The greats of the tenor saxophone inhabit the very walls of London’s premier jazz venue. A picture of the late Ronnie Scott himself looks down from above the bandstand, occupying the “0” of “50” in the club’s fiftieth anniversary year. While I was waiting for my companion to fetch a coat, I nodded sheepishly to both Sonny Rollins and visiting Missourian Ben Webster, a man known for always carrying a knife when visiting the club. I doubt if there were any knives being carried tonight, but for half a century Ronnie’s has been definitely the place for tenor saxophonists to do battle. And Dave O’Higgins (above), following this tradition, had laid on a lively treat of tenors locking horns for a bustling, sizeable and enthusiastic Monday night audience at the club.They were also promoting their new album from Jazzizit Records.

O’Higgins’ guest and sparring partner tonight was Eric Alexander, from Chicago by way of New York. By his own admission he was jet-lagged, but there was no sign of it in his energetic and fluent playing.

What you mostly get at this kind of gig is uptempo burners with both protagonists sparring. One of the greats of British jazz described this occasion to me once. He says you can expect to hear so many notes, that someone will have to come and sweep them up off the floor afterwards. That’s the convention, the tradition, you go with it.

Platform demeanour showed up an interesting contrast: while O’Higgins was soloing, Alexander strolled off into the shadows, escaping most of the way into 49 Frith Street. But during Alexander’s solos, O’Higgins stayed ever-watchfully on stage, seeming to play the role of the pupil who didn’t want to miss a single semi-quaver of his masterful guest Alexander’s playing.

But for my ears the most jaw-dropping tenor playing of the evening actually came from O’Higgins in his arrangement of “I can’t give you anything but love.” Pianist Tom Cawley had insistently repeated an “out” note -sharp five? – at the end of his solo. This seemed to act as an invitation and a spur for O’Higgins to keep revisiting it as the solo gathered momentum, and use it as a launching pad into several energetic choruses leaving the chords for dead. Mesmerising, totally commanding “out” playing which will stay in my ears…. .

Oases of repose did come in the one slow ballad by each player in each set. In the first set it was Alexander’s turn, and he gave a poetic account of Jimmy Van Heusen’s “All The Way,” with a narrative ease reminiscent of Ike Quebec, in which I also liked the sensitive brushwork of Danish drummer Kristian Leth. O’Higgins then featured in the second set on Brazilian Chico Chagas’ “Brixton.” This time Leth was careful and creative on hot-rods. In both ballads, and throughout the evening Arnie Somogyi was flawless and big-toned on bass.

Their final number was Blue Mitchell’s joyous calypso on Rhythm changes, “Fungi Mama.” O’Higgins’ solo was an inventive meander in sub-tone. And a highlight was pianist Tom Cawley’s solo, in which he seemed to want to lose the first beat of the bar without trace. But just when I imagined he would have to pick it up from lost property in the morning, the whole band were emphatically back in for a rousing final chorus of the calypso, giving off a joyous and friendly collaborative vibe.

This was a tenor battle to rank wth the greats of the past. After two more nights at Ronnie’s, Alexander and O’Higgins will be storming round Germany.

O’Higgins’ quintet were playing opposite Claire Martin’s very classy band of Gareth Williams, Laurence Cottle and James Maddren. A highlight of their first set was a deliciously intense, spacious account of the much-missed Esbjorn Svensson’s “Love is Real.” It inspired the Ronnie’s crowd to offer up that rare and wondrous thing: a perfect, rapt, pin-drop silence.