Textile Structure
how cloth is put together
Concept

Denting — where it appears

How many warp ends are drawn through each opening of the reed, which groups the warp and beats against the weave repeat. Where it shares a factor with the repeat the beat is coarse and visible, and where it does not the mark closes up and disappears.

Named by 8 essays across 3 fields — each of them below, with the objects they name alongside it.

Which dentings leave a mark. Every combination of ends per dent and weave repeat, with how many ends the grouping takes to come back into step. A small number means the reed treats every repeat the same way and the grouping shows as a stripe at the dent pitch; a large one means the grouping walks across the weave and there is nothing periodic for the eye to find. The rule is one word: dent so the two share no factor.

The reed leaves its own mark

A reed does not space a warp evenly. It groups it, several ends to a dent, and the grouping beats against the weave repeat — so a denting that shares a factor with the repeat treats every repeat identically and shows as a stripe, and one that does not is invisible.

pattern · Moire The reed is not the sett. Twelve ends held at the reed's pitch above and at the cloth's pitch below, for a sheeting whose weft crimp is 14.61 per cent. The count is the same in both rows and only the spacing changes: the cloth is 12.75 per cent narrower, so a reed at 24.43 ends per centimetre produces a cloth at 28. The crimp comes from the Peirce solution at this cloth's quoted construction.

The reed is not the sett

A reed holds the warp at a pitch, and the cloth that leaves it is narrower — by exactly the weft's crimp, with nothing fitted and nothing approximated. On a close balanced sheeting that is 12.75 per cent, on an open scrim 1.87, and a weaver who allowed one figure for both would be wrong by a factor of nearly seven.

setting · Take-up What the two setts can be set to. Two rules on one scale from 8 to 40 threads per centimetre. The upper carries the 49 warp setts a metric reed catalogue reaches at one to four ends per dent; the lower carries the 4825 pick densities a change-wheel take-up reaches. The mean spacing is 0.656 threads per centimetre in the warp and 0.0066 in the weft, a ratio of 99. The widest gap in the reed's range is 2.10 threads per centimetre.

The setts a loom can reach

Transposing a draft gives a perfectly good draft, and every count this site takes off a matrix either is symmetric under exchanging warp and weft or has a mirror twin. The loom is not symmetric at all: over the range ordinary cloth is woven in, it can choose a pick density 99 times more finely than a warp sett — and the warp sett cannot be changed once the warp is drawn in, at any granularity whatever.

setting · Take-up The same error twice: scattered, and in a period. Two bands of 96 ends, drawn at spacings that differ from the reed's by the same root-mean-square amount — 6% of a dent, which is 25 µm. The upper band's errors are independent; the lower band's repeat every 8 ends, which is what one shaft set forward or one dent of the reed too wide produces. The displacement is drawn 8 times over scale, because at true scale it is half a pixel and both bands are picket fences; the arithmetic below it is at the true amplitude. The upper band reads as an even cloth with a little texture in it and the lower one has stripes, and nothing about the eye is needed to say why: at 96 ends the periodic arrangement is 7.7 times stronger at its own frequency than the scattered one is at any frequency, and over the 256 ends a buyer takes in at once it is 12.8. The ratio grows as the square root of how much cloth is looked at, which is why a fault-finding sweep is done at a distance rather than close up.

A random error hides and a periodic one shows

A warp whose threads vary by fifteen per cent looks perfectly even. One dent of the reed a tenth of a millimetre wide makes a streak that gets the piece rejected. The same amount of error, arranged two ways — and the ratio between them is √(2n/π), with nothing fitted in it.

pattern · Variation Where a muslin's warp jams, over 40 ends. 40 ends drawn at their own diameters, with every neighbouring pair's combined width plotted beneath. A cloth cannot be set closer than its threads will lie, and the pair that decides that is not the average pair — it is the widest one anywhere across the warp, which here is ends 8 and 9 at 205 µm apiece against a mean of 167 µm. Over the 2000 ends of a real warp rather than the 40 drawn here the worst pair is 42% above the mean, and it goes on growing with the width of the cloth: the same yarn in a wider loom jams sooner. The naive estimate that treats every window as an independent try overstates it by 0.48%, which is small enough to say that the overlap between neighbouring windows is not what is going on here.

