Lewis & Short

irrătĭōnābĭlis (inr-), e, adj., without reason, irrational (post-class.; not in Quint., v. Spald. ad Quint. 2, 16, 16): error, App. Dogm. Plat. p. 21: motus, Amm. 31, 12, 15.
Of musical intervals, = logica, proportional, harmonic: irrationabilia (sunt) quibus non subest ratio, Mart. Cap. 9, § 949.
Subst.: irrătĭōnābĭlĭa, ĭum, n., unreasoning creatures, Lact. 2, 2, 17.
Adv.: irrătĭōnābĭlĭter, irrationally, Amm. 19, 10, 1; Tert. Poen. 2; Cael. Aur. Acut. 2, 37, 199.