The weave index
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A subject's natural index is a list of its objects, and the objects here are drafts. There are 24 of them below, and every column is computed from the matrix while the page is built: the longest float, the interlacings per intersection, how many separable cloths the draft describes, its plane group, how much of the face each thread system takes, the number of shafts a loom needs to hold it, and the closest the weave can be set in a yarn 1/40 inch across.
A catalogue copied out of a manual would be a table of assertions. This one is a table of measurements, which is a different kind of object: a row cannot say something the draft it names does not do, because the row is produced by asking the draft. If a figure elsewhere on the site disagreed with a number here, neither would be published: the two are computed from one model, and a disagreement between them is refused rather than settled.
The column worth reading first is layers. Every draft here interlaces everywhere and every one of them looks like cloth on point paper; 4 of them are not one cloth. Nothing about the drawing says so, and that column is the whole reason this site exists.
Shafts is the newest column and the only one that is not about the cloth. It is the number of distinct columns in the matrix — what a loom charges for — and it is a property of the machine rather than of the fabric: two drafts needing four shafts and sixteen are the same cloth to wear and a different purchase to make. It runs from 2 to 16 here. Where it is set in bold, the repeat is wider than the harness that weaves it — 6 of the 24 rows — which is the whole economics of a dobby and is invisible in every other column.
Plain and its derivatives
| Draft | Repeat | Float | Interlacings | Cloths | Group | Warp face | Shafts | Sett |
|---|---|---|---|---|---|---|---|---|
| plain the most interlaced cloth there is, and therefore the most openly set Plain, twill and satin · Interlacings and firmness | 2 × 2 | 1 | 1 | 1 | p4m |
50% | 2 | 20/in |
| 2/2 basket plain weave with its threads doubled — the same interlacing order, half as often Interlacings and firmness | 4 × 4 | 2 | 0.5 | 1 | p4m |
50% | 2 | 27/in |
| 3/3 basket three and three; the float grows with the group and the firmness falls with it Interlacings and firmness | 6 × 6 | 3 | 0.333 | 1 | p4m |
50% | 2 | 30/in |
| 2/2 warp rib plain weave extended in the warp — the picks pair up and the cord runs across the piece A cord is a stripe with no colour in it | 2 × 4 | 2 | 0.75 | 1 | cmm |
50% | 2 | 20/in |
| 2/2 weft rib the same doubling in the other system; the two densest setts stand at three to four A cord is a stripe with no colour in it | 4 × 2 | 2 | 0.75 | 1 | cmm |
50% | 2 | 27/in |
| 3/3 warp rib three picks to a group; the imbalance widens to two to three and the unit to six A cord is a stripe with no colour in it | 2 × 6 | 3 | 0.667 | 1 | cmm |
50% | 2 | 20/in |
Twills
| Draft | Repeat | Float | Interlacings | Cloths | Group | Warp face | Shafts | Sett |
|---|---|---|---|---|---|---|---|---|
| 2/1 twill the smallest twill; warp-faced, and the smallest repeat with a diagonal in it Plain, twill and satin · Twill direction, and how it is named | 3 × 3 | 2 | 0.667 | 1 | cmm |
66.7% | 3 | 24/in |
| 2/2 twill the jacketing twill, balanced, four ends of repeat Plain, twill and satin · The diagonal is not a thread | 4 × 4 | 2 | 0.5 | 1 | pmg |
50% | 4 | 27/in |
| 3/1 twill denim — three warp on the face for every one under, which is why it fades on one side Twill direction, and how it is named · The float decides | 4 × 4 | 3 | 0.5 | 1 | pmm |
75% | 4 | 27/in |
| 1/3 twill the same twill turned over; every count identical, the face the other system Twill direction, and how it is named | 4 × 4 | 3 | 0.5 | 1 | pmm |
