Plain, twill and satin

Almost every woven fabric in ordinary use is one of three structures or an obvious variation on one. Not because weavers lack imagination — the possible drafts on even eight shafts number in the millions — but because these three sit at the useful points of a single trade, and most of the space between them is not worth occupying.

Plain weave: every crossing, every time #

The rule is one line: alternate. Warp up, warp down, warp up; and the next pick does the opposite.

Two ends and two picks describe it, which means it can be woven on two shafts — the simplest loom there is — and that alone accounts for a great deal of its ubiquity.

The consequences all follow from that maximum. It is the firmest structure for a given yarn and sett, because every thread is gripped at every opportunity. It is the most resistant to threads slipping or being pulled out. It has no float longer than one, so there is nothing to snag. And it is the most open of the three: every one of those interlacings makes a thread bend, and a bend takes room, so plain weave has to be set more loosely than anything else in the same yarn.

Muslin, calico, poplin, taffeta, canvas, organdie and most shirting are plain weave. So is nearly all the cloth ever woven anywhere, which is what happens when a structure is simultaneously the easiest to make and the hardest to pull apart.

Twill: the same idea, shifted #

The rule is barely longer. Choose a sequence of ups and downs — three up and one down, say — and shift it by one end for each successive pick.

That shift produces the diagonal, and the diagonal is the thing everyone notices and the thing most often misdescribed. No thread in a twill runs diagonally. The warp runs one way and the weft the other, exactly as in plain weave; what runs diagonally is the pattern of which one is on top, which is a different sort of object entirely. The essay on that works through why the mistake is so persistent.

A twill’s floats are as long as its runs, so a 2/2 twill has floats of two and a 3/1 has warp floats of three. Halfway between plain weave and satin in every respect, which is the point of it: firmer than a satin, more supple and denser-settable than a plain weave, and with a surface interesting enough to be worth looking at.

Denim, gabardine, drill, serge, tweed and herringbone are twills. So is the cloth in almost every pair of trousers ever made.

Satin: interlace as little as possible #

The rule is different in kind. Instead of a repeating run, a satin places exactly one interlacing per pick, stepping across the ends by a fixed move.

The point is not to have few interlacings — a long-float twill has few too — but to have them scattered. A twill’s interlacings line up into a diagonal that the eye follows immediately. A satin’s are placed so that no line forms, and the surface reads as an unbroken expanse of warp.

The move cannot be chosen freely. It must be coprime with the order, or the interlacings revisit ends before covering them all; and it must not be one or one less than the order, or they line up and the weave is a twill. That condition has a consequence famous among weavers and provable in a line: there is no regular satin on six ends.

Satin, sateen, damask grounds and most linings are satins. The lustre is not a finish and not a fibre property: it is specular reflection from a long uninterrupted length of thread, and it is available in cotton exactly as much as in silk.

The variations, and why they are variations #

Between the three sit a great many named cloths, and nearly all of them are one of the three with a small modification. Knowing the modification is worth more than knowing the name.

Basket takes plain weave in groups: two ends and two picks treated as one, so the alternation happens every two threads instead of every one. Floats of two, half the interlacings of plain weave, and a noticeably softer cloth in the same yarn. Hopsack and Panama are basket weaves.

Rib takes the groups in one direction only, so the cloth has pronounced cords across it. Poplin is a fine warp-way rib — more ends than picks, so the weft is completely covered — and grosgrain is a coarse one.

Herringbone reverses a twill’s direction at intervals, so the diagonal zigzags. Broken twill reverses it without the mirror, which removes the pronounced diagonal and is why denim’s characteristic look is a broken twill rather than a plain one in some mills.

Crepe weaves scatter interlacings irregularly rather than by a rule, to give a surface with no visible direction at all. They are the case where a designer is working cell by cell, and therefore the case where the integrity check earns most of its keep.

