Textile Structure
how cloth is put together
Concept

Colour-and-weave — where it appears

A coloured warp and weft threaded into a weave, giving surface patterns the interlacement never hints at. Two very different drafts can give the same coloured surface, so the pattern a reader sees is not a faithful record of the cloth beneath it.

Named by 11 essays across one field — each of them below, with the objects they name alongside it.

Colour and weave — 2/2 twill. One interlacement, threaded in two colour orders. What a reader sees is the colour of whichever thread is on the face, so the visible pattern can be something the draft gives no hint of.

Colour and weave

Thread the same weave with a different order of coloured ends and a pattern appears that is nowhere in the draft. Houndstooth is an ordinary two-and-two twill, and nothing about its interlacement is unusual at all.

pattern · Pattern Three different weaves, one cloth. Drafts drawn from one collision class, with the blind intersections marked, and the single surface all of them produce. Where the two crossing threads are the same colour the weave leaves no trace, so the cloth cannot report what it is.

Colour and weave as a two-colour problem

Where the two threads crossing are the same colour, the intersection looks identical whichever is on top. Half of them are, so 22,874 drafts collapse onto 256 surfaces — eighty-nine weaves apiece, and no way to tell them apart.

pattern · Pattern A tartan sett in 2/2 twill. A pivoted sett of 70 threads used in both systems, which is what makes a tartan a tartan rather than a check. On the left, the cloth at block scale: the squares on the diagonal have one colour in both systems and the rest are mixtures. On the right, one mixture rectangle at thread scale, where the weave decides. In 2/2 twill the reflection survives on 50.0 per cent of a mixture's intersections, against a ceiling of 75 per cent that no weave can reach. The three tints stand for the three colours of the sett and carry no other meaning here.

A check is two stripes and a tartan is one

A tartan is quoted as one sett of thread counts because the warp and the weft carry the same order. That is said to make it symmetric about its diagonal, and the arithmetic says it cannot be — the ceiling is three quarters, and a 2/2 twill reaches one half.

pattern · Stripe 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 Two weft colour orders thrown on a loom with boxes at one side. Weft colour orders thrown pick by pick on a shuttle loom that picks alternately from the two sides. For an order with runs of four, two, two and four, every throw finds a shuttle of its colour on the side it leaves from, so the order can be woven. For an order with runs of three and three, pick 4 has to be thrown from the right in a colour whose shuttle is on the other side, and the order cannot be woven. On a loom with boxes at one side the box opposite holds only the shuttle just thrown, which the next pick must throw straight back, so colour can change only between pairs of picks. What the drawing cannot show is the mechanism that drops the boxes, which decides how fast a change can be made but not which changes are possible.

A weft stripe is counted in pairs of picks

A warp's colour order is laid out once at warping and the loom never has to think about it. A weft's is thrown, one pick at a time, by shuttles that cross the cloth and stay where they land. On a loom with boxes at one side that makes every coloured band an even number of picks; with boxes at both sides it admits odd bands and pays for them in shuttles; and a tartan, which uses one order in both directions, is designed for its weft whether its designer knew it or not.

pattern · Stripe A warp pinstripe in a 2/2 twill, 1, 2, 3 threads wide. A light stripe of ends in a dark 2/2 twill, drawn as the face a reader sees at 1, 2, 3 threads wide over 3 repeats. A single stripe thread is on the face at 50% of the crossings and goes under for up to 2 at a time, so it draws a broken line. Adjacent threads of the same colour cover one another's gaps, and the line becomes unbroken at 3 — the fewest neighbours for which, at every crossing, at least one is on the face — though an unbroken line is not a solid one, and beneath each panel is how much of its width is light, which varies along it until the line is a whole repeat wide. What the drawing cannot show is distance: a broken line whose gaps are a fraction of a millimetre reads as a fainter unbroken one from arm's length, and how far that is depends on the sett and on the eye.

No weave draws an unbroken line one thread wide

A pinstripe is drawn on point paper as a single coloured column, and in cloth a single end is on the face only where it is up — so in every weave that interlaces, a line one thread wide has gaps in it. Neighbours of the same colour fill each other's gaps, and the fewest that leave no gap is a property of the weave: two in a plain weave, three in a 2/2 twill, and in a warp-faced sateen two across the warp and eight across the weft. Unbroken is not solid either — an eight-pick bar in that sateen has no gap and is an eighth light.

pattern · Stripe The named colour-and-weave effects, sorted by the loom their weft needs. Each named colour-and-weave effect with the shortest band in its colour order and the cheapest loom that can throw that order in the weft, on a loom with 4 boxes a side. end-and-end, runs of 1 and 1, needs picking at will; hairline, runs of 1 and 1, needs picking at will; log cabin, runs of 1 and 1, needs picking at will; tattersall, runs of 1 and 9, needs picking at will; birdseye, runs of 2 and 2, needs boxes at one side; crow's foot, runs of 2 and 2, needs boxes at one side; step pattern, runs of 2 and 1, needs boxes at both sides; three-and-one, runs of 3 and 1, needs picking at will; houndstooth, runs of 4 and 4, needs boxes at one side; shepherd's check, runs of 6 and 6, needs boxes at one side; gun club, runs of 4 and 4 and 4 and 4, needs boxes at one side; glen check, runs of 4 and 4 and 4 and 4 and 2 and 2 and 2 and 2, needs boxes at one side. The warp costs nothing, because a colour order in the warp is laid out once at warping; the weft is thrown one pick at a time by shuttles that stay where they land, so an effect's price is its weft order alone. What the bars cannot show is the pattern, which is in neither the order nor the weave but in what they make of each other.

