Concept

Shift-rule — where it appears

The property of a weave whose every column is a rotation of one column, which plain, twill, satin and sateen all have. Having it means the whole draft is one column and a step, so the weave can be threaded straight and treadled in sequence.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

$What four notations can say. Four ways of writing a weave down, with how many of the 426 four-by-four cloths each can express and whether expressing one identifies it: point paper, 426, identifies; a four-part draft on 3 shafts and 4 treadles, 110, identifies; a fraction name, 5, does not identify; a longest-float specification, 426, does not identify. A longest-float specification names every cloth and separates them into only 3 classes.$

Four ways to write a weave down

A weave's name in the trade is a pair of numbers — 2/2, 3/1, five-end satin — and the notation is so universal that it is easy to forget it is a notation. It has an image and the image is computable: of the 426 cloths at four by four, five have a name of that kind, and there are four names for the five.

cloth · Notation

The strain across a harness. The warp strain each shaft of a 24-shaft harness puts into its own ends, from 0.460 per cent at the front to 1.728 per cent at the back. Shafts within a budget of 1.0 per cent are drawn in one colour and those outside it in another; the budget is reached at shaft 13.

The back shaft works hardest

How hard the loom is on a warp end is the product of two numbers from different worlds — how often its column changes sides, which is a property of a binary matrix with no millimetre in it, and the strain of the shaft it happens to be on, which is a property of a machine with no weave in it. Neither knows about the other, and the threading that joins them is a decision nobody makes on structural grounds.

mechanics · Shed

Flexes per end in the same check, ground a pick along. One bar per warp end above the draft of the same check, ground a pick along, each the number of times that end changes sides in one repeat — which is the number of times the shed drags it through its heddle eye. The counts run from 6 to 10, and they are the same numbers that give the cloth its interlacing rate of 0.500 per intersection.

A figure is harder on its warp

Every basic weave flexes all its ends exactly as often as each other — plain, twill, satin and sateen alike, and it is a one-line theorem. Figure one of them on another and that evenness goes, or does not, depending on where the ground weave was started relative to the figure. The same invisible offset that decides whether a fine figure holds together decides, at a coarse one, how unevenly the loom works the warp.

mechanics · Shed

Named alongside it

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

Heddle Interlacing Loom Shaft Shed Threading Warp strain Abrasion Block figure Catalogue Damask Expressiveness

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