Muqarnas — the vault from its plan
This page is a scroll-driven three-dimensional piece. As you scroll, a
medieval vault design is drawn, solved, and raised before the camera; this
section carries its full narration in reading order.
A muqarnas — Arabic muqarnaṣ — is the stalactite vault of Islamic
architecture: tiers of small carved cells, ring upon ring, that turn a
dome's underside into stepped concavities of light. By the eleventh century
it crowned portals and domes from Samarkand to Córdoba. In the fifteenth,
the astronomer al-Kāshī wrote down the masons' method — one module, one
curve, one table of measures. This site raises a vault his way, from a
single thirteenth-century drawing.
I — the square and the circle. A square room, a round dome: they do not
meet, and whatever the dome stands on, the corners are left over. The zone
of transition is the gap between the room a builder can make and the dome a
builder wants; everything that follows is its answer.
II — the module. One measure runs through everything: the miqyās, the base
of the largest facet; a cell stands exactly two of it tall. The masons'
recipe as al-Kāshī wrote it: strike an oblique at thirty degrees, divide it
in five, fold two fifths onto the vertical — a facet, one sixth of a
circle, a ramp, nothing else. The taʿdīl coefficient, 1;43,33,48,40 in
sexagesimal, turns a cell's facet-bases into its surface; the manuscript
tables 1;43,33,45,41, the difference entering through al-Kāshī's facet
height, isolated by Dold-Samplonius five centuries later. Two profiles face
to face make the niche every cell is cast from.
III — the alphabet. Two seeds, the square and the forty-five-degree
rhombus; their divisions and remainders give eight letters — halves, the
jug, the almond, two bipeds. Cells wear roofs; bipeds only connect. The
full drawing spells the sky with 632 letters yet uses only four of the
eight kinds.
IV — the plan. The master rules frame, seams, and diagonals, and writes one
quarter from a corner in toward the crown — 157 letters in this
digitisation's count. Symmetry turns it four times, four diamonds stitch
the seams, and the word is whole: 632.
V — the lift. This is not a rosette; it is a building seen from above. The
first tier stands, two cells to a corner — the family Harb proposed for the
plate, and the one this site raises.
VI — tier on tier. Each ring stands on the roofs of the ring below; nothing
floats, or the whole reading is refused. The crown closes to a ring, not a
point. Stand beneath it: everything the drawing knew is over your head.
VII — the same plan, twice. A vault stands: one reading, seventeen tiers to
the crown ring. It descends into its plan; the plan holds; it rises again,
differently — same projection, different building, both correct. The
drawing does not determine the building, and the master's knowledge was
never fully in the plan.
VIII — the day. Nothing moves except the sun. Each cell is a cup set at its
own angle; as the light walks the horizon every cup fills and empties in
its own time, and when the sun returns to where it began, nothing has
looked the same twice.
IX — the return. The ember hour: ring gives back ring, down through the
tiers, into the plan, into the module, into the point it was struck from.
Everything here grew out of this, and goes back into it. Good night.
After the return, a separate free-look viewer presents the completed
reconstruction as an object rather than another scroll scene. Activate
the viewer, then drag to turn the vault from any side and from beneath;
pinch or ctrl-scroll zooms, a slider walks the low light around the
horizon, and a close control returns to the page. A fuller scholarly
account, with sources, is on the about page.
Muqarnas
muqarnas (مقرنص) — the honeycomb
vaulting of Islamic architecture: tiers of small carved cells, corbelled ring
over ring, that turn a dome's underside into stepped pockets of light.
By the eleventh century it crowned portals and domes from Samarkand to Córdoba.
In the fifteenth, the astronomer al-Kāshī wrote down the masons' method — one
module, one curve, one table of measures. This site raises a vault his way, from
a single drawing, before your eyes.
I — the square and the circle
A square room. A round dome.
I
They do not meet. Whatever the dome stands on, the corners are left over.
I
The zone of transition — the gap between the room a builder can make and the
dome a builder wants. Everything that follows is its answer.
II — the module
One measure runs through everything that follows: the miqyās, the base of the
largest facet. A cell stands exactly two of it tall.
II
The masons' recipe, as al-Kāshī wrote it down: strike an oblique at thirty
degrees, divide it in five, fold two fifths onto the vertical. A facet, one sixth
of a circle, a ramp — nothing else.
II
0;00,00,00,00
The taʿdīl: multiply a cell's facet-bases by this length and you have its
surface — the facet counts whole, the tapering roof counts half. The manuscript
tables 1;43,33,45,41; the difference enters through al-Kāshī's facet height,
isolated by Dold-Samplonius five centuries later.
II
Two of them, face to face: the niche every cell is cast from. The whole
alphabet wears this one curve.
III — the alphabet
Two seeds, one rib: the square, and the rhombus of its half-turn — forty-five
degrees and its complement. Everything else is a division or a remainder.
III
Bisect each seed for its halves. Cut a quarter octagon from the square's corner:
the jug, and the large biped it leaves behind. Drop perpendiculars inside the
rhombus: the almond, and the small biped around it.
III
Eight letters. Six know their apex — the marked corner, its two module sides
the curved ones, where the profile rises. The seeds decide theirs only when
placed. Cells wear roofs; bipeds only connect.
III
Letters into words: the plate's own corner, where the readings this site
raises begin. The
full drawing spells the sky with 632 letters, yet
uses only four of the eight: 248 squares,
360 rhombi, 16 half-rhombi,
and 8 jugs paired on the diagonals. No almond, no
biped — a word never needs the whole alphabet. That word is next.
IV — the plan
The drawing board again, and the same square field. The master rules the frame,
the seams, and the diagonals — and begins in a corner.
IV
One quarter is enough to draw: 157 letters, written
from the corner in toward the crown — the same order the vault will be built in,
because the outermost ring is the lowest tier.
IV
Symmetry does the rest, a right angle at a time. This is the medium's own
economy: the Takht-i Sulaymān plate records only a quarter — the turning was
understood.
IV
Four diamonds stitch the seams no quarter can hold, and the word is whole:
632 letters. Now it stops being a drawing.
IV → V
This is not a rosette. It is a building, seen from above.
V — the lift
The first tier stands. This reading begins in the corners, two cells to a
corner — the family Harb proposed for the plate, and the one this site raises.
VI — tier on tier
Each ring stands on the roofs of the ring below. Nothing floats: a cell must
land where the tier beneath will carry it, or the whole reading is refused.
VI
Halfway up, the geometry begins doing what it is for: the cells cup the low
light, and the vault carves itself into shadow and blade.
VI
The crown closes to a ring, not a point — the plan was an annulus all along,
17 tiers to its rim. Stand beneath it: everything the
drawing knew is over your head.
VII — the same plan, twice
A vault stands: one reading of the drawing, seventeen tiers to the crown ring.
VII
The vault returns to its plan. The plan holds.
VII
It rises again — differently. Same projection, different building, both correct.
The drawing does not determine the building, and the master's knowledge was never
fully in the plan.
VIII — the day
Nothing will move now except the sun. Watch what the geometry was for.
VIII
Each cell is a cup set at its own angle. As the key walks the horizon, every
cup fills and empties in its own time — the same plaster, read differently by
the hour.
VIII
The sun comes back to where it began. It was the only thing that moved, and
nothing looked the same twice.
IX — the return
The ember hour. Ring gives back ring, the way it was raised.
IX
Down through the tiers, into the plan. The day lowers to ember, and the ink
rises back through the warm plaster — the drawing was under the building all
along.
IX
Into the module. Into the point it was struck from. Everything here grew out
of this, and goes back into it. Good night.
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