A selvedge holds only where its edge end changes face

Every thread in a woven cloth is held by its crossings, and the thread with fewest goes first. There is one place in the cloth where that argument has a special form, because the thread in question is not straight: the selvedge, where the weft reaches the edge of the warp and comes back.

A shuttle weft is one continuous thread. It crosses the warp on one pick, turns round the outermost end, and crosses back on the next. Whether that turn holds is a single question about a single end: is the edge end on the other face on the second pick from the one it was on for the first? If it is, the weft goes over it one way and under it the other and is wrapped round it — the turn is caught. If the edge end stays up, or stays down, the weft passes the same side of it both times and the loop has nothing to wrap. It can slide along the edge, draw in, or pull out, and the edge end beside it is held by nothing on that side.

That question has an exact answer for every weave at every width. Plain weave catches every turn. Most weaves do not, and a large share of all weaves cannot catch every turn at any width whatever — which is why cloths so often have a selvedge woven differently from their body.

A turn is caught where the edge end changes face #

Put a weave between two selvedges and the weft turns at the right edge after one pick, at the left edge after the next, at the right after the next, alternately. At each turn the question is asked of the end at that edge, between the two picks either side of the turn.

In plain weave every end changes face at every pick, so every edge end answers yes at every turn, whatever the width and whichever side the first pick is thrown from. Plain weave’s selvedge holds by construction, and plain weave is the only weave in which that is true without conditions.

In a 2/2 twill every end changes face every second pick. So at each edge the end changes face at every other pick boundary — and the weft turns at that edge at every other pick boundary too. Whether the two coincide is a question of phase, and it has two answers. Thrown from one side, the turns fall exactly where the edge ends change face and every one is caught; thrown from the other, they fall exactly where the edge ends do not, and every single turn slips.

Plain weave holds everywhere, a 2/2 twill at half its widths #

A weave’s repeat can be cut at any end on either side, so a width of cloth puts one of its repeat’s columns at the left edge and one at the right. For a four-end repeat there are sixteen such placements, and for each the first pick can be thrown from either side.

Plain weave holds at all sixteen, from either side. A 2/2 twill holds at eight — and at each of those eight, from exactly one side. So a weaver of 2/2 twill who has chosen a width has an even chance of a width that can hold, and then a starting side that must be got right; the other side unravels the same width completely.

A 3/1 twill, its reverse the 1/3 twill, and a 2/2 hopsack hold at none of their sixteen placements from either side. A 2/1 twill holds at none of its thirty-six, and a five-end satin at none of its twenty-five. For the 3/1 twill the failure is precisely half: at every placement and from either side, each edge catches exactly half its turns and lets the other half slip, so both selvedges are loose at every other turn and no width or starting side changes it.

An edge end that floats past two picks always lets a turn slip #

The reason the long-float weaves fail is not a coincidence of these few weaves. The weft turns at a given edge at every other pick boundary. An edge end that stays on one face for three picks spans two consecutive pick boundaries without changing face — and one of any two consecutive boundaries is a turn at that edge. So any edge end with a float longer than two picks lets at least one turn slip, whatever the width and whichever side is thrown first.

That was checked, not only argued: across all 22,874 four-by-four drafts in which every thread interlaces, and every one of the 52,352 edge placements that does hold all its turns, both edge ends float at most two picks. A float of two is necessary and not sufficient — its middle boundary has to fall between the edge’s turns, which is the alignment the 2/2 twill has to get right — but a float of three is always fatal.

It explains the whole list at once. A 3/1 twill’s ends float three picks on the face, a 1/3 twill’s three on the back, and every satin’s edge end floats for all but one of its picks. A hopsack’s ends float only two, but all of them change face on the same picks, while the weft turns at the two edges on alternate picks — so whichever edge its changes suit, the other edge’s turns fall between them. A weave that is valued for long floats cannot hold its own selvedge, and the longer the floats the further it is from holding one.

Four drafts in ten cannot hold a selvedge at any width #

Across all 22,874 four-by-four drafts, the sixteen placements with the better starting side at each sort the drafts into a long tail. 9,636 — 42 per cent — hold at no placement at all. 9,552 hold at between one and four; 2,952 at five to eight; 720 at nine to fifteen; and 14 at all sixteen.

A cloth usually has to be a whole number of repeats wide, so the placement it actually gets is the repeat’s first column at one edge and its last at the other. 3,262 drafts — one in seven — hold their selvedges at a width of whole repeats. The other six in seven either need a width that cuts a repeat, which the arithmetic of fitting a repeat to a warp already makes awkward, or cannot hold at any width.

A floating end at each edge catches every turn #

The practical answer is to stop asking the weave. A floating selvedge is an extra end at each edge that is threaded through no shaft of the pattern at all: it lies in the middle of every shed, and the shuttle is passed over it going in and under it coming out, or the other way, so the weft is over it on one pick and under it on the next. It changes face at every pick, which is exactly plain weave’s edge, and so it catches every turn — whatever weave is beside it, at whatever width, from whichever side.

Checked on a 3/1 twill, a hopsack, a 2/2 twill and a five-end satin with a floating end added at each edge, every turn is caught. The same result is what a woven selvedge weave buys on a power loom: a few ends at each edge threaded to plain weave or to a weave whose edge ends change face at every pick, costing their own shafts on a dobby — the shafts a draft never lists because the selvedge is not in its repeat.

That also puts a number on why a cloth’s edge and its body are drafted separately. The body’s weave is chosen for its face, its handle and its floats; the edge’s weave has one job, to change face at every pick, and only plain weave does that job unconditionally.

