Monoterpene synthase producing mainly (+)-alpha-terpineol (44%) and (-)-limonene (33.6%) and lower amounts of (E)-geraniol (5.9%), linalool (5.0%), myrcene (3.4%), (-)-alpha-pinene (3.3%), (+)-sabinene (3.0%) and alpha-terpinolene (1.6%). (2E)-geranyl diphosphate + H2O = (R)-alpha-terpineol + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. Belongs to the terpene synthase family. Tpsb subfamily.