Back in 1994, when he was first lauded in these columns, it didn't take a genius to predict that Chris Thile was going to be an incredible mandolin player when he grew up.

Heavens, at 13 he was incredible already.

Foreseeing the one-man musical entertainment phenomenon that held this audience in thrall for two hours might not have been so easy then. But it's been coming for a while.

The Bach sonatas and partita that formed this concert's spine - and that Thile performed with beautifully caressed gentle phrases, superbly articulated passing chords and a certain occasional bluegrass rigour - were at least partly revealed on his previous Edinburgh visit with his pace-setting band Punch Brothers.

This "Bachtoberfest" alone would have earned five stars; the "stuff" in between made Thile frankly adorable. His own songs ranged from the melodically involved (Stay Away) to jaunty, if warped, power pop (Set Me Up With One Of Your Friends) to a musical hall-kabaret piece of knowing, self-effacing mischief; he also celebrated Fiona Apple, side-swiped the Louvin Brothers and drew on American Civil War folklore. All of these he sang with major personality, superb sincerity and a fantastic array of vocal timbres and linked with brilliant comic timing and endearingly offbeat observations of perhaps not entirely trustworthy, but mightily entertaining, research.

What impresses most of all, though, is Thile's ability to switch instantly from wag to mandolin riches, be it the Bach pieces or his repertoire of improbably fluent, quicksilver runs, bouncy rhythms, impish harmonics and sonic moods that produce both wonderful purity of tone and almost washboard-like grooving. He wants to come back more often: any time, sir.