Textile Structure
how cloth is put together
Concept

Greatest common divisor — where it appears

The largest number dividing two others, which turns up wherever two periodic things in a cloth have to be asked whether they come into step. Where it is one the two things never come into step and the beat runs the whole repeat; where it is large the pattern closes early.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

What a second guide bar buys. Independent fabrics left by each lapping across 12 wales, counted by walking the wale graph and checked against the greatest common divisor of the shogs with the width. A bar that leaves more than one is not making cloth; a second bar can put right what the first could not.

What a second guide bar is for

One warp-knit bar leaves the wales in as many independent fabrics as its shog shares factors with the width. Two bars leave the greatest common divisor of both — so a pair of shogs that each fail alone can succeed together, and a pair that share a factor cannot.

knits · Warp knit Which dentings leave a mark. Every combination of ends per dent and weave repeat, with how many ends the grouping takes to come back into step. A small number means the reed treats every repeat the same way and the grouping shows as a stripe at the dent pitch; a large one means the grouping walks across the weave and there is nothing periodic for the eye to find. The rule is one word: dent so the two share no factor.

The reed leaves its own mark

A reed does not space a warp evenly. It groups it, several ends to a dent, and the grouping beats against the weave repeat — so a denting that shares a factor with the repeat treats every repeat identically and shows as a stripe, and one that does not is invisible.

pattern · Moire A colour order against a 2/2 twill. The visible face of a 2/2 twill under 2 colour orders, drawn at the repeat the divisor arithmetic allows and outlined at the repeat the surface has. A filled cell is a dark thread on the face, which is the warp's colour where the warp is up and the weft's where it is not — so none of these patterns is in the draft, and the draft is the same in all of them. The colour period and the weave repeat beat exactly as a reed's grouping beats against a weave: the surface repeats on the least common multiple of the two, which here is 8×8 and 4×4. What the panels cannot show is colour: the two threads are drawn as filled and empty, and two colours of similar value make a pattern far weaker than this.

A colour order beats the weave it is threaded on

The reed's grouping beats against the weave repeat and the arithmetic is a least common multiple. A colour order is a second grouping of the same warp and the arithmetic is identical — but where the reed's beat is a fault to be dented out of a cloth, the colour order's beat is the pattern the cloth is sold for. Across 472 colour orders on four weaves the divisor bound is the surface's exact repeat in 470 or more, and the handful that beat it have no pattern left at all.

pattern · Moire

Named alongside it

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

BeatCoprimeDentingPeriodReedRepeatColour-and-weaveConnectivityCoverLappingMoirePlane pattern

All concepts