Two layers of cloth are laid face to face and run through metal cylinders under pressure. Some of the weaves are flattened, others left standing, and the wave that results is never the same twice. That is moiré, technically a gros-de-Tours here, invented in Italy and common enough in Renaissance painting to turn up behind the Madonnas of Bellini and Crivelli. In Venice it was called amuèr and pasted onto palace walls, which is more or less what is happening here.
The cloth is Trevira CS, so it is inherently flame-retardant, with the silky surface that goes with it. Twenty-two colourways, produced to order, 135 cm wide and sold by the metre. Certified to EN 13501-1, ASTM E-84 and IMO 5. Made in Italy.
One thing to know before specifying it: because the watering is made by hand, the pattern will not align across a join. The irregularity is the character of the cloth, not a fault in the hanging.