A skew steps at every seam and a bow at none

Every account of matching a pattern so far has taken the pattern’s rows to be square to the cloth. A repeat has to fit the width between the selvedges and fit the panel along the length; two lots drift apart down a drop because their repeats are different lengths. In each of them a row of motifs ran straight across the width, at right angles to the selvedge, and the only question was where along the length it fell.

A finished cloth’s weft rarely does that. The temples on a loom grip the cloth at its edges, and the middle of the cloth is held only by its own stiffness, so the weft comes off curved; a stenter pulls one selvedge a little ahead of the other, and the weft comes off slanted. A straightener in finishing exists to take both out, and neither ever comes out entirely. On a plain cloth nobody can see where a weft row goes. On a woven pattern every weft row is a pattern row, and the two errors are the most visible things about it.

They are not two sizes of one error. One of them breaks every seam and the other matches at every seam without help, and the difference is one fact about where each moves a row.

Two ways a weft row stops being square #

A skew is a weft row that runs straight but slants: it is lower at one selvedge than at the other, by a fraction of the width. A 140-centimetre cloth skewed two per cent has every row 28 millimetres lower at one edge than at the other.

A bow is a weft row that curves: its two ends are level and its middle dips below the straight line between them, again by a fraction of the width. A 140-centimetre cloth bowed two per cent has every row 28 millimetres lower at its centre than at its edges.

Measured as a fraction of the width the two are the same size, and on a single width of cloth hung on its own they look like errors of the same order: a row 28 millimetres out somewhere. Put two widths side by side and they part company completely, because a seam between two widths joins them at their selvedges, and only one of the two errors moves a row at a selvedge.

A skew steps at every seam #

Hang three widths of a skewed cloth side by side, each cut so that its pattern starts at the same height — hung level, the way a heading is sewn. Every width’s rows start at its left selvedge at the same height and finish at its right selvedge 28 millimetres lower. At the seam, the next width’s rows start again at the top.

Every seam carries the whole step: 28 millimetres. It is the same at the top of the drop and at the hem, the same on the first seam and the last, and it does not depend on the size of the repeat, because it is a property of every row. A one per cent skew steps 14 millimetres and a half per cent 7.

A step across a seam is exactly what a pattern match is supposed to remove, and 28 millimetres is nine times the three-millimetre offset the lot essay took as reading matched. A skew of two per cent does not make a pattern slightly out; it makes every seam in the hanging visibly stepped.

A bow does not step at all #

Now hang three widths of a cloth bowed two per cent and skewed not at all.

Every row starts at its left selvedge at the top, dips 28 millimetres at the middle of the width, and comes back up to the top at its right selvedge. At the seam, the next width’s row starts at the top as well. The rows meet exactly, at every seam, with no matching done at all.

The error has not gone anywhere. It has moved from the seams to the middle of every width, where the rows scallop: a festoon of shallow arcs across the hanging, each 28 millimetres deep. But a scallop is the error a seam cannot show, because a seam only ever compares one row’s end with another row’s start, and a bow leaves every row’s ends where they belong.

Matching a skew turns its steps into a climb #

A hanger who sees the steps can take them out, and a skewed cloth is matched by dropping each width 28 millimetres below the one before it, so that its rows start where its neighbour’s rows ended.

Every seam now matches. The rows run across the whole hanging as unbroken lines — and each of those lines falls 28 millimetres in every width it crosses, so a hanging four widths wide has its pattern rows 112 millimetres lower at one end than at the other. The headings of the widths are staggered by the same amounts, or, if the widths are cut so their headings are level, the tops of the widths start at four different points in the pattern.

So matching a skew does not remove it. It converts a step at every seam into a climb across the whole hanging, and a climb is read against a different edge. A step is seen against the pattern on the other side of the seam; a climb is seen against the curtain pole, the ceiling, the sill and the hem, all of which are level.

One row across the whole hanging #

Follow one pattern row across four widths of a cloth skewed two per cent and bowed one, hung each way.

