Thanks again everyone for the replies. DOC! I was beginning to think you fell ill, GOD forbid. Haven't heard from you in a while. When I started this thread, I posted some rather different requirements. I had reasons for this. Mostly, I didn't want the standard replies.
What I am really after is a sub that can go super low so I can get to the frequencies you can feel, but not hear. Yes it's true most people may not be able to hear below 20 hz, but I figure if a sub is good to 10 hz. It should be awesome at 17. Kind of like having headroom in an amp I suppose. But I also want a sub that will be more than capable for HT and music, especially music, even at lower levels when I don't want the music to be the only thing I can hear in the house. I'm not convinced I can get all of that out of the same sub. I could however be wrong. I certainly hope no one feels as tho I wasted their time, if so my humblest apologies, but as I stated I wanted something different from the usually recommended stuff.
With all that cleared up, where do I start. TLS, if this sub is a poor choice, what would you recommend and what type of enclosure. Budget is not an issue, although the higher the price tag, the longer it will take to complete. Size could be an issue if it gets too huge, but I'm willing to work with about anything. I will figure out how to make it look good in the room somehow. It kind of all has to come together, pros vs cons, as with any sub it seems.
The trouble is you are fixated on low F3. That will lead you astray. The most important parameter for any speaker is its sound quality. The crux of the error of your thinking is that "if a sub is good at 10 Hz, it will be awesome at 17 Hz." Almost certainly with a cone driver it will be lousy at 17 and above.
The most important parameter is the quality of the bass, especially that it be non resonant or close to it.
The other issue is that you don't have to get the F3 into the teens or single digits to feel bass. I don't use a sub, or sub drivers, but I can certainly feel bass with these speakers. In room F3 is almost exactly at 20 Hz. I have watched the opening night of the Proms several times now. I can feel the huge RAH organ on many occasions and the effect created is just the same as in the Albert Hall.
The problem comes in the home of getting bass out of a fairly small box. As I have so often pointed out, a speaker cone is a terrible and inefficient coupler to an acoustic space, and the larger the space the worse it is.
All closed boxes have a much higher F3 then driver Fs. So brute force becomes mandatory with Eq and high power. Even then if you pursue low F3 you still need a heavy cone and less efficiency and the spring (suspension) still has to be sloppy.
If you use a Qb4 vented enclosure, then you end up with horrid high Q "extended bass" alignments, rather then the optimal alignment. My advice is to never sacrifice bass extension for bass quality.
Now there are good reasons in physics why the pipes of an organ like the one on the RAH as so massive. It all has to do with filling the space evenly and cleanly at high spl.
Speakers are no different. However we live in small houses. Never the less, building speakers of the dimensions dictated by physics, and not building ones forced to perform by brute force, will always win the day. It all comes down to acoustic transformation. To perform optimally in the lowest octave, cone speakers need an acoustic transformer. The best options are pipes or horns.
To cut to the chase, for domestic purposes, a speaker system built round a driver with an Fs around 20 Hz and a Qts in the range of 0.3 to 0.4 is optimal. I personally think around 0.35 is the real sweet spot.
As you know some members have built subs, I have designed. They seem to really like them. I don't have to play the numbers game and get the lowest F3. However in practice, I bet mine sound as if they have a better bass than a commercial offering designing for lowest F3.