THE ROLLING STONES might be best understood as a band with a split personality. On one side there have been those who hogged the front of the stage—Mick Jagger, Keith Richards and Ronnie Wood—musicians who didn’t so much play their instruments as flaunt them. But the band’s sound was rooted in its rhythm section: Bill Wyman on bass and, particularly, Charlie Watts on drums. If the lead musicians were dishevelled and dangerous, the backline was stylish and steady. It was a winning combination that formed the basis of one of the world’s most successful rock outfits.

Mr Watts, who died on August 24th aged 80, did not have rock and roll coursing through his veins. He was brought up on the jazz music of Charlie Parker and Gerry Mulligan. Indeed it was hearing Chico Hamilton drum on Mulligan’s “Walkin’ Shoes” that first persuaded him to take up the instrument. He had bought a banjo, with plans to play in a skiffle group. But, unable to get along with it, he removed the neck, placed it onto a stand and turned it into a snare.

He had never taken a lesson. Instead he learned simply by watching other drummers, in clubs like Ronnie Scott’s in London, and by imitating his jazz heroes’ recordings. Getting to see them in the flesh was difficult in Britain in the 1950s, though. The musicians’ union forbade America’s best swing and jazz bands from crossing the Atlantic to play, for fear they would be doing local musicians out of a job. (Instead they flew right over Britain and settled in Paris which, to Mr Watts’s annoyance, quickly became the jazz capital of Europe.)

After Mr Watts had spent years jamming around with jazz musicians, in 1961 Alexis Korner asked him to join his band, Blues Incorporated, to form the rhythm section with Jack Bruce, later of Cream. It was, according to London musical lore, the country’s first amplified rhythm and blues group, and the forerunner for the great British blues wave of the 1960s, that stretched from Led Zeppelin to Fleetwood Mac to, of course, the Rolling Stones. Mr Watts took the leap of styles in his stride. “Blues to me was just Charlie Parker playing slow,” he later said.

He took that measured sensibility with him when he joined the Stones in 1963. While contemporary drummers on the London scene, such as Ginger Baker and Keith Moon, would assault their snares and cymbals like brawlers in a pub car park, Mr Watts’s beat would instead coax Stones’ songs forward. The swing time he had grown up playing in his jazz days gave the band its heartbeat: incessant, vital and yet often taken for granted.

When you play the Stones’ more raucous records in your imagination—think “Jumpin’ Jack Flash”, say, or “Brown Sugar”—it is likely you hear the drums as pounding and aggressive. Concentrate on the actual recordings, however, and most will be surprised at just how understated Mr Watts’s playing really is. In both of those examples it at once allows Keith Richards’s bombastic guitar riffs to take centre stage, while also binding them into the overall song. It is the tension between the guitar straining at the leash, and Mr Watts’s steady grip on the choker, that gives a sense of exhilaration to the best Stones songs.

Indeed, Mr Watts spent his life confounding the image of the Neolithic rock drummer. He was usually to be found in bespoke Savile Row suits. He by and large avoided the narcotic excesses (although he did, for a while, succumb during the 1980s). And while other drummers’ equipment grew ever more extravagant—with added gongs, cowbells and a circumference of tom-toms—Mr Watts kept his kit modest, true to his jazz roots. Using the “traditional” grip, in which one stick is held overhand and the other one under, gave him the light-touch feel that was his trademark.

Yet Mr Watts was, still, a versatile musician. For a while the Stones would “adapt with what music was in the air”, as Mr Wood once put it. That might require a four-on-the-floor disco beat, as on “Miss You”, the reggae feel of “Hey Negrita” or the samba of “Sympathy for the Devil”. But it was always jazz that seemed to pull him back. In between world tours, he would convene a big band, and record an album or play the clubs. Perhaps he never really had rock and roll in his blood. Ironically, that is one reason he became one of the best rock drummers who ever lived.