What Is a Skeleton Tieup? (Fair Warning: This Post Involves Math)

 

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's Rudimentary Treadle Reducer 🙌

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.

____________________________________________________________________

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!

How to 'Downsize' a 14-Shaft Pattern for 8 Shafts... and even 4 Shafts

Let's start with just one draft, because -- while these principles can apply to many designs -- I recently had to downsize a point-twill design, which happens to be one of my favorite weaving patterns.

It's a historic 14-shaft draft, fondly known as "The Earl," derived from a tablecloth that was used as the canvas for a 1626 painting of the Earl of Mar in Scotland. (To read the original 2020 post about "The Earl," click here.)

Above is the original Gebrochene pattern (in German that means "broken," while in English we call it Ms and Ws). Marjie Thompson, master weaver and lover of historical patterns, shared the WIF with me some time ago. Thank you, Marjie!

But not everyone has 14 shafts, right?

"Shaft envy" is what weavers call it. What can you do if you love this design but you have just 8 shafts? The answer is to "downsize" the threading, tieup, and treadling, following the shapes of the original 14-shaft threading but systematically reducing the peaks and valleys as best we can by using a ratio for each twill line (or block, depending on how you want to define your terms). And that ratio may have to vary across the threading. It gets complicated.

In keeping with that explanation, here's what the Earl might look like on 8 shafts. 

Not bad, eh? Not quite as ornate as the original design, of course, which is what happens when you're weaving with fewer shafts. But it's a pretty good adaptation, in my view. 

So how to do this? Since the design is tromp as writ (treadled as threaded), all one has to do is reduce the ups and downs of the threading to fit into 8 shafts, then repeat the threading in the treadling and create a tieup that mimics the original.

Let's start with the first twill line. For the 14-shaft version, you have a descending twill line, from upper right to lower left, which can easily be reduced from 14 to 8 shafts.

Original twill line on 14 shafts

Same twill line reduced to 8 shafts. This is the easy part ;o)

For the second motif, forming a "V," the original threading has a descent and an ascent of 6 shafts each, beginning at shaft 14, descending to shaft 9, and then ascending back to shaft 14. To keep the draft within 8 shafts, I began the "V" at shaft 8 and then descended to shaft 5 and back up to 8. That means the "ratio" is now 6 shafts reduced to 4 shafts -- not quite following the ratio of 14 shafts to 8 shafts, but creating a "V" threading that looks like the original pattern.

The Earl on 14 "V" threading (second motif from the right in original threading).

6 ends going down, then going back up

The "V" motif (aka descending-point-twill block) reduced to 8 shafts

This might not be true for all weavers, but when I downsize a pattern, I'm not looking to maintain an exact ratio for every block in the threading, as if 14 to 8 would be the rule throughout. (Besides, it just won't work out mathematically, because sometimes you would have to round up or down accordingly in your numbers.) More important, in my view, is to try to follow the original silhouette of the draft. So, for the above portion of the threading, a 6-shaft descent in the original 14-shaft threading becomes a 4-shaft descent in the 8-shaft version.

Moving on to the next descending twill motif: the line in the original descends 10 shafts beginning on shaft 14. For 8 shafts, the line begins at shaft 8, the topmost shaft (as with the original design) and descends 6 shafts. Again, the ratio differs from the original 14 to 8 -- in this case, the ratio is 10 to 6. So I'm adhering to the form of the design rather than exactly to the numbers.

On 14 shafts, the third twill block descends from shaft 14 to shaft 5

On 8 shafts, the third twill block descends from shaft 8 to shaft 3

The next twill line, ascending from the right to the left: the design rises 5 shafts in the original and 3 shafts in the 8-shaft adaptation. I could continue describing the pattern adaptations, but I think that you get the idea....

As you can see, there's a method to the madness here. Basically, you want to preserve the overall form of the threading. This means you don't have to be precise as much as you have to be painterly, you might say, creating a simpler line that follows a similar shape of the original, but with shallower ascents and descents.

The bigger challenge is when you want to reduce a complex design on 14 shafts to just 4 shafts. It can be done, certainly, but you lose a lot of detail.

Here's how you might design The Earl on 4 shafts.

