speakers on hardwooed floors

Smaller than your room....

Consult she who must be obeyed.  There is no audiophile input on this one.

Question-
How hard did you woo them?

First of all you will want to get a spectrum analyzer. Take measurements from 14 different locations. Map out frequency response in three time domains. Take the average of the worst two at two different points. Write down the dB errors. Take the absolute value. ie -6dB is 6, +8dB is 8. Those are the length and width of your area rug. You're not done. Take the best one, the greatest +/- error is your shag thickness. You're not done. If above 1kHz then the rug must be red. If below, a neutral gray or brown. 

Either that, or you buy one that looks nice and fits the area. Never could keep those two straight.

He must have used Jeffrey Osborne's   "Woo, woo, woo" song.

Consult she who must be obeyed? Yikes, mine is and always will be the only input.

The following link is to a room size/rug size tutorial with various furniture placement options.

The rug should cover the area between the speakers and the listening spot(s), and not look stupid/out of place while laying there.

I’ve read that natural fibers are better (I use large 100% cotton rag rugs over unnatural carpet because I like the way they look/feel).

https://www.wayfair.com/sca/ideas-and-advice/guides/how-to-choose-the-right-rug-sizes-T456?refid=GX4...

DeKay