Monoterpene synthase which catalyzes the conversion of (2E)-geranyl diphosphate (GPP) to (R)-alpha-terpineol and (4S)-limonene, as well as small quantities of linalool, myrcene, (-)-alpha-pinene, (+)-sabinene and geraniol (PubMed:18541135). To a lower extent, catalyzes the conversion of (2E,6E)-farnesyl diphosphate (FPP) to beta-bisabolene (PubMed:18541135). (2E,6E)-farnesyl diphosphate = beta-bisabolene + diphosphate (2E)-geranyl diphosphate + H2O = (R)-alpha-terpineol + diphosphate (2E)-geranyl diphosphate = (4S)-limonene + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family. Tpsb subfamily.