A fee or tax paid to a lord for the privilege of grinding grain at his mill; a milling charge or grain dues.
From Old French 'grain' (grain) plus the suffix '-age,' which denotes a fee, tax, or right of use (as in 'perage,' 'passage,' 'tonnage').
In medieval times, lords controlled the only mill in town and charged high 'grainage' fees, making them wealthy from something as ordinary as processing grain—it was basically medieval monopoly!
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