The shuttle’s alternation decides stripes and selvedges alike #

The whole question exists because a shuttle is always on the side it last arrived at. That one fact is also what decides which weft stripes a box loom can throw: a shuttle that has to come back before a new colour can go makes a one-sided loom throw its colours in pairs of picks, and an odd band cannot be thrown at all without boxes at both sides.

The selvedge is the same alternation seen from the edge instead of the box. Every pick ends in a turn at the side the shuttle has reached, the turns alternate sides exactly as the shuttle does, and a weave’s edge columns are asked the question only on the picks their side receives a turn. A weft stripe changes colour between pairs of picks on a one-sided loom, and the edge that turn sits on is set by the same parity. A designer who throws a stripe order on a one-sided box loom is also fixing which edge every one of its turns lands on, and so which of the weave’s edge columns has to change face where.

A repeat has no selvedge to hold #

The census counts a property the repeat does not contain. A weave’s draft tiles the plane and has no edges, which is why a tube, a double-width cloth and two separate cloths are the same draft and differ only at their free edges. A selvedge is a property of a finite piece — of where the repeat was cut to put a column at each edge — and nothing computed from the repeat alone can say whether that edge holds.

That is also why a cloth’s selvedge is the reference its grain is measured from. A bias cut is taken at forty-five degrees to the selvedge because the selvedge is the one line in the cloth that is certainly straight along the warp; a selvedge that has drawn in at its slipped turns is a reference that has moved.

On shuttleless looms the question disappears, because the weft is cut at every pick and there is no turn. The edge then has to be held another way — tucked back into the next shed, or bound by a pair of ends crossing each other as a leno’s do — and both of those are selvedge weaves by another route: ends whose only job is to hold what the body weave cannot.

What a slipped turn does to the cloth #

A slipped turn is not immediately visible. The weft still goes out and comes back; it simply does so without wrapping the edge end. What follows depends on tension. With the weft drawn tight, the loop pulls in towards the body of the cloth and the edge end is left outside it, lying loose along the selvedge — a loopy or drawn-in edge, and an edge end that can be pulled free for the length of the slipped turns. With the weft left slack, the loops stand out beyond the edge end and snag.

The pattern of the looseness is itself a record of the draft. A 2/2 twill woven from the wrong starting side slips at every turn on both edges, so both selvedges come out uniformly loopy from the first pick. A 3/1 twill slips at every other turn on both edges whichever side it starts from, so its selvedges alternate — one tight turn, one loose — in a regular rhythm two picks long. And a weave that holds at one edge placement but not at the width it was given slips only at the edge whose column is wrong. So a slack selvedge can be read back: a uniform one points to a starting side, an alternating one to an edge end with a float of three, and a one-sided one to the width.

Either way the edge end is held on that side only by the crossings inside the cloth, which is exactly the situation of a thread at a cut edge: it is gripped by the crossings between it and the next thread in, and nothing outside it. A selvedge that does not hold is a woven edge that behaves like a cut one, on the side of every turn it failed to catch.

And it is why a weave’s edge is where its looseness shows first. The least-interlaced thread inside a cloth is held by crossings on both sides; the edge end of a weave that cannot catch its turns is held by crossings on one side only, at exactly the picks where its float means it interlaces least.

What was counted, and how #

For each draft, each choice of left and right edge column and each starting side, the weft’s turns were placed between every pair of picks at alternating edges, and each turn was scored as caught if the edge end at that side was on a different face on the two picks either side of it, cyclically round the repeat. A placement holds if some starting side catches every turn.

The named weaves were confirmed to hold at sixteen, eight, none, none and none of their sixteen placements — plain, 2/2 twill, 3/1 twill, 1/3 twill, hopsack. A floating end at each edge, changing face every pick, was confirmed to catch every turn of a 3/1 twill, a hopsack, a 2/2 twill and a five-end satin. The census was confirmed to find 3,262 drafts holding at a width of whole repeats and 13,238 at some placement. And every one of the 52,352 holding placements was confirmed to have both edge ends floating at most two picks.

Where the model stops #

A caught turn is not a perfect edge. A turn wrapped round the edge end still depends on the weft’s tension, the temple’s grip and the beat-up to lie straight, and a selvedge that catches every turn can still draw in or wave. The count says which edges can be sound, not which are.

The edge is taken as one end. Real selvedges are several ends wide and often doubled or tripled in the heddle, so the outermost group changes face together. A doubled edge end behaves as one thicker end for this question, and the answer is the same as for one.

Shuttleless looms are different. A rapier or air-jet loom cuts the weft at every pick and the turn does not exist; the edge is held by a tucked-in or leno selvedge instead, and this essay’s question does not arise.

And only four-by-four drafts are counted. Larger repeats offer more placements and the same theorem: a float of three at the edge always slips, and a float of two holds only when its changes of face fall in step with the turns.

Still open: how many cloths are woven with a selvedge weave they need #

The census says four drafts in ten cannot hold a selvedge in their own weave, and a named 3/1 twill never can. The question the count raises is how often, in real cloth, the edge weave is the body weave anyway — on hand looms without spare shafts, on narrow fabrics, on cloths whose edges are cut off — and whether those edges show the loose, loopy selvedge the count predicts at exactly the edges it predicts.

A survey of edges of twill and satin cloths with and without a separate selvedge weave would answer it directly: the slipped-turn side is predicted edge by edge from the draft and the starting side, and a loopy selvedge on the other side would be evidence that something else — a floating end, a doubled edge, a tension habit — is doing the catching.

Who worked it out #

Floating selvedges are standard handweaving practice and selvedge weaves standard mill practice, and both are prescribed for twills in weaving manuals because weavers found the twill’s own edge unreliable. The rule that an edge end must change face at every turn is the mechanism under that advice. The census, the placement counts and the float theorem were computed directly.