You need to know mass and tension. Torque wrenches just aren't precise enough, in my experience.

Back in the days of coin-operated musical instruments (before recorded music made jukeboxes possible) they used actual fiddles, "bowed" woth a rosin-covered wheel (like a hurdy-gurdy). There were no tuning pegs, and pitch was maintained by using a roller for a nut and hanging different weights at the end of each string.