I think the shade is 1970s Murano glass, probably by Tony Zuccheri. He did a series of molded objects with the same distinctive indentations.
I have seen tons of these shades around, usually with 1970s-ish chrome hardware. Most Murano shades were sold without hardward, and purchased by lamp companies that assembled them. I vote that the base is a marriage, or assembled by a style-challenged lamp distributor.
The hanging shade could be P&P. Barovier also did something similar called 'efeso.'