25% | 4 | 27/in |
| 4/4 twill eight ends of repeat, floats of four; the point at which a twill starts behaving like a satin The float decides | 8 × 8 | 4 | 0.25 | 1 | pmg |
50% | 8 | 32/in |
Satins
| Draft | Repeat | Float | Interlacings | Cloths | Group | Warp face | Shafts | Sett |
|---|---|---|---|---|---|---|---|---|
| 5-end satin, move 2 the smallest regular satin; moves 2 and 3, mirror images of one another There is no satin on six ends · Why satin shines | 5 × 5 | 4 | 0.4 | 1 | p4 |
80% | 5 | 29/in |
| 7-end satin, move 2 the smallest order with two essentially different satins There is no satin on six ends | 7 × 7 | 6 | 0.286 | 1 | p2 |
85.7% | 7 | 31/in |
| 8-end satin, move 3 the satin of lining and damask; seven ends of warp on the face for every one of weft There is no satin on six ends · Why satin shines · Floats and abrasion | 8 × 8 | 7 | 0.25 | 1 | cmm |
87.5% | 8 | 32/in |
| 12-end satin, move 5 moves 5 and 7 only — an order with many small factors is a poor one Which satins are worth weaving | 12 × 12 | 11 | 0.167 | 1 | pmm |
91.7% | 12 | 34/in |
| 16-end satin, move 3 floats of fifteen, which almost no yarn will carry; the arithmetic runs out long after the cloth does Designing to a float limit | 16 × 16 | 15 | 0.125 | 1 | p2 |
93.8% | 16 | 36/in |
Reversals
| Draft | Repeat | Float | Interlacings | Cloths | Group | Warp face | Shafts | Sett |
|---|---|---|---|---|---|---|---|---|
| 2/2 herringbone (clean) the reversal that duplicates no end; the float grows from two to three Broken and herringbone twills | 8 × 4 | 3 | 0.5 | 1 | pmg |
50% | 4 | 27/in |
| 2/2 herringbone (point) the point reversal; two ends per repeat are duplicated and the float doubles Broken and herringbone twills | 8 × 4 | 4 | 0.438 | 1 | pmg |
50% | 4 | 29/in |
| 2/2 broken twill direction kept, phase displaced — no end duplicated, because nothing was reflected Broken and herringbone twills | 8 × 4 | 3 | 0.5 | 1 | p2 |
50% | 4 | 27/in |
More than one cloth
| Draft | Repeat | Float | Interlacings | Cloths | Group | Warp face | Shafts | Sett |
|---|---|---|---|---|---|---|---|---|
| double cloth two complete fabrics in one repeat, and the layer count is the assertion that they are two Backed and stitched constructions | 4 × 4 | 3 | 0.5 | 2 | pmg |
50% | 4 | 27/in |
| double cloth with 1 stitch one intersection turned over, and the two cloths are one; half of them would do it Backed and stitched constructions | 4 × 4 | 3 | 0.5 | 1 | cm |
43.8% | 4 | 27/in |
| a draft that is two cloths every end interlaces, every pick interlaces, and it is two fabrics lying on one another Does it hang together | 4 × 4 | 3 | 0.5 | 2 | cmm |
50% | 4 | 27/in |
| 3-layer cloth on 6 ends three complete cloths in six ends, which is the ceiling for that repeat How many layers a draft can have | 6 × 6 | 5 | 0.444 | 3 | pm |
50% | 6 | 28/in |
| 4-layer cloth on 8 ends four cloths on eight ends — at the ceiling, and with warp floats of seven How many layers a draft can have | 8 × 8 | 7 | 0.375 | 4 | pm |
50% | 8 | 29/in |
What the whole census says
The table above lists the drafts worth naming. The enumeration behind it does not stop at the ones with names.
Of the 65,536 four-by-four binary matrices, 22,874 have every end and every pick interlacing at least once, which is the honest minimum for calling something a weave. Of those, 144 describe more than one cloth.
90 of them are balanced — two up and two down in every end and every pick — and 0 of those separate. Balance appears to force integrity at this size. That is a measurement rather than a theorem, and the essay on balance says so.
Restricting to twills on eight ends, the 64 up-and-down sequences collapse onto 21 classes once rotation and reversal are quotiented out, which is a smaller number than the catalogues suggest.