just got to add my 2p's worth here.
Now whilst I do not claim to have the mathematical know how, nor wish to claim that I know more than the clearly knowledgeable previous posters I would like to share my experiences of setting up a normal living room for critical monitoring.
The only claim I make to knowledge is that I have a good ear and the recording and mixing work I have done in less than ideal environments is testament to this.
As for proper speaker placement it will depend on speaker design (closed box, front ported cabinet, rear ported cabinet, passive reflex, etc) however, the basic things I learnt were:
1) Form an equilateral triangle with your head at the apex
2) Tweaters should be at around ear height
3) if you're in a square room, or rectangular room standing waves could be a problem, rooms with uneven geometry are less likely to cause issues.
4) these can be offset and ameliorated with soft furnishings or commercially available bass traps in the corners of the room
5) you can use line of sight to work out reflection points (behind your head, above your head, behind the speakers etc) these should be treated with some form of reflection damping. You can make perfectly usable and effective reflection dampers using rockwool, a wooden frame and some kind of decorative fabric covering, or you can buy commercially available aurlalex foam
6) Sofas, bookshelves etc all affect the geometry of the space you are listening in as they will absord some frequencies and ignore others. Unless you are working in a tailored environment ( in which case, go to a professional) the only real guide you have is you 'ear'
There are no hard and fast ways of setting up any real world space for critical or even just good old high fidelity listening.
My best suggestion would be to follow some basic guidelines (see above) and then find someone who can sort you out with a cd or tape of low, mid and high frequency tones played from low to high c at the same db and listen for any that are either overly pronounced or inaudible...
If, when in the listening position, you can hear all tones with the same perceived level then your system is optimal.
This kind of process has allowed me to set up studio monitors for critical listening in adverse conditions on more than one occasion. I have used it to set up my hi-fi and found it to have similarly pleasing results.
Hope this is of interest to folks out there in audio land.
-freedom is what we do with whats been done to us- J.P Sartre
Luxman L-100 - SL-150 Mk2, SME 3009, Shure M97xE-Marantz CD 75Mk2 SE KEF Cadenza, Event 2020 BAS