Broken and herringbone twills

A twill is a rule: step the interlacing one end along at every pick and let it run. It produces a diagonal, it produces it forever, and there is nothing in it to look at twice.

The cheapest way to make something out of a rule is to break it. Run the twill one way for a few ends and then the other way, and the diagonals meet in a chevron; keep alternating and the cloth is a herringbone. Every tweed jacket, most suiting, and a great deal of upholstery is made this way, and the construction costs a weaver nothing but a change in the threading.

What this essay is about is the seam. There are two ways of mirroring a twill that produce drafts a reader cannot tell apart at a glance, and they differ in a way that is perfectly visible in cloth and completely invisible on paper.

Two ways to turn round #

Mirroring means reflecting the column index. The question is what it is reflected about, and there are two natural answers.

Reflect about the last end before the turn — end number $w-1$, if the reversal is every $w$ ends — and the mirror sends end $w$ back onto end $w-1$. The two ends on either side of the seam then receive the same rule and produce identical columns.

Reflect about the turn itself — the line between end $w-1$ and end $w$ — and end $w$ receives the rule that end $w$ would have had going the other way. No two ends coincide.

Both are used. The first is called a point reversal, because the threading turns on a point, and it is what a weaver gets by threading 1-2-3-4-3-2-1 on four shafts. The second requires threading 1-2-3-4-4-3-2-1 or an equivalent, and gets a variety of names.

What the enumeration finds #

The two constructions can be generated at every reversal width and measured, which turns a piece of workshop lore into a pair of statements that hold generally.

A point reversal duplicates exactly two ends per repeat, at every width. Not sometimes, not at narrow widths: always two, because a repeat of the herringbone contains two turns and each turn duplicates one pair. Widening the reversal does not dilute the defect, it merely spaces it further apart.

A reversal about the turn duplicates none, at any width. That is the whole of the fix, and it costs one extra heddle position.

The second finding is about floats, and it is the one that is genuinely unobvious.

The reversal lengthens the longest float, and by different amounts for the two constructions. A two-two twill has a longest float of two. Reversed about the turn, the longest float in the repeat becomes three. Reversed on a point, it becomes four — twice the twill’s own.

The reason is worth seeing. At the seam, a weft float running one way meets a weft float running the other way, and if they are on the same pick they join into one longer float. How much longer depends on the phase the mirror leaves them in, and the point reversal leaves them exactly in step.

That is a real consequence rather than a curiosity. A float of four in a cloth designed around a float of two is a place that snags, wears, and reflects light differently — a line down the seam that is visible for optical reasons as well as for the doubled thread. The two defects reinforce each other, which is why a cracked herringbone is so conspicuous.

The third way: break rather than mirror #

There is an alternative to mirroring, and it is the one used in the cloths where the seam has to be invisible.

Instead of reflecting the twill, displace it. Keep the direction, keep the rule, and shift the second half of the repeat by a fixed number of ends. The line does not turn round; it jumps. That is a broken twill, and satin drill, the broken twills of shirting, and a good deal of denim’s cousins are made this way.

The measurement is the striking part. At reversal widths of three and five, a broken twill’s longest float is two — the twill’s own, unchanged. At widths of two, four, six and eight it becomes three. So the break is free at odd widths and costs one at even ones, which depends on where the reversal falls and is precisely the kind of thing that is not worth reasoning about in the head.

That is the case for enumerating rather than arguing. The rule “break rather than mirror” is right; the rule “and it costs nothing” is right only half the time, and which half is not obvious from the construction.

The reversal that stops being a cloth #

Running the enumeration over every width turns up one row that is not like the others, and it is the reason the census exists.

A point reversal every two ends does not describe one cloth. It describes three separable pieces. Over the whole family of reversals — two constructions at six widths apiece, plus the broken twills — it is the only failure, and it happens at the tightest reversal there is.

The mechanism is the one from the integrity ladder. At a two-end point reversal the duplication and the mirror between them leave a pick that never goes under anything: a row of solid squares on the paper and a weft thread lying loose on the surface in the cloth. The digraph reports three components and the assertion refuses the figure.

