Let's start with this 8-shaft draft. Most weavers with 8-shaft jack looms would, at first glance, decide that they can't weave it because they don't have 16 treadles. Typically, 8-shaft jack looms have 10 treadles. (It works that way for most jack looms: 4 shafts, 6 treadles; 8 shafts, 10 treadles; 12 shafts, 14 treadles; 16 shafts, 18 treadles. I assume it's this way so that weavers can always weave tabby along with a pattern -- for selvages, perhaps, or for weaving popular patterns like overshot and Summer and Winter.)
The pattern shown above, pattern #42887 on Handweaving.net designed by Eugenio Poma of Italy in 1947, is an intriguing double-weave design that gives you the illusion of squares that rise above the surface of the cloth, in a sort of embossed effect.
Folks with 8-shaft table looms could weave this, because they have a direct tieup (one lever always lifts the same single shaft) and thus can weave any possible combination of 8 shafts (way more than 16, because the number of combinations any particular number of shafts can weave is a factorial -- but that is definitely another blog post).
But with 10 treadles that are fixed (tied up), you have only 10 possible combinations of shafts.
Still, take another look. If you study the tieup carefully, you'll see that, in 4 instances, 3 treadles lift the same shafts. Perhaps it's because these repetitions in the tieup helped the designer "build" the pattern on a straight draw (and perhaps that helps the weaver understand how the illusion of the embossed squares is created).
Anyhow, let's break it down so that we can eliminate the duplications in the treadles.
Treadles 1, 5, and 9 all lift shafts 1, 2, 3, and 6. So you let's combine all these for treadle 1.
Treadles 2, 6, and 10 all lift shafts 3, 6, 7, and 8 -- same thing, so these 3 identical treadles are treadle 2.
Treadles 3, 7, and 11 all lift shafts 1, 3, 4, and 8 -- they become treadle 3.
Treadles 4, 8, and 16 all lift shafts 1, 5, 6, and 8 -- they become treadle 4.
So we've brought 12 treadles down to 4. We have 6 more to play with, but the final reconfiguring requires just 4 treadles.
We will make the "new" treadle 5 the same as the original treadle 12, to lift shafts 1, 2, 4, 5, 6, and 8. The new treadle 6 will be the same as the original treadle 13, lifting shafts 2 and 6. The new treadle 7 is the same as the original treadle 14, lifting shafts 2, 3, 4, 5, 6, and 8. And finally, the new treadle 8 is the same as the "old" treadle 15, lifting shafts 4 and 8.
There you have it! We've combined all of the treadles that lift the same shafts and retained the 4 original treadles that are one-offs, meaning that they appear only once in the original tieup.
Here's the result.
Please remember that this is NOT a skeleton tieup. It's merely a rearranged, reduced-to-the-lowest-number-of-shafts-lifted kind of tieup. But I've started with this exercise to give you the basic idea of how you can break down a 16-treadle tieup to just 8 treadles and weave the same pattern.
So what is a true skeleton tieup? I think of it as connecting two (or sometimes even three) bones, as in a real skeleton, to achieve one function -- like a leg or an arm, you might say.
Let's start with this design: an 8-shaft double-weave pattern, using a parallel threading, that calls for 16 treadles. While it can't be woven on 10 treadles using the tieup below, it can be woven on 10 treadles using a skeleton tieup.
Here is the 16-treadle tieup and treadling, enlarged.
Now, here's what the skeleton tieup looks like, using only 10 treadles. This lets you weave the same design.
The details, for those who have the patience to read them: You can see that for pick 1, you step on treadle #3, lifting shafts 2 and 8. For pick 2, you step on treadles 3 and 7, which combined lift shafts 1, 2, 3, 5, 7, and 8. On pick 3, you step on treadle 2, lifting shafts 1 and 7, and then for pick 4, you step on treadles 2 and 8, which together lift shafts 1, 2, 4, 6, 7, and 8. (No matter that shaft 8 is lifted by both treadles; it gets the job done.)
Looking closely, you'll see this tieup is really the identical treadling as in the preceding diagram: on the first pick shafts 2 and 8 are raised; on the second pick you're raising shafts 1, 2, 3, 5, 7, and 8; on the third pick, you're raising 1 and 7; and on the fourth pick, you're raising 1, 2, 4, 6, 7, and 8. The skeleton tieup uses the same liftplan, reduced (or broken into patterns) to use just 10 treadles.
In the days before computers, I'm guessing that, to create a skeleton tieup, a dedicated weaver had to sit down and figure out which groups of shafts could be combined in a pattern that would work with another group of shafts in tandem to lift the total number of shafts needed. It's all about math, which dovetails quite nicely with the computer era we're in. Which brings us to...
Tim McLarnan is the Tremewan Professor of Mathematics Emeritus at Earlham College in Richmond, Indiana. And, for the mind-bending ease of weavers everywhere, he created this online tool. With a few short steps, you can reduce a lengthy tieup to a skeleton tieup, allowing you to weave more intricate patterns in double weave, overshot, and summer and winter, among others.
(Please note: There are many complicated tieups that can't be reduced to a skeleton tieup. The treadle reducer will let you know that in a dismally short period of time.)
Here's how it works. First, you're asked to plug in how many shafts you have, how many treadles are in the original tieup, and how many treadles you have.
After that, these diagrams pop up.
You fill in the original tieup, click on how much time you're willing to wait for an answer, and then click on "Find Reduction."
If you're lucky, you will get a skeleton tieup. This is what the Treadle Reducer shows you at that point.
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And there you have it! But you're not quite yet done, because, for those of you who use Fiberworks or other weaving software -- or for those of you who use graph paper, for that matter -- you will have to draft a new tieup and treadling to match the Treadle Reducer's directions. Which takes some time. (In the fifth image from the beginning of this blog post, you can see the results of changing the tieup in Fiberworks to create the skeleton tieup for the 8-shaft example I'm using. By the way, you'll have to click on "Allow Multipedal Action" in the Treadling drop-down menu.)
This may seem like a lot of work, but it's a lot less work than figuring out a skeleton tieup using pencil and paper -- and you get to weave the pattern you want on the loom you have.
Here's a sample of the pattern in double weave, woven with cotton and wool wefts
(then washing in soap and hot water and agitating, so that the wool fulls
and the cotton pleats for a differential-shrinkage effect).
Skeleton tieups demystified. Thanks to Professor Tim and thanks for reading!
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