Lincoln Center could have been forgiven if it had gone a little crazy in celebrating the reinstallation of the lovable Kuhn organ in the renovated Alice Tully Hall, now the only pipe organ in a major concert hall in New York. From the time of the instrument’s removal in 2006 until it was finally put back in place in recent months, fearful, not to say paranoid, organ fanciers greeted the center’s repeated assurances that the instrument would return in all its glory, and then some, with unalloyed skepticism.

Now here it was, on Tuesday evening, restored and fitted out with the latest technology to make it more user friendly and give it greater sonic heft. But from the moment the inaugural concert was announced, with the young wizard Paul Jacobs playing the third book of Bach’s “Clavierübung” (“Keyboard Exercise”) as part of Lincoln Center’s new White Light Festival, it was clear that this would be a dignified affair. And if the choice of repertory — a single, daunting 100-minute work familiar in its entirety only to organ buffs and Bach devotees — was not an obvious one, it was in some ways ideal.

As one of Bach’s great late compendiums, ranking alongside the B minor Mass, “The Art of Fugue” and “A Musical Offering” (and part of a larger compendium, the other books of the “Clavierübung” encompassing the six keyboard partitas, the “Italian Concerto” and “French Overture,” and the “Goldberg” Variations), the work merits broader exposure. And written, in Bach’s words, “for the refreshment of the spirit,” it meshed perfectly with the White Light Festival’s cause, spirituality in music....