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.