Anatomy of this year's Christmas towels

 Quite a few years ago, I read a paper called "Designing with Farey Fractions" by Ralph Griswold.  Ralph was a computer scientist with a penchant for weaving drafts and weaving design.   I did some designing using a Farey sequence as the threading for an 8 shaft draft and wrote about the process here in this blog. https://bannermountaintextiles.blogspot.com/2013/07/farey-fraction-towels.html    The results were interesting (to me) but recently I began to think about other things that might be done with this Farey sequence used as a profile draft. 

I digress a bit here to tell you that I don't understand the mathematics involved.  Yes, I've looked at the papers and most of it is just out of my league.  However, using mathematical sequences in weaving design is very much something that I understand and can use.

I started thinking about how I might weave green and red towels for Christmas sales without the problems of green and red crossing one another and blending into brown.  The solution appeared to be to use blocks of weave structure so that the colors of red and green would appear more or less solid against one another.  Which comes back to using a profile draft and translating it to satin and block twills to weave my towels.    I selected the Farey sequence above for my threading profile and converted it into a series of drafts using 5 thread satins and 5 thread twill blocks. 8 blocks times 5 thread structures translates to 40 shafts.  How lucky for me that I have a loom that will weave these designs!

In preparing the ideas for my warp color, I used stripes of red and green which used portions of the profile that would give a different design for the two color stripes.  Red and green yarns were another problem.  I didn't have any of the specific value in my stash that I wanted for the warp, so I wound off 2800 yards for the green warp stripe and 2800 yards for the red warp stripe. I dyed each of the 2800 yards in the same pot so that I would get exactly the same colors - although, a variation in the warp color stripes could have been interesting too.

 1/5 and 5/1 twill blocks

 This towel was woven with 5 thread satin blocks making it a damask cloth.  And all without a Jacquard Loom!

Accidental Christmas trees appeared in this variation.  Again, the structure is 5 thread satin.

I was able to weave 11 different towels on this 12 yard warp and still had designs left that I could have woven.  This last towel was woven with a dark green weft which almost changed colors once it was planted on the lighter green and the red warp stripes.  I'm always amazed at the differences you can get from variations in weave design and weft colors and must say that I didn't tire of what kept emerging as I wove.

I guess the final question is whether or not I'm done with Farey Fraction sequence weaving.  Probably not.  I expect that the next warp will expand the sequence into a larger design - but who knows, it may take me years to come around to the next iteration in my fascination.

Postscript!

For more about Farey and his fractions, here is a Wikapedia article  and a photo of the Farey Fraction sequence up to 8.  Use the denominators for your own sequence work.

If you are interested in satin weaves and  their various counters, here are a couple of resources that help to explain how they are formed. The documents contain almost identical information but in somewhat different format.  If you eyes aren't glazed over when you finish with these documents, I don't know what it will take☺

http://www2.cs.arizona.edu/patterns/weaving/webdocs/mo/D/SatinCounters.pdf

https://www2.cs.arizona.edu/patterns/weaving/webdocs/gre_satn.pdf

Farey fraction towels

I'm finally getting around to putting up the post that shows the some of variations on the  Farey Fraction Denominator threading.  Some of them are very busy, one or two show a good solid design and some didn't show the complexity of the threading at all.

These towels are all woven on the same warp using different tie ups and mostly a point treadling.  I used an advancing treadling on one towel.



 This is the most elegant design. The pattern is clear and varies across the warp.

 This towel is the end of the warp.  I used up all of the odds and ends of yarn left on pirns. It was interesting to see how the weft color influenced the design.

 I actually like this towel a lot.  The pattern shows up in both the red and dark purple areas and it seems almost like embroidery. The reverse of the towel (folded back) shows a redder pattern.

 

 This close up shows how the design alters across the warp.  The weft color worked well with the warp; always a surprise which wefts are good and those that are just ho hum!

 

 

 The towel in this photo shows two very different looking faces.

This was a worthwhile exercise in design work even though my original idea of the red stripe design showing up between bars of dark stripes didn't translate the way I imagined it would.  The main feature of the designs are an embroidery like appearance to the cloth.  However, the designs are small and so detailed, that they can seem overly busy. 

Designing with Farey Fractions

This post may be a bit premature because I haven't yet woven off my Farey Fraction designs on this towel warp.  Who knows if the designs will meet my expectations or not.

The journey started with needing to do a paper for the Computer Aided Design Exchange for Complex Weavers.  I did the paper, had some errors that needed fixing and then got into a nervous nelly fit about whether or not my designs would actually weave into anything that looked like the vision I had in my head.  I don't know about you, but once I start doubting myself, it can be hard to go forward.  I kept the paper on a back burner and decided to weave some of my ideas on a towel warp which would either prove the design value or let me know that it was just a gimmick.

The paper is based on Farey Fraction denominator sequences used in weaving design.  That's a mouthful, isn't it, but not nearly as intimidating  in practice as it sounds.  Ralph Griswold wrote a paper about designing with the sequences  and you can find his work here.   I learned about the sequence and its design possibilities from a FaceBook post by Marg Coe, so I'm not working with brand new ideas, just trying to expand them with my own touch.

I found an online calculator to make the math part easy for me.  From there, I just used the denominators as a threading sequence and experimented with various tie ups and treadling sequences.  My idea was to have a complicated threading that could be woven with a simple treadling sequence on my Baby Wolf.  When I got right down to warping the loom, however, I decided that I would put in on the AVL, add a basketweave selvedge and treadling my threading to avoid threading errors.  To top off the complications, I saw a natural color sequence in my draft and it was awkward  because I used a sett of 20 epi and my color sequence was 12 red and 11 navy, which made every bout I wound had to be calculated for color.

Let's get down to a sample draft.  Start with a denominator sequence based on the number 8.  Here is the threading.

I then advanced the threading one step seven times. (This creates a threading that comes back to the original threading after the seven advances. What you see below is only a portion of the threading sequence and is still in the 8 shaft form before selvedges were added.   I have done 12 different tie ups and a variety of treadling sequences for my 12 yard towel warp.  Once they are off the loom, tell me if you think they they were worth the fuss!

 

What I like about this design is how the pattern changes in each red warp section - sort of like looking through a fence.  Some of the drafts are better with a light colored weft which shows off the design in the wine colored warp.

 

And, no, I don't mind if you use this draft or expand on it for your own use.  I really think it would make a good draft for a weaving demonstration - change your tie up and you get an entirely new design peeking at you through the fence.