Guitarist Eliot Fisk. (Jesse Weiner)

Eliot Fisk, the distinguished American guitarist, played the first of a pair of concerts at the National Gallery on Saturday afternoon. Like his mentor, ­Andrés Segovia, Fisk’s influence on the world of classical guitar, particularly in the United States, has been significant.

After graduating from Yale, he established the guitar department there, where he continues to teach, as well as at the Boston Conservatory and the Mozarteum University of Salzburg.

This weekend’s performances were devoted to Fisk’s own guitar transcriptions of Bach’s six suites for solo cello.

Transferring music conceived for a bowed stringed instrument to one with plucked strings poses considerable challenges. But, as Fisk pointed out in his remarks, the only surviving manuscript source of these pieces in Bach’s hand is a transcription he made of the Suite No. 5 for baroque lute, another plucked instrument.

That provided Fisk with a starting point and model.

The results, as evident in the first, fifth, and third suites he played Saturday, added up to the most engaging and stimulating hour of music-making I’ve heard this season.

For all the earnest sincerity of Fisk’s playing, he is also a consummate stylist.

His vividly authoritative characterization of the suites’ component baroque dances were a delight.

With a nod toward the French harpsichord tradition, the preludes sounded almost improvisatory in character. Some of the most exhilaratingly virtuosic playing occurred in the quick courantes, while the lively gigues concluded each suite with an air of culminating inevitability. The slow, richly embellished sarabandes were particularly eloquent, rising to a ferocious pathos in the C minor Suite and, in the joyful C major Suite, bathed in an aura of calm repose.

Throughout, Fisk’s uncanny ability to convey Bach’s intricate polyphony, always over a sturdy bass, impresses most.

— Patrick Rucker