I would put it in the category of a tenor bass, though that is defined by a 4 string bass in A standard tuning or a 5 string bass in E standard tuning.I’m certainly not opposed to using a conventional name, I just don’t know that there is one for what I have. The tuning puts it the range of a baritone guitar based on the lowest string. However based on the strings I need to buy it is a piccolo bass. It’s also an extended range with the BEAD so it’s not exactly a piccolo bass at an octave up from a standard 4.
The naming oddity I was pointing out wasn’t any particular confusion on my part. I just think calling something a piccolo bass is like needing a medium shirt and buying a small large, or would that be a large small…
I think I’m kinda stuck calling it a piccolo bass tuned BEAD. Oh, and it’s a short scale. Can’t forget to shoehorn that in there.
But I'd say close enough, only 2 half steps away, certainly closer to that definition than what is conventionally considered a bass piccolo tuning.
So I would call it a tenor bass in B standard tuning.