THERE is a school of thought that says the best way to prepare for a jazz gig is to play dozens, if not thousands, of jazz gigs beforehand. Pianist Brian Kellock has some sympathy with this thinking. The busiest musician over the ten days of Edinburgh Jazz & Blues Festival, which begins on Friday, might also put forward another form of preparation: a course in logistics.

On at least one occasion during a run of – at the last count – eleven gigs, Kellock is due to finish one gig a mere half an hour before starting another in a different venue half a mile or so away. And that’s before we factor in the different style of jazz and different format, in this case sextet to duo, to say nothing of a different piano to get used to almost immediately.

“With the cockiness of youth I might once have said, with absolute confidence, that playing is the best form of preparation,” says Kellock. “Now I probably just hope that this is the case.”

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This element of doubt isn’t shared by his fellow musicians. Saxophonist Tommy Smith, Kellock’s long- time duo partner, calls the pianist his own personal orchestra for his ability to provide a style of accompaniment that dispenses with the need for any other instruments. Smith also enthuses about Kellock’s breadth of repertoire in a relationship that will frequently see them deciding what to play minutes before taking to the stage.

Resourceful is the word that springs to mind, and a fine example of Kellock’s resourcefulness involves this newspaper’s arts editor and the Scottish Jazz Awards a few years ago. Kellock was the house pianist on this occasion and as is the way of such events, his trio played everyone onto the stage – including winners and people who were presenting awards – with an appropriate tune.

Coming up in the second half he spied our Mr Bruce. What on earth do I play for the arts editor of the Herald, Kellock asked himself. Getting no response, during the interval he asked someone else, who was able to suggest that something by Elvis Costello would fit. Kellock didn’t know any Costello songs so his helper crooned one into his ear, Kellock took a few notes on a napkin and the trio played Mr Bruce up to make his presentation with Oliver’s Army as if they’d been playing it for ever .

There may be a few more tunes crooned into ears during Kellock’s Edinburgh marathon. Some of his playing partners – trumpeter Ryan Quigley for one – have played duos with Kellock before. The baritone saxophonist Bill Fleming, a regular with the Scottish National Jazz Orchestra, and Kellock actually made a point of rehearsing a few weeks in advance and the singers Liane Carroll and Fionna Duncan are performers Kellock knows well.

“I played with Bill on the Scottish National Jazz Orchestra’s Ellington concerts and he’s a lovely player,” says Kellock. “And because he also plays bass clarinet he can bring that along and we can pay tribute to Joe Temperley, who played both instruments as well for Ellington.”

Kellock has a particular affinity with singers, provided they’re the sort who interact and are as happy to follow him as they are for him to follow them, and he loves the tightrope walk (“you hold my hand and I’ll push you off,” he jests) of a situation where both participants are exposed.

“I don’t always know the words to the songs we’re playing, to my shame,” he says. “But I love responding in the moment to a lyric, especially when the phrasing being sung isn’t exactly as it was written. Audiences react to spontaneity – if it’s working – because I think they feel part of what’s happening onstage.”

Audiences also react to the camaraderie, he says, that develops offstage in conversations that might have nothing to do with music but become part of the performance in that they break the ice and help everyone to relax. Football might be the pre-gig topic of conversation for Kellock’s long-standing trio with bassist Kenny Ellis and drummer John Rae as they reunite for a rare appearance, but it’s less likely to figure when he gets together with the Ear Regulars from New York.

Trumpeter Jon-Erik Kellso and saxophonist Scott Robinson play on Sunday nights at the Ear Inn in Greenwich Village. Kellock has never met them but he likes the modern take on mainstream jazz that the Ear Inn fosters, and he has invited them to Edinburgh in a mountain-coming-to-Mohammed scenario.

“I was in New York once, playing a gig at Small’s jazz club with Tommy [Smith] and it was only later that I found out that our hotel was just round the corner – two minutes away – from the Ear Inn and that these guys were playing that night,” says Kellock. “So when the festival asked who I’d like to invite to Edinburgh, I immediately thought of them.”

They’ll probably meet just before the gig, but the background to it sounds like the start of another conversation.

edinburghjazzfestival.com