At the time 'Take Five' seemed like the epitome of cool sophistication; it also attracted the biggest audience jazz has ever had. Released as a UK single in October 1961, it made it to No 6 in the pop charts (it had reached No 25 in the US) and appeared on jukeboxes everywhere. The album it came from, Time Out, became a coffee-table accessory long before Sgt Pepper, the abstract painting on the cover hinting at all kinds of high-toned delights within. Even Brubeck and Desmond's horn- rimmed glasses seemed to signify their status as jazz intellectuals.
For some hardened jazz fans, however, the formula was too cute; to them, the mixture of jazz, pseudo-classical references and high-culture packaging seemed, in the argot of the times, square. As the Mad magazine parodies of the time had it, jazz like Brubeck's was for would-be hip suburbanites to drink dry Martinis to while talking psychoanalysis. Despite a follow-up single called 'Unsquare Dance', Brubeck has never entirely been forgiven for his prodigious success. 'Take Five' was actually composed by Paul Desmond, but Brubeck, now 71, his horn-rims long ago replaced by contact lenses, says he acted as its midwife. 'The tune was born in my front room,' he told me at his London hotel last week (he is in the UK for concerts with his new quartet). 'I had asked Paul and Joe Morello to come up with tunes in 5 / 4 because that was the rhythm that Joe played the best. Paul had two themes and I put them together. When I called it 'Take Five' he said he didn't like the title.'
Although Brubeck and Desmond (who died in 1977) had their disagreements, musically it was a perfect partnership: Desmond's soaring lyricism given a holding counterweight by the pianist's heavy block chords. 'I thought I had to provide a balance to him,' Brubeck says, 'though I could be very lyrical too if I wanted to be. Desmond was very inventive, night after night, and much more consistent then me. His tone was the best I've ever heard. He could play an octave above his range and still sound good.'
The famous Oberlin College recording of 1953 (released on Fantasy, the label Brubeck founded, as Jazz at Oberlin) displays Desmond at his most swinging and is probably the best of all Brubeck's records. 'There you hear Paul where I wanted him,' Brubeck says. It was the entry of the drummer Morello into the group that helped lead to the experiments of Time Out.
According to Brubeck: 'Joe made us evolve into complex time signatures because Paul liked the rhythm section never to intrude. He would have preferred to play ballads all the time if he could, but Joe and I knew that Desmond had the most fantastic rhythmic sense that he didn't want to use.'
Brubeck is often perceived as someone who came to jazz from a background in classical music but this, he says, is a misunderstanding. Though born into an intensely musical Californian family - his mother, a piano teacher, had studied in London with Myra Hess - Brubeck always gravitated towards jazz. 'My classical experience was so minimal that I'd call it nothing. Through jazz I listened to classical composers but I never played the classical repertoire.' After service in the Second World War, he studied composition with Darius Milhaud at Mills College. Milhaud - who thought jazz was the authentic American music - encouraged Brubeck to do whatever he wished. A brief encounter with Arnold Schoenberg, by contrast, disillusioned Brubeck with the contemporary classical world. 'It had to be absolutely his way, while with Milhaud you were absolutely free.'
The preoccupation with complex time signatures began very early; 'I have always thought in terms of poly-rhythms and poly-tonality.' Rather than seeking to take jazz closer to the classical tradition, Brubeck insists that he was trying to recapture some of its African heritage. 'After giving complete credit to African-Americans for jazz, many musicians now feel that the New Orleans tradition was very much a mixture of Africa and Europe. There's a strong European tradition in jazz; 'Tiger Rag' is a Belgian march with a syncopated beat and you'll find the form of the march in many early rags and street music.'
Brubeck's experiments developed further when a record dealer played him a copy of Denis Roosevelt's field recordings from the Belgian Congo. 'I realised how far we were from this music, that the jazz tradition was so European and not at all as African as we had thought. I wondered what the music in Congo Square (where New Orleans freed slaves were allowed to play their drums) must have sounded like.' Brubeck felt vindicated when, at the School of Jazz in Lenox, Massachusetts in 1960, Dr Willis James, a black anthropologist, stood up and sang an African worksong in 5/4.
Though critics have sometimes carped (an extraordinary 1959 essay by Raymond Horrocks blames the pianist for not being poor, black and Charlie Parker, among other things), Brubeck feels that leading jazz musicians have always respected him. Indeed, Cecil Taylor - at the avant-garde end of the modernist line as far as jazz piano goes - used to sit by Brubeck's left hand night after night when the pianist played Birdland in New York in the 1950s. 'Generally, the guys who were on the cutting edge liked me,' says Brubeck, 'Mingus, Parker, Kenton, Benny Carter, Miles Davis, Ellington, were always very favourable. Miles and Charlie Parker would come to Birdland and Miles would come to see me at the Black Hawk in San Francisco. Cecil said I filled in a gap, but he didn't say between what and what.'
Brubeck's current quartet is a hot one, featuring the brilliant clarinet player Bill Smith (who, like Desmond, was a member of Brubeck's octet in 1948). His latest quartet album, When I Was Very Young (PolyGram), is also impressive. Though since 'Take Five' Brubeck has busied himself with some rather portentous compositions, including oratorios, masses, cantatas and ballet music, and has performed for Presidents and Popes, as a small group leader he remains a genuine star. He's also an authentic jazzman, in touch with the tradition in a way few other performers are these days. 'Serious music is feeding from jazz now,' he says. 'The classical people see the communication that exists in great jazz groups as something that they want to get hold of for themselves.'
The Dave Brubeck Quartet: Manchester, Free Trade Hall tonight; Edinburgh, Usher Hall, 14 Oct; Glasgow, City Hall, 15 Oct and London, Festival Hall, 19 Oct