When reading upon the Shroud of Turin it was noted that it uses a distinct 3-1 Herringbone weave. Many textile experts say there is no evidence of this weave existing in the first century middle east but other sources say it is consistent with first century Syrian design, and it’s hard to make out which sources are biased or accurate when many sites claim one or the other. (Either way even if it did exist I’m aware no 1st century Jewish burial shroud we know of was more complex than a simple two-way weave I’m just wondering if the 3:1 weave in general existed)
The weave of the Shroud was closely examined by Gabriel Vial of the International Centre for the Study of Textiles in Lyon, in Turin in 1988 (The Shroud of Turin: A Technical Study, at shroud.com). Professor John Tyrer of the Manchester College of Technology also wrote a detailed analysis of the weave, based on photographic studies (Looking at the Turin Shroud as a Textile, also at shroud.com), and finally Piero Vercelli, of the Quintino Sella Technical Institute, wrote La Sindone nella sua Struttura Tessile.
All these people thought that the Shroud must have been woven on a four-shaft loom, and, being believers in the authenticity of the Shroud, made some attempts to establish the existence of such a loom in the ancient Middle East, without success. Two alternative looms should be considered, the upright, warp-weighted loom and the flat, treadle-loom. The first was common in the Middle East, and all over Europe, from antiquity, while the second appeared in Europe in around the twelfth century. Only the second can be demonstrated to have involved four shafts. There is no archaeological evidence for a four-shafted warp-weighted loom, either in terms of the loom itself, illustrations of looms in ancient paintings, or the textiles it might have produced. The theoretical loom illustrated on the front cover of Vercelli's book is an optimistic reconstruction of what he hoped might have existed, rather than anything which did.
Determined authenticists then looked to examples of 3/1 twill from antiquity, and came up with several bands, belts or straps, and also some pieces of Syrian damask, all of which have weft threads which go over three and under one warp thread in a more or less regular series, which is what twill is. However, these were demonstrably not woven using the kind of loom necessary for the Shroud. In theory, anybody could set up a set of warp threads, and then manually manoeuvre a shuttle of weft in and out across them, to produce any pattern they wanted. Or they could hook all the threads they wanted the weft to go under, to a shaft, and by lifting the shaft make a 'shed,' and pass the weft through it, and then re-set the shaft for the next pass. This was how the Syrian damask was made. While it would be possible to weave any pattern of cloth using these methods, it would be absurd to suppose that if the weaver made an error in his shuttling, or warp-hooking, he would repeat it all the way through the weave. The Shroud, however, shows exactly that, demonstrating that all the required sheds were set up, using the four shafts, at the beginning of the weave, after which it would have been very awkward to reset them after an error had been discovered.
Finally, I have asked two weavers to produce some 'Shroud material' for me, using both treadle and warp-weighted looms. Ruth Gilbert made some on a treadle loom (Replicating the Weave of the Turin Shroud and Weaving the Shroud, A Reproduction by Ruth Gilbert, both at shroud.com) but Antoinette Olsen found it impossible on a warp-weighted loom (The Shroud of Turin and the Extra Sheds of Warping Threads, at exarc.net).