It's hardly recognizable, you might say.  

And yet... this is still an Ms and Ws pattern, with interesting motifs throughout, worth weaving into a scarf or a tea towel. (It also might work as a great threading for overshot. But that would be another post.) If you look back at the threading of the original draft, you'll see that this 4-shaft version does follow the hills and valleys of that threading, even though much is lost in the details of the pattern. 

I invite you, dear reader, to share in the comments your own method of adapting a draft to fewer shafts. Someone else might have a more exacting approach, for certain. (Perhaps someone really savvy could use AI, come to think of it.) And certainly some patterns (other than twill) may lend themselves better or worse to a reduction in shafts. In any event, the approach I've outlined works well for me.

Thanks for reading!

Here's to John Erskine, 2nd Earl of Mar, painted by Adam de Colone, 1626.

(Still, we're more interested in the canvas.)

How to Paint One Warp and Get Two Colors

 Last month's blog post promoted a workshop I'm teaching in April in Bucks County, PA, on how to weave a "Harriet Tubman Shawl."

Here, once again, is a photo of the scarf (as seen in last month's post). It honors the heroism of Harriet Tubman, who spent her last years in Auburn, NY,  near where I live. She was photographed at least a couple of times during those years wearing a shawl over her shoulders. I admire her greatly, as so many of us do.

If you look very closely, you'll see that the warp is painted -- but, because it's Echo, you need at least two colors in the warp. Again, looking closely, you'll see that one warp thread is painted and the next one is black. Painted/black/painted/black -- that's how the colors of the warp are arranged for my parallel threading.

Another clue about the two warp colors: Just look at the two colors 

in the twisted fringe, with a painted thread alternating with a black thread.

That's the secret to achieving two colors in your warp while painting one warp: wind a warp of natural and black threads together. Black yarn does not show the dye, so you can paint right over it.

In this case, I've wound the warp in 24/3 cotton, which is the same grist as 16/2 cotton, but I find it's a bit sturdier thread. The drawdown for this warp is 8 shafts and, while the warp count in this case was about 840 ends, the warps for the workshop will call for 400 ends. (Not many people want to wind 840 ends for a workshop, I believe.)

So here are the steps in the dyeing process. I'm actually giving away a good portion of the instructions for the warp prep in this workshop, but I enjoy the results so much I thought I'd share it. The complete directions can be found on the ProChemical and Dye website, under MX Fiber Reactive Dyes: the instructions are for warp-painting on cotton and silk. (Please note: I don't use print paste in this process, so you can ignore the step that calls for making print paste as well as the instructions for making thick dyes.)

Step 1) As you wind your warp, do not use choke ties. Instead, use twining every 18". (If you use choke ties, they will resist the dye and you'll get little white lines across your painted warp.) Of course, you will want to use a choke tie at the end of the warp, where you cut it, and at the beginning of the warp, where you secure it around the back tie-on rod. (I warp back to front.) Also, you'll want to secure the cross quite snugly. But otherwise, use twining, as you often see when you purchase a skein of yarn. Here's a photo of what twining looks like.

Step 2) Soak your warp for at least 30 minutes in a soda-ash solution, according to the directions. (This assumes that you have already scoured the warp to get rid of any oils, dirt, or sizing in the yarn.)

Step 3) Prepare the urea water. Urea basically helps the dyes to stay active longer. I use 4 cups of urea for 1 gallon of water. Make sure the urea is completely dissolved. This is your basic water solution for making your dyes.

Step 4) Put on your respirator mask and gloves. Make sure you're wearing old clothing, too.

Me rockin' my respirator mask

If the water is really hot, I use these humongous gloves. 

Otherwise, I use food-preparation gloves or the cleaning gloves 

you can get at the grocery store.

Step 5) Mix your dyes.

I alter the recipe a bit, using 1 and 1/2 teaspoons of dye powder for one cup of urea water. This gives me a medium shade that I like.

8 different colors all lined up and ready for painting.

