NEW YORK — When Holly Williams says she could have put on a cowboy hat, called up a record company and been on her way to making a living as a country musician, she’s not bragging.

The Nashville, Tenn.-based singer-songwriter is simply acknowledging that with her musical pedigree — she’s the daughter of Hank Williams Jr. and granddaughter of country music icon Hank Williams — she probably could have taken a shortcut to success.

Instead, Williams started playing small clubs right out of high school and has been honing her formidable songwriting skills ever since. She independently released her third album, “The Highway,” on her own label, Georgiana Records, last month. It debuted at No. 146 and No. 18 on Billboard’s 200 albums and country albums charts, respectively. “I’m assuming I could’ve called a record company and said, ‘Find me 10 hits,’ ” the 31-year-old said. “And there is nothing wrong with that, but that was not what was natural to me. I truly love playing my guitar and piano and writing stories.”

Williams wrote or co-wrote all the songs on her new album, which features Jackson Browne, Gwyneth Paltrow, Jakob Dylan and Dierks Bentley.

The singer is on a tour that wraps July 28 in Lincoln, Neb.

She said about her family history and being labeled a country singer:

“Definitely. I still get identified like, ‘Oh, the country singer Holly Williams,’ and there’s nothing wrong with ‘country singer.’ ... Hank Williams had a famous quote that said, ‘I don’t know what you mean by country. I just write songs’ and that is what I live by. Some are so slow, some are fast, some are stories, but they’re just songs.”