On Oct. 4, 2015, Van Halen performed at the Hollywood Bowl in what proved to be its last show, capping a decadeslong run as one of rock’s most successful and influential acts. The amphitheater is about 30 minutes from the 800-square-foot house in Pasadena, Calif., where the Van Halen brothers — drummer Alex and guitarist Eddie — grew up. But the journey between those spots took the group all over the world, through the highest highs and lowest lows of rock ‘n’ roll glory, excess and tragedy.

Alex, 71, has learned to be grateful for every moment of it. During a video call one morning in September from his home in the Los Angeles area, he cited an old saying: “‘In the effort lies the reward.’” He was dressed casually in a blue button-down check shirt underneath a leather jacket, sunglasses on and dark hair brushed back. On an otherwise bare wall behind him hung a gold record for Van Halen’s 1978 self-titled debut album.

“That’s exactly how Ed and I felt,” he said. “The ride was the reward. And it’s been a hell of a ride.”

That trek — the first 30 or so years of it, at least — is chronicled in “Brothers,” a book that will be published Oct. 22, which Alex was moved to write after losing Eddie, his younger sibling by roughly 20 months, to cancer in October 2020. He characterized the project, told with New Yorker writer Ariel Levy, as “a painful experience.” But, he said, “you’ve got to go through the pain to get to the other part.”

Alex was a commanding presence onstage, especially in Van Halen’s early years (recall him bare chested, furiously bashing away behind a massive drum kit in the 1981 video for “Unchained”), but he was always more reserved with the press. He ceded the role of mouthpiece to the band’s exhibitionist singer, David Lee Roth, and his brother, who was routinely hailed as one of the greatest guitarists of his generation.

Despite Eddie’s yearslong battle with various cancers, his death at 65 was not necessarily expected. “We were getting ready to make another record,” Alex said of the period after the Hollywood Bowl show. The news elicited an outpouring of emotion from fans, family, friends, bandmates and some of the biggest names in the music world. But Alex issued only a brief public statement.

“Brothers” breaks his silence. Why did he write it? “To add a little more depth to the understanding of what Ed was all about,” he said. Addressing the intensity of the attention heaped on his brother, whether for his transformative guitar playing or, later in his life, his addiction and health struggles, he added, “When you’re in the spotlight, people tend to speak for you. I wanted to remind people that Ed was not a commodity. He was a complex human being.”

Alex, more than anyone, would know; even for siblings, they were very close. “Every day, the first thing I’d do is call him,” he said. “We would talk, we would yell and scream at each other. But we were always supportive.”

Donn Landee, the engineer and producer who worked beside the brothers on Van Halen’s first eight albums, said Alex and Eddie were “a unit,” who were “either fighting or defending each other from everybody else. But absolutely locked together.”

Early on, it was for survival. The family, headed by their Dutch jazz musician father, Jan Van Halen, and Indonesian mother, Eugenia (“tiny but tough,” Alex writes), emigrated to America in 1962. Alex was 8, Ed, 6; they rode for many days on a boat from Holland to New York, impressing the crew and fellow passengers by performing classical pieces on a Rippen piano that was one of a few possessions the family brought across the ocean. Today, the instrument sits in the hallway of Alex’s home.

“It’s representative of the whole trip of us coming here,” he said, turning his camera to display the weathered upright. What did he learn on it? “I learned to dislike it,” he answered with a laugh.

The family made its way to Southern California, where Eugenia had relatives, and the brothers were entranced — by the blazing SoCal sun; by the stream of “Felix the Cat” cartoons on TV; eventually, Alex writes, by the “wildness and rebellion” of rock ‘n’ roll. But they were also outcasts. Neither spoke English, and the family was often in turmoil; their parents argued, and Jan struggled to find steady work and music gigs, developing a worsening drinking habit along the way.

Alex was the tough one, at times coming to physical blows with his father; Eddie, in his view, was “more sensitive.” In the book, he recalls his mother hearing Eddie practice guitar in his room and referring to his soloing — something that would come to evoke joy and awe in millions of listeners — as “that high crying noise.” “If our mother didn’t like the sound of that wail, can you blame her?” he writes. “It’s hard to hear your kid suffer.”

When the brothers hooked up with Roth, a Midwest transplant from a well-off family, they recognized a shared experience despite their very different upbringings. “He was basically the same as us,” Alex said. “He felt himself an outcast.” Together, the three (along with bassist Michael Anthony) manifested a flamboyant, virtuosic band that made music filled with high-voltage riffs, earworm melodies and lead-guitar heroics.

“Brothers” effectively ends in 1984, around the time of Van Halen’s initial split with Roth. As Alex explained, this period, from when the band formed through Roth leaving, defined “the real, vibrant spirit of the band.” He addresses his own struggles that followed — with alcohol until the mid-’80s; with benzodiazepines after an old neck injury flared up a decade later — but allocates more space, both on the page and emotionally, to his brother’s battles.

Eddie, he writes, had “flashes of genuine ingenuity” — the brain-scrambling tapping licks in “Eruption”; the indelible keyboard salvo that opens the chart-topping “Jump.” These moments, which made him so beloved by so many, Alex posits in the book, also haunted him. “You can spend your whole life trying to make what happened before happen again,” he writes. “I honestly believe that’s what cost my brother his life.”