Step 6) Paint your warp. Make sure you thoroughly saturate the threads with color -- so for me that means using 2"-wide sponge brushes and turning the warp over as I paint, so that both sides get painted. I don't follow any particular color order, just using the colors randomly. Also, I try hard (although I don't always achieve this) not to paint horizontal stripes with my dye colors. Instead, I work to paint each color at an angle on the warp, which makes the warp more interesting visually. For each color, I paint a 2-4" long swath of color, no longer than that. (Don't want the weaving to get boring.) So each of the colors is about the same length on the warp.

Step 7) Wrap the warp entirely in plastic so that none of the dye leaks out onto your floors or tabletop or any surface. One thing I do to avoid leakage is that I sop up the excess dye on the sides of the warp as I paint, using old bath towels. (This makes for some very colorful towels that I continue to use for dyeing after washing and drying them. Somehow, with no soaking in soda ash, the dyes do adhere to the cotton towels.)

Step 8) Cure the dyed warp for 24 hours in a room that is at least 70 degrees Fahrenheit. This is really important. If your room isn't warm enough, your dyes won't strike (adhere) to the yarn and you'll be rinsing and rinsing to the get color out, only to wind up with faint colors. There are many ways to achieve a temperature of 70 degrees or higher. In my case, I take the warp (rolled in plastic and then put in a plastic bag) and place it on top of my boiler in the basement, which is hotter than 70 degrees. Some folks use those grow-mats for keeping seeds warm. Others use electric blankets but somehow that makes me nervous....

Step 9) Rinse out the warp. I have two stationary tubs, so I load one plastic bucket in each tub and rinse the warp in warm (maybe 100 degrees) water until it's filled with color (and it usually is). Then I transfer the warp to the other water-filled bucket and repeat the process. I do this until the water, with the warp in the bucket, runs nearly clear. To be honest, I have yet to achieve perfectly clear water in rinsing a warp with fiber-reactive dyes. But a pale-colored water is good enough for me.

Step 10) Hang the warp to dry. Understand that, at this point, the warp will look pretty tangled. I urge you to leave it this way until it is completely dry. Tangles come out much better when the yarn is dry. What I do, when it's dry, is wind the loop at the end of the warp on a hook and walk back the entire warp until it's taught, stretching and snapping it straight as I go. Even then, there will be some tangles. These will have to be combed out as you dress your loom.

So there you have it! Two colors for the effort of painting one warp. Although I almost always use this for Echo and Jin designs, I have used the same process for a striped warp in 60/2 silk -- black stripes alternating with painted stripes -- and then woven in a turned twill, going in one direction for the black stripes and the other direction for the painted stripes. The effect is always beautiful, because we all love color, don't we?

Feel free to ask any questions in the comments section. And thanks for reading!

Interested in an Upcoming Workshop in Bucks County, PA?

This shawl, pictured above, is a tribute to Harriet Tubman, who guided some 70 slaves to freedom, through wilderness in the dark of night, chased by bounty hunters, guided only her instincts, her visions, and the North Star. She reportedly made 19 trips back to the South and notably never lost anyone.

I called it "Harriet's Shawl" because in her later years she was often pictured weaving a large wrap around her shoulders. (By the way, she spent her later years in Auburn, NY, near my hometown of Rochester. It never ceases to amaze me to feel so close to greatness.)

Why did I dedicate it to Tubman? Because the motifs remind me of the forest, of darkness, of the stars she followed. And I did my best to make it beautiful, because her courage and strength are worthy of the best work I can create. (Not-so-humble brag: The scarf did win first prize at the faculty show at NEWS a few years ago, which makes me very proud.)

So what does this have to do with a weaving workshop? A dear friend, Hedy Lyles of Willow Grove, PA, passed away a short time ago and she had planned this workshop. We're doing it for the love of Hedy. Here she is at the loom she sold me, a 16-shaft Toika that I really like. (Except when it's hot and humid and the shafts stick, but that's another story.) Here, she's painstakingly showing me how to put the loom together.

