10/05/2013 AT 10:30 AM EDT
's transformation from a small-town Michigan girl to provocative pop superstar has become the stuff of legend.
But in a revealing new essay in November's Harper's Bazaar
, the singer, 55, opens up about a harrowing experience she went through when, as a 20-year-old, she was struggling to make it in New York City: She was raped a knifepoint.
"New York wasn't everything I thought it would be," the mother of four writes. "It did not welcome me with open arms. The first year, I was held up at gunpoint. Raped on the roof of a building I was dragged up to with a knife in my back, and had my apartment broken into three times. I don't know why; I had nothing of value after they took my radio the first time."
Madonna did not elaborate on the attack, which she previously discussed in a 1995 interview and which was chronicled in a 2007 biography, according to the Hollywood Reporter
. But she did share the highs and lows she experienced while trying to strike it big in New York.
"The tall buildings and the massive scale of New York took my breath away," writes the pop diva, who still calls the city home. "I felt like I had plugged into another universe."
"But I was also scared sh–less and freaked out by the smell of piss and vomit everywhere, especially in the entryway of my third-floor walk-up," she describes.
To earn money, she posed nude for art students. But even then, her signature grit already shone through.
"I was defiant. Hell-bent on surviving. On making it. But it was hard and it was lonely, and I had to dare myself every day to keep going," she recalls.
The candid essay also touches on other parts of Madonna's life, from her modest beginnings in her small Michigan town to her devotion to Kabbalah
to her decision to adopt
two children from Africa.
It's a journey that the pop star has navigated with fierce resolve and an individualistic spirit – qualities that she's keen to pass on to her own kids.
"I have been blessed with four amazing children. I try to teach them to think outside the box. To be daring. To choose to do things because they are the right thing to do, not because everybody else is doing them."