Nobody weaves a two-end herringbone, so the failure has no commercial consequence. It has a methodological one. A designer working out a fancy reversal by hand has no way of knowing whether the construction they have arrived at is on the near side or the far side of that line, and the drawing will not say.

How many things there are to reverse #

The reversal is applied to a twill, so the size of the family is the number of twills times the number of widths, and the first of those is a count worth having.

Three distinct twills on a repeat of four; twenty-one on eight. Multiply by a handful of reversal widths and three constructions and the family a designer is working in runs to several hundred cloths, every one of which is generated by a rule short enough to write on a card.

That is the appeal of the construction and also its trap. A space that large cannot be inspected by eye, and the two properties this essay measures — the duplication and the float at the seam — are exactly the two that a designer flipping through samples would not think to look for, because both of them are properties of a boundary rather than of a pattern.

What a weaver does about it #

The lore is worth setting beside the arithmetic, because the two agree and arrived independently.

The standard remedy for a cracked line in a hand-woven herringbone is to thread the turn on a doubled shaft — 1-2-3-4-4-3-2-1 rather than 1-2-3-4-3-2-1 — which is precisely the reflection about the turn rather than about the last end. Weaving manuals give it as a rule with no derivation and sometimes with an explanation that is not the reason: that the doubled shaft “balances the threading”. It does not balance anything. It moves the mirror line by half an end, which is enough to stop two ends receiving the same rule.

The second remedy is to accept the duplication and use it, which is what the boldest herringbones do. A cracked line at a wide reversal reads as a deliberate stripe, and cloths are designed around it. Both remedies are correct; what neither of them is, in the sources, is counted.

The third possibility only exists on a loom with independent control of every end. A jacquard has no threading in this sense, so the reversal can be placed anywhere and the mirror can be put wherever it does least harm. That freedom is the reason large figured cloths are the ones where reversal defects are least common and float defects are most common — the constraint moved from the threading to the float limit, which is the constraint a jacquard designer actually works under.

What the duplication buys, which is why it survived #

The point reversal is treated above as the inferior construction — two duplicated ends, a float of four instead of three, a visible cracked line — and it is still what a great many herringbones are threaded as. That is worth explaining rather than putting down to habit, because the arithmetic gives it a defence.

Count the threading. A point reversal at every w ends is threaded 1, 2, … w, … 2, 1 and repeats, so its repeat is 2w − 2 ends. A reversal about the turn is threaded 1, 2, … w, w, … 2, 1, and its repeat is 2w.

The point reversal has a repeat two ends shorter, at every width, and the two ends it saves are exactly the two it duplicates. The defect and the economy are the same fact.

A quarter of the threading, at the width a herringbone suiting is actually woven at. That is not a rounding: a drawing-in of a thousand-end warp is a day’s work, the repeat is what a drawer-in reads from, and a shorter repeat is fewer positions to keep count of and fewer chances to make an error that runs the length of the piece.

And the saving is largest exactly where the defect is least conspicuous. A four-end reversal has its cracked lines two per repeat and very close together, which reads as a texture rather than as a fault; a twenty-end chevron has them far apart on a plain diagonal ground, where every one is visible — and there the saving has fallen to five per cent. So the two curves run opposite ways and the trade’s practice sits where they cross: point reversals at the narrow widths and clean ones at the bold, which is what the manuals recommend without saying why.

Two things follow that are worth keeping separate from the recommendation.

The shafts are unaffected. Both constructions use w shafts, because the set of distinct columns is the same either way — a shaft is a distinct column and duplicating an end adds no column. So the saving is entirely in the repeat and none of it is in the harness, which is the opposite of where a weaver would look for it.

And the float is not bought back. The point reversal’s float of four is a real cost that the shorter repeat does not offset, since it lands on the seam where the cloth is already conspicuous. The honest summary is that the point reversal trades a float and a visible line for a quarter of the threading, and that on a narrow reversal in a busy tweed that is a trade most weavers would make again.

What the reversal does not change #

Three invariances, because the list of what stays put is as useful as the list of what moves.

