A jacquard is every end its own shaft

The jacquard has a reputation as the machine that can weave anything, and the reputation is close enough to be misleading. It cannot weave anything. It removes one specific constraint completely, replaces it with a different one, and the design work it makes possible is shaped by the replacement rather than by the removal.

The constraint it removes is the threading. On a shaft loom, ends that hang on the same frame do the same thing forever, so a designer chooses the behaviours first and then arranges ends among them. A jacquard has no frames. Each end of the repeat is lifted by its own hook, on its own cord, and can do anything on any pick independently of every other end.

The count that replaces the shaft count #

A jacquard is sold by its hooks: 400, 600, 900, 1,344 are the classical sizes, and the number means what a shaft count means, one level down. One hook drives one end of the repeat.

So the repeat is bounded by the hook count and by nothing else. A 600-hook machine weaves a repeat of at most 600 ends, and the cloth is made by repeating that across the warp — a 1,800-end warp carries three repeats of it, comb-wise, all lifted by the same 600 hooks through a harness of cords that fans out from the machine to the loom.

The arithmetic that follows is the arithmetic a designer actually does. At sixty ends per inch, 600 hooks is a repeat ten inches wide. At a hundred and twenty ends per inch it is five inches. The same machine gives half the motif for twice the fineness, and the trade-off between how large a figure may be and how finely it may be drawn is the central fact of designing for one.

What the freedom is, exactly #

It is tempting to describe the jacquard’s freedom as unlimited and to leave it there. It is worth counting instead, because the count says something more precise than “unlimited” and rather more interesting.

On any pick, a machine with h hooks may raise any subset of them. So the number of distinct lifting plans available per pick is 2^h — for 600 hooks a number with about a hundred and eighty digits, which is not a useful thing to print and is the honest answer to “how much can a jacquard do”.

The point of computing it is the comparison. A sixteen-shaft dobby has 2¹⁶ = 65,536 possible lifts per pick, and a designer does not experience that as a limitation either. What separates the two machines is not how many lifts each can make; it is that the dobby’s lifts are lifts of groups, and the group memberships were fixed when the loom was dressed. The jacquard’s freedom is not that it has more instructions. It is that its instructions are addressed to individuals.

The constraint that arrives in its place #

Removing a constraint on the kind of design and replacing it with one on the size is not a straightforward improvement, and a designer feels the exchange.

The repeat is now a hard edge in the cloth. A shaft loom’s repeat is small and vanishes into texture. A jacquard’s repeat is large enough to be seen as a repeat, so a figure ten inches wide comes round every ten inches across a fifty-inch cloth, and the repeat becomes a plane pattern a reader can see and the eye finds the rhythm immediately. Managing that — turning the repeat, staggering it, dropping it half a repeat each time — is most of the craft of the trade, and none of it would be necessary on a machine whose repeat exceeded the cloth.

The cost scales with the ends. A hook, a cord, a mail and a lingo per end of the repeat, plus a card position per hook per pick. Doubling the fineness of the drawing doubles the hardware. On a shaft loom, refining a design within its blocks costs nothing.

Every end must still be bound. This is the constraint that catches designers and has nothing to do with the machine. A hook can leave an end up for two hundred picks, and the resulting float is a two-hundred-pick float lying on the surface of the cloth waiting to be snagged — or, if it never comes down at all, an end that can be pulled straight out, which is precisely the failure the integrity criterion exists to detect. The freedom to lift each end independently is the freedom to make a cloth that is not a cloth.

What “any subset” does not include #

The freedom is a freedom over subsets of ends on a single pick, and it is worth being exact about what that does and does not reach, because the machine’s reputation quietly extends it in two directions where it does not go.

It does not free the weft. Every pick is one thread crossing the whole width. A jacquard can decide which ends rise, and it cannot make the weft be two different yarns in two places at once — that requires extra shuttles, and a figure made with them is a brocade rather than a damask. So the design’s freedom is one-dimensional per pick: any subset of ends, one weft.

It does not free the order. The ends stay in the order they were drawn in, forever. Nothing in a jacquard makes end 40 cross end 41; a hook lifts an end and puts it down in the same place. So the whole family of constructions this field goes on to — leno above all, where the ends genuinely change places — is as far out of a jacquard’s reach as out of a shaft loom’s, and needs its own mechanism.