She was also a terrific weaver, as you can see by this photo of her work:

So the workshop must go on, honoring both Tubman and Hedy. Here are the details:

GUILD: Handweavers of Bucks County

DATES: April 8-10, 2026

VENUE: Trinity Buckingham Church, 231 Durham Road, Buckingham, PA

WORKSHOP DESCRIPTION: For anyone who can read a draft and warp a loom. For looms from 4 shafts to 16 shafts. Each weaver will first, with guidance from the instructor (on Zoom), paint her warp using alternating black and beige yarns in 16/2 cotton. (The trick is you'll automatically have two differently colored yarns for an Echo threading, as the beige yarn will dye colorfully and the black yarn won't take the dye.) You will come to the workshop with your warp dressed and ready to weave. For your "Harriet Shawl," you will weave a series of structures on your Echo threading, using different tieups and treadlings to weave Echo, Jin, Decorated Jin, and double weave. You'll also experiment with different weft yarns and colors, including active yarns such as wool/stainless steel, which will be provided by the instructor. You'll come away with a colorful, textured scarf with a multitude of patterns, colors, and textures that will be unlike any scarf you've woven to date, I boldly venture to say.

To give you a taste of what you're you'll be weaving, here's the double-weave design for the 8-shaft version: 

That's just one of the varied designs you'll be weaving in different colors and textures.

We're looking for a few more weavers to sign up for this workshop. If you're interested you may contact me at kovnatdenise[at]gmail.com

I look forward to hearing from you!

By the way, I want you to know that I do try faithfully to write one blog post a month. December got away from me (not surprising, right?) so (fingers crossed) you'll be getting another blog post toward the end of January. Gotta meet those deadlines, right, even though they're self-imposed....

Thanks for reading!

 

Making Plans...

The image above is part of a drawdown of a design I call "Azteca," which refers to the indigenous people who founded the Aztec empire as well as to their culture. They flourished in central Mexico from 1300 to 1521 C.E., founding their capitol, Tenochtitlan, on the site that is now Mexico City. To me, the warm, vivid colors and the geometric motifs have the feeling of Aztec art. 

Architectural model, Mezcala, 1st-8th century, Metropolitan Museum of Art

(Public domain)

Coronation stone of Moctezuma, Xocoyotzin, 1503, Art Institute of Chicago

I'm thinking of weaving this pattern to create a tunic that derives from the art of the traditional Azteca women's tunic known as a huipil (pronounced wee-PEEL), worn by indigenous women from central Mexico to Central America. The garment's history predates Spanish colonization, with designs and weaving traditions pass down through the centuries. These designs represent a complex tradition of communication, with weaving and embroidery symbolizing the wearer's ethnic community and identity. Traditionally, huipils were woven in cotton on backstrap looms, such as the one seen below.

As for my plans for this modern-day huipil: I aim to weave it in 16/2 cotton and rayon/bamboo on my 32-shaft Louet Megado, with a width in the reed of 24.75 inches. I figure this gives me plenty of width to weave a rectangular shape that can be folded in half to fit an average-sized woman. Further, I want to decorate it with an inkle-woven band or two, maybe adding beads, giving it a look similar to the images below -- which are, by the way, from the wardrobe of Frida Kahlo.

In fact, I found a "Frida Huipil" sewing pattern on the website of the Victoria and Albert Museum. Here's the link: Frida Huipil V&A.

The design is a 4-color parallel threading, based on a design line that is basically Ms and Ws.

The tieup makes it a Jin pattern, and the treadling is an advancing point twill (with tabby shots in between the pattern shots, in keeping with Jin).

I would like to make this more of a garment for show rather than an everyday piece, so I may embellish it with beads and -- get this, real gold thread! (It's actually gold-plated, I guess you'd say, not solid gold, because that would be unaffordable.)

There is so much that weaving has to say, non-verbally but beautifully, to celebrate other cultures, traditions, and beliefs. Textiles awaken us to our connections and our individuality as well.

Now, off to the warping reel!

Thanks for reading.

The Huipil de la Malinche, one of the oldest huipils 

ever found, carbon-dated to the 1700s.

Creating an Optical Illusion in Block Double Weave

Please note that, unbeknownst to me as I worked on weaving this image, it is, in fact, an ancient, sacred pattern from the Itneg people of the Philippines. Here are the words of a reader who pointed this out:

"This is an optical art pattern from my culture which originates from the Itneg indigenous people's group in the Philippines. Its dizzying pattern is said to scare away malevolent spirits, so this is a heritage motif in my culture."

