Catalyzes a mixture of sesquiterpenoids from (2E,6E)-farnesyl diphosphate in fragrance biosynthesis. Catalyzes the formation of alpha-santalene, beta-santalene, epi-beta-santalene and exo-alpha-bergamotene, as well as traces of alpha-farnesene and beta-farnesene. (2E,6E)-farnesyl diphosphate = (1S,5S,6R)-alpha-bergamotene + diphosphate (2E,6E)-farnesyl diphosphate = (+)-alpha-santalene + diphosphate (2E,6E)-farnesyl diphosphate = (-)-beta-santalene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. kcat is 0.91 sec(-1) with (2E,6E)-farnesyl diphosphate as substrate. Belongs to the terpene synthase family. Tpsb subfamily.