An Etymological Dictionary of the German Language/Herrschaft
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Herrschaft, f., ‘lordship, dominion, master and mistress, employers (as used by servants),’ from MidHG. hêrschaft, f., OHG. hêrscaft, hêrscaf, f., lit. ‘lordship,’ then ‘high rank, manor, magistracy.’ Allied to Herr, but probably not to hehr.