Subwoofer for classical music listener

Personally I like RELs. I have listened to Storm IIIs, G2s (2500 - 3000 used), and Studios ($3500-4500 used). I prefer the older generation ported downward firing woofers (such as the Storm and Studio) because their sound is more nuanced, effectively allowing mid-range sound to come to the fore.
Too often, the subwoofers that I have used, although fast and precise, have been overpowering. I felt like I was spending as much time tuning the subs to my room as enjoying good listening. Good luck in your search, and do post about your experience.

I listen to a lot of rock classical and bebop jazz. I noticed that the B&W 802D2’s that I have didn’t go low enough for me to feel the music, and I did notice a low frequency drop-off. I looked for tight musical subwoofers and decided on a Rhythmic F15HP 15" ported servo driven subwoofer. It did take a bit of fiddling with room placement, and I set up the unit by experimenting with crossover points on the mains and subs while listening to slow bass sweeps. Eventually I got my system dialed with even sustainable perceived volume levels through the test bass sweeps.

The tight articulation and integration of the subwoofer and mains has made the music way more engaging. I’m sure someone knowledgeable with calibration software and a mic, would have been able to dial things in quicker, and possibly better but I am extremely happy with the decision to integrate a tight sub into my audio setup.

I’d recommend Rythmik, but servo loaded subs from a company like Velodyne which I heard are easier to calibrate, but they are over twice the cost.

They aren't servo loaded, but I've alos heard good things about SVS subwoofers.

Link to tone generator I used:

http://onlinetonegenerator.com/subwoofer.html

For $1,000 & sealed sub(s), there's only 1 choice that makes sense IMO: the SVS SB-1000. It's a compact, powered, sealed 12" sub. I use one in my home office (where I have a relatively refined desktop audio system). It sounds very good and I only wish there was room for a second one.

With your speakers, you'd probably only want these dialed in at 50-60 Hz, tops. Because they're sealed, the bass doesn't go quite as deep as it would w/the ported version--but that's actually better, since the sealed design (in my experience) outputs more natural sounding bass.

Forgot to say the SB-1000 costs $500 each; X 2 = $1000 (done).

Here's my 2 cents and it may just be worth that!
I've done a lot of research on subs and am an advocate of REL's. My system is dual purpose, 2-channel music and 5.5 channel home theater. When I say 5.5, meaning I have 5 subwoofers. A loudspeaker is only designed to generate frequencies to a certain level, typically around 40 Hz for floor standing and 60 Hz for quality bookshelf's. Therefore, why not allow every channel you have produce a full range from 20-20K? Anyone who does an A/B of a system with and w/o a sub quickly discovers something missing without the sub. We live in a full range world. If accurate reproduction of a musical performance is what we're after, then it's important to reproduce everything that was present during the original performance.
As far as REL's are concerned, they are integrated using a high level signal tapped directly from the speaker tap of the amp. This way the sub gets the signal at the same exact time and the same exact signature at the corresponding speaker. Setting the crossover and volume can be a bit tricky however, once set correctly, it's a seamless integration. You shouldn't hear your subwoofer. You should hear the system!
A subwoofer should cost roughly what a loudspeaker cost, or more! It's much more complex and it's the subwoofers job to integrate in the system, not the pre-amps or external crossover's!
I encourage anyone looking to buy a sub, to consider a REL. Don't just look at the pretty box, READ the technology behind it, how it's integrated, and why. Most other subs rely on the pre-amp's crossover or a separate external crossover. If buying extra gear to display is your thing, go for it. If you want a system that is truly integrated, synergistic, and sounds like its all "one" system, read about how the REL works....