Textile Structure
how cloth is put together
Concept

Fundamental domain — where it appears

The smallest region of a pattern that the symmetry group repeats to fill the plane. Its size divides the repeat's, so counting cloths rather than drawings is a division by the orbit and the domain is what is left after it.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

2/2 twill: written at 4×4, repeating on 4. On the left the draft as written, with the smallest rectangle that tiles it outlined. On the right the same draft with every translation that leaves it unchanged marked from the top left corner: there are 4 of them, so a fundamental domain holds 4 intersections rather than the 16 the rectangle claims and the 16 the point paper carries. Nothing in the drawing on the left says so.

What a repeat repeats

Point paper is ruled in squares, and the rectangle a draft is written on is a decision by whoever drew it. The unit a cloth actually has is smaller — two intersections for a plain weave, four for a 2/2 twill — and it is not a rectangle at all.

cloth · Repeat Plain weave, doubled. Plain weave, then the same weave with its picks grouped in 2, its ends grouped in 2, and both — which are a warp rib, a weft rib and a hopsack — and a 2/2 twill beside them for comparison. The rules under the drafts bracket the threads that lift together on every pick and so lie touching. Each doubling multiplies the cloth's own unit by 2: 2, then 4, then 8 intersections. The hopsack and the twill interlace equally often and are drawn from different rules. The setts under each draft are the densest that weave may be set at with a 0.25 mm yarn, and a rib's two are 0.750 apart where every other weave here is square.

A cord is a stripe with no colour in it

Warp rib, weft rib and hopsack are plain weave with its threads doubled, in the warp, the weft, or both. Six of the nine measures this site takes off a matrix cannot tell a 2/2 hopsack from a 2/2 twill, and the three that can are not the ones a weaver quotes.

weaves · Rib weaves Grouping the two systems by different amounts. Plain weave with its ends grouped by one number and its picks by another, over a grid of both. The four weaves the trade names are the corners of this space — plain at one and one, a warp rib down the first column, a weft rib along the first row, a hopsack on the diagonal — and the interior is the oblong matt, which has a name and no literature. Every cell weaves on two shafts, so the harness cannot tell any of them apart; the fundamental domain is exactly 2ab, so the notation's cost is the product; and the longest float is the larger of the two groupings. The two densest setts move with the two groupings separately, so the sett ratio is one exactly on the diagonal and nowhere else — a 3×1 matt sets at 1.50 and its transpose at the reciprocal. What the grid cannot show is the cord: the diagonal has no directional relief at all and everything off it does, in the direction of the larger grouping.

The four named weaves are corners of a family

Plain, warp rib, weft rib and hopsack are one construction with two knobs, and the trade turns both together or neither. Group the ends by two and the picks by three and the result is an ordinary cloth with a name, no literature and a fundamental domain of twelve intersections on two shafts — and the family's three quantities all have closed forms: two shafts everywhere, a unit of exactly 2ab, and a longest float of the larger grouping.

weaves · Rib weaves 4 drops of 250 cm cut from one roll of a 64 cm repeat, three ways. 4 matched drops of 250 cm cut one after another from one roll of a cloth with a 64 cm repeat, drawn along the roll at its own scale, with the cloth lost between drops shaded and its length written below. A straight match has one place in the repeat where every drop must start, ticked above the roll, so each gap is 6 cm and 18 cm is lost. A half-drop's alternate widths start half a repeat lower, ticked below. Cut in the order the widths hang, A B A B, every gap goes from one class to the other and costs 38 cm, 114 cm in all; cut A A B B, the like gaps cost 6 cm and the job loses 50 cm. What the strip cannot show is the pattern itself, which is the same cloth in every row.

A half-drop wastes less, cut in the right order

A straight match has one place in the repeat where every drop may start, so a cutting room loses half a repeat between drops on average and a whole one at worst, in any order. A half-drop has two, because alternate widths start half a repeat lower — and that gives the cutter a choice the straight match never offers. Cut in the order the widths hang, a half-drop loses exactly what a straight match loses. Cut with like drops together when the remainder favours it and alternated when it does not, four drops of a pair of curtains lose a third less, and a long run half as much: (r/4)·n/(n − 1) a gap, against r/2. The rule needs one subtraction before the first cut.

cloth · Repeat

Named alongside it

The objects these essays reach for when they reach for this one.

FloatHopsackPlain weaveRepeatSettShaftsThread groupWarp ribWeft ribBurnsideCensusCutting

All concepts