Andalusi woodwork: lazo, artesonado, taracea.

In al-Andalus and the Mudejar Spain that followed it, the geometry went into timber. The interlaced ribs of a lazo ceiling, the sunken coffers of an artesonado, the inlaid seal of a taracea door, the turned lattice of a celosia: four vocabularies, one construction, and a guild of carpenters who wrote the geometry down as a set of set squares.

Andalusi woodwork is the carpentry of Islamic Spain and of the Mudejar craftsmen who carried its methods on under Christian rule, and its subject, more than any other decorative tradition in the peninsula, is geometry. Where the tile-cutters of Granada and Fez worked the star patterns in glazed clay, the carpinteros worked them in pine, walnut and cedar: as the interlaced ribs of a ceiling, as the coffers between those ribs, as inlay on a door or a minbar, and as the turned bars of a screen. The vocabulary is Spanish because the craft outlived the caliphate by three centuries, and it is worth learning, because each word names a different way of making the same construction.

Lazo: the interlace

Lazo, "the knot", is the Spanish name for the star-polygon interlace itself, and the carpenters classified it by its symmetry: lazo de ocho, de diez, de doce, the eight-, ten- and twelve-fold families, the same three the studio derives. In a ceiling the lazo is not painted on but built: the pattern lines are the cintas, wooden ribs applied to or worked into the boards and rafters, which cross one another over and under, and the stars where the ribs converge are the sinos, often dropped as pendant bosses. A wheel of interlace around a central star is a rueda. The structural roof that carries all this, the paired rafters and collar-beams of the Mudejar tradition, is the armadura, and a lazo ceiling is properly an armadura de lazo: the geometry and the structure are one object.

The finest surviving example is the ceiling of the Hall of Ambassadors in the Comares Palace of the Alhambra, a fourteenth-century Nasrid work of many thousands of pieces in which a lazo of stars rises in stepped tiers to a central cupola, read since the nineteenth century as the seven heavens of the Qur'anic cosmos. Mudejar Toledo, Seville, Zaragoza and Teruel are full of lesser ceilings built the same way, and the Salón de Embajadores in the Alcázar of Seville has a lazo dome of 1427 to stand beside the Nasrid one.

Artesonado: the coffers

Artesonado names a coffered ceiling, from artésón, a trough: a ceiling of sunken compartments framed by ribs. The word is now used loosely for any Mudejar ceiling, but strictly it names the ones in which the geometry is not the interlace but the field it leaves behind. The star-and-cross at depth one, the fusion where the motif closes into a solid tessellation with no ground, is exactly an artesonado seen from below: every face of the pattern is a coffer, every line a rib, and there is nothing that is not one or the other. A flat ceiling of this kind, on beams rather than rafters, is an alfarje.

Taracea: the inlay

Taracea, from the Arabic tarsi', is marquetry: a surface veneered with small pieces of contrasting wood, bone, ivory and sometimes metal, cut to the faces of a geometric pattern and glued down edge to edge. The tradition was practised in Nasrid Granada on doors, minbars, chests and the small caskets that were exported across Europe, and it continued in the city as a craft industry into modern times. In taracea the polychrome logic of zellige is followed literally: each congruence class of face takes its own material, walnut for one, boxwood for another, bone for a third, with the strapwork line cut as a thread of ebony between them. The studio's class-by-class colouring is the same rule, and a taracea panel is what a pattern looks like when the rule is obeyed with a saw.

Celosia: the turned lattice

A celosía is a lattice screen, the Iberian cousin of the Egyptian mashrabiya and the Indian jaali, built not by piercing a slab but by joining turned wooden spindles and small blocks into an open net. Its geometry is the simplest in the family, usually the six-fold hexagram or a square grid, because a turned lattice can only follow lines that a lathe can make. It is also the most functional: a celosia lets a room see out without being seen into, and lets the air move on a Seville afternoon. Drawn as line only, the hexagram field is a celosia's cutting list.

The set squares

The clearest evidence that this geometry was understood rather than copied is a book. In 1633 the Seville master carpenter Diego López de Arenas published his Breve compendio de la carpintería de lo blanco, a treatise on "white carpentry", the structural and geometric joinery of the armadura, and in it he set down the guild's method for laying out lazo. Its instrument is the cartabón, a set square, and the carpenters kept a family of them named for the division of the circle each carried: the cartabón de ocho, whose acute angle is an eighth of a half-turn, for eight-fold work; de cinco and de diez for ten-fold; de doce for twelve-fold. A carpenter laying out a lazo de ocho set his ribs with the eight square, and every angle in the ceiling followed from it.

The angle of the cartabón de ocho is 22.5 degrees, and its tangent is √2 − 1, the eight-fold star depth the studio derives from the khatam's own chords. The guild had the number without the algebra: it was the shape of a tool in the workshop, and the tool was cut to the geometry. That is the whole of this studio's claim about the tradition, in a piece of seventeenth-century oak.

In the studio

The Andalusi Woodwork Series in the studio's social plates renders the timber register from the engine: the marquetry seal, a coffered depth-one field, the ten-fold lazo, a carved boxwood rosette, the twelve-fold lazo wheel and the hexagram celosia as line only, a panelled wainscot and a two-level marquetry panel. The constructions are the ones this journal derives everywhere else; the colour sets are walnut, honey, boxwood and bone. Derived, not generated.