An Etymological Dictionary of the German Language/Annotated/Zeche
Zeche, feminine, ‘rotation (of duties), succession, hotel bill, share in a reckoning (at an inn), drinking party (each paying a share), corporation, guild, club,’ from the equivalent Middle High German zëche, feminine (which also means arrangement, association); also in Middle High German zëchen (Old High German *zëhhôn), weak verb, ‘to arrange, prepare, bring about,’ also (late), ‘to run up a score at an inn.’ In Old High German only the word gizëhôn, ‘to arrange, regulate,’ from this stem is found; compare the allied Anglo-Saxon teohhian and teógan (from *tëhhôn, tëhwôn, tëhôn), ‘to arrange, determine, regulate,’ and teoh (hh), ‘company, troop.’ A Teutonic root tē̆hw, tē̆gw (tē̆w), is indicated by Gothic gatêwjan, ‘to ordain,’ têwa, ‘order,’ têwi, ‘troop of fifty men.’ These imply a pre-Teutonic root dē̆g, ‘to arrange, regulate’ (to which Greek δεῖπνον, ‘meal,’ for deqnjom?, is allied). The numerous senses in Middle High German may be easily deduced from the primary meaning.