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Small Angle-X-ray Scattering Tensor Tomography (SAS-TT) is a relatively new, but powerful technique for studying the multiscale architecture of hierarchical structures, which is of particular interest for life science applications. Currently, the technique is very demanding on synchrotron beamtime, which limits its applications, especially for cases requiring a statistically relevant amount of sample. This study reports the first SAS-TT measurement at a macromolecular X-ray crystallography beamline, PX-I at the SLS, with an improvement in data acquisition time from 96 h/Mvoxel in the pilot experiments to 6 h/Mvoxel, defining a new standard for fast SAS-TT and allowing the measurement of a full tomogram in 1.2 hours. Measurements were performed on the long and lenticular process of the incus bone, one of the three human auditory ossicles. The main orientation and degree of alignment of the mineralised collagen fibrils are characterised, as well as the size and shape of the mineral particles which show relevant variations in different tissue locations. The study reveals three distinct regions of high fibril alignment, most likely important pathways of sound throughout the ossicular chain, and highlights the potential of the technique to aid in future developments in middle ear reconstructive surgery.