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Because of the importance of bone in the biomedical, forensic and archaeological contexts, new investigation techniques are constantly required to better characterize bone ultrastructure. In the present paper, we provide an extended investigation of the vibrational features of bone tissue in the 0.1-3 THz frequency range by time-domain THz spectroscopy. Their assignment is supported by a combination of X-ray diffraction and DFT-normal modes calculations. We investigate the effect of heating on bone tissue and synthetic calcium-phosphates compounds with close structure and composition to bone mineral, including stoichiometric and non-stoichiometric hydroxyapatite (HA), tricalcium phosphate, calcium pyrophosphate and tetracalcium phosphate. We thus demonstrate that the narrow vibrational mode at 2.1 THz in bone samples exposed to thermal treatment above 750 °C arises from a lattice mode of stoichiometric HA. This feature is also observed in the other synthetic compounds, although weaker or broader, but is completely smeared out in the non-stoichiometric HA, close to natural bone mineral composition, or in synthetic poorly crystalline HA powder. The THz spectral range therefore provides a clear signature of the crystalline state of the investigated bone tissue and could, therefore be used to monitor or identify structural transitions occurring in bone upon heating.