Do I need a subwoofer? Which brand and model?


I mainly listen to classical and jazz - mostly trumpets and violins, with the occasional piano, viola or bass guitar. A couple of my friends have been suggesting to me that my ensemble lacks bass and having a subwoofer will address it. My setup includes a 2 ch. NAD C365BEE integrated amp, Wharfdale EVO 50 loudspeakers (pair), and an Oppo BDP 105 Bluray player as a CD player. The setup is in the living room, with three walls, and the fourth side open to the dining room. The living room itself would have been 18' L X 12' W X 18' H = 3888 cu. ft, but the fact that it opens up to the dining room makes the entire space more like 40' L X 18' W X 12' = 8540 cu. ft. Would I benefit from a subwoofer and which one should I get? Budget $1000 or close to that.
shugho
The build quality is fantastic - beyond my expectations. it's heavy too. I ordered the piano black finish by the way. Will let you know how it sounds after cables arrive.
Finally set everything up today. I was confused about the cables (got a single one from Blue Jeans, then had to order a Y adapter to connect to the stereo outputs). Also, you cannot connect this to Pre 1 on the NAD as there is a hard connection (bridge?) between that and Main, and no sound comes out of your front speakers if you take it out. NAD has a handy Pre 2 with a volume control on its own :) Having figured this out, next challenge was the settings on the sub itself. Initially, the presence was not felt or very minimal. I put the frequency to LFE, the Phase to the other end of 180 degrees (0 degrees ?), and the volume on both pre and sub to max. Now it is making its presence felt :) I can distinctly hear the bass guitars on it, much more pronounced than I ever have. This is precisely the aspect my friends had complained about, Current placement is left of left front speaker, pointing towards center of room where current listening position is. SVS recommends putting it in the corner of the room, which I can also try. For the moment, I am happy, but I will need to keep tweaking and start measuring. I also changed the cables between the Oppo and the NAD amp with a Blue Jeans stereo cable, separately, and that had already improved the sound level at least. I am now a believer in subs and am already looking forward to a second! Also, I am wondering if an audiophile grade rack (not a bank breaker) would further improve anything. I need a new rack for better organization, but was wondering about an audio one. Thoughts welcome,
I am getting my turntable back and will conduct some digital vs audio tests in the near future. Also, I am thinking of adding a tube phono stage to the setup - thinking of a Bellari VP 130 which has good reviews for bang for buck. Thoughts welcome.
After talking to SVS support, I realized that the crossover was too high, and that phase apparently is not something I need to worry about. I learnt about localization. I still have my crossover high and I don't think it is that localized - I suppose every room is different and tastes differ as well, I am liking it with the crossover high at least with piano, as the low frequency piano notes are now a lot more audible and I like that. Not sure if this is the wrong thing to do but I am ignoring that advice.