Today it means: In Ancient Greek musical theory, the lowest-pitched fixed note in the farther tetrachord on a lyre, always pitched a perfect fourth below the nete, with two movable notes between them, the trite (lower in pitch) and the paranete (higher in pitch). The paramese was higher-pitched than the mese (the highest-pitched fixed note in the nearer tetrachord on a lyre) by a ratio of 9:8. Full definition →
Unadapted borrowing from Latin paramesē, from Ancient Greek παραμέση (paramésē, literally “next to the middle [string]”).
Etymology from Wiktionary, CC BY-SA 4.0.