The conversion of vibrating periods to densities through the calibration of the Anton Paar DMA 512 vibrating tube densimeter (VTD) to perform P-rho -T measurements on fluids is examined. After reviewing various calibration models with their detailed internal characteristics, a new one is proposed that accurately extends the use of the densimeter over a wide range of densities, including vapors under low pressures, compressed liquids and near critical fluids. A good accuracy is obtained by fitting only two mechanically defined parameters on liquid reference density data. Detailed considerations on the mechanical model and on the calibration procedure are exposed and illustrated through sample results.