It does not free the geometry. Every end is under the same tension from the same beam. A construction wanting two warps at two tensions needs two beams, which is a property of the loom rather than of its shedding, and is why a pile fabric on a jacquard is a jacquard and a second beam.

Put together, those three say something worth carrying into the rest of this field. The jacquard removes the constraint on which ends may act together, and leaves untouched every constraint on what a thread system may be. That is a large freedom within one encoding, and it is not a freedom to leave the encoding — which is exactly the boundary the constructions in the rest of this field sit on the other side of.

Binding, which is the designer’s real work #

The practical answer to that last constraint is a binding weave: a satin or twill imposed over the whole design, so that within any area of figure the ends interlace at the satin’s spacing whatever the outline is doing.

That turns the design problem into a layered one. The outline decides which areas are figure and which are ground; the binding decides how the ends within each area interlace; and the two are combined by the machine. A designer draws the first and chooses the second, and the second is what stops the cloth falling apart.

It also explains an otherwise puzzling feature of figured cloth, which is that the same binding is used at very different scales. A satin binding on an eight-end repeat is the natural choice at any figure size, because the constraint it satisfies — no float longer than seven — is local, and locality is exactly what a large figure does not otherwise provide.

The harness tie, which is where the repeat is actually decided #

A hook does not reach the warp directly. It pulls a cord, the cord runs down through a board and ends in a mail carrying one end, and the arrangement of those cords is the harness tie. It is the jacquard’s equivalent of a threading, and it is the thing a designer specifies rather than the hook count.

A straight-through tie gives the plain reading assumed so far: hook k drives end k of every repeat across the warp, so the repeat is the hook count and the design steps across the cloth unchanged.

A point tie does to the harness what a point draw does to a threading. The cords run out and back, so a machine of 600 hooks drives a repeat of about 1,200 ends — a figure of double the width, symmetrical about its centre line. The gain is exactly the gain of the previous rung, arriving one level down, and the cost is exactly the same: the design must be a mirror image of itself, which suits a border or a medallion and rules out anything that has to read one way round.

A mixed tie does both in different regions, typically a straight-through field with a point-tied border, and a repeating tie drives several ends from one hook to coarsen the drawing where fine detail is not wanted.

So the hook count is a bound on the number of independent behaviours, not on the width of the figure — which is the same distinction the shaft essays drew, and it is worth noticing that it survives intact into the machine that was supposed to have abolished it.

A harness tie is a threading, and it economises for the same reason #

The ties above are usually presented as a list of arrangements. They are not a list: they are the same economy the bottom of this ladder computes, applied one level up, and saying so makes the fourth one predictable rather than surprising.

The shaft count is the number of distinct columns — two ends that are up on exactly the same picks may hang on the same shaft, because nothing can ever tell them apart. A hook is in precisely that position. Two ends of a jacquard design with identical columns could share a hook, and the harness tie is the mechanism for making them do so.

Read that way the three ties are three sources of duplicate columns. A straight-through tie exploits translation: end k of one repeat has the same column as end k of the next. A point tie exploits reflection: a design symmetrical about its centre line has each column appearing twice, so 600 hooks drive 1,200 ends. A repeating tie exploits deliberate duplication, coarsening the drawing by making neighbours identical.

So the hook count is not a bound on the ends. It is a bound on the design’s distinct columns, which is the same statement the shaft essays make, with a larger number in it.

And that explains why the economy has to be designed in. On a shaft loom the repeat is four or eight picks long, so columns collide constantly by chance — there are only sixteen possible columns over four picks, and any draft wider than sixteen ends must repeat one. A figured design’s columns are a thousand picks long, and two of them agreeing by accident is out of the question.

A shaft loom’s economies are mostly found and a jacquard’s are entirely made. The machine did not abolish the constraint the previous rungs are about; it moved it into the harness, where a designer has to put the symmetry there deliberately or pay for every end.

How much instruction a figure costs #

The card is worth an arithmetic, because it is the part of the machine that scaled worst and it explains a good deal about what figured cloth cost.

