How to diagnose the need for room treatment?

Another option if you have a PC is Room EQ Wizard (for PC and free - a vry cheap solution) or Fuzzmeasure Pro 3 (for Mac $150) - you'll need a measurement microphone and a pre-amp like a Dual Art USB pre and off you go - measure to your hearts content.

Make sure you have a measurement microphone - an omnidirectional condenser type. For example the Behringer ECM-8000. An ordinary microphone is not suitable

SPL meter readings could be a LOT worse - a few observations.....

No kidding. The bass response is superb - almost to the point of being suspicious - hardly any room is ever that good without being treated.The broad dip in the midrange is probably just "midrange scoop" - most speakers are weak off axis in the upper midrange and your ears and SPL meter will sense this.

Since you have positioned your speakers in the middle of the room (15 feet out) they will not excite the room length mode nor its harmonics - as the speakers sit at a pressure null. I think this is the principal reason you are getting such good bass - as usual "acoustic physics" dictates how it will sound...

I wonder if treble beaming could be a factor as well, assuming the tweeters are pointed straight ahead. Should be easy enough to check, by toeing the speakers in a little, and re-measuring.

Only very high up (at 10 Khz and above), however,the 804S is a typical B&W with the "midrange scoop" - they run the excessively large midrange up to 4 Khz and the tweeter has no waveguide. This means you get beaming on the midrange and which causes the mids to lose energy between 1khz and 4Khz when in a room. Above 4Khz the energy returns as the tweeter takes over with its typical wide dispersion pattern in the absence of a waveguide.The power response would show a "scoop" in the midrange and a stereophile horizontal dispersion plot would show this hole at 60 degrees off axis. Perceptively this sounds laid back in the mids but with plenty of presence detail - it creates a very nice sound with emphasis on articulation that B&W is known for.

The only B&W's I know that do not exhibit this "midrange scoop" are the B&W silver signature, the B&W 805N (Nautilus and not the "S" version) and their top of the line 4 way Nautilus. It is actually not uncommon for most two ways with large 6 inch midranges and a tweeter crossed over high to sound this way.

The in room HF roll off is quite typical anyway - that would be completely normal for a room that size.

Here is a useful chart to explain how the speaker will sound. You can see why B&W would choose to voice it this particular way: bass string pluck, drum and guitar attack and vocal presence will all be increased- giving the impression of more detail compared to a flat power response.

Of course some people believe that measurements are like the zodiac and reading the position of planets ....i.e. "completely meaningless" ....just don't tell that to the engineers mixing/mastering your music. They use many rules of thumb based on measurements - a good engineer will know exactly what to do to create a desired effect and so will a speaker designer....

Al,

That is roughly correct but beaming starts a little earlier. If you look at figure 3 you will see that the prototypical 6" woofer and combined midrange should not really be used above 1.8 Khz - like was done in the famous Energy Pro 22 speaker.

So why do we see so many speakers with 6 inch woofer/mids and a tweeter with a crossover much higher than 2 Khz?

Cost is the answer - unfortunately few tweeters can handle SPL requirements at that low crossover point - not without distortion and risk of failure. However to avoid having to add another driver (increased cost/complexity) the designers make do with beaming in the midrange...odd really in what is ostensibly an audiophile design and given we have known about the physics of loudspeakers for donkeys years and considering this frequency region is where our hearing is the most acute and discerning.