This rehearsal is about bringing to life some of the songs Haines wrote on his dinky midi keyboard in London last year where he and wife Jaimie now live.
He hasn't met most of the horn players until today, and wanders along the line shaking hands and introducing himself. It's all rather gentlemanly.
They start working methodically through a track that will end up being called Frontier West, before moving on to the beautiful, eerie Lament.
During Frontier West there is a sense of some tension between Haines and horn section leader Mike Booth as they figure out the intricacies of the track. But you soon realise that it's the mechanics of making a jazz record. And that's the thing about this difficult and eloquent music; though it is a little like a business transaction, the true magic comes out in the phrasing and the passion of the playing.
That rehearsal was back in the second week of February. Just over a month later, Haines is at the offices of Warner Music New Zealand for a day full of interviews. He mentions his record company a lot over the course of our chat and you can tell he feels lucky - almost indebted, which he probably literally is - to them for supporting his "jazz music".
He was out DJing at Ponsonby Social Club until 2am the previous night and although he says he's a little tired he looks fresh and bright. The album, entitled Vermillion Skies, a name taken from the lyrics of lead single First Light, is ready to go and will be released on March 29 to coincide with Haines' performance at the Waiheke Island International Jazz Festival on Good Friday and the National Jazz Festival in Tauranga the next day. The songs TimeOut heard in their raw form during rehearsal have polished up well. Frontier West is the most lively of the bunch, with its delightful zah-zah-zah dramatics ("I wrote it on the keyboard in London and it really reminded me of a 60s western."), and Lament has become an eerie and haunting closer to the set.
Haines says he wanted to build on the classic jazz sound of The Poet's Embrace but fill it out with more instrumentation, hence the reason he brought in the six-piece horn section made up of two flugelhorns, two french horns and two trombones.
"Whereas The Poet's Embrace was more like a vehicle for improvising, on this one I wanted to bring more of a movie soundtrack vista to it," he says.
There's also the smoky and smouldering Lady Lywah, which is dedicated to his Chinese mother ("because she was a dancer in the 60s so she's a stylish woman. My father is the musician but it's my mum who has the artistic flair"), and two vocal tracks, Navarino Street and First Light, where Haines shows off his smooth inviting croon.
"I've always been very scared of singing and I always knew that I wouldn't really come into it until I was in my 40s, which I am now," he says. "Singing is terrifying, but I'm finally getting comfortable with it and it's feeling more and more natural as I get older. And I think my next record will be a full vocal record."
The sweet and catchy First Light, with the great line "Facing down the dawn, whiskey in my hand", is a nod to his and wife Jaimie's new life in London, where they moved last year. And it's a love song of sorts, too.
"It's based on Jaimie and I being up all night - the sun comes up at 4am in London - and you're at a party and everyone's high. I guess it's a big thing for me and Jaimie to move our lives over to London and I wanted to put that into a song. She has chosen to be with me, and me with her, and so I guess you could say it's a love song, without being cheesy," he laughs.
It's these vocal tracks that make the album more accessible than The Poet's Embrace. Not that that album was purely for jazz lovers, because it sold solidly and spent a month in the top 20 album charts. But Haines is hoping Vermillion Skies is even more commercially viable, which is key because as well as Warner bankrolling much of his recent music, Haines has also put everything he has into it.
"I put my life savings into this record. But I'm at a point in my life where these things are very important to me and you have to put everything on the line," he says.
Because the move to London Coming to an arrangement
has also been expensive. But, he says, it was necessary to capitalise on the success of The Poet's Embrace, which has given his international live career a new lease of life.
"It's beginning to pay off now and for me personally what makes me most happy is to be able to play music with my friends. I enjoy being on the front line."
With so much at stake he doesn't mind admitting he wants to sell some records.
"We are going international with this one. We're looking for a bigger audience. I'm making music for the public and I always have an audience in mind and it's never a selfish project. It [Vermillion Skies] is quite different and I wanted it to be a little bit more accessible."
In the past few years Haines has changed the way he approaches writing and recording music. He pondered things like the "terrible" reviews he got for 2010's not that bad Heaven and Earth, and the mixed reactions to 2003's dance jazz cross-over hit Squire For Hire ("But that was my defining album I guess, and it sold more than anything I've done."), and resolved to play classic jazz.
"I got to a point a couple of years ago with my music where I thought, 'Where am I going to go with this?'."
Haines admits he's had some pretty hairy times, like the late 90s when he was hooked on heroin. But then he cleaned up, released 2000's Sound Travels, and started touring the world, which he's been doing ever since.
However, that era also ushered in what he calls his "haphazard 30s when my ear and natural talent got me by".
So he realised there were some big holes in his technique that needed fixing. "I really owed it to myself and to the tradition that I'm from. I thought, 'I'm going to go into the deeper darker areas of what I do and not coast along'.
"And for this record [Vermillion Skies] I was just as inspired by Johnny Cash as John Coltrane, but I am a saxophone player and from the jazz tradition."
And now he's focused on - hopefully - doing an album every year for the next 10 years of his life. "Yes, I would like to do an album every year, and the guys, ... I mean my [jazz] heroes, they just kept on making music continual through all sorts of fashions.
"Donald Byrd, who passed away just last month, he was playing with Art Blakey in the 50s and 60s, and then made all these amazing jazz funk records in the 70s, so I would like to be able to do that. That's if Warners are interested," he says with a smile.
Lowdown
Who: Nathan Haines, saxophone-playing jazz man
New album: Vermillion Skies, out March 29
Also listen to: The Poet's Embrace (2012); Squire For Hire (2003); Sound Travels (2000); Shift Left (1996)
Playing: Waiheke Jazz Festival, The Bay, Matiatia, March 29; National Jazz Festival, Baycourt Theatre, Tauranga, March 30; Album release show, Q Theatre, April 6. Tickets from qtheatre.co.nz
More info: nathanhaines.com