I would be careful not to overdamp the room. Curtains can suck the life out of your music.
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Try it all ways possible; first the curtains without, then pin one layer of baby blanket material, and finally two layers.
You do not have to use a baby blanket material. Perhaps a treated fabric like "black out material" would be superior in many respects. This is a fabric coated such that it blocks out light completely, which is what several layers of baby blanket material would do as well, I believe. The black out material would be lighter most likely and may have a better sonic property of absorbing some of the sound waves but still reflecting enough that it would not sound like a sonic black hole. You are trying to recreate the effect of a wall, not a sound absorption panel. :)
You should have a strong preference for one of them. :)
My guess is you need to balance out your room. It's not only high frequencies giving you fits. It's reflections and a frequency imbalance within the two sides of your room. When you select curtains look for natural materials opposed to synthetic materials. Synthetics are frequency selective and natural materials will give you a more balanced sound. What's the other side of your room like?
Absorption panel it is not. Whatever you hear thru the curtain held in front of you will reflect from the glass. Curtains should help at high frequencies but you might think of some fiberglass absorption panels. I'm putting twelve 2'x4'x2" high density fiberglass (Johns Manville 817) panels on the wall behind sofa I'm sitting on (first reflection point) knowing, that they work only from approx 200Hz up. I wish I could use 4" panels but it looks worse on the wall (WAF).
Look at 812 1" panels. Their absorption coefficient shows good damping from 1kHz up. Thickness of the curtains in comparison to 1" thick panels suggests that curtains will help only at tweeter frequencies.