Ann McCrary remembers going into the room where her father, the Rev Samuel McCrary, used to rehearse with his group, legendary gospel harmonisers the Fairfield Four, and thinking that they must have left something musical in the air for her and her sisters to breathe in and sing out.

"We'd hear them rehearsing in there and, as soon as they were finished, in we'd go and continue the music," she says. "We didn't know about the technique of singing harmony. We thought this was something that everybody did. We just sang songs and all found a note to sing that blended with the others' voices."

It took 40 years for those four sisters' voices to come together on a recording, after the gospel-rock singer Mike Farris featured them in his shows in the noughties and started an avalanche of requests for a McCrary Sisters CD. Much had happened in the meantime, or as Ann has it, "life got in the way".

Sister Regina had sung back-up for Stevie Wonder, Elvis Presley and Bob Dylan, as well as losing her 21-year-old son, a murder victim, at the turn of the millennium. Deborah had become a nurse and didn't want anything to do with singing for a living, and Alfreda had got married and turned to music ministry with her husband.

For Ann, the night that one of the female groups in the Fairfield Four's travelling party persuaded her to go onstage and tell her father that she wanted to "shing" was the start of a career that has included countless recording sessions in almost every musical style on Music Row in her home town of Nashville.

"I was only three years old and couldn't even talk properly yet, hence the "I want to shing" demand," she says. "But my father felt me tugging on his pants leg, looked down and handed me the microphone, and the audience – I don't remember this but I've been told – loved this little girl singing to them. After that, my father never left home without me. I'd only been allowed to go with him that time because I'd thrown such a tantrum at him leaving that my mum had packed me a suitcase and told him to take me with him. But from then on I became the mascot."

She travelled with her father into her teens, experiencing the highs and lows of touring in America, being refused service in certain restaurants and hotels and seeing her father, a very strong, proud man, she recalls, being humbled by white traffic cops in one incident that still upsets her. Whatever happened en route to the gig, or afterwards, however, the music kept their spirits up.

When her father came off the road to concentrate on preaching, she joined with other family members in CBS (Cousins, Brothers, Sons) and sang all over Nashville and its neighbouring towns. Much to her father's disappointment, however, this group lacked the discipline to succeed and they all went their separate ways until Ann and Regina were invited to sing together on a television programme starring gospel singer Bobby Jones.

"People started to call us for sessions together after that," she says. "We'd been busy doing other stuff separately but we were still sisters and we could still sing closely together, and after we'd done some recordings with Buddy Miller and Patty Griffin, people started asking where our CD was. But it was only when Mike Farris needed a three-part harmony and we said we have a sister, Freda, who could come in and do the top part that the idea of the four of us singing together again took hold."

Deborah was initially reluctant to join them but relented in time to record the Our Journey album in 2010. Then in May last year she suffered a stroke, and although for a time she encountered paralysis down her right side, she's back singing with the group.

"I really believe that music has healing powers," says Ann, "and for Deborah, being involved in singing with us again has been a blessing. The four of us don't always agree on everything – well, we are sisters after all – but if we start to argue, our parents come into my mind and I can see them saying: 'What are you doing?' I'd say that 90% of the time we get along just fine, which is better than getting along for 10% of the time."

Their songs, she says, carry a positive message.

"You know, life can get hard and you just have to keep moving," she says. "Our music is really about the lessons we've learned and we sing to pass on the good part of our experiences. When you've come through darkness into the light, it's good to share that with people."

The McCrary Sisters play Perth Theatre as part of the Southern Fried festival on Saturday and the Palazzo Spiegel in George Square as part of Edinburgh Jazz & Blues Festival on Monday.