As suggested in a comment by Valorum, you're looking for Charles Eric Maine's novelette "The Boogie Matrix", which was published in the British magazine Authentic Science Fiction Monthly #41, January 1954, available at the Internet Archive.
The story is set in 21st century "Nyok City". In a post-apocalyptic technocratic dystopia, somebody finds an ancient phonograph with a recording of "Honky Tonk Train Blues" by Meade Lux Lewis. (Lewis is not mentioned by name in the story, but the piano player in the illo on p. 63 looks like him, and "Honky Tonk Train Blues" is his most famous work.)
But the girl had produced a small cranked handle from the lid, and, inserting it in a hole in the side of the box, busied herself by winding up an unseen mechanism that creaked and groaned as though burdened with a century of rust and dirt. Then she pushed a small lever near to the turntable, and the latter began to revolve. Carefully, she picked up the long cylindrical tone arm, and dropped the needle on to the shiny black recording. Bax listened—horrified, but
The quality was atrocious by twenty-first century standards. There was an almost intolerable hiss and mush from the needle point, and the reproduction was tinny and unreal, but the music that came from the grille was recognisable. It was a recording of a pre-Inferno instrument, a primitive hammer and string device that produced music from the out-moded Reversionist twelve-note chromatic scale. But as he listened the rhythm of the music seeped into his brain.
It was a sound that had not been heard in the world for nearly a hundred years, a type of music utterly foreign to a humanity that knew only the synthetic discords and subtle rhythmic interplay of tones and harmonics produced by an audio-permutator from a metal matrix, inscribed with curves and lines, corresponding to mathematical equations and formulas. It gripped him and hypnotised him. He felt his feet tapping instinctively in time with the precise beat and the dynamic syncopated chords and melody.
It was piano music. It was wonderful piano music. He was listening to boogie-woogie, to the Honky Tonk Train Blues, played by an acknowledged master of his craft. It was Reversionist and primitive, while he was a technocrat and a world-famous composer, but he was entranced.