Hung level, the row is a saw-tooth: 28 millimetres down across each width, straight back up at the seam, with a 14-millimetre dip in the middle of every width from the bow. Matched, it is one straight line falling 112 millimetres across 5.6 metres, with the same dips. The bow is the same in both, because no hanging moves a row’s middle relative to its ends.

The climb has a property the steps do not. A matched hanging falls by the skew times its total width, which is the same whether the hanging is sewn from four widths of 140 centimetres or two of 280. Cutting a wide cloth into narrower widths makes each step smaller and adds more of them, and it leaves the matched climb exactly where it was. The skew is a slope, and a slope across 5.6 metres is 112 millimetres however the 5.6 metres are divided.

Turning a width over cancels a skew; turning it round does not #

A hanger has two ways to change a width without cutting it: turn it round, end for end, or turn it over, face to back. They do opposite things to the two errors, and one of them cures a skew outright.

Turning a width end for end keeps its skew. A row that falls from left to right, rotated half a turn in the plane of the cloth, still falls from left to right: its old right selvedge is now on the left and now at the top. The same half turn inverts a bow, so a dip becomes a hump. Turning alternate widths round therefore does nothing for the steps and changes a festoon into a wave — and it also turns a directional pattern upside down, which rules it out for most designs anyway.

Turning a width over reverses its skew. Face to back is a mirror image left to right, and a row that fell to the right now rises to the right, while a bow, being the same at both ends, is unchanged. Hang the widths level with every other one turned over, and each seam joins a row that has fallen 28 millimetres to one that starts 28 millimetres down and rises back — every seam matches exactly, with no width dropped at all.

The rows no longer fall across the hanging. They zigzag within one step, 28 millimetres down across one width and 28 back up across the next, and a four-width hanging’s ends are level. The skew has been turned into a chevron, and a chevron is read as a pattern where a fall is read as a fault.

The price is that alternate widths show their backs. A cloth whose back is the same as its face pays nothing. A woven figure usually pays everything, and a damask pays in a very particular way: a damask is its own complement, so its back shows the figure where the face shows the ground, and a damask hung with alternate widths turned over has its figure and ground trading places at every seam. The cure for its skew is exactly as visible as the skew.

A match needs a skew under a quarter of a per cent #

Turn the question round, as the lot essay did. If a step of three millimetres still reads as matched, how much skew can a cloth carry and still hang level with its seams matched?

The step is the skew times the width, so the tolerance divided by the width is the answer: 0.21 per cent for a 140-centimetre cloth, 0.25 for a 120, and 0.11 for a cloth 280 centimetres wide.

That is a small number against the distortions a straightener is working on, and it gets smaller as the cloth gets wider. A wide cloth is harder to match than a narrow one of the same skew, not because its pattern is any different but because its selvedges are further apart and a slope is multiplied by the distance.

The bow has no such number. It never steps at a seam, so there is no skew-like tolerance for it; the tolerance on a bow is how deep a scallop the eye forgives inside a width, which is a question about the pattern and the hem rather than about the seam.

Down a seam, a skew is constant and a lot difference grows #

A seam runs down the whole drop, and two errors can put an offset across it. The skew’s step is the same at every height. A lot difference — two widths woven with their warps held a little differently — grows from wherever the two were matched, at the rate their repeats differ.

For 140-centimetre widths skewed one per cent, the step is 14 millimetres from top to hem. Two lots a tenth of warp tension apart drift at 12.2 millimetres a metre, reaching 30.4 at a 250-centimetre hem. The drift overtakes the skew 115 centimetres down: above that the seam’s offset is mostly the finishing, below it mostly the weaving. At two per cent skew the crossover is 230 centimetres down, at the hem of a full-length curtain.

The two do not care which way the other runs. When they run the same way they add, and the seam is 44 millimetres out at the hem. When they run opposite ways they subtract, and something odd happens: the seam matches exactly at 115 centimetres and nowhere else, and a hanger who matched it there by eye has matched a skew against a lot difference and will find both at the ends.

