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As it is well known, the power loss of transformer core steel depends on a series of parameters which vary in the final core in complex ways. The aim of the present study was to investigate the corresponding dependencies for the second key characteristic, i.e., magnetostriction (MS), as the most significant source of no-load noise. The MS-performance of core material was investigated by means of a rotational single sheet tester (RSST). Compared to loss, the peak-to-peak MS in rolling direction (RD; as the direction of strongest strain) shows similar increases with increases of both induction and axis ratio a. On the other hand, the shape of induction pattern B (t) proves to be rather insignificant, MS being similar for elliptic and rhombic magnetization. While increased dynamics of the pattern yields rising eddy current loss, MS remains unaffected. However, the harmonics show increases as being of relevance for audible noise. While mechanical tension in RD yields slight decreases of MS for alternating magnetization, MS for rotational magnetization increases for both tension and compression. As in the case of loss, MS shows significant increases for DC-bias which correlates with reports of increased noise. The study also included local measurements on a 2-limb, 1-phase model core and on a 3-limb, 3-phase core. MS remains in the order of 0.5 ppm for the 1-phase core, except from its corners. On the other hand, T-joint regions of the 3-phase core show values up to the order of 6 ppm, in accordance to RSST-results. Moderate DC magnetization, as being possible in practice as a long term phenomenon, yields distinct increase of MS intensity and MS harmonics with strong regional differences.