Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.
Rules · Entablatures · Spacing · Geometry
The Doric corner conflict
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)
Vitruvius reports that some architects, Pytheos and Hermogenes among them, refused to build Doric temples at all because of this “embarrassment”. The column axis stands inside the corner of the frieze by half the depth of the architrave; a triglyph centred on the corner column therefore stops short of the corner, while a triglyph pushed out to the corner leaves the adjacent metope too wide by about half a triglyph.
The Greeks chose to keep the corner triglyph and the square metopes, and paid with the intercolumniation; Vitruvius and the Renaissance kept the axes and ended the frieze with a half-metope. The widened metope, the third way, was used in some early buildings and generally avoided. Switch between the three solutions in the figure.
Related rules
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
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)
To end the frieze with a triglyph at the corner and keep every metope square, move the corner column inward: make the last intercolumniation narrower than the others by the amount the corner triglyph is displaced.
contraction c = e − t⁄2; Parthenon: 4.29 m normal, 3.68 m at the corners (c ≈ 0.61 m)
Keep every triglyph centred over a column and every intercolumniation equal, and finish the frieze at the corner with a half-metope half a module wide.
corner semi-metope = ½ M (Vitruvius); equal intercolumniations throughout
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
Cite this page Chris Paton, “The Doric corner conflict”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/doric-corner-conflict. Text, drawings and models licensed under CC BY-NC 4.0.