Thrilling Bach from Mahan Esfahani at Wigmore Hall

Glenn Gould, Angela Hewitt, Grigory Sokolov – Bach's piano music has attracted legions of great musicians over the ages, drawn by a profusion of melody, counterpoint, harmonic progression, rhythmic variation which provides seemingly endless opportunity for the performer to create.

There's an important thing wrong with that last sentence: Bach did not write for the piano. Its early incarnation, the fortepiano, was invented midway through his lifetime, and he was not impressed. To reach the mother lode of Bach's keyboard music, you have to listen to it on harpsichord and today no performer embodies that mother lode more than Mahan Esfahani.

What distinguishes Esfahani's playing is the range of colours that he is able to extract from his instrument. There is light and shade, there is tension and free flow, there is focused directness or meandering exploration. And given that he is playing an instrument whose notes have no intrinsic sustain, Esfahani spins an extraordinary cantabile.

Last night's all-Bach recital at Wigmore Hall started with the Sonata in A minor after Reinken, BWV965. Esfahani sat at the keyboard and paused for a moment, as if to determine his bearings, before embarking on the opening Adagio, unhurried, contemplative. It feels as if the composer is exploring different pathways in a quest for the right harmonic structure – and then, in the fugue, he finds it, with a vengeance. The notes cascade out; each voice that comes in stands out from the rest until it is gradually subsumed into the wash and a newly arrived voice takes over. Sometimes, Esfahani breaks from the pattern to emphasise one of the sets of accompanying figures. Always, he has an eye for subtle acceleration or deceleration – on the tiny scale of an individual phrase, or over the arc of a whole movement.

The Allemande shows Bach in free flow, a stream rather than a flood. As the music ranges the length of the keyboard. Esfahani is notable in the way he reaches for high or low notes: there's just a touch of rubato to keep you waiting for the note that you know is coming, giving a profoundly satisfying sense of release when it arrives.

The notes at the low end are impressive. Esfahani is playing (for the first time in London) what he calls “the harpsichord of the future”, an 16-foot beast with a carbon fibre soundboard designed and built for him by Finn and fellow Prague resident Jukka Ollikka. The clarity and depth of each note is outstanding, most unusually so in the low registers where there is no trace of a rapid flow of notes becoming limp or turning to mud. In the closing Gigue, gentle thunder works its way up the keyboard until the music breaks into its dance rhythm, making me want to leap out of my seat and dance in a way that, presumably, would not have met with the Wigmore Hall audience's approval.

The extremes are ably demonstrated in the English Suite no. 3. The Prelude contains a wonderful cantabile, shining brightly through the surrounding arpeggios, juxtaposed with death-defying plunges into the lowest register. The Allemande gives relaxation: an unsatisfying harmony at the end of one section turns out to be merely the cue for the resolution that will arrive in the next. The Courante falls a fraction flat: for once, I lose my sense of direction in the flow, for it to return in the elegiac, trance-like Sarabande. The English Suite no. 4 is most memorable for the unexpected harmonies of the Allemande and the pure joy of the closing Gigue.

The last programmed work, the Toccata in D major, BWV912, grabs me the most. Esfahani takes the opening at breakneck speed before becoming more deliberate. What's so extraordinary is the way in which Bach messes with your head: he leads you by the nose in some harmonic direction and then turns on a sixpence to take you somewhere joyful that you had no idea was coming. There is a slow fugue in which every change exudes a profound sense of rightness; there are echoes of church organ sound – you might have thought this impossible, given how opposite in timbre an organ is from a harpsichord, but it works. The return to the dotted rhythm original motif and the subsequent ending are mind-blowing.

After the encore, there is a moment of tenderness as Esfahani presents an award for his teacher Zuzana Růžičková – posthumously, alas – to Růžičková's great-niece, and they remember her devotion to music and her unique personality (a perpetual optimist and perfection-seeker who at 90, five days before her death, was deciding that she needed a new Rabbi). It sums up the evening: an event about the life that can be breathed into music.