October 2012. I remember being at my desk in the Sunday Herald office when the sad news filtered through that Michael Marra had died, aged 60. Earlier that same day I'd been reading a diary piece written by The Hazey Janes - the four-strong Dundee band who count Marra's children, Alice and Matthew, in their ranks - concerning their ongoing European tour as support for Wilco. I remember checking their gig dates and hoping they hadn't been far from home when Scotland lost one of its greatest songwriting sons.

"We'd been back in Dundee for about two hours," Alice Marra reassures me when we meet up in her home city on a surprisingly warm day in May. "It was literally out of the van and up to the hospital, which was surreal. We'd just driven from Valencia to Dundee, and I'm sure I was walking down Perth Road with a sombrero on. I remember thinking, for weeks and months after, that the tour was like a bit of a dream because it ended so abruptly. A very strange time."

Today, basking in the sunshine outside Dundee Contemporary Arts centre with three-quarters of the band - keyboard-guitarist Alice, her bass-playing brother Matthew and singer-guitarist Andrew Mitchell (drummer Liam Brennan is otherwise engaged) - there's a lot of laughter when Michael Marra comes up in conversation.

"We had a great afternoon with Michael and [his wife] Peggy a day or two before the tour," says Andrew. "I remember being in the garden with them, and Michael was really excited."

"He wanted to get in the van with us," adds Matthew. "It made him really happy to know that, in the last two weeks of his life, we were with Wilco every night," says Alice. "Apparently it was all he talked about for the whole fortnight."

"Peggy says he was like, 'Where are we on tour tonight?'" laughs Andrew. "And she was like, 'The bairns are in Barcelona.'"

Earlier in 2012, The Hazey Janes and Michael Marra had shared time together in the studio recording the six-track Houseroom EP, which consisted of six of Marra's previously unreleased songs, chosen by the band from about 20 demos he offered them.

"It was fun," Alice remembers. "We did it fairly quickly, in two or three days. He was already ill by that point, so it wasn't quite as silly as it might have been. Although I'd done a lot of bits and pieces with him over the years, I'd never been in a proper studio set-up before and I was very impressed with his first-take vocals, that sort of thing."

"Michael was just my friend's dad for many years when I was about 15 or 16," explains Andrew. "Then it was, 'Oh, he does what I'd like to do.' Then it was, 'Wait a minute: he's really good at doing what I'd like to do.' And quickly he became someone I'd aspire to be. So, personally speaking, it was such a massive thing for me, a dream getting to know him."

Even without that Wilco tour, Marra had every right to be proud of his offspring and their bandmates: they've been making excellent records ever since their self-titled mini-album was released in 2004. Two years later, debut album proper Hotel Radio set the template for a laid-back west-coast America style married to a more insistent UK indie sensibility, with warm vocal harmonies working hand-in-hand with sunny pop melodies.

Unfortunately, the band's early momentum was knocked off track when their second album, Hands Around The City, was shelved because of a legal dispute (it remains unreleased but they've since recorded a live version of it in its entirety which may, one day, plug the gap for completists). Undaunted, they swung back into action with 2011's The Winter That Was and have consolidated their return to the forefront of the Scottish music scene with Language Of Faint Theory, out tomorrow.

Picking up in Spain again where the Wilco tour left off, The Hazey Janes returned to the studio in El Puerto de Santa Maria where they'd recorded Hotel Radio, in order to work again with producer Paco Loco. They'll admit to one day off for a boat trip to Cadiz, and they rhapsodise about the food ("that black rice paella…"), but, in all fairness, they set themselves a tough task: to be in and out of the studio in two weeks, making the most of its non-digital devices.

"We recorded everything on two-inch tape and mixed down to quarter-inch," Andrew explains. "It was all analogue, and the desk was from a studio called Scorpion Sound Studios in London that had been used by Queen, Supertramp and T. Rex in the 1970s."

Decide for yourselves if the spirits of those particular rock ghosts haunt the new album, but the colours of Spain certainly soak their way into some of the songs. There's a neat bit of Spanish-style guitar on (I'm) Telescoping, while the title track features a trumpet solo that surely owes a debt of gratitude to Miles Davis's Sketches Of Spain (as well as boasting a rare lead vocal by Alice).

One of the album's highlights is recent single The Fathom Line, a song that's more overt than usual in its tribute to the band's home city, past and present. If anything, those euphoric harmonised choruses capture the optimism that seems to be tangible in the Dundee air these days, as the city reshapes its riverfront and pushes itself into the cultural spotlight.

"It's nice that somebody gets that because it's definitely one of the things we were going for - that plight-of-the-underdog type of sentiment," Andrew admits. "To be unashamedly writing about where you're from and being okay with that, as opposed to always looking beyond. We've got something really great here in the city - what's going on, and what's been in the past as well."

Once the album's out, the band immediately take on a set of headline gigs and festival appearances, with an eye in September to playing live dates down south and then, at some point, returning to Europe. If the latter is ground won through touring with Wilco ("I think we were just happy to get the Jeff Tweedy seal of approval," says Alice) then the former might be a bit easier this time round thanks to their late 2013 tour supporting a band with a few Dundee connections of its own. "We made a lot of new friends in England when we were on the Deacon Blue tour," notes Alice, "so hopefully some of them will come back out and say hello."

"Doing the Deacon Blue shows, we weren't really sure how it was going to work, but their audiences were great," says Andrew. "Really kind, really professional audiences." What do you mean by that, exactly? "They know how to give the support band their time. It was amazing for us to get to play places like the Royal Albert Hall and Liverpool Echo Arena - but still feel we had a connection with the audiences. A great tour."

"We just need to wait and see what happens with the album first, and take it from there," adds Matthew, more cautiously, "because we're having to book everything ourselves, which is not the easiest."

If The Hazey Janes have a heads-down-get-on-with-it attitude, then perhaps that is something they inherited from Michael Marra. I get the feeling this is the case when we talk about the Celtic Connections tribute gig that Rab Noakes pulled together only a few months after Marra's death.

"It was fantastic, one of the best nights of my life, in a strange way," says Alice, who sang with special guests right across the programme and, of course, appeared with the band for their contribution.

"I think it was different for all of us," Andrew admits. "I think Alice just put on Michael's head and adopted that acting role for the night to get through it. I was incredibly nervous."

"That whole period, though," says Matthew, "we just seemed to work right through. It seemed like the only thing we could do."

"But that was always his advice to us," notes his sister. "'Whatever you do, don't stop working. Just keep working.' And it seems to be working for us."

Language Of Faint Theory is released by Armellodie Records tomorrow. The Hazey Janes play Hootananny, Inverness as part of goNORTH on June 5, Queen's Hall, Edinburgh (June 6), Fat Sams, Dundee (7), Broadcast, Glasgow (13), Fyne Fest, Achadunan (14), The Lemon Tree, Aberdeen (20), The Old Bridge Inn, Aviemore (21) and Twa Tams, Perth (28), www.thehazeyjanes.com