Well the obvious choice (see my username) would be a lathe. :)

Similar to what is done to make fluted columns, you could mount stock between revolving centers and build a trammel to hold a router that makes cuts angled to the stock.

e.g. 

![lathe trammel][1] 

(Except imagine one end of the platform higher than the other to make a cone.


  [1]: https://i.sstatic.net/lzZpl.jpg

Technically, you wouldn't even need a true lathe, just a couple of sharpened bolts in a frame to create points about which the stock can rotate.

image via: http://customfurnitureandfab.com/how-to-make-fluted-or-beaded-columns