Textile Structure
how cloth is put together
Concept

Regular satin — where it appears

A satin whose mark advances by the same number of picks at every end, which requires that number to share no factor with the repeat. It is the usual construction rather than the definition, and the condition it adds is exactly what fails at four and six ends.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

Which satins exist. For each order, the moves that give a satin — a step coprime with the order, and not the steps of one and one less which give a twill instead. Four and six admit none, so no regular satin exists on four ends or on six.

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.

weaves · Satin How much a draft agrees with itself. On the left the draft; on the right its correlation at every offset, one cell per offset, with the offset of nothing at the top left. Warp-up counts as plus one and weft-up as minus one, so the number in each cell is agreements minus disagreements out of 64. The correlations away from the origin sum to exactly -64, whatever the draft — structure can be moved about and not removed.

A crepe cannot be structureless

A crepe weave is designed to have no line in it anywhere. The correlations of a draft with itself sum to a number fixed by the repeat alone, so structure can be spread and never removed — and on eight ends the floor turns out to be half the repeat, set by a fact about binary words with nothing textile in it.

weaves · Texture weaves The lattice under 8/3 and 10/3. Satin marks drawn as points over two repeats, the 8-end satin on a move of 3, whose closest marks are √8 apart and next √10, so its marks line up 45° off the weft; and the 10-end satin on a move of 3, whose closest marks are √10 apart and next √10, two equal directions at right angles and so no single diagonal. For a regular satin the blue arrow is the shortest lattice vector and the red the next, and the faint lines run along the shortest through every mark — the diagonal the marks make. What the drawing cannot show is whether an eye finds that diagonal in woven cloth, where the marks are not points but short interruptions of a float, and where the yarn's own twist lies across them at an angle of its own.

Most satins still have a diagonal

A satin is chosen so that no diagonal forms, and its move is ranked by how far apart its interlacings sit. But the interlacings of a regular satin lie on a lattice, every lattice has a shortest step, and the marks line up along it. Only when two shortest steps tie is there no row to follow — and between five and forty ends the best move manages that at twelve of the thirty-five orders.

weaves · Satin What an irregular satin buys, order by order. For each order, the best regular satin's and the best irregular satin's scatter at the order's own best spread — the largest share of the closest pairs that point in one direction, where one is a line and less is a scatter. 5 ends: regular 0.50, irregular none at the best spread; 6 ends: regular none exists, irregular 0.25; 7 ends: regular 1.00, irregular 0.33; 8 ends: regular 1.00, irregular none at the best spread; 9 ends: regular 1.00, irregular 0.25; 10 ends: regular 0.50, irregular none at the best spread; 11 ends: regular 1.00, irregular none at the best spread. Irregularity buys something at 6, 7, 9 and nothing at the rest, and where it buys it scatters over four directions with no more than a third in any one. What the bars cannot show is whether a reader sees the difference, which is a question about a visual system.

An irregular satin scatters where a regular one lines up

A regular satin's marks lie on a lattice, so its closest pairs all run along one vector and make a row. An irregular satin has no lattice at all, so its closest pairs may point several ways at once — and at seven and nine ends, where every regular satin at the best spread has a row, an irregular one reaches the same spread with its closest pairs scattered over four directions and no more than a third in any one. At eight and eleven ends there is no such satin: the best spread is reached by regular satins alone, and irregularity has nothing to offer.

weaves · Satin 8/3 at 1.00 and 8/3 at 1.29, drawn in cloth. Satin marks drawn over two repeats at the spacings of a cloth, with the pick direction stretched by the sett ratio — ends per centimetre over picks per centimetre — and every closest pair of marks joined. 8-end satin, move 3 at a sett ratio of 1.000: closest pairs point one way: a row; 8-end satin, move 3 at a sett ratio of 1.291: closest pairs point 2 ways: no row. What the drawing cannot show is the float each mark interrupts, which is what a reader of the cloth actually sees.

A satin's row belongs to its sett

Point paper draws an end and a pick as equal squares, and every result about which satins have a row was taken there. A cloth is not square: it is set at so many ends and so many picks a centimetre, and in cloth the ties that made twelve satin orders row-free are ties between steps of different shape, which break at the first per cent of unequal sett. The reverse happens too. An eight-end satin, rowed on paper, has no row at exactly 1.291 ends per pick; an eleven-end at 1.265 and 1.528. And the only scatter that survives a range of setts is an irregular satin whose closest steps are mirror images — which nine ends has from the first per cent and ten only by 1.3.

weaves · Satin

Named alongside it

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

SatinMove numberScatterSymmetryCensusAutocorrelationConservationCoprimeCrepeEnumerationFloat lengthPlane group

All concepts