After a phone call to my weaving guru, Joyce Robards, I now know more about taqueté. It's actually Summer and Winter without tabby, but with a pattern weft alternating with a tie-down weft. That means it's usually a two-shuttle weave. The beauty of this pattern is that it's turned, and I'm weaving with just one shuttle, alternating between a pattern pic and a tie-down pic. Here's a closeup.
For the most part, all you can see are the pattern warps (the long floats on the surface of the fabric). If you look very carefully -- or if you can double-click on this photo to enlarge it -- you might be able to see the tie-down wefts hiding among the pattern warps....
It's a complex structure, calling for lots of counting on my part. I have notes taped onto my loom to outline my treadling order: my left foot taps out the "bass line," alternating between treadles 1 and 2, while my right foot plays the melody on treadles 3 through 8.
The original design by Mary Berent takes up the entire page. Very complicated and not to be attempted when the weaver is sleepy or has had a glass of wine or two.... You see the pink paper clip? That's the middle of my towels, where I reverse the pattern. No way I can count beyond that with any accuracy. Not without a computerized loom!
Joyce tells me that taqueté was often used for elegant fabrics, similar to a Jacquard weave, because it shows off the colors and pattern so beautifully. I have a plan to tie onto this warp, using it as a dummy warp, with some leftover hand-dyed 20/2 silk in purple, fuschia, green, and gold. More adventures!
Once again, here's a link to the Berent pattern on "Weaving Today."