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Confused about normals on a conical shape

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Hey guys, I'm working on this piece, still WIP of course, so please disregard the seam and poor material definition.

I like to do things by the book, so I like the normals on the left side - perpendicular to the surface, how it's probably supposed to be.
But there's an obvious lighting difference between the conical shape and the tip. The normals on the right though - I moved them to point like cylinder normals would and the lighting is so much better now. It's more shiny and there's less discontinuation between meshes.

I could just leave it like in the right picture and call it a day, but I'm having hard time understanding how proper normal direction just gives you this bad effect. What am I missing here?

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