CHAPTER XII¶
On the Orders and Spacing (Intercolumniations / Tetrants) of Round Columns in Buildings, and How the Architect Must Adapt Symmetry to the Site and Load (Vitruvius Book V).
Having shown how round columns are carved and proportioned in themselves, we now explain for those who must erect them in buildings the ancient and modern rules for their spacing or intercolumniation (intercolumnium, which we also call tetrante).
The Five Classical Intercolumniations (Vitruvius III.3.1–6)
When setting up a row of columns plumb (a livello) upon their stylobates and foundations, the Ancients spaced them apart from one another by the following multiples of one column thickness (lower diameter):
One and a half column thicknesses (:math:`1frac{1}{2},D`, Pycnostyle), or even one single thickness (:math:`1,D`): Found by travelers in ancient temples at Athens and Alexandria in Egypt, and in many places in Rome; strongest of all for bearing immense loads.
Two column thicknesses (:math:`2,D`, Systyle): Commended by Vitruvius for combining strength with dignity.
Two and a quarter or two and a half column thicknesses (:math:`2frac{1}{4},D` to :math:`2frac{1}{2},D`, Eustyle): Commended above all others by our Vitruvius (più commenda… a vaghezza) both for visual beauty (venustà) and for convenient passage, provided the load of the epistyle (architrave), frieze, and cornice overhead is not excessive!
(Note on the term **Tetrante*: By tetrante is understood any rectangular space or interval bounded by parallel lines that tends toward a square—thus we used tetrante in Chapter IV for the space between two corner horns of the capital’s abacus, here for the intercolumniation between two standing columns, and in Chapter XIII for the metope interval between two :term:`*triglyphs <tygraphi>`*!)*
Verbatim Authority of Vitruvius (Book V, Chapter 6) on the Architect’s Practical Judgment in Adapting Symmetry to the Site and Materials
Before erecting his columns, the wise architect must always weigh on the spot (in sul facto) the load to be supported, the nature and narrowness of the site, and the available marble and timber—keeping always as close as possible to the square and the circle and their rational parts (or at least their geometric lines when numbers fail). As our Vitruvius concludes in that golden passage of his fifth book (V.6.7):
Nec tamen in omnibus theatris symmetriae ad omnes rationes et effectus possunt respondere, sed oportet architectum animadvertere quibus proportionibus necesse sit sequi symmetriam et quibus rationibus ad loci naturam aut magnitudinem operis temperare. Sunt enim res quas et in pusillo et in magno theatro necesse est eadem magnitudine fieri propter usum, uti gradus, diazomata, pluteos, itinera, ascensus, pulpita, tribunalia, et si qua alia intercurrunt, ex quibus necessitas cogit discedere a symmetria ne impediatur usus. Non minus si qua exiguitas copiarum, id est marmoris, materiae, reliquarumque rerum quae parantur in opere defuerint, paulum demere aut adiicere, dum id ne nimium improbe fiat sed cum sensu, non erit alienum. Hoc autem erit, si architectus erit usu peritus, praeterea ingenio mobili solertiaque non fuerit viduatus.
(“Yet not in all theaters can the symmetries answer to every theoretical ratio and effect; rather, the architect must observe in what proportions it is necessary to follow strict symmetry, and in what respects they must be tempered to the nature of the site or the size of the work. For there are certain parts which, on account of practical use (propter usum), must be made of the exact same size in a small theater as in a great one—such as the steps/seats (gradus), walkways (diazomata), parapets (pluteos), passages, stairs, stages (pulpita), boxes (tribunalia), and the like, where necessity compels one to depart from pure proportional symmetry lest practical use be impeded. Likewise, if a scarcity of materials—such as marble, timber, or other supplies—occurs during the work, it will not be amiss to subtract or add a little, provided this is done judiciously (cum sensu) and not clumsily. And this will be achieved if the architect is experienced in practice and not devoid of nimble wit and resourcefulness!”)
And to this very end—so that you and all other craftsmen and men of science may have a mirror of true proportion to adapt to every site—I have labored through long nightly vigils to set forth in this book the five regular bodies and their dependent bodies with the canons for forming infinitely many more, as the divine philosopher Plato makes manifest in his Timaeus.