Combine a hipped lower roof with a gabled upper roof, the triangular gable set back from the end of the building; count one main ridge, four gable ridges and four hip ridges: nine in all.
The Song called the form jiuji dian, the nine-ridged hall; later Chinese builders called it xieshan, the Japanese irimoya and the Koreans paljak. It is the favourite roof of East Asia because it combines the protection of a hip, which throws water off all four sides, with the ventilation and light of a gable, and because the gable, filled with a carved or painted board, gives the silhouette a crown. In the Song and later the gable was set in from the end column line (shoushan) to adjust the proportions of the upper roof.
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.
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
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 hip-and-gable: nine ridges”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/xieshan-nine-ridges. Text, drawings and models licensed under CC BY-NC 4.0.