Waltzes, suites, airs, fantasies, inventions — these kinds of pieces have formed the Western classical-piano repertoire for centuries, as anyone who has ever wound a metronome knows. And as anyone who has ever heard Billy Joel also realizes, that studious tradition has always underlaid his music. So this collection of pieces for solo piano written by Joel and performed with highly extroverted skill by Richard Joo represents, in essence, Joel’s roots album. As a restless rock & roller, and now as a composer, he restages the scarlet-hued nineteenth-century thrusts and taxing engagements of legendary Russian and German composers. But Joo begins this collection breathing Joel’s “Reverie (Villa D’Este),” which exhales delicate French colorations and impressionistic dissolves. Elsewhere, Joo plays a number of showy waltzes, explores Verdian melodicism on “Aria (Grand Canal),” and climaxes the sequence with “Air (Dublinesque),” whose piquant folk-based strains almost meld this new Joel of scales and arpeggios with the always hummable Joel of popular song. Fantasies doesn’t always jell this satisfyingly, but for the most part, Joel doesn’t let his delusions get the best of him.