One card per pick, one position per hook. A 600-hook machine weaving a design 1,200 picks long needs 1,200 cards of 600 positions, which is 720,000 punched holes-or-not, cut once and laced into a loop. At forty picks to the inch a 1,200-pick design is thirty inches of cloth before it repeats, so a tablecloth design might run to several thousand cards.

Compare that with the previous rung’s dobby, where the whole instruction set for a four-shaft cloth is four lifts and the length is carried by a sequence. The jacquard’s instruction count is not merely larger, it scales with the design’s own dimensions in both directions, and this is the real sense in which the machine is expensive. The loom is a capital cost paid once; the card set is a cost paid per design, and it is why jacquard designs were repeated for decades and why a change of pattern was a serious commercial decision rather than an afternoon’s work.

Electronic control removed that cost entirely and did nothing else to the machine, which is a fair summary of what changed in the twentieth century.

Why it did not replace the shaft loom #

A machine that removes a constraint completely might be expected to displace the machines that have it. The jacquard did not, and two centuries later the great majority of woven cloth is still made on shaft looms.

The reason is that most cloth does not want a figure. A plain weave, a twill, a satin, a check: every one of them is a small repeat, every one is cheap on a shaft loom, and a jacquard weaving a plain weave is an expensive machine doing arithmetic no one needed. The hooks would be lifting six hundred ends into two groups.

So the two machines divide the work along the line this ladder has been drawing all along. If the design’s ends fall into few behaviours, buy the harness. If they do not, buy the hooks. The dividing line is the shaft count — the number of distinct columns — which is why that count, computed at the bottom of this ladder from one pass over a matrix, turns out to be the number the whole industry is organised around.

What was counted, and how #

Very little here is enumeration, and it is worth saying so plainly rather than dressing the arithmetic up.

The hook arithmetic is division: a repeat of r ends at a sett of s ends per inch is r/s inches wide and comes round e/r times across a warp of e ends. The model refuses a repeat wider than the hook count, which is the one thing about a jacquard that is a hard bound rather than a judgement.

The lifting-plan count is the size of the power set, reported as its logarithm because printing a hundred-and-eighty-digit integer beside a figure would be theatre rather than information. That choice is itself the point being made about the number: its magnitude is not what distinguishes the machine.

The one genuine enumeration in this essay is borrowed. The float-length distribution over the four-by-four census is the evidence that unbound ends are the failure mode a free machine invites, and it was computed for the integrity essays rather than here.

Where the model stops #

A hook is not quite an end. In many mountings several ends share a hook through a repeated harness tie, which is how a machine of 600 hooks dresses a warp of thousands; and in others one hook drives several ends deliberately, to coarsen the drawing and save hooks. The identity of hooks with ends is the design abstraction, not the plumbing.

The lingoes decide the shed as much as the hooks do. An end comes down because a weight pulls it down, and a machine running fast with light lingoes does not clear its shed. Nothing in the matrix knows about the mass hanging off each cord.

Nothing here is about the card. How the lifting plan is stored — punched cards, then paper rolls, then electronic files — is a genuine part of the machine’s history and is a question about instructions rather than about cloth. The previous rung counted instructions; this one counts hooks; and the two never meet in the matrix.

Who found it, and when #

Joseph-Marie Jacquard’s machine of 1804–5 is a combination of three earlier devices rather than an invention from nothing, and the combination is the achievement. Basile Bouchon had punched paper controlling a row of needles in 1725; Jean-Baptiste Falcon put the same idea on chained cards in 1728; Jacques de Vaucanson mounted the mechanism over the loom in 1745. Jacquard’s contribution was the arrangement that worked at production speed and could be retrofitted, and it spread with a speed that had a good deal to do with what it replaced — a drawloom needed a draw boy per loom, and the machine did not.

The often-repeated line about the punched card leading to the computer is true in a limited and specific way: the storage medium travelled, and Babbage’s Analytical Engine took its cards from exactly this source. What did not travel is the more interesting part. The jacquard’s card holds a lifting plan — a set of simultaneous states — rather than an instruction to be executed, and that is a different idea about what a stored pattern is.

Where the ladder goes next #

The machine has been described and its two exchanges counted. What it was built for is damask, and the arithmetic of that cloth is a pleasant surprise: figure and ground turn out to be the same weave, on the same threading, with the same float statistics, so the thing the jacquard is famous for weaving costs it far less than its reputation suggests.