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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 particularly relevant to life science applications. Currently, the technique is very demanding on synchrotron beamtime, which limits its applications, especially for cases requiring a statistically relevant number of samples. This study reports the first SAS-TT measurement at a macromolecular X-ray crystallography beamline, PX-I at the Swiss Light Source (SLS), with an improvement in acquisition time from 96 h/Mvoxel in the pilot experiments to 6 h/Mvoxel with comparable sampling, defining a new standard for fast SAS-TT with a micrometer beam size and allowing to record a full tomogram in 1.2 h. Measurements are 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 technique's potential to aid in future developments in middle ear reconstructive surgery.