A warp jams where its threads are thickest

The closest a cloth can be set is decided by its worst pair of neighbours, not its average thread — and the worst pair depends on how many pairs there are. The same yarn in a wider loom jams sooner, which makes a jammed sett a property of the machine as well as of the yarn.

setting · Sett A colour order against a 2/2 twill. The visible face of a 2/2 twill under 2 colour orders, drawn at the repeat the divisor arithmetic allows and outlined at the repeat the surface has. A filled cell is a dark thread on the face, which is the warp's colour where the warp is up and the weft's where it is not — so none of these patterns is in the draft, and the draft is the same in all of them. The colour period and the weave repeat beat exactly as a reed's grouping beats against a weave: the surface repeats on the least common multiple of the two, which here is 8×8 and 4×4. What the panels cannot show is colour: the two threads are drawn as filled and empty, and two colours of similar value make a pattern far weaker than this.

A colour order beats the weave it is threaded on

The reed's grouping beats against the weave repeat and the arithmetic is a least common multiple. A colour order is a second grouping of the same warp and the arithmetic is identical — but where the reed's beat is a fault to be dented out of a cloth, the colour order's beat is the pattern the cloth is sold for. Across 472 colour orders on four weaves the divisor bound is the surface's exact repeat in 470 or more, and the handful that beat it have no pattern left at all.

pattern · Moire 8-end satin at 1 a dent and 8-end satin at 5 a dent, marks and nearest neighbours. Regular satin marks drawn at the positions a reed leaves the ends in, over 16 picks and a whole period of reed and satin together, with each mark joined to its nearest neighbour. Inside a dent the ends sit closer than the average spacing by the stated share, and the gap at the wire takes up the rest. 8-end satin, no reed grouping, every end evenly spaced: links point one way: the row; 8-end satin, 5 ends a dent, ends in a dent 30.0% closer: links point 2 ways: no row. Links along the undented row's own step are drawn in one colour and links in any other direction in another. What the drawing cannot show is how much of a reed's grouping a finished cloth keeps, which is the input every one of these depends on.

A reed can dent a sateen out of its row and not a satin

A reed pulls the ends in each dent closer together than the average spacing, so a satin's marks stop lying on a lattice, and a step that fits inside one dent shortens. For the eight-end satin, four or five ends to a dent scatter its row once the ends in a dent sit 22.5 per cent closer than average. Five shares no factor with eight, so that denting leaves no reed mark. But a warp-faced satin's ends are set too close to close up that far, and what replaces the row is the reed's own stripe. Two ends to a dent never scatter any satin's row, and they give the one row-free satin the trade weaves a row.

weaves · Satin A 2/2 twill line's ends where the reed leaves them. A light warp line 3 ends wide in a dark 2/2 twill, with the ends drawn at their true places at a cover of 60% and both boundaries traced. Set evenly the edge swings 2.00 thread spacings. With 3 ends to a dent, closed by 40% of a spacing so that they touch, and the line on the dent's edge, it swings 1.20. One end along in the same reed it swings 2.40, more than if it had been set evenly. The weave and the reed are the same in the last two. Only where the line starts has changed.

A stripe's edge is cleanest inside one dent

No weave can draw a line with a straight edge, since the thread at the boundary must go under somewhere. A cloth has one freedom its weave lacks, which is the spacing of its ends, and it looked as though crowding a stripe's outer end could halve the swing. It cannot, in most cloth: two ends stop at a diameter apart, so the swing falls only as far as the cover. The freedom that costs nothing is another one. A line's narrowest unbroken width is exactly its swing plus one, so it fits one dent of a reed, and the same reed gives 1.2 thread spacings or 2.4 according to which end of the dent the line begins on.

pattern · Stripe

Named alongside it

The objects these essays reach for when they reach for this one.

ReedSettBeatPeriodCoefficient of variationContractionCoprimeCoverGreatest common divisorLoomPopulationRepeat

All concepts