An arch pushes outward on its supports as well as down. For the same load and span the horizontal push grows as the rise falls: halve the rise and you roughly double the thrust.
H ≈ w·s² ⁄ 8f (uniform load w per metre, span s, rise f)
Rules · Façades · Proportion · Columns
The scene: twice the orchestra
Make the scaena twice as long as the orchestra is wide; raise its podium a twelfth of the orchestra diameter, its lower columns a quarter, their entablature a fifth of the columns; above, a parapet half the podium and columns a quarter shorter than those below.
L = 2D; podium D⁄12; columns D⁄4; entablature ⅕ col.; upper parapet ½ podium; upper columns ¾ lower
The whole elevation of the stage front is derived from one dimension, the diameter of the orchestra, in the way the orders are derived from the module. Vitruvius adds at once that the rules cannot always be kept: steps, aisles and stairs must be the same size in a small theatre as in a large one, and materials may run short, so an experienced architect must know how far to depart from symmetry.
The surviving scene buildings (at Orange, at Aspendos, at Sabratha and Leptis Magna) rise in two or three storeys of columns framing the three doors, with niches for statues, projecting aediculae and a roof over the stage.
Related rules
Raise the central nave above the lean-to roofs of the aisles and pierce the upper walls with a row of windows, the clerestory, so that the middle of a wide hall is lit from high on both sides.
nave height ≈ 1½–2 × nave width; one window over each bay of the arcade
Make the corner columns thicker than the rest by a fiftieth of their diameter, because, seen against the open sky, they look thinner than they are.
D corner = D × (1 + 1⁄50); Parthenon: 1.95 m against 1.905 m
Divide the height from floor to ceiling into three and a half parts and give two and a half to the opening; make a Doric door five and a half twelfths as wide as it is high (an Ionic one two-fifths), and narrow it slightly at the top.
h = 2½⁄3½ H; Doric w = 5½⁄12 h, Ionic w = h ÷ 2½; top narrowed by ⅓, ¼ or ⅛ of the jamb as h ≤ 16, ≤ 25, ≤ 30 ft
Architecture depends on order (ordinatio), arrangement (dispositio), eurythmy, symmetry, propriety (decor) and economy (distributio).
A column is narrower at the top than at the bottom, but the taller the column the less it should be diminished, because distance already makes its top look smaller.
upper Ø : lower Ø = 5⁄6 (≤15 ft) · 11⁄13 (15–20 ft) · 6⁄7 (20–30 ft) · 13⁄15 (30–40 ft) · 7⁄8 (40–50 ft)
Cite this page Chris Paton, “The scene: twice the orchestra”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/scaena-proportions. Text, drawings and models licensed under CC BY-NC 4.0.