Introduction
Historical Remarks
Muqarnas is the Arabic word for stalactite vault, an
architectural ornament developed
around the middle of the tenth century in north eastern Iran and almost
simultaneously, but apparently independently, in central North Africa.
Two points about these new forms are of importance. One is that, from the late
eleventh century on, all Muslim lands adopted and developed the muqarnas,
which became almost as common a feature of an elevation as the Corinthian
capital was in Antiquity. The second and far more important point is that,
from the moment of its first appearance, the muqarnas acquired four
characteristic attributes, whose evolution and characteristics form its
history: it was threedimensional and therefore provided volume wherever it
was used, the nature and depth of the volume being left to the discretion
of the maker; it could be used both as an architectonic form, because of
its relationship to vaults, and as an applied ornament, because its depth
could be controlled; it had no intrinsic limits, since not one of its
elements is a finite unit of composition and there is no logical or
mathematical limitation to the scale of any one composition; and it was
a threedimensional unit which could be resolved into a twodimensional outline.
The fifteenth century Timurid mathematician Ghiyath alDin Mas'ud alKashi
(~1380  1429) defines the muqarnas
in his practical way as: "The muqarnas is a ceiling like a staircase with
facets and a flat roof. Every facet intersects the adjacent
one at either a right angle, or half a right angle, or their sum, or another
combination of these two. The two facets can be thought of as standing on a
plane parallel to the horizon. Above them is built either a flat surface, not
parallel to the horizon, or two surfaces, either flat or curved, that
constitute their roof. Both facets together with their roof are called one
cell. Adjacent cells, which have their bases on one and the same surface
parallel to the horizon, are called one tier." [1]. In addition there
are intermediate elements which connect the roofs of adjacent cells.
(For a more detailed explanation, see the example in the following chapter.)
AlKashi distinguishes four types of muqarnas: The Simple Muqarnas and
the Clayplastered Muqarnas, both with plane facets and roofs, as well
as the Curved Muqarnas, or Arch, and the Shirazi,
in which the roofs of the cells and the intermediate elements are curved.
The plane projection of a simple element (either cell or intermediate element)
is a basic
geometrical form , namely a
square, halfsquare (cut along the diagonal), rhombus, halfrhombus
(isosceles triangle with the shorter diagonal of the rhombus as base),
almond (deltoid), jug (quarter octagon), and large biped (complement to a jug),
and small biped (complement to an almond). Rectangles also occur.
The elements are constructed according to the same unit of measure, so they
fit together in a wide variety of combinations.
AlKashi uses in his computation
the module of the muqarnas, defined as the base of the largest
facet (the side of the square) as a basis for all proportions.
The muqarnas is used in large domes, in smaller cupola, in niches, on
arches, and as an almost flat decorative frieze. In each instance the
module as well as the depth of the composition is different and adapts to
the size of the area involved or to the required purpose. The muqarnas is
at the same time a linear system and an organization of masses.
There is a relatively unbroken tradition of architectural practice in the
Islamic culture. From the Ilkhanid period until
today, 700 years later, the elements mentioned above did not change, but at the
same time more elaborate muqarnas were constructed in which we find elements
like five, six, or sevenpointed stars.
Here is a link to the website with a great survey on plans of Muqarnas, ordered
by there geographic and historic relations:
www.tamabi.ac.jp/idd/shiro/muqarnas/
In this
detailed picture of a
muqarnas at Bastam
(an Ilkhanid shrine situated midway between Tehran and Mashad) you see a
few cells and the
correlating plan. These
cells consist of two facets, or vertical sides, with their curved roof.
In general a roof can be
a flat surface, not parallel to the horizon, or two joint surfaces, either flat or
curved. The roofs of two adjacent cells can be connected by intermediate
elements consisting of one surface, or two joint surfaces. A row of cells,
with their bases on the same surface parallel to the horizon, is called a tier.
On the lower tier we see from right to left (in the plan: beginning at the upper
right corner of the nonshaded area): an intermediate element based
on a small biped, a cell based on a rhombus, then two broken intermediate
elements, a cell based on a quarter octagon, an intermediate element based on
a small biped, a cell based on a quarter octagon, again an intermediate element
based on a small biped and a cell, with only the right facet visible, based on
a quarter octagon. On the tier above: a cell based on an almond, a cell based
on a quarter octagon, three cells based on an almond with a fourth one being
barely visible.
