On a wet Monday morning in Glasgow's west end, I am telling two-fifths of Camera Obscura my theory of Glasgow.

It goes something like this. All the things that this city tells the world about itself are wrong. Glasgow likes to pretend it's the city of the stare, no mean city, a place full of hard words and harder men. And it's not true. Or rather it's partly true, but it's by no means the whole story.

Here's the thing. Look at the music that's come out of this place over the past 30 years. None of it is hard. None of it is macho and aggressive. Were you to chart Glasgow's contribution to pop music from the early 1980s to now, it's more or less the opposite. From Postcard Records via The Pastels and Belle And Sebastian to the members of the band sitting in front of me, musically Glasgow is a soft city.

"I understand what you're saying, yeah, absolutely," says Tracyanne Campbell, the lead singer, lyricist and face of the current incarnation of my notional new soft. "It does have an image as something that doesn't truly represent it at times. It's a soft place. And it's an emotional place and they're emotional people here, and people aren't scared to express their emotions.

"I think it's the lack of pretension that allows that to happen," adds keyboard player (and adopted Glaswegian) Carey Lander. "We don't like people to be up themselves. We don't reward that. It's not about how rich you can get and how much you can show off. And I think the music reflects that. It's a really melodic tradition of music. You can't help but be influenced by the kinds of bands that are around you."

And in some ways you could argue that Camera Obscura are the acme of this strain of Glasgow sound. A band who sing love songs that namecheck books (The Heart Is A Lonely Hunter gets a mention on their new album Desire Lines) and pop stars (perhaps their most familiar song is a belated answer song to Lloyd Cole's Are You Ready To Be Heartbroken; and Billy Joel, of all people, gets a mention on the new LP – see the panel above). A band who don't so much rock as skip, painting emotions in honeyed, sometimes country-inflected harmonies.

Some people have taken that the wrong way over the years. Words such as "fey" and "bookish" are tossed around. Campbell has heard them. "It doesn't bother me. I think sometimes people have this image of us as being shy and bookish and sort of snotty, maybe. But I don't think we are."

"I don't mind being called bookish," says Lander. "I just don't like it when people try to get us to dress up as schoolchildren for photoshoots. We're actual adults."

"We go from 31 to 41," Campbell points out. "We're not children. We're not little innocents. I don't dwell on it very often but sometimes I think: how have I presented myself to the world? Have I presented myself as some little twee, asexual bookworm? I really hope not because that's not the reality."

The fact that she's currently five months pregnant probably gives the lie to that. And while Desire Lines itself is bookish, it's certainly not asexual (the lyrics of Do It Again go: "You were insatiable/ I was more than capable" – and Campbell is presumably not talking about crosswords).

But it's also a richer sounding and more sombre record than any they've done before. The former comes from recording in Portland, Oregon with Tucker Martine (Neko Case and My Morning Jacket's Jim James popped in to do some backing vocals) and from giving everyone in the band the chance to shine. "I think you can tune into people's strengths," says Campbell. "You can listen to the guitar and keyboards and drums and the bass and they're all really great. They've got a lot of personality in this record. Everybody's a bit more exposed. I think that's a good thing."

And as for the emotional richness? Well, parenthood, mortality and a brush with serious illness will do that to you, I guess. But before we go there, let's back-track a little. Where does the story of Camera Obscura begin? Maybe in Tracyanne Campbell's granny's house.

"Even at a very young age I always remember being surrounded by music and it making me feel certain ways," she says. "I used to play Puppy Love by Donny Osmond over and over again. And I remember getting to that bit of the song – 'Help me - Help me - Please' – and physically feeling something, excited or sad. I think I always had that relationship with music."

Camera Obscura made their first tottering steps into the world in 1996. ("I was still at school in those days," admits Lander.) "I was just out of school," says Campbell. "I remember the first show we played was in Hyndland Church Hall. I remember being physically sick before it and having this battle with myself. 'Why am I doing this?' There was a great need to do it and a great desire to do it. A pull. But at the same time my body was rejecting it. When you're sick your body's rejecting something. And it was like that for a long time."

Still, everyone who was anyone in the Glasgow music scene was at the gig that night and in the years since stage fright has receded and over five increasingly confident albums Camera Obscura have been finding their feet. Lander, from Maidstone in Kent, joined just over 10 years ago. Their last album, My Maudlin Career, saw them arrive on 4AD. The trajectory was upwards. Then life came along and gave them a bit of a kicking.

Some of that was inevitable perhaps. Campbell came off touring the last album feeling flat and jaded. "It started off as a general cliched burnt-out feeling I'd never felt before."

That was bad enough. But then Lander was diagnosed with cancer in 2011 and had to take time off for treatment. "Obviously when something like that happens, your whole world changes and your priorities become completely different," explains Campbell. Was there a suggestion that it might mean the end of the band? "There must have been a fear at some point with some of us that things were definitely going to change and perhaps that was that. But I don't think it lasted too long. I think Carey was determined that we got on and wrote songs in her absence, which we did."

On top of that, guitarist Kenny McKeeve became a dad in 2012 but lost his mother suddenly this year. "I think if this had been our second album maybe we wouldn't have made it because everything would have seemed too difficult, too fractured," adds Lander, "but because we've been doing it for so long we know we can do it and it was worth holding on."

"And we also owed it to each other as well." Campbell again. "We're all there to keep each other going after a fashion."

"It just would have been an awful ending," concludes Lander, "after all the good things that have happened and all the success we've had. To fizzle out would not have been a way to stop it all."

The result is an album that's not unperky but has a deeper undertow to it. Desire Lines talks to where the band is and has been, Lander says. "It's personal - but not all about her," she says, looking at Campbell.

Has it been all about her in the past, I ask the singer? "No. I've always written other things. I think people tend to think all I do is get brokenhearted or something which just can't really be true. God, what a tragedy [that would be]."

In the end the word that defines Desire Lines, and Camera Obscura for that matter, is not "fey" but "thrawn". They have taken the blows and come back from them. And they've made an album that doesn't betray their past but improves on it.

"I think it shows our determination, really," says Campbell. "Our stubbornness, our endurance."

What does that make Camera Obscura? Not as soft as you think.

Desire Lines is released on 4AD on Monday. Camera Obscura play the Liquid Room, Edinburgh, on Tuesday and RockNess on June 9