The values of the shear v s and longitudinal v l wave velocities were calculated for 14 selected titanium oxynitrides TiN x O y using the known values of Young's modulus and Debye temperature. The errors Δ of the calculations did not exceed ±0.01%. It turned out that some TiN x O y samples are able to compete with artificial diamonds in terms of v l values and can potentially be used in acoustic resonators for intelligent chemical and biochemical sensors. A number of elastic, thermodynamic and thermophysical quantities were calculated, and graphical dependencies between them were plotted. The established correlations were used to develop two algorithms for predicting the properties of TiN x O y alloys based on a single experimental parameter, namely the X-ray coefficient of thermal expansion or pycnometric density. The highest accuracy was shown by the method based on the experimental density, which allowed to estimate, with acceptable errors, the values of the shear v s and mean v m wave velocities (Δ = ±(1-5)%), the minimum thermal conductivity λ min within the framework of the Cahill‒Pohl model (Δ = ±(0-3)%), the isobaric C p and isochoric C V heat capacities (Δ < 1%); while the known experimental methods and alternative models for determining these quantities are characterized by wider error intervals: Δ(v s) = ±(1-10)%, Δ(λ) = ±(1-10)% and Δ(C p) = ±(1-3)%.