PARIS — The music industry, the first media business to be consumed by the digital revolution, said Tuesday that its global sales had risen last year for the first time since 1999, raising hopes that a long-sought recovery might have finally begun.

The increase, 0.3 percent, was tiny, and the total revenue, $16.5 billion, was a far cry from the $38 billion that the industry took in at its peak more than a decade ago. Still, even if it is not time for the record companies to party like it’s 1999, the figures, reported Tuesday by the International Federation of the Phonographic Industry, provide a psychological boost.