These are the tools I use on all my horn work.
Left to Right:
Flat ended with a sharpened tapered left side edge. For hollowing out base plugs after a 1" pilot hole is drilled with a spade bit.
Standard Parting tool.
Small Skew, lots of uses, smoothing, making beads, layout, thin lines, the list goes on.
Large Skew, same as small only for larger work and gets use a lot on flattening pieces.
Large Round nose, used for concave work.
Small Round nose, same as above only for smaller work.
Even smaller Round nose for smaller work.
Kind of an offset Parting/Scraping/Bead making/V cutting/overall tool, made from a power Hacksaw blade. A real go to tool. You can see where I filed some "U"s in it to try it for bead making, didn't like it.
And a large Gouge for the rough work.
I also use files and rasps as needed.
Tim C.