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
Rules · Optics · Geometry · Bases
The stylobate rises in the middle
Do not lay the stylobate dead level: raise it gently toward the middle of each side, for a perfectly flat platform looks to the eye as if it sagged.
Parthenon: rise ≈ 11 cm over 69.5 m (flanks), ≈ 6.5 cm over 30.9 m (fronts), about 1 : 600
Vitruvius says the level of the stylobate should be “increased along the middle” by means of scamilli impares (literally “unequal little benches”) and promised a figure at the end of his book that has not survived. For centuries the phrase was a riddle. Penrose’s survey of 1846–47 showed that at the Parthenon the platform really does rise, in a smooth curve, toward the centre of each side, and that the curve runs up through the columns into the entablature. One persuasive reading, noted in Morgan’s commentary, is that the scamilli were sighting blocks of graded height used to set out the curve along a stretched line.
The figure exaggerates the curve. At its true size it is invisible as a curve, yet it keeps the long horizontals of the building from looking slack. Rainwater, incidentally, runs off a crowned platform, but the precision of the curves goes far beyond what drainage requires.
Related rules
Set the outer columns so that they incline slightly inward, toward the cella wall, the middle columns of the fronts plumb on their own axes and the corner columns leaning both ways.
Parthenon: lean ≈ 6–7 cm over 10.43 m (≈ 1 : 150); the axes would meet some 2 km above the ground
Give the shaft a continuous convex curve from base to necking, departing from a straight taper by only a few hundredths of a diameter, so that the column seems to flex under its load rather than to pinch.
Parthenon: greatest departure ≈ 1.7 cm on a shaft 9.6 m high (≈ 1⁄110 D)
A Doric frieze cannot obey all three of its rules at a corner: triglyphs over the column axes, a triglyph turning the corner, and metopes as broad as they are high. One of them must give way.
displacement of the corner triglyph = e − t⁄2 (e = half-depth of the architrave, t = triglyph width)
Plan a Greek theatre by inscribing three squares in the orchestra circle; the side nearest the scene fixes the front of the stage (proscaenium), and the scene is set back to a line tangent to the circle.
proscaenium at r cos 45° ≈ 0.71 r from the centre; logeion 10–12 ft high
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 stylobate rises in the middle”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/stylobate-curvature. Text, drawings and models licensed under CC BY-NC 4.0.