The pattern in that list is worth noticing: almost every variation moves along the same axis. It changes how often threads interlace and how far they run between interlacings, and the effect on the cloth is predictable from where it lands.

The trade, quantified #

Everything above is one variable seen from three positions, and it is worth seeing the numbers rather than the adjectives.

Plain weave interlaces at every intersection — a firmness of one on the scale used here — and can be set to about twenty threads per inch in a yarn a fortieth of an inch across. An eight-end satin interlaces at one intersection in eight and can be set to about thirty-two. The same yarn, sixty per cent more threads, and a completely different cloth.

That is why weight and thread count cannot be read as quality without knowing the weave. A dense satin and an open plain weave in the same yarn will differ enormously in count while being the same amount of thread doing different jobs, and thread count as a measure fails for exactly this reason among others.

What each trade buys #

Rather than a table of adjectives, the consequences with their mechanisms.

Abrasion. Plain weave wins, because no length of thread is exposed. A satin’s floats take the wear on a small fraction of the surface and go first; a worn satin shows its weft through the face where the floats have gone.

Tear strength. Satin wins, which surprises people. A tear propagates by breaking threads one at a time; in a loosely interlaced structure the threads can slide and group together at the tear, so several share the load and the tear is arrested. In plain weave every thread is gripped where it is and takes the load alone.

Drape. Satin wins, and by a long way. Bending a cloth means bending its threads, and a thread that interlaces at every intersection is bent at every intersection already and has no compliance left. Fewer interlacings mean a limper cloth.

Lustre. Satin, for the specular reason above.

Crease recovery. Twill tends to win, because the diagonal structure lets threads move without the whole cloth having to.

None of these is a fibre property. All of them are consequences of one number.

The two faces are not the same #

One structural fact that plain weave hides and the other two make obvious.

Plain weave is balanced: as much warp on the face as weft, and both faces identical. A 2/2 twill is balanced too. But a 3/1 twill has three times as much warp on the face as weft, so its two sides look nothing alike — and a satin is the extreme case, with almost the whole face warp and almost the whole back weft.

That asymmetry is designed for. A warp-faced cloth puts the better yarn where it shows and takes the wear, and puts the cheaper or softer yarn against the skin. Denim does exactly this, and so does most lining satin.

The count in that figure is not an aesthetic judgement, and it is exactly zero for the warp-faced weaves — a warp-faced draft has more filled squares than empty ones, so no operation can turn it into its own complement. Balance is decidable from the matrix, like everything else here.

Crimp, which the three do differently #

One more number separates them, and it is the one that decides how a cloth behaves when it is pulled.

A thread in a woven cloth is longer than the cloth it crosses, because it goes over and under. The excess is crimp, and it is bought entirely by face changes: a thread that stays on the face for a long run travels straight, and a thread that changes face at every intersection is travelling up and down the whole way.

The ordering — plain, then twill, then satin — is the same ordering as everything else on this page, which is the point. It also explains a practical fact that catches people out: a plain-weave cloth extends more in its own thread directions than a satin does, despite being firmer in every other sense, because there is more crimp available to be pulled out. That extension is a rearrangement rather than a stretch, and it is why a shirt gives a little at the shoulders while a satin lining does not.

Why three and not thirty #

Three points on one axis is a strange number to converge on, and it is worth asking why the trade did not settle on five or on a continuum. Two answers, and the second is the interesting one.

The axis is not evenly sampled, because the loom is not. Plain weave needs two shafts, a twill needs as many as its repeat, and a satin needs its order. So the three sit at two, four and five — which are the first three shaft counts that buy anything, and the gaps between them are gaps in what a loom cost. Everything between a 2/2 twill and a five-end satin exists and is weavable and buys very little that either of its neighbours does not, at a shaft count that is not obviously cheaper.

And the properties saturate. Read the consequences above and each of them changes fast between plain and twill and slowly between twill and satin: the interlacing rate goes 1.00, 0.50, 0.40, so the first step halves it and the second takes off a fifth. A twelve-end satin’s rate is 0.083, which is a further factor of five — and its float is eleven, which is past every float limit anybody weaves to.

