Jean's comment on the differences on right and left (or top and bottom) made me do what I have thought to do for a long time: can the differences be avoided?
So I started with my "normal", looking at both sides:
Seeing that both sides are the same (one side clean, the other jagged) made me suspect that it can't be "fixed", as long as one is interested in a reversible result.
By adding (or subtracting) two ends at the jagged side, one can get clean cuts at both sides.
... but the back will then get both sides jagged:
Personal conclusion: until I feel the urge to take the exchanging layers to twill, I will continue to weave two picks per layer, and live with the un-equal sides because of the reversibility of the result.
Others may have other ideas...
Yesterday I stopped before doing what I always do: rearranging the treadling for easiest actual weaving:
Unless I have very fat yarns in my double (in this case triple) cloth, I try to arrange the treadling so that I can do two picks per shuttle (layer).
It is so much faster to do two picks before having to change shuttles...
(Yes, it shows in the end product:
These are two not quite focussed pictures of double-layer shawls.
They are approximately 2 x life size, and has the ends one-by-one and the picks two-by-two.
The warps are a combination of cottons, 16/2, 20/2, 22/2 and maybe a few 30/2.
The wefts are of course only one quality per shuttle, but I don't remember which grist. The sett was probably somewhere about 10 ends/cm (25 epi).
And no, I haven't tried it for three layers.)
So: here is what I would do before sitting down to actually weave.
First: use the existing tieup, but rearrange the colour sequence.
Next: rearrange the new treadling to straight:
As I weave from bottom to top, and have an overhead beater, this is the treadling I would use, namely start in the bottom layer, working up to the top layer, as seen in the widest section of the warp.
(Yes, on the loom there will be "gaps" where the layers change. I have never seen these gaps after wet finishing - see pictures above.)
Remembering one of my doodlings from yesterday (which did not reach publication) - another way of making more-than-two-different narrow stripes - a shift in the warp sequence can accomplish that:
So, the question was: how to make a three-layer weave, with warp-wise layer changes?
(and preferably on 12 shafts "only")
This is how I approached the problem:
(To all Swedish readers (and Ellen: hi, Ellen!): note that all tieups are for rising shed. This means that the layers/colours will be reversed if the tieup is used "as is" for a CM.)
Started with a three-layer (three independent layers) weave - for plainweave layers, that takes six shafts.
For instance like this:
I made the top layer turquoise, the middle layer purple, the bottom layer red-orange. The three layers do not interact at any point. (Note that the difference in nuances between warp and weft makes It easy to see that the bottom, red-orange, layer has a correct interlacement, even without using the "back view".)
Now, we wanted a lengthwise (warpwise) layer exchange. I decided the left hand side is a good place. Thus, to start the construction, assume another "block" of the same threading and colour to occur at the left side. Like so (left pic):
The same threading on a new set of shafts (= a new block), with the same colour order. We want to shift the layers, so I let them "cycle": the middle, purple, layer goes on top - the bottom, red, goes in the middle and the top, turquoise, layer has to go to the bottom.
OK, I hear you: how do I do this?
I am using Fiberworks PCW (silver, if that matters).
By clicking in the drawdown, I can get ends/picks to the top (for instance).
Middle pic above: all purple threads, both warp ends and picks, are taken to the top.
Next is to fix the interlacement: right-hand pic above. Note that the interlacement should be a continuation of the purple plainweave in the right-hand (first) three-layer block.
Now to fix the middle layer, the red-orange one. Click all ends and picks so that they are under the purple layer, but on top of the turquoise (left picture below). Fix the interlacement - easy because of the difference between the red and the orange - right-hand picture below.
For the bottom (turquoise) layer, it is easier to use "back view".
As it happens, all turquoise threads are already at the bottom... fix the interlacement, go back to "front" view again:
Unfortunately, all the 12 shafts are now used.
As we want another stripe, we add another block (6 shafts) - now the total is 18.
The same procedure again: make the red-orange layer top, the turquoise will be in the middle and the purple layer will go to the bottom layer:
In the hopes that I had missed something important, I let the software analyse my result - alas, I had not: it really takes 18 shafts to do this.
What if: let one of the layers stay in the same position for two stripes: this will reduce the goal to two blocks. With the three "open" layers on the right-hand side of different widths, and several narrow-ish stripes on the left-hand side... voilà, only 12 shafts. An alternative?
(As I, personally, prefer straight threadings whenever possible, I rearranged it for this final picture, showing both front and back:
(Remember: click pictures to enlargen)
So is it possible to use dräll pulleys for other than two-block "opposite" weaves?
To refresh your memory, here is one illustration from my web page on dräll pulleys, with 6 shafts mounted:
The question came up in another context, and I tried to construct some examples.
Starting with a 2/2 twill - this is one "normal" way to thread and tie it up:
As can be seen, that tieup will not work. Starting from the left, the first column will work. The second will not, as shafts 1 and 4 both go up (in the Swe notation), while shafts 2 and 3 both go down). Third column is "opposite", fourth is not.
So what can be done? We need to do something to both column 2 and 4, trying to get them "opposite". One way is this:
Next try, an 8-shaft even tieup (by "even" I mean that all sheds have half of the shafts up, half down, in various combinations - see a discussion on "even" weaves here)
Started with the leftmost column - and got the fourth correct as a bonus.
However much I tried, I could not fix more than 4 columns/treadles.
Maybe I could modify the pattern some, and still like the result? So I marked all the ties that conformed with the rule:
Started to take out/put in ties in the possible positions... this was the best result I could come up with:
Would I weave this? No, but then, I am on a countermarche...
Compare it to my starting point:
I tried various other even tieups with much the same results, and in the end I decided that there is a good reason the pulleys are called "dräll" pulleys: they are excellent for two-block "opposite" structures! For all the others, there are countermarche looms...