Sometimes Lisa-Kaindé Díaz will be wandering around her apartment, singing to herself, only to find twin sister Naomi singing exactly the same song, at exactly the same part.

“It is not strange to us for that to happen,” she says. Or at least I think Lisa-Kaindé says it – their tendency to complete each other’s sentences, disagree furiously mid-sentence, or just tumble their thoughts over the top of each other’s makes it hard to untangle exactly who is saying what.

“With music, we just look in each other’s eyes, and we know,” adds Naomi (or at least I think it’s Naomi, etc etc).

The 19-year-old French-Cuban sisters are currently putting their musical sixth sense to good use as Ibeyi, adding an electronic edge to their piano and percussion compositions to produce what they describe as “contemporary negro spirituals”. Much of their inspiration comes from Yorùbá tradition, from the chants brought over to Cuba from Nigeria and Benin on slave ships. These songs have always been an integral part of their lives thanks to their mother, who grew up singing them. Ibeyi’s unique combination of the ancient and modern is no doubt what persuaded XL boss Richard Russell to sign them and produce their self-titled debut album.

The sisters’ story is pretty remarkable. Their father was the famous Cuban percussionist Miguel “Angá” Díaz, a conguero who played with the Buena Vista Social Club, among others, before his death in 2006. Asked what musical lessons he gave them, Lisa-Kaindé gestures a “zero” sign: “He would ask if we wanted to do music and we would say, ‘No, we want to go to the beach!’ So he let us do that.”

The girls credit their Venezuelan mother (who also acts as their manager) for really pushing them and inspiring their love of Yorùbá culture. Yet their father’s influence seems undeniable: the day after he died, Naomi picked up her first instrument – the cajón – and began playing.

“It was an unconscious thing,” she says, reflecting on the synchronicity.

“But I do think there was something spiritual about it,” says Lisa-Kaindé. “It was our father’s new instrument, and one he wanted to be better at. [Naomi] didn’t know about this instrument and yet she started playing it … so there is something there.”

They also remember vividly the only time their father cried – when he found them arguing about the television. He delivered a speech: “You girls have to help each other and not fight – you are sisters, you must find a way to love each other every day.”

The way they eventually found was music – in fact, they say music is the only way they can communicate with each other without ending up in a screaming match.

“Oh, we scream a lot,” laughs Lisa‑Kaindé. “We were screaming just two hours ago!”

The reason they argue is also the reason their music works so well: they have polar opposite personalities. Naomi, the impulsive, energetic party girl, looks after production and percussion, as well as bringing her love of hip-hop, dancehall and electronica to the mix; Lisa-Kiandé, the more studious homebody, listens mainly to old soul and jazz artists, and concentrates on the compositional side. Musical disagreements seem to fuel their best songs, and although there is plenty more screaming during writing and rehearsal sessions, it melts away when they get on stage.

“People say we communicate in a really beautiful way on stage,” says Lisa-Kaindé. “It can be like therapy.”

Like therapy?

“When we have a person that is here with us, we don’t argue,” says Naomi, nodding towards me. “The audience is the same. So being on stage is the therapy, and the audience is like …”

“... the psychoanalyst!” says Lisa-Kaindé. “It’s true! In a way it’s like that.”

“It’s weird though,” laughs Naomi. “We sound weird.”

Behind their laughter is a serious point. The songs on Ibeyi – which is Yorùbán for “twins” – address their late father (Think of You) and also their older sister (Yanira), who died in 2013 from a stroke. Lisa-Kaindé says that whenever they play live, it allows them to re-enact the pain in the songs but emerge with strength.

“That’s why I love songs,” she says. “It’s like living your pain again, but winning. At the end of every song I’m like, ‘I won the war, I won this pain, this is over.’”

Music, it becomes abundantly clear, is not something the sisters deal with lightly. Many of their songs are inspired by – and structured like – prayers, with their use of repetition and lyrics, such as recent single River’s “come to the river, wash my soul”.

Of course, taking music so seriously means making sure the songs are as good as can be, which means more disagreements. And more screaming.

“When she writes the songs, I will listen after and say ‘it’s shit’ or ‘it’s not shit’”, says Naomi.

Lisa-Kaindé nods forlornly: “She is really tough.”

But you appreciate the criticism, right?

Lisa-Kaindé: “No.”

Naomi: “No, but in a way, yes!”

Lisa-Kaindé: “No, sometimes I do not.”

Naomi: “But in a way, you do.”

Lisa-Kaindé: “No! Of course you don’t appreciate when you make a song you are so happy with and someone tells you it’s bullshit.”

“No,” says Naomi, pausing for a second: “But in a way, yes!”

While I’m laughing, Lisa-Kaindé concedes that she wouldn’t want someone telling her everything is wonderful all the time: “I wouldn’t want to make music she doesn’t like. Because in the end, the music sounds like a part of me and a part of her. It will only work if we both like it, because …”

She pauses for a micro-second, so her sister can chime in, with perfect timing: “We complete each other.”