figure of the twelve signs of the zodiac, when they are making computations from the musical harmony of the stars. Taking that one of these triangles whose side is nearest to the scaena, let the front of the scaena be determined by the line where that side cuts off a segment of the circle (A-B), and draw, through the centre, a parallel line (C-D) set off from that position, to separate the platform of the stage from the space of the orchestra.

> Latin: 6.1. Ipsius autem theatri conformatio sic est facienda, uti, quam magna futura est perimetros imi, centro medio conlocato circumagatur linea rotundationis, in eaque quattuor scribantur trigona paribus lateribus, ⟨quae paribus⟩ intervallis extremam lineam circinationis tangant, quibus etiam in duodecim signorum caelestium ⟨astrologia⟩ astrologi ex musica convenientia astrorum ratiocinantur. ex his trigonis cuius latus fuerit proximum scaenae, ea regione, qua praecidit curvaturam circinationis, ibi finiatur scaenae frons, et ab eo loco per centrum parallelos linea ducatur, quae disiungat proscaenii pulpitum et orchestrae regionem.

[¶43] 6.2. 2. The platform has to be made deeper than that of the Greeks, because all our artists perform on the stage, while the orchestra contains the places reserved for the seats of senators. The height of this platform must be not more than five feet, in order that those who sit in the orchestra may be able to see the performances of all the actors. The sections (cunei) for spectators in the theatre should be so divided, that the angles of the triangles which run about the circumference of the circle may give the direction for the flights of steps between the sections, as far as up to the first curved cross-aisle. Above this, the upper sections are to be laid out, midway between (the lower sections), with alternating passage-ways.

> Latin: 6.2. Ita latius factum fuerit pulpitum quam Graecorum, quod omnes artifices in scaena dant operam, in orchestra autem senatorum sunt sedibus loca designata. et eius pulpiti altitudo sit ne plus pedum quinque, uti, qui in orchestra sederint, spectare possint omnium agentium gestus. cunei spectaculorum in theatro ita dividantur, uti anguli trigonorum, qui currunt circum curvaturam circinationis, dirigant ascensus scalasque inter cuneos ad primam praecinctionem; supra autem alternis itineribus superiores cunei medii dirigantur.