A cutter cannot cut a skew out #

Every cutting room has a remedy for a slanting row, and it is worth seeing why the remedy moves the error rather than removing it.

A width can be cut across along a weft row — torn along a pick, or cut following the pattern — so that its heading follows the skew. Then the pattern is square to the heading and slanted to the selvedge: the width’s top edge falls 28 millimetres from one side to the other, and when the heading tape is sewn level across it, the width hangs rotated, its selvedges no longer vertical. Or the width can be cut square to its selvedges, and its rows fall across the heading instead.

There is no cut that squares a skewed pattern to both the selvedge and the heading, because the skew is the angle between them. A cutter chooses which of the two edges carries it. The only complete remedy is upstream, at the straightener, before the pattern has an angle to its edges at all.

A bow has its own version of the same trap. A heading cut along a bowed row is curved, so it cannot be sewn to a straight tape without either easing the middle in or letting the selvedges stand proud; cut straight, the heading crosses the rows, which dip below it by the bow at the centre of every width. The cutter again chooses where the error lives, and nothing at the cutting table makes it go away. What the bow does not do is spread: whichever edge it is given to, it stays inside its own width, because both of its ends are already level.

A printed pattern hides a skew in the drape #

A printed pattern is laid on the cloth after finishing, by a screen or a roller that runs square to the cloth’s edges. So a printed pattern on a skewed cloth is square to the selvedges while the weft beneath it is not: the seams match perfectly and the threads under them are skewed.

That does not make the skew harmless. It moves it out of the pattern and into the cloth’s behaviour: a width whose weft slants hangs with its threads off the vertical and horizontal, and a cloth pulled off its grain skews again as it shrinks and shears as it hangs. A woven pattern shows its skew at the seams on the day it is hung. A printed pattern shows it later, as a drop that twists or a hem that will not hang level after cleaning.

Rows, selvedges and one slope #

A pattern row across a width is taken as a straight line at the skew plus a parabola of the bow’s depth, zero at both selvedges and deepest at the centre. Widths hung level all start their rows at the same height; widths hung matched are each dropped by the skew’s step so that every row continues across every seam. The step at a seam is the height of one width’s row at its right selvedge less the next width’s at its left. The offset down a seam is the skew’s constant step with the lot drift from the relaxation model added or subtracted.

The step at every seam was confirmed to be the skew times the width exactly, for three widths, three skews and three bows; matched, every seam was confirmed to be continuous and each width to sit one step below its neighbour; a bow alone was confirmed to step at no seam and to dip by its depth at the centre; at a skew of the tolerance over the width the step was confirmed to equal the tolerance; and down the seam the lot drift was confirmed to overtake a one per cent skew’s step where the step divided by the drift’s rate says, a little over a metre down.

What the rows leave out #

The skew is uniform and the bow a parabola. A real cloth’s weft can be skewed more at one end of a piece than the other, bowed off-centre, or bowed into an S; each moves where its error shows, and none changes the rule that only what moves a row at a selvedge can step at a seam.

The widths come from one piece, in one orientation. Widths hung from two pieces, or with one turned, can carry different skews; the seam then steps by the difference between them rather than by either.

The tolerance is a stand-in for an eye, as it was for the lot drift, and a climb across a hanging is judged against a pole or a ceiling that the arithmetic knows nothing about.

And the cloth is rigid in its own plane. A soft cloth can be eased across a seam by a few millimetres, which reduces a small step, and a hanging cloth shears under its own weight, which can move its rows by more than a small skew; neither is computed.

Still open: how much skew a finished piece carries #

Every number here is conditional on a skew, and the skew a finished patterned cloth actually leaves the straightener with is a measurement nobody’s arithmetic supplies. It is easy to take: lay a width flat, rule a line square to one selvedge through a pattern row, and measure how far the row is from the line at the other selvedge. Done on every piece of a design, it would give the distribution of residual skew a finishing works delivers, set against the quarter of a per cent a matched hanging needs; and done at both ends of each piece it would show whether a skew is steady down a piece or grows, which decides whether a cutter can correct it once or has to correct it every width.