The interlacing count barely moves. A reversal rearranges which end does what; it does not change how often the threads change face, except locally at the seam. So the firmness of a herringbone is essentially the firmness of its parent twill, and it can be set at essentially the same density.

The balance is unchanged. A two-two twill shows half warp and half weft; so does every reversal of it, at every width. Reflection and displacement both permute the intersections without altering how many are warp-up.

The cross-section along an end is unchanged. Any single warp end in a herringbone follows exactly the sequence it would follow in the parent twill — over two, under two — because reversing acts on the relationship between neighbouring ends and not on any one of them.

Wider reversals, and where the family goes #

Reversing every four ends gives the small chevron of a herringbone suiting. Reversing every twenty gives a chevron proper, a bold zigzag with the diagonal clearly visible on each limb. Reversing in both directions — the threading mirrored and the lifting plan mirrored — gives a diamond or goose-eye, where the pattern turns in the weft as well as the warp.

Every one of those is the same construction at a different scale, and every one of them has the same seam question. The wider the reversal the smaller the fraction of the cloth the seam occupies, but the seam does not improve: a duplicated end at a twenty-end reversal is still a duplicated end, and it is now surrounded by enough plain diagonal to make it stand out more rather than less.

The other direction the family runs in is towards the satin, which is what a twill becomes when the step is chosen so that the interlacings scatter instead of aligning. A herringbone breaks the diagonal by reversing it; a satin breaks it by stepping so far that the eye cannot follow it. They are the two answers to the same complaint about twills, and they belong to different rungs of the same ladder.

What the pictures cannot show #

The figures on this page draw the seam as a change in the pattern of filled squares, which is what it is on point paper and not what it is in cloth.

In cloth the seam is a place where two families of floats meet, and what a viewer sees there is dominated by light. Floats lying in opposite directions catch the light differently, so a herringbone shows alternating light and dark bands that have nothing to do with colour and nothing to do with the duplication — they are the same yarn seen at two orientations. Point paper cannot show that and neither can any figure here.

The duplicated end is likewise drawn as two identical columns, which is a true statement about the draft. What it looks like in the fabric is a single thread of twice the diameter, because the two ends have nowhere to go but alongside each other and no crossing thread separates them. The count in the caption is the honest version; the picture is the schematic one.

Where the construction came from #

Herringbone is old. Woven fragments with reversed twills survive from Iron Age Europe, and the name comes from the resemblance to a fish’s skeleton, which nobody has improved on. The construction requires no mechanism a plain twill does not require — only a threading that goes up and comes back — so it is available on the simplest shaft loom and appears wherever twill appears.

The vocabulary, on the other hand, is a mess, and it is a mess for a reason worth knowing. Herringbone, chevron, broken twill and point twill are used by different trades to mean overlapping things, because they were named by people looking at cloth rather than at drafts. Herringbone and chevron differ only in the width of the reversal, with no agreed boundary. Broken twill sometimes means the displaced construction described above and sometimes means any twill whose diagonal is interrupted, which includes the reversals.

The naming confusion is the same one this site keeps meeting. Names attached to appearances do not partition the space of constructions, because two constructions can look alike and one construction can look like several things at different scales. The three quantities this essay measures — duplication, longest float, layer count — do partition it, and they are not what any of the names are about.

Two later developments belong to the same family. The diamond or goose-eye reverses in both directions at once, which requires the lifting plan to be mirrored as well as the threading and produces a cloth whose seam question has to be asked twice, once in each direction. And the entwining or rosepath threadings of Scandinavian weaving are point reversals at several widths at once, which multiply the number of seams and, on the arithmetic above, the number of duplicated ends with them.

Where the ladder goes next #

The next rung of the weaves ladder leaves the plane entirely: backed and stitched cloths, where a second complete fabric is woven behind the first and the interesting quantity is how few intersections it takes to join them.

The companions are the two quantities this essay kept measuring: the float, which the reversal lengthens, and the interlacings, which it does not. And the rung below is the direction itself, where reversing a twill was a symmetry rather than a construction.