NEW YORK — On a recent Thursday afternoon, the pianist Jeremy Denk sat at the small kitchen table of his Manhattan apartment, seemingly searching for the right words.

We had been discussing the sheer athleticism — the gymnastic precision — required to play the most demanding works of the piano repertoire. Having mastered his share of violently percussive, finger-twistingly avant-garde music in recent years, Denk, 42, understands this athleticism as well as any pianist. It’s just that he’d like to find a better way of describing it.