A strap is very useful if your horn is anything above wine glass size. A popular method of fixing is to drill a hone in the solid tip of the horn and attach a ring of wire to the horn through this hole. (Make sure you drill through the solid tip or you'll have a leak!) then tie a loop slightly smaller than the mouth of the horn in a thong, leather strap, length of tablet braid or whatever and slide it up towards the mouth of the horn. Tie the other end of the strap through the loop at the horns tip.
If you're good at metalwork you can get more elaborate and put fancy patterned metal horn mounts around the mouth of the horn and on the tip. Horn tips in the shape of stylised birds were quite popular.
For carving, some suggest using a Dremel tool, with a fine bit. Wood-working tools can be used, but be careful: the curved surface makes slips much more likely....
Using and working with Horn - Making a Drinking Horn. Copyright ©
1996, 2001, 2005 I. Marc Carlson
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