Finally, approximately 50 years after its contents were recorded, The Beatles’ Live at the Hollywood Bowl (Universal/Apple) has been released on CD. The occasion is the album’s de facto status as the soundtrack to Ron Howard’s new documentary, The Beatles: Eight Days a Week—The Touring Years. But the performances stand on their own.

They’d been released before, in 1977, as an LP titled The Beatles at the Hollywood Bowl. But once it went out of print, it stayed there, becoming the only album by the world’s most popular rock ’n’ roll band excluded from the digital age.

The reason usually given was that no existing technology could effectively separate John, Paul, George, and Ringo’s playing from the hordes of female fans whose shrill screams made the original three-track recordings more a fascinating pop-cultural document than a consistently pleasurable listening experience.

But the technology improved. And when Capitol Studios gave the original tapes to Giles Martin (the late Beatles’ producer George Martin’s son), he and a crew of dedicated technicians were able to “demix” their contents, effectively bringing the music to the fore with unprecedented clarity.

It’s now possible, for instance, to distinguish one instrument from another. And never again will anyone question the ability of The Beatles—who would soon stop touring altogether and popularize the idea of using the studio itself as an instrument with Sgt. Pepper’s Lonely Hearts Club Band—to rock the house in real time.

And how do the shrieking teenagers fare in the new mix? They still play a large role, but it’s a supporting one, leaving the singing and playing to sound as it probably would have through the onstage monitors if The Beatles had, in fact, had any.

Another bonus is that Martin and Co. were able to salvage four extra tracks, effectively providing the 1977 version of the album with an encore and bringing the total running time to just over 43 minutes. Like the original album’s 13, they’ve been carefully spliced together from Hollywood Bowl shows that actually took place one year apart (Aug. 23, 1964, and Aug. 30, 1965, to be specific).

Taken together, the 17 performances create the most convincing illusion of a complete Fab Four show to date. And they’ll continue to until the complete 1964 and 1965 shows, the tapes of which exist, get the demix treatment and give disillusionment a good name.

Sounds of McCartney

Another reason for Beatles fans to celebrate is Pure McCartney (Hear Music), the recently released definitive overview of Paul McCartney’s solo career.

The collection comes in two-disc and four-disc editions, each mixing greatest hits with deep album cuts. If the bigger edition includes too many examples of McCartney’s mooncalf optimism (“Ebony and Ivory”’s brotherhood bromides play especially poorly amid weekly Islamic-terrorism headlines), it also makes a more persuasive case for his multifaceted talent.

Both editions contain the previously unanthologized gems “Mrs. Vandebilt” (1972), “My Valentine” (2012), “Only Mama Knows” (2007), and “Sing the Changes” (a 2008 collaboration with Killing Joke’s Youth, credited to “The Fireman”). But only the deluxe edition includes “Don’t Let It Bring You Down” (1978), “Baby’s Request” (1979), “Good Times Coming/Feel the Sun” (1986), and “Appreciate” (2013), songs that combine the unpredictable and the catchy as confidently as “Band on the Run” or “No More Lonely Nights.”

There are more where those came from. And if those more had included “Beware My Love” (1976), “Girls’ School” (1977), “So Bad” (1983), and “Cut Me Some Slack” (which won a “Best Rock Song” Grammy in 2014 and deserved to), the collection would’ve been better yet.