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Have a 1/2 decent AV set-up with Mordaunt Short satellites & centre speaker with a pair of Jamo front speakers with a Yamaha RX-V679 amp.
Our current TV stand has 3 shelves which has the amp on the bottom with the centre speaker on top of the PS4 on the 2nd shelf and TV on the top.
I'm guessing that the centre should, really, be at ear height to work the best but that's not possible with the height of the TV.
So, question is where's your centre speaker?
Similar to yours, have been looking at a new stand to elevate the screen and put the centre on the top of the stand, but it was about £400 to get the one I wanted and I didn't want it *that* much!
Directly under the TV but in the stand.
I had it made out of oak to accommodate the speaker and the amp and other peripherals (set top box, DVD, blu-ray).
So centre is about 2 foot off the ground so maybe a bit below ear height, but sounds much better than near the floor.
Get it as close to ear height as you can, or could you maybe try and angle it up slightly?
My TV unit has a place for a centre under the TV but the speaker is too tall to fit in, so it goes down on the shelves with the amp. They do have an open/grated front.
This has reminded me to buy a new, lower profile centre speaker!
Ideally it should be in line vertically with the screen. Height doesn't really matter. </2p>
Trouble with putting it at ear height is that conflicts with your screen eye level.
Luckily it can be angled to achieve the same effect.
Pretty much the same sat on the shelf with the TV works very well.
I suspect sonically above the screen would probably be better but visually below. TV is wall mounted, speaker wall mounted just below it.