Divide the inside of a dome into coffers that shrink in step with the meridians as they rise, so that their perspective deepens the dome and draws the eye to the light of the lantern.
Rules · Capitals · Geometry · Ornament
Mauch’s volute: each turn half the one outside it
Draw the Ionic volute seven eye-diameters high and six wide, with the eye four diameters below the top; lay three turns about centres set out in the eye so that each winding is half as wide as the one outside it and the spiral runs into the top of the eye.
height = 7 e, width = 6 e; eye centre 4 e below the top; radii from the eye centre (e = 16 parts): 60, 52, 44, 36, 30, 26, 22, 18, 15, 13, 11, 9 → 8
Mauch devised this construction for the capitals of the Erechtheum. The vertical diameter of the eye is divided into sixteen parts; the middle two, four and eight parts form the sides of three nested squares whose corners are the twelve centres for the quarter-turns. Because each turn is half the width of the one outside it, the start and end points of every quadrant can be calculated rather than found by trial.
He found that it matches a cast of an Erechtheum corner capital closely, though the original’s eye is a little larger, and that it serves for the other capitals of the temple of Minerva Polias but less well for the Ilissus temple, whose eye is about a fifth of the volute’s height. Later, Roman-derived capitals follow Vitruvius’s construction instead, shown on his Plates 51 and 52.
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)
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
Take the plan, the orders and the details from the builders’ pattern books, simplified for timber and for the carpenter: a symmetrical front, a central hall and stair with rooms either side, a doorway under a pediment or fanlight, and mouldings drawn to be made with the plane.
Cite this page Chris Paton, “Mauch’s volute: each turn half the one outside it”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/mauch-volute. Text, drawings and models licensed under CC BY-NC 4.0.