Rules · Vaults · Ornament · Structure
Fill a half-dome, squinch or cornice with tiers of small concave cells, each tier corbelled forward from the one below and each cell set over the junction of two cells beneath.
height = tiers × module; each tier projects inward
Muqarnas appear almost simultaneously in the eleventh century in north-eastern Iran, Iraq and North Africa, perhaps developed from the squinch, the small arch across the corner of a square room that carries a dome. Multiply the squinch into a honeycomb of little niches and you have a surface that turns a corner, fills a vault or crowns a portal with a play of light and shadow that seems to dissolve the masonry.
Some muqarnas are structural, corbelled in brick or stone; many, especially later, are a hanging skin of plaster or wood beneath a real vault. Either way the design is systematic: a small set of cell shapes, a constant module of height, and a rule that each tier steps forward over the joints of the tier below.
To set a round dome on a square bay, imagine a sphere passing through the four corners of the square; cut it by the four vertical planes of the sides and by the horizontal plane of their crowns. The four spherical triangles left in the corners are the pendentives; the circle at their top carries the dome.
sphere radius R = S⁄√2; arches = sphere ∩ side planes (radius S⁄2); ring at h₀ + S⁄2 with radius S⁄2
Pierce the base of the dome with a close ring of windows between buttressing ribs, so that the shell seems to float on light rather than to rest on the arches.
Hagia Sophia: 40 windows and 40 ribs; dome ≈ 31 m across, crown 55.6 m above the floor
To turn a domed square into a long church, open two of its great arches into semidomes of the same radius, and open the semidomes in turn into smaller exedrae, so that the space expands by stages from the central dome.
Hagia Sophia: central square 31 m; two semidomes of radius ≈ 15.5 m; four exedrae; interior ≈ 31 × 70 m
Make the prayer hall of identical bays of columns and arcades, so that it can be enlarged by adding aisles or bays without changing its character.
hall = n aisles × m bays of one module
Where the available columns are too short for the height you want, stand a pier on each column and carry the roof on a second, upper tier of arches, bracing the piers with a lower tier of horseshoe arches.
height ≈ column + pier + upper arch; lower arch = brace
Alternate voussoirs of two colours (red brick and pale stone, or black and white stone) to make the structure of the arch legible as ornament.
Cite this page Chris Paton, “Muqarnas: a vault of small niches”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/muqarnas-tiers. Text, drawings and models licensed under CC BY-NC 4.0.