I need a musical sub under 500,,,,new or used.

Lots of suggestions so far. I'd just add, at this price level, avoid anything with a woofer more than 10" in diameter. The amps in the cheap subs and even in some more expensive ones (like your 15" Velodyne) are not capable of controlling that woofer cone. They are "slow" and sloppy, as you have heard.
Find a sub with a 10" or two 8" woofers made by a company that also makes good speakers for music.
You didn't say what speakers you're using, so I can't say where to set the crossover. But, from what I've seen, a lot of people have their subs set way too high in the frequency range, over-lapping the performance of their main speakers, and that's why they sound so bad.

Hsu distributed by Ascend Acoustics or Parts Express sells a sub. These would be two options.

The Aperionaudio 12 recently had quite a good review.

VMPS New larger subwoofer..it sells for 700$..I don't think you can find a used one..no one sells them on the used market..why?/because they are so good.....

B&W ASW 600 sounds good to me. 10 inch 150watts. $500. I'm fairly new to the high-end stereo game but this is what I own and it's nice and tight for music. Some of the others that I listened to(including HSU) sounded way to boomy for me. I have a pair of B&W 602's and the sub blends in perfect with it. You can't tell that it is there.

Paradigm PDR-10 ($350) or HSU VTF-2 ($500)

Technically, the Hsu is as good as it gets at this price point. That doesn't mean it'll sound best to you, in your room, with your mains. But it is worth an audition. (Try to find somebody who has one; otherwise, you've got to order one on the 30-day plan.)

Adire Audio - rava $399. Sealed 12" Shiva based sub. I am real impressed with mine.

Believe it or not, about ten years ago Pioneer made a subwoofer called the "SW-1000" that is remarkably fast and musical.... I have one in my second system and while it's certainly not as quick and won't go as deep as my REL Strata II, or play as loud, it performs a lot better than you might imagine. The Pioneer has speaker-level inputs which are very transparent-sounding and 12" paper cone woofer that is quick and tuneful. It is without doubt more musical than bandpass-type subs (like the Paradigm PS1200) and IMO more musical than the budget Velodyne, Klipsch, JBL and other low-end (10" woofer) subs. I've seen them go for about $100 on ebay which is a stone-cold bargain considering the performance you can get from this 20" square black box. As an added extra the Pioneer is quite attractive looking with a piano-black top and front-mounted controls. Oh and BTW, I use mine with an ASL Wave 8 tube monoblocks and Triangle titus speakers and it holds its own with this budget audiophile gear.

Paradigm PS-1200 Subwoofer. This is a really good sub for music and movies. Alot of reviews on Audioreview about it.