WITH all the multi-disc jazz boxes that have come out in recent years —

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the complete Miles Davis on Columbia, the complete Charlie Parker on Savoy, the complete Duke Ellington on RCA and so on — it’s hard to believe that any significant tapes by any major musician might still be languishing undiscovered in a record company’s archives.

Yet Verve has just released “Twelve Nights in Hollywood,” a four-CD box­ed set of Ella Fitzgerald si­nging 76 songs at the Cr­escendo, a small jazz club in Los Angeles, in 1961 and ’62 — and none of it has ev­er been released until now.

These aren’t bootlegs; the CDs were mastered from the original tapes, which were produced by Norman Granz, Verve’s founder and Fitzgerald’s longtime mana­ger. They capture the sin­ger in her peak years, and at top form: more relaxed, sw­ing­ing and adventurous, than on the dozens of other albums that hit the bins in her lifetime.

Richard Seidel, the producer of the boxed set, first heard the tapes early this year. He was driving to Massachusetts from his home in New Jersey and brought al­ong some rough CD transfers to play in the car.

“I was feeling kind of down that day,” he recalled, “and the more I listened, I could not help but start to smile. I’ve worked on doz­ens of Ella projects over the years, but there was something different about this one — the sheer rhythmic joy she projects, the endlessly inventive improvising.”

There’s nothing rare ab­out a joyous Ella Fitzgerald recording; the woman exuded joy in nearly every note she sang. Yet the level on these sessions soared higher and plumbed deeper.

Gary Giddins, the veteran critic and author of “Jazz,” agrees. “This ranks on the top shelf of her live recordings,” he said. “It’s ab­out as good as it gets.”

Why these tapes stayed locked in the vault for ne­arly half a century — and what it took to set them free — is a tale of a producer’s neglect, a jazz sleuth’s obsession and a string of happy coincidences.

The 1961 Crescendo gig, which took place from May 11 to 21 (with one night off), was booked as an afterth­ought to begin with, a time filler between a European tour that Fitzgerald and her quartet had begun in February and a month-long stay at the Basin Street East in New York that June.

Granz took the unusual step of taping every set. But in the next year alone he and Fitzgerald recorded six studio albums, most of them with large orchestras, incl­uding two of her eight heavily promoted songbook albums, each devoted to standards by a prominent American composer.

In this context it’s not so surprising that the Crescendo tapes received short sh­rift. “My guess,” Seidel said in a phone interview, “would be that Norman Granz was just recording Ella so much at the time, and was probably focused much more on her big studio projects.”

Granz did pull 12 tracks from the roughly 14 hours of material recorded at the Cr­escendo and released them that year as an LP called “Ella in Hollywood.” But the album didn’t do well.

Whatever the reasons for the flat reviews and scant sales, the executives of Verve — which Granz had sold to MGM in 1960 — put the Crescendo tapes in the vault, where they were forgotten for the next 27 years.

In 1988, Phil Schaap, a jazz scholar was contracted by PolyGram (which had recently bought Verve) to compile a discography of all the recordings — issued and unissued — that Fitzgerald ever made for the label.

Early on in the task, riffling through PolyGram’s vast tape facility, then in Edison, NJ, Schaap unearthed the never-released tapes of a 40th-birthday concert that Fitzgerald recorded at the Teatro Sistina in Rome on April 25, 1958. He urged PolyGram’s executives to release them. When they did, as an album called “Ella in Rome,” on the concert’s 30th anniversary, it soared to No. 1 on Billboard’s jazz chart.