THERE is no mystery as to why East London band Tigercats have called their new second album Mysteries.

“I was thinking a lot before we picked a title about the idea of mysteries in the songs and how songs are supposed to be a mystery,” says songwriter, singer and guitarist Duncan Barrett, assessing the collective theme of their first release for the Fortuna POP! label.

“There’s more to these songs than you might think on the first listen, which I really like in a song, where something can suddenly really hit you after a few years and a lyric becomes more significant. There are songs on this album that might sound like a love song or a song about a girl but they’re not; there’s more there.”

Tonight at the Wharf Chambers in Leeds and on Saturday at the Fulford Arms in York, on the closing night of Tigercats’ ten-date tour, Barrett will be airing his indie-pop songs with their complex structures and beautiful arrangements in the company of his brother Giles on bass, Laura Kovic on keyboards and vocals, Jonny Evans on drums and latest recruit Paul Rains, from Allo Darlin’, on guitar.

“People have to listen to songs and gradually they put their own meaning into them; that’s how songs stay alive,” suggests Duncan. “I do think you can have mystery in the way a song is written; there are so many songs that sound cheerful, then you listen to the lyrics, and they’re not cheerful at all; I love playing with songs like that.”

At the same time, as was the case on Tigercats’ 2012 debut, Isle Of Dogs, Duncan believes “absolutely that it’s important to have immediacy in your music if you’re trying to make pop records”.

“You can worry about different labels being given to your music, but I aspire to make pop music,” he says.

Whereas Isle Of Dogs fizzed with jangly punk, Afro rhythms and spoken-word passages, Mysteries is a sophisticated pop creation, effervescent and spirited, the songs taking shape over two years of touring before the band headed into the studio.

As serendipity would have it, bassist Giles’s day job was at Soup Studios in Limehouse, where the studio was being built from scratch. “We were helping with that, and it was a big project, so in between band bookings there, we were able to do our own sessions,” says Duncan. “At one point, Giles worked out that it was a saving of £30,000 for us.”

Having almost unlimited time to work on the recordings allowed Tigercats to “take every song as far as it could possibly go” as Giles puts it. The process also made for a more cohesive album. “We wanted to make a record that hangs together, whereas the first album was a collection of songs from where we were at that point,” says Duncan .

“For this one, we thought about the overall sound, how the songs would sit together, so it’s cleaner and there’s a crispness to it.”

• Tigercats play Wharf Chambers, Leeds, tonight and the City Screen Basement, York, on Saturday.