So the useful part of the axis is short, its ends are fixed by two different constraints, and the interesting middle is one weave wide. Three is what a bounded axis with a cliff at each end has room for, and the cliffs are the shaft count at one end and the float limit at the other.

That reading also says what a fourth foundation weave would have to be. Not a longer float, which the float limit forbids; not a shorter one, since plain weave is the minimum; but a structure that reaches a different arrangement of the same interlacing rate — which is exactly what a crepe is, and exactly why the trade names it as a fourth class rather than as a variation. A crepe scatters the same number of interlacings that a twill lines up, and the difference is not on this axis at all.

Where the rules came from #

The three are not a modern classification imposed on a messy tradition; they are genuinely the three that emerged.

Plain weave is prehistoric and universal, because it is what happens when anybody interlaces anything. Twill appears wherever there are more than two shafts, which is most places by the Bronze Age — the Hallstatt salt-mine textiles from around 800 BC include twills and even a herringbone. Satin arrived much later and from one place: China, where the drawloom made long-float figured weaves possible, and the technique travelled west along the routes that carried the silk itself. The word comes from Zaitun, the Arabic name for the port of Quanzhou.

The classification into three is a nineteenth-century tidying-up, and it is a good one. Every other weave in ordinary use — basket, rib, herringbone, satin derivatives, crepe — is a modification of one of the three, and naming the base tells a reader most of what the cloth will do.

What the rules do not settle #

Two limits worth stating.

A rule does not guarantee a cloth. Plain, twill and satin all hang together comfortably, but a draft is not obliged to. The integrity check exists because designed weaves — as opposed to rule-generated ones — can and occasionally do describe two fabrics rather than one, and the failures cluster among exactly the long floats that make a satin attractive.

The matrix knows nothing about yarn. Everything on this page is structure. A satin in a hairy woollen yarn will not be lustrous, a plain weave in a very fine yarn can be softer than a coarse satin, and finishing changes all of it again. The weave decides the direction of each property; the yarn and the finish decide the magnitude.

Which of them hangs together #

All three pass the check this site is built around, and it is worth saying why rather than only that.

Plain weave is the most thoroughly tied structure possible, so its integrity is not in doubt. A twill ties every end once per repeat at minimum. And a satin ties every end exactly once — the minimum that is possible at all, since an end tied no times would be lying loose on the surface.

That last one is the interesting case. A satin sits exactly at the boundary: one tie per end per repeat, which is the least that still makes cloth. Reduce it further and the structure is not a weave.

That is a good way to understand what the satin rule is for. It is not an aesthetic convention; it is the arrangement that reaches the minimum-tie limit while still scattering the ties so no diagonal forms, and the arithmetic of the move is what makes the scattering possible with a rule.

What happens when the rule is broken #

All three rules here run uninterrupted, which is what makes them rules. The obvious next move is to break one, and it has a consequence worth knowing before it is made.

Reversing a twill at intervals gives a herringbone, which is the cheapest way of turning a rule into a figure. Two ways of doing the reversal produce drafts a reader cannot tell apart, and one of them leaves two adjacent ends doing exactly the same thing — a doubled thread down the seam that the trade calls a cracked line. Broken and herringbone twills counts them, and finds the duplication is exactly two ends per repeat at every reversal width.

Where the ladder goes next #

The quantity doing the work throughout is the float, which deserves its own account.

The theorem hiding in the satin rule is the absence of a six-end satin, which is a one-line proof about common factors.

And the mechanism behind the setting numbers is interlacings and firmness, where the trade is derived rather than tabulated.

What the pictures here cannot show. Every figure on this page is a draft, and a draft is structure without yarn. Lustre, hand, weight and drape are all consequences of these structures in a particular yarn at a particular sett with a particular finish, and none of those is drawn anywhere here.