Give the hipped roof (wudian) to the highest halls, the hip-and-gable (xieshan) to the next, and the gabled roofs, overhanging (xuanshan) and flush (yingshan), to lesser buildings and houses; double the eaves for the very highest.
double wudian > double xieshan > wudian > xieshan > xuanshan > yingshan
In the Forbidden City only the Hall of Supreme Harmony and a handful of other buildings have double hipped roofs; the gate-towers and secondary halls have hip-and-gable roofs; the offices and storerooms have gables. Colour ran in parallel (yellow glazed tiles for the emperor, green for princes and temples, grey for everyone else), and so did the number of small beasts on the hip ridges, usually an odd number up to nine, with ten on the Hall of Supreme Harmony alone.
The same hierarchy was known in the Song, which called the hipped roof si’a (“four slopes”) and the hip-and-gable jiuji (“nine ridges”).
For a great hall, measure the distance between the front and back eave purlins and raise the ridge purlin above them by one third of it; for lesser halls, by about a quarter.
rise = ⅓ × depth between eave purlins (halls); ≈ ¼ (+ a small addition) for ting-tang halls
Draw a straight line from the ridge purlin to the eave purlin and lower the first purlin below the ridge from it by one tenth of the rise; from that point draw a new line to the eave purlin and lower the next purlin by one twentieth; continue, halving each time.
drop₁ = H⁄10 · drop₂ = H⁄20 · drop₃ = H⁄40 · …
Give each rafter span a fixed slope, increasing from the eaves to the ridge: half-pitch (5 jǔ) for the eave span, then about 6½ or 7, 7½, and 9 tenths for the span below the ridge.
rise of span k = run × (0.5, 0.65, 0.75, 0.9) for four spans
From the intermediate bracket set of the second bay the rafter ends advance progressively outward, so that at the corner the eave projects further (by 4 cun for a hall of one bay, 5 for three bays, 7 for five bays) and rises with the corner beam.
With the palace at the centre facing south, place the ancestral temple on its left (east) and the altar of soil and grain on its right (west); put the court in front and the market behind, each one fu (a hundred paces) square.
Project the eaves from the centre of the eave purlin by 3½ chi for rafters of 3 cun diameter and 4 to 4½ chi for rafters of 5 cun; beyond them add flying rafters projecting six-tenths as far again.
eave projection ≈ 3½–4½ chi · flying rafters = 0.6 × eave projection
Cite this page Chris Paton, “The roof declares the rank”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/roof-hierarchy. Text, drawings and models licensed under CC BY-NC 4.0.