Donald Trump Jr and his wife Vanessa, both 29, had a baby girl Saturday afternoon in New York City. Kai Madison weighed in at 6 lbs 14 oz.

"Everyone's great," Trump Jr. said in a phone call from the hospital to People. "Baby's great, Vanessa's great – and I'm getting used to the idea [of being a father]."

And what's the origin of the baby girl's unusual name? "Her [maternal] grandfather," he says. "It's Danish. He's a Danish musician and we wanted to keep it as a family name."

Kai wasn't due for another two weeks. She joins her Uncle Barron, Donald Trump's one-year-old son.

The elder Trump told the New York Post that being a granddad was "terrific." "Well, it's not something I had necessarily in mind, but it feels very nice," he said.