Stereo Speakers behind a perforated screen- How much loss in sound?

There will be some loss of upper treble, the amount of loss depends on the screen, but usually less than 1dB, just have the speakers as close to the screen as possible.

Are you using a center? Subs? where are they?

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I'd never, ever put a screen or anything else between me and my speakers for critical 2-channel listening.  Acoustically transparent screen???  Yeah right.  Unless my speaker designer meant it to be there, it's gone.  Can't you just raise the screen for stereo listening?

I agree that there is some loss of fidelity with using acoustic transparent screen, therefore, not ideal for critical two channel listening. I have two separate setups, home theater with the aforementioned acoustic transparent screen and B&W 804 diamonds behind screen, and a large HTM1 for center, and B&W 15 inch sub behind screen as well. I have a 3 foot deep pocket behind screen which is great for placing speakers behind screen. For the critical two channel setup, which is also on its own dedicated circuits, I optimized the room for stereo listening, vice the typical muted and overdamped with lush wall to wall carpet rooms. Used spot throw rugs, absorbers, diffusion, etc. Home theater is 7.1, 4 in wall speakers, 34x20. 

Understandimg that each enthusiast has there own set of issues and compromises, if you can’t go a separate two channel setup, make sure that the speakers are dynamic, and efficient, maybe horns, which offer greater projection authority and perhaps make up for the loss of upper treble and mids which would occur with a screen. I ran separate HDMI, coax, Digitial, XLR, RCA, to my stereo rack in the theater, listening room from the AV rack in another room, to give me further options for connectivity.

By by all means, stereo will still work and can sound great behind a screen, but it will not be fully optimized, especially if you are used to a certain label of fidelity and clarity. Good luck.  

for audiophiles, its a no no.

for big altec or jbl  type horns, the screen doesn't really stop the sound for theater.

How locked into your existing screen? ... there are some electric retractable AT screens out there.
I have Centerstage AT fabric for a DIY that I never got to in old house where I had a huge HT room ... and now looking at a retractable one for the new place to overcome some space issues.

Oh ... and tab-tensioned too, of course

Aside from screen permeability to pass sound, you also give rise to odd reflections etc.

Only solution I can see is the one I've used - a screen that retracts when you want to listen to two channel (and in my case a different preamp/amp that sounds better but has lower output than my AV amp path).

My main speakers around now outside the screen area in my new listening/viewing room, but in my old smaller room, the speakers were right behind the screen - minimal loss of SPL if you get a quality screen made for audio transparency.