All the lyrical skills of the rapper from Compton will be on display Tuesday night when he plays a sold-out Tacoma Dome.

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In popular perception, Los Angeles rapper Kendrick Lamar currently holds the distinction of greatest rapper alive.

It’s possible that the idea of greatness is more important in rap than any other genre. Conversations among fans, especially online, pit the genre’s biggest stars against one another in terms of album sales, cultural relevance and lyrical acuity.

Drake has sold more records, and Kanye is (largely by his own volition) more prominent in pop-cultural conversations, but Lamar, who plays the Tacoma Dome on Tuesday (Aug. 1), is a tireless striver who takes an ascetic approach to his craft. He’s also more popular than ever. “DAMN,” the record he’s touring behind, has gone double platinum and is one of the year’s most streamed releases.

Concert preview

Kendrick Lamar, Travis Scott, D.R.A.M.

7:30 p.m. Tuesday, Aug. 1, Tacoma Dome, 2727 E. D St., Tacoma; $35-$215 (800-745-3000 or ticketmaster.com).

It’s fitting that LeBron James, the best basketball player of his generation, is an outspoken fan of an artist who many consider the best rapper of his. But while greatness is relatively easy to measure in sports — points are scored, games are won or lost — it’s less clear in an abstract, subjective form like music.

Lamar raps like there’s no room for doubt. He can seamlessly switch flows and cadences, embody multiple characters within the same track, and construct detail-rich lyrics that invite scrutiny and analysis. (On lyric-annotation website Genius, he’s the second-most popular artist of all time behind Drake.) At least one prominent website’s review of “DAMN” compared listening to Lamar to watching a masterful athlete go to work.

Though it’s easy to focus on Lamar’s pure virtuosity, he’s also forged an undeniable connection with audiences. On this tour’s opening night in Phoenix, Lamar cut out to let the crowd sing the words to “DAMN” standout “HUMBLE” for nearly a full minute. That song’s chorus — ”Sit down, be humble” — is directed at his competition, but it also reads like a mission statement for an artist who, at least outwardly, is less interested than most in the trappings of fame.

Like each of Lamar’s previous records, “DAMN” expands his music’s scope and ups its stakes. Mainstream breakthrough “good kid, m.A.A.d city” was a loosely conceptual exploration of Lamar’s childhood in Compton and 2015’s “To Pimp a Butterfly” examined the black experience in America over instrumentals crafted by a cadre of experimental jazz musicians.

Lamar’s lyrics on “DAMN” show his focus has again turned inward, but the music’s reach is broader. He raps about his insecurities, his youth and the burden of being famous and talented. Though the music draws from his life, the songs have monolithic titles, stylized in all caps, that imply universality: ”PRIDE,” “LUST,” “FEAR” Lamar’s music has plenty of appeal to old-school rap listeners, but like the most effective pop music, it expands the personal to widescreen proportions.

While Lamar’s music exudes focus and gravitas, the two openers on Tuesday occupy very different lanes. Travis Scott’s manic stage presence draws from arena rock’s theatrics; on this tour, he’s taken to performing some of his songs while riding a huge animatronic bird above the stage. D.R.A.M. had a hit last year with “Broccoli,” an easygoing, sing-songy track that is something like the antithesis to Lamar’s earnest approach.