After controlling for age, voice pitch was a highly accurate predictor of the number of children a man fathered, and those with deeper voices fathered significantly more. The researchers estimated that voice quality alone could account for 42 percent of the variance in men’s reproductive success. The quality of women’s voices was unrelated to how many children they had.
This research fits with other findings that women are drawn to more masculine men, other things being equal -- taller, stronger, square-jawed, high testosterone, and smelling of more male hormones.
It happens that we were watching "Capote" last night. Philip Seymour Hoffman won an Oscar for his portrayal of the very gay Truman Capote, including his distinctive, high-pitched voice. Research on "sounding gay" has found suggestive evidence for a "gay voice" among some gay men. Most of this research has focussed on lisping, but one of the features of the gay voice is its higher-pitched, nasal tone -- like Truman Capote's.
Putting these two bodies of research together suggests -- but only suggests -- that how masculine men's voices sound probably correlates with how many children they produce.
[In case you are wondering: low bass, three kids. Not that anecdotes prove anything.]