Catalyzes a mixture of sesquiterpenoids from (2E,6E)-farnesyl diphosphate. Catalyzes the formation of exo-alpha-bergamotene, as well as (E)-nerolidol, (Z)-alpha-bisabolene, (E)-beta-farnesene and beta-sesquiphellandrene. Also has activity towards geranyl diphosphate, but to a much lesser extent. (2E,6E)-farnesyl diphosphate = (1S,5S,6R)-alpha-bergamotene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. kcat is 0.033 sec(-1) with (2E,6E)-farnesyl diphosphate as substrate. kcat is 0.00026 sec(-1) with geranyl diphosphate as substrate. Optimum pH is 8.0. Belongs to the terpene synthase family.