Never covet thy neighbour's wife, unless it helps your songwriting.

Cage The Elephant's charismatic singer Matthew Shultz is in full flow, discussing their third album, Melophobia, and seeking a way of explaining it.

"I just had a string of little discoveries that led me to discover where I'm going with my songwriting," he says.

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He says he has moved on from subject matter that may be socially acceptable or cool to creating work that is more honest or tells a personal story.

"For me, I wanted to get to a place where it was about transparency. A friend of mine told me that if you're not writing lyrics that you are somewhat embarrassed to sing, then you're not writing honest enough lyrics. That really resonated with me. Could I write a song about being tempted by my neighbour's wife? Because to write about that is to be real."

Quite what it might do among Shultz's local community is another matter, but the singer himself seems too relaxed to be bothered by anything.

It has been a difficult couple of years for the Kentucky band, who delivered two early records full of screaming and shouting, teamed with chunky, Southern fried riffs. Although the ingredients were familiar, the quintet infused them with a lively energy and their live gigs were often thrilling. Yet the recording of Melophobia, a complex record that veers towards the experimental, was a laborious process.

"On this record it was the first time we'd been apart for a bit and started writing as individuals before we got together again," explains Shultz.

"So we all had pretty solid ideas about where the band should move, and they were all polar opposite ideas.

"The challenge was to marry these polar opposites, which gave the record way more depth."

Shultz returns the subject to the honesty that he feels is at the heart of Melophobia.

If their previous songs could often display a clear lineage to the past, then this time he feels they've created an identity of their own.

That includes his own singing voice, where the full on shriek that characterised hits like Ain't No Rest For The Wicked has seemingly been rested.

"On this record I wanted to sing more and scream less. In the past it was somewhat monotone melodically, and just going full throttle as a singer. At the time I thought it was more punk rock, or more 'legitimate' to sing like that, and on this record I wanted to be free of that baggage and not care about a particular image."

That's not to say the group will be reaching for the pipe and slippers just yet. Their current jaunt on British shores is supporting the rock band Foals, another group who have wedded more complex ideas with rousing guitar-anthems.

The tour calls at the O2 Academy in Glasgow on Sunday evening, and Shultz is delighted to be travelling with Foals again.

"One of our first tours in the UK was opening for Foals, and it was a great time. They were one of the first bands we befriended over there and it's great things have come full circle and we're touring again."

They will, however, be missing a member. Having finally got through the recording process of Melophobia and released it last autumn, the band were then hit with another blow, when guitarist Lincoln Parish announced he was leaving.

For a group who've been friends for years, it left Shultz on the back foot.

"It was a bit out the blue. There was so much adversity behind this record, when we finished it there was a sigh of relief, and it felt like we were closer than ever. Then it was a major surprise and a major blow.

"There's no animosity there, Lincoln was 15 when he joined the band and when we moved to the UK we had to become his legal guardians. To tour for five years straight after that, he missed out on his adolescence. It was just a very difficult thing to have to deal with for us."

Yet the band are still standing, and Shultz is looking ahead with optimism as to what lies ahead.

"I definitely see infinite possibilities in the future now, whereas before it was like walking through a minefield. Now I'm like, let's just fly over it…"

Cage The Elephant support Foals at Glasgow's O2 Academy on Sunday.