And in a second comment, the writer states, "...(T)his particular motif is a sacred pattern that means something spiritually. Other people brought it to other parts of the world through colonization. As weavers, I think it's important to honor the original stewards of that material culture. It's not just weaving or weaving patterns. It's so much more."

So, with that reflection and understanding, I hope that bringing this image to the loom is a respectful act. To be truthful, for me, this did not come from any source that I recall other than the idea that weaving blocks can create optical illusions. At that point I saw that I had re-created a pattern familiar to weavers. Now that I know its history, I share this ancient illusion with a deeper understanding of the reverence felt by the people who created it. 

Below is my original post.

________________________________________________________

Perhaps it's because our brains just want to see patterns -- but do you see expanding circles in this drawdown?

But it's all squares, right? What's going on?

This is known as a "fiction illusion," in which the brain perceives a shape or figure that is not actually present in the image. Optical illusions involve different ways in which the brain and the eye process visual information, such that the perception is different from the reality. 

Why does this happen? Quoting from my Google search: "Your brain uses patterns, past experiences, and context to make sense of visual input, but illusions exploit these processes by presenting confusing or conflicting information, causing the brain to 'fill in the gaps' in a way that leads to a perception that doesn't match reality." 

Aha! Confusing or conflicting information, differences between perception and reality -- this is where weaving can createsome interesting patterns!

Our immediate perception of this black-and-white version of the pattern above: It's full of flowing lines that intersect, dilate, and compress.

But, in the weaving pattern, it's all black-and-white rectangles, increasing and decreasing in length and width. In weaver-speak, it's just double-weave blocks.

I'm in the process of dressing my loom with this design, which is simple block double weave on 8 shafts. Here's the threading:

Two blocks, that's it. But, if you look at the top of the threading, you'll see that the units of 1, 2, 3, and 4 descend from 9 to 8 to 7, etc., in number, all the way down to 3 -- and then they begin to expand again. This means that the widths of the two different warp blocks get progressively smaller, and then they reverse and get larger again.

The treadling is "tromp as writ," meaning that it's identical to the threading. ("Treadle as written" is my rough translation.)

Looking at the weft, you'll see the same progressive increases and decreases in the number of units per block -- from 9 units in the first block to 8 in the second to 7 in the third and so on down to 3, where the number of units begins to increase again. This means that the height of the blocks changes, getting progressively longer and then progressively shorter.

The beauty of double weave is you get solid colors: In the case of my drawdown at the top of this post, green weaves with green, in alternating blocks that are either on the top layer or the bottom layer. And red is doing the reverse. Double weave makes for bold colors and graphic patterns, which is probably why weavers like it so much.

Here's the tieup. It's a double-weave tieup, so that the first 4 shafts on the first treadle lift just shaft 3, while the second 4 shafts weave the bottom layer, which is being woven upside down. This means that, effectively, shaft 7, which is technically down, is the only shaft lifted on the upside-down bottom layer. Then, on treadle 2, the layers exchange, so that shaft 8 is lifting the warp on the top layer while shaft 2 is "lifted" on the upside-down bottom layer. You're exchanging the top layer and the bottom layer to form differing rectangles. And effectively you're weaving plain weave on both layers. (Caveat: I don't consider myself a double-weave expert, so I simply created a tieup that works for me.)

The structure itself gives you two layers of cloth that exchange (top to bottom) in the pattern we talked about, squares that 

increase and decrease in height and width. In my case, I'm threading everything in beige -- but one layer is 20/2 wool and 

the other layer is 17/2 nm silk noil. Using differential-shrinkage techniques (where the wool fulls and draws in 

and the silk noil buckles and puckers because it's being drawn in by the wool), I hope to end up with a fabric that has a 

really interesting texture. But I haven't finished threading yet ;o) because I had to re-thread to get the pattern just right....

(Please note that yes, this is an unusual double-weave tieup. A friend pointed this out and, to be honest, 

I created it because that's how I puzzled it out. I hope to fix the tieup in the next few days....)

And my loom's acting up, but that's another story. Fingers crossed. 

Thanks for reading!