Textile Structure
how cloth is put together
Weaves

Plain, twill and satin

Three rules, and everything else in weaving is a variation on them. What separates the three is not appearance but one trade — how often a thread changes face against how far it runs when it does not.
15 min read 10 figures A weave is a matrixThe float decidesStructure before fibre

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.

The weaves everything else is built fromPlain, twill and satin on point paper. Reading across, the floats lengthen and the interlacings fall — and every property a weaver cares about follows from that one trade.plainfloat 1 · 8 interlacingsfirmness 1.002/2 twillfloat 2 · 16 interlacingsfirmness 0.505-end satinfloat 4 · 20 interlacingsfirmness 0.40a filled square means the warp is on the facecounted from the matrices, not from the pictures
Fig. 1 The three, on point paper. Reading across, the floats lengthen and the interlacings fall. That is the whole trade, and every difference in how the resulting cloths behave comes out of it.

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 plainThe plain on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.plainlongest float 18 interlacings per repeat1 separable clothrepeat 2 × 2generated, then counted2×2
Fig. 2 Plain weave, drawn over three repeats. Every intersection is an interlacing and no thread is ever on the face twice in a row. Nothing else can be more thoroughly interlaced, because there is nowhere left to put another crossing.

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.

The 3/1 twillThe 3/1 twill on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.3/1 twilllongest float 316 interlacings per repeat1 separable clothrepeat 4 × 4generated, then counted4×4
Fig. 3 A three-and-one twill: denim. Three warp on the face for every one weft, so the face reads as warp and the back as weft — which is why one side of a pair of jeans is indigo and the other is pale.

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.

8-end satin, move 3A satin, drawn from its move. Almost the whole surface is warp, broken by one weft point per pick, and those points are placed so that no diagonal forms — which is what distinguishes a satin from a twill of the same float length.8-end satin, move 3warp floats of 7moves available: 3, 532 interlacings per repeatone weft point per pick, scattered8 ends
Fig. 4 An eight-end satin. One weft point per pick and warp floats of seven, with the points placed so that no diagonal appears. That scattering is the difference between a satin and a twill of the same float length, and it is entirely a matter of where the interlacings sit.

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.

The basketThe basket on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.basketlongest float 216 interlacings per repeat1 separable clothrepeat 4 × 4generated, then counted4×4
Fig. 5 A two-and-two basket: plain weave with the threads taken in pairs. The interlacing count halves and the cloth becomes softer and denser-settable, which is the same trade the twill makes by a different route.

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.

What an interlacing costsEach weave's interlacing count beside the closest it can be set in the same yarn. The two run opposite ways, because a thread that changes face often has to bend often and a bend takes room.weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch
Fig. 6 Interlacing count against the closest each weave can be set in the same yarn. The two run opposite ways, without exception and by a mechanism rather than by convention: a thread that changes face has to bend, and a bend needs room.

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.

A draft is a two-coloured patternFor each weave, the symmetries that leave warp-up as warp-up and those that exchange the two. Only a balanced weave has any of the second kind, because exchanging warp and weft is only a symmetry when there is as much of one on the face as the other.weaveleave the faces aloneexchange themplain1616basket16162/2 twill16163/1 twill16none5-end satin20noneevery candidate operation tried against the repeat
Fig. 7 The structural signature of that asymmetry. Some symmetries of a draft leave warp-up as warp-up; others exchange the two, which physically means the cloth looks the same from the other side. Only the balanced weaves have any of the second kind.

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.

A warp end in section — plainOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spansplainwarp crimp 22.3%8 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility3 face changes
Fig. 8 A warp end through a plain weave, with the wefts it crosses shown end-on. The thread deviates at every crossing because it changes face at every crossing, and the crimp is correspondingly large. The thread thickness is exaggerated for legibility, so the figure overstates the effect.
A warp end in section — 8-end satinOne warp thread drawn through the cloth, with the weft threads it crosses shown end-on. The thread is longer than the cloth it spans, and the excess is the crimp — measured here from the drawn path rather than quoted beside it.the cloth this thread spans8-end satinwarp crimp 3.2%32 interlacings per repeatso the crimp shown exceeds a real cloth'sthread thickness exaggerated for legibility1 face change
Fig. 9 The same measurement in an eight-end satin. Seven crossings out of eight are travelled straight along the face, and only the eighth costs anything, so the crimp is a fraction of plain weave’s.

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.

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.

The 8-end satinThe 8-end satin on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.8-end satinlongest float 732 interlacings per repeat1 separable clothrepeat 8 × 8generated, then counted8×8
Fig. 10 The boundary case. Every end is tied down exactly once in eight picks, which is the fewest ties a structure can have and remain one cloth — and it is the same fact as the satin’s long floats and its lustre.

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.

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.

Where this goes next

5-end satinwarp floats of 4weft floats of 120 markedruns measured round the repeatfloat 4 The float decides How far a thread runs on the face before it goes under is one number, and it sits behind lustre, drape, snagging, abrasion, tear strength and how densely the cloth can be set. Almost nothing else in the subject has that reach. weaveinterlacingsdensest settingplain1.0020 per inch2/2 basket0.5027 per inch2/1 twill0.6724 per inch2/2 twill0.5027 per inch3/1 twill0.5027 per inch5-end satin0.4029 per inch8-end satin0.2532 per incha geometric jamming model, circular sections, yarn diameter 1/40 inch Interlacings and firmness Every time a thread changes face it has to bend, and a bend takes room. That one sentence decides how densely a cloth can be set, how firm it feels, and why the two run in opposite directions. ordermoves that give a satinhow many3 endsnone — every step shares a factor with the order04 endsnone — every step shares a factor with the order05 ends2 326 endsnone — every step shares a factor with the order07 ends2 3 4 548 ends3 529 ends2 4 5 7410 ends3 7211 ends2 3 4 5 6 7 8 9812 ends5 7213 ends2 3 4 5 6 7 8 9 10 111014 ends3 5 9 114enumerated from the coprimality condition, not recalled3–14 There is no satin on six ends Weavers have known it as a rule for centuries. It is a theorem with a one-line proof about common factors, and it rules out four ends as well.