Textile Structure
how cloth is put together
Concept

Equivalence — where it appears

Two weaves counted as one because some operation turns one into the other: shifting the start, turning the cloth over, reading it end for end or mirroring it. Which of those operations a count allows decides its number, so a census of twills is only stated once its equivalence is.

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

How many twills there are. Every way of writing a twill on each repeat, reduced by the two operations that leave the cloth unchanged: starting on a different pick, and turning it over. What is left is the number a designer actually chooses between.

How many twills a repeat admits

Sixty-four ways of writing a twill on eight ends, and twenty-one twills. The difference is two operations that leave the cloth unchanged, and a catalogue that does not quotient by them is counting notations rather than fabrics.

weaves · Foundation weaves The 2/1/2/3 twill and its own back. The 2/1/2/3 twill on 8 ends drawn on point paper, face and back, with warp up shaded. The back is every cell's face changed and the ends read from the other side, so its diagonal runs the other way. The warp floats on the face are 2, 2 and on the back 3, 1. This twill is not reversible. The matrix has no yarn in it, so what cannot be shown is how each face reads when a yarn's twist lies with one diagonal and across the other.

A balanced twill need not have two equal faces

Up to six ends, a twill with as much warp as weft on its face is the same cloth on both sides, and the trade's word for one has done duty for the other. At eight ends the two part: 2/1/2/3 shows warp floats of two and two on one face and three and one on the other. By eighteen ends only one balanced twill in ten is reversible, because half a reversible twill's word fixes the rest. Counting the motions properly also moves the count of twills itself, and shows that no twill is ever the same on both faces in a real yarn.

weaves · Foundation weaves

Named alongside it

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

TwillCensusCompositionFloatFloat lengthHandednessRepeatReversalTwill direction

All concepts