That would be a coaxial driver. It's still a tweeter, it's just located in the center of a speaker where the dust cap would normally be.
You've probably never played through a cab with a really high quality tweeter. Tweets typically used in bass and PA cabs are of the metal diaphragm, compression horn type. They're built to be loud and durable, not for sound quality. You will never find this type of tweeter in a decent stereo speaker, because they don't sound very good.
Speakers built for sound quality use a number of different types of tweets; ribbon, planar, and soft dome are all common. Ribbon and planar tweeters sound really nice but they're delicate and don't handle much power. Soft dome tweeters (also called textile or silk dome) can be had with decent power handling capabilities, and if they're horn-loaded, they're efficient enough for use in bass and PA duty.
And they sound way, WAY better than compression horns. They do cost more, although not all that much more.
About the only production bass cabs that I know of that use dome tweeters are Accugroove and Acme.
A good tweeter doesn't sound like a tweeter; it blends seamlessly with the other speakers, so you get smooth, unobtrusive high end. When you play a bass cab with the typical Foster/Fostex horn, unobtrusive is the LAST thing that comes to mind.
It's also important that a tweeter be crossed over at the correct frequency. Too low, you'll blow the tweeter; too high, and you get a gap in your frequency response. Most bass cabs with a Foster horn are crossed over too high, usually around 5k; very few woofers can do anything above 3~4k, so you get a pretty big hole in the frequency response. And that is exactly what those cabs sound like - lows plus some sizzling highs layed on top, nothing in the middle.
I find high frequencies really critical for note definition. Even with the best woofers, by themselves, it can get pretty hard to tell the difference between a low C and C# (it ain't my basses - Modulus and Dingwall). A good tweeter makes a big difference. You don't really notice the tweeter's sound by itself, it just kind of clarifies the notes.
I was tweeter-free for nearly 20 years. Never was happy with the lack of clarity. Then I started using some PA cabs that had compression horns. Very clear sounding, but no amount of tweaking would get the high end sounding just right. I could get close, but it'd still be either inaudible or still have that harsh quality. When Accugroove came out, I saw they were using soft domes; they use a pair in order to get adequate efficiency. I was planning a 2x10 to biamp with a 1x18, and started looking at dome tweeters, intending to use a pair like Accugroove does. THEN I ran across the particular Peerless tweeter I recomended earlier. It's got good power handling, adequate efficiency, and it goes a lot lower than most tweeters (down to 1k) so it's easy to crossover with nearly any woofer. No need for a midrange. Gave it a try, and it's a beautiful thing...........