The finest colour-and-weave effects need the rarest loom

A houndstooth, a shepherd's check and a gun club check are thrown by the cheapest shuttle loom there is. A hairline, an end-and-end and a log cabin are thrown by none — a colour on every other pick is thrown from the same side every time, so its shuttles pile up at the far end of the loom and never come back. The dividing line is the parity of the bands and nothing else, which is why it survives the fact that no two sources agree about how wide a shepherd's check is.

pattern · Stripe A 2/2 twill with warp 1/1 and weft 2/2, as drawn and woven across. A 2/2 twill coloured 1/1 in the warp and 2/2 in the weft, drawn as the face of the cloth, and the same cloth turned through a right angle, which is what the loom makes if the two colour orders are exchanged and the weave turned with them. As drawn the weft order is 2/2 and needs boxes at one side; woven across the weft order is 1/1 and needs a loom picking at will. What the drawings cannot show is whether the cloth's two systems can be exchanged, which depends on their yarns and setts.

A colour-and-weave look costs its cheaper order

The finest colour-and-weave effects need the rarest loom because a weft order is thrown pick by pick and a warp order is laid out once, so an effect's price was said to be its weft. That is true of a construction and false of a cloth. The same cloth can be woven lying across the loom, with its warp order thrown as weft and its weft order laid in the warp, and then it costs the other order. Over every two-colour look twelve small weaves make with orders up to six threads — 4,036 of them — 55 per cent need a loom picking at will as drawn and 31 per cent need one either way round. The looks turning rescues are the ones fine in one direction only, and not one of the trade's named effects is among them.

pattern · Stripe What a pair of colour orders does to the catalogue. Dark ends in the warp across against dark ends in the weft down, for the sixteen two-colour orders at four ends. Each cell gives the blind intersections of sixteen and the number of distinct surfaces the 22874 drafts collapse onto. Every cell stands for between one and thirty-six colour orders and they all behave identically, so the arrangement of the colours does not matter and only their counts do. The corner at four against nought is blind nowhere and separates every draft.

The colour order that hides least

A caption on this account's top essay left a question: whether a warp of long runs against a weft of short ones hides less than either would against itself, and called it a lever nobody uses. Sweeping all sixteen orders against all sixteen says the lever is real and the caption named the wrong variable. Run length has nothing to do with it — the blind count, the separation and the largest confused class all depend on the two orders' colour counts and on nothing else, and what a mixed pair saves is exactly the square of the difference between them.

pattern · Pattern Every way to make 4 intersections blind. The number of distinct surfaces the 22874 four-by-four drafts collapse onto, for every shape a set of 4 blind intersections can take, in however many colours it needs. 1×1 + 1×1 + 1×1 + 1×1: 3,632 surfaces, touching 8 threads, 4 colours needed; 1×1 + 1×1 + 1×2: 3,352 surfaces, touching 7 threads, 4 colours needed; 1×2 + 1×2: 3,102 surfaces, touching 6 threads, 3 colours needed; 1×2 + 2×1: 3,100 surfaces, touching 6 threads, 4 colours needed; 1×1 + 1×3: 3,038 surfaces, touching 6 threads, 3 colours needed; 1×4: 2,744 surfaces, touching 5 threads, 2 colours needed; 2×2: 2,402 surfaces, touching 4 threads, 3 colours needed. The same number of blind intersections keeps more of the catalogue apart the more threads it is spread over. What the chart cannot show is whether an eye can tell the surfaces apart.

A blind set hides less the thinner it is spread

Two colours showed that where a cloth's threads match in colour the draft underneath is invisible, and that how many intersections match is not what decides how much is hidden. More colours say what does. A third colour lets the blind count take every value from nought to ten; a fourth lets the blind intersections sit one to a thread. At a fixed count, the catalogue keeps more of its cloths apart the more threads the blind set is spread across — 3,632 surfaces for four scattered blind cells, 2,402 for the same four in a square.

pattern · Pattern The advantage of spreading a blind set, against the repeat. The number of distinct surfaces a blind set keeps when its cells are spread one to a thread, over the number it keeps when they are gathered into a block, against the size of the repeat: 4 blind, 1.512 at 4, 1.254 at 5, 1.129 at 6, 1.064 at 7, 1.032 at 8, 1.008 at 10, 1.002 at 12; 8 blind, 1.080 at 8, 1.020 at 10, 1.005 at 12. Sampled from forty thousand surfaces at each point. The dashed curves are the closed form — each thread the set misses must interlace on its own, which fails once in 2^(n−1) — and the sampled points sit on them from six threads up; at four and five the form overstates, because a thread the set does touch can still fail there. At four by four spreading keeps half as much again; at eight, a few per cent; at twelve, nothing to speak of. What the chart cannot show is whether an eye can tell the surfaces apart.

A blind cell costs half the cloths at any real repeat

At four by four, spreading a blind set over more threads kept half as many cloths apart again as gathering it. At eight by eight the same rule holds, and it is almost nothing: three per cent for four blind cells, eight for eight. The reason is one factor. A blind set's surfaces are the count's bound, 2^(n² − b), times the chance that every thread it misses interlaces on its own, and at eight threads a thread lies all on one face once in 128 tries. So shapes that touch the same number of threads tie exactly, whatever their rectangles; every blind cell costs very nearly half the catalogue; and by twelve threads the arrangement is free.

pattern · Pattern

Named alongside it

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

Colour orderCensusBlind intersectionCheckStripeTartanFaceAppearanceCollisionEnumerationHoundstoothPivoted sett

All concepts