Join Date: Jan 2016
Location: San Francisco Bay Area
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I am a big fan of Rythmik, but at your price point, I believe you should take a different alternative. The biggest issue you are going to have is your room. You have a square 10'x10' room which means your modes will be doubled up leading to some huge bass peaks and suckouts. Specifically, you have stacked modes in the bass at 56hz, 90hz, 112hz, and 125hz (there are more further up but they become less of a factor). As such, with any subwoofer you are going to have some big peaks and suckouts that will result in some stuff sounding very boomy and other stuff like the bass is missing.
The best remedy is to get the SVS SB12-NSD or RSL suggested (I would lean towards the SVS) and take the remaining $200 and purchase a Mini DSP 2x4 and UMIK-1. First with careful setup (try the crawl method), then using the UMIK to measure and the Mini DSP as your crossover and parametric eq, you will be able to significantly knock down the peak modes. You will need to spend time reading how to use the Mini DSP and REW with the UMIK, but done properly, will give you better sound than you will get with any sub, regardless of price, without.
The most important thing to keep in mind when using DSP and equalization is that the equalization is primary used to knock down the peaks. It is nearly impossible to equalize the nulls and will often result in overdriving the subwoofer. As such, you really never want to use more than about 3db of boost. If you use only jriver or roon for your music sources, you could skip the Mini DSP, measure and manually equalize in jriver or roon.
Finally, you could use room treatments to help with the bass issues, but it will be expensive and take up a lot of room, as room treatments that control bass need a lot of space. A hemoltz resonator would work for you 56hz peak, but again, expensive and takes space.