What’s the story on the female jazz musician who lived as a man?

From the Straight Dope:

You think I could forget the story of Billy Tipton? Yes, she lived as a man from age 21 till the day she died at age 74. Yes, her three sons (all adopted) never suspected a thing. But that’s not the bizarre part. She lived with five women in succession, all of them attractive, a couple of them knockouts. She had intercourse with at least two of them and, who knows, maybe all five. But of the three we know about in detail, none tumbled to the fact that her husband was a woman (one figured it out later). At first you might think: man, I thought my spouse was oblivious. But the more charitable view is that they were taken in by one of the great performances of all time.