If this isn’t the greatest rock-and-roll album ever recorded, it’s pretty damn close. Disdained at the time of its 1972 release, “Exile on Main St.” today is regarded as the Rolling Stones’ best work — a chaotic double-record set comprising a few classic songs and a jumble of bits and pieces. There’s a lot of filler on “Exile” — but it’s great filler.

Now for a controversial assertion: “Exile” is not only the Stones’ best album, but it’s so much better than anything else they’ve done that you’re left gaping in wonder. I’ve said that about two other albums on the list — Derek and the Dominos’ (i.e., Eric Clapton’s) “Layla” (No. 6) and Van Morrison’s “Astral Weeks” (No. 12). But I think most people would agree with me in those cases. Making that same argument about any album by the Rolling Stones, though, flies in the face of classics like “Beggars Banquet” (1968), “Let It Bleed” (1969) and “Sticky Fingers” (1971) — not to mention the live “Get Yer Ya-Ya’s Out!” (1970), my second-favorite Stones album, largely on the strength of Keith Richards’ amped-up guitar.

Well, I’ll stick with it. Mick Jagger has a reputation for being a control freak, and the other albums, for all their raw power, are just a little too perfect. “Exile,” largely recorded while the band members were literally tax exiles holed up in France, is right on the verge of veering out of control, more Keith than Mick. Not to glorify drug use, but Richards had a raging heroin habit at the time, and that led to some weird lineups, such as guitarist Mick Taylor playing bass on “Tumbling Dice” instead of Bill Wyman.

Let me linger on “Tumbling Dice” for a moment, because I think it’s the Stones’ single greatest song — which is saying a lot. It opens with a classic Richards riff and features a gospel choir, supposedly inspired by Jagger’s attending the concert at which Aretha Franklin performed the songs that became her album “Amazing Grace” (No. 22). There are little touches that kill me every time I hear them. Charlie Watts marking time during the outro, only to come crashing back in. Keith’s now-you-hear-him-now-you-don’t harmonies. Mick’s wail seguing perfectly into a slide guitar. Something magical and desperate was captured that night. I’ve only seen the Stones once, but I’ve listened to “Tumbling Dice” on several live albums, and it’s flat and uninspiring by comparison. That’s really saying something for a band whose songs usually sound better live than in the studio.

Beyond that, it’s hard to pick favorites. “Rocks Off” for the great line “The sunshine bores the daylights out of me.” “Happy,” maybe Keith’s best vocal performance. “Hip Shake,” “Casino Boogie,” “Torn & Frayed,” “Turd on the Run,” “Ventilator Blues,” “Just Want to See His Face” — what we used to call deep album cuts, with a ragged, not-quite-finished quality. “Black Angel,” “Loving Cup,” “Let It Loose” and “All Down the Line” are all melodic and beautiful while still rocking hard.

The Stones recorded some fine albums after “Exile,” most notably “Black and Blue” (1976) and “Some Girls” (1978). And they’ve remained an excellent live band, not to mention a vibrant cultural force well into their 70s. From “Satisfaction” to their COVID song, “Living in a Ghost Town,” they have been a welcome presence in our lives for more than 50 years.

On “Exile,” though, they achieved something higher: transcendence.

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