Sound Absorbing Drapes

I think it is fair to say that a room will be at its best when a microphone is used along with computer software to read room modes and learn what can be done within the space using absorption/diffusion..

The aesthetic of the selected treatment can't be disputed for the impression made on the selector's eye and the integration with the space's decor. Beauty is in the eye of the beholder.

Without Data being recorded, any explanation for the effect of a material used within the space for mode control will be conjecture. Even if the user of the room detects a change to the end sound presentation, there is also the risk that remaining within the room are modes/nulls and a speaker positioning that are not ideal.

It makes sense to get the space mapped to learn a methodology to treat the room.. 

I had cellular shades, then added foam behind shades, finally put diffusion panels in front of window and preferred that sound the most. I like depth and dimension.

I have - and continue use - heavy cotton drapes. And the last ones were reinforced with another absorbent fabric. And they hung over windows on the wall behind the speakers. There were also columns of Tube Traps along the walls, but I was glad to have the cotton drapes over the window in contrast to even more Tube Traps everywhere else.

Tube Traps are fantastic, but one must be willing to move them individually by inches to see where they kick in. Even I misplaced them in my family video setup anad had them 1" out from optimum, and the gutted the lower midrange and made it hollow. 

So, All acoustic improvements should consider experimenting, once the speakers appear to be in the correct position, then acoustically putting  panels or acoustic improvements in the best location you can hear  vis a vis the speaker.