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 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 luck 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.
For more about Farey and his fractions, here is a Wikapedia article.