The pianist Brad Mehldau is quick to point out that After Bach – the result of a joint commission by Dublin's National Concert Hall, New York's Carnegie Hall and others – is not another exercise in "jazzing up" the music of the great German composer.

Not, he hastens to add, that he has anything against that particular strand of jazz, popularised in the 1960s by Jacques Loussier and the Swingle Singers, but Mehldau’s homage to Bach is both more faithful and more flagrant.

Presented here are five pieces from The Well-Tempered Clavier, each followed by a Mehldau composition inspired thereby.

That the great composer’s celebrated book of keyboard solos has played a part in the formation of Mehldau’s technique has always been clear from his ambidextrous, densely contrapuntal approach to jazz standards.

Here he acknowledges the debt explicitly, taking the form and grammar of Bach’s keyboard works and refracting them through a lens that gathers light from many sources, from Brahms and Bartók to Coltrane, the Beatles and Radiohead.

This glimpse behind the curtain into the mind of one of the greatest and most fluent improvisers in contemporary music may infuriate Bach purists, but that would be just an added bonus. bradmehldau.com