This is a very old lampshade, it must be at least 30 years old. The construction of the shade itself is very easy: because of the pattern of this fabric, it was made as a cylinder with a channel for a drawstring at each end. The cylinder is slightly bigger than the wire construction, and sewed with attention to the pattern.
The fabric was bought.
The warp is a thin cotton. I think the warp yarn is the same all over, but it is hard to tell. The weft is the same, except for the closer bands: that yarn might be a thin singles linen.
Here is the drawdown:
I gave the presumed linen a different colour, to make reading the construction easier. (The detail picture does obviously not contain a whole repeat - fill it in yourselves)
The crammed warp stripes has 24 ends each; for more open parts I did not even try to count the number...
Also, I did not check the sett, but my guess is that the crammed stripes has double the number of ends per unit (this is the reason I left every other "heddle" empty).
The same goes for the weft: the crammed bands have 12 picks, the two first end the two last in each band go in the same shed. I guess that the linen weft is double the thickness of the other yarn (and I think the other weft is the same as the warp).
Each square is roughly 2 cm - maybe 1/2 cm for the crammed stripe/band, maybe 1 1/2 cm for the open square.