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. Also acts with (Z,Z)-farnesyl diphosphate isomer, producing alpha-endo-bergamotene, alpha-santalene, (Z)-beta-farnesene, epi-beta-santalene, and beta-santalene. (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 0.34 sec(-1) with (2E,6E)-farnesyl diphosphate as substrate. Belongs to the terpene synthase family. Tpsb subfamily.