What’s the best voice for influencing others and dominating the herd? A recent study found that male horses with the deeper whinny appeal more to female horses and generally fared better in the DNA sweepstakes.

Similar studies have found advantages of a parallel kind for humans. Researchers at Duke University’s Fuqua School of Business analyzed speech patterns of 792 chief executives at major publicly held companies. Male CEOs with lower-pitched voices tended to manage larger companies, make $187,000 a year more than their higher-pitched peers, and last in office on average five months longer.

A study a few years back found that the U.S. Presidential candidate with the lower voice won in every election since Calvin Coolidge.

But apparently it’s not enough just to have a lower voice. What you do with it also matters. Another researcher, UCLA acoustic scientist Rosario Signorello, conducted studies of leaders speaking French, Italian and Portuguese, including François Hollande, the current president of France, and Luiz Inácio Lula da Silva, a former president of Brazil. He also studied speeches given by two Italian politicians, Umberto Bossi and Luigi de Magistris, and by former French President Nicolas Sarkozy.

Then he asked his research subjects – ordinary people – to rate the voices on their charisma.

What he found was surprising. Here’s what he says: “In the three languages, I see a similar pattern,” he said. “My research shows that charismatic leaders of any type in any culture tend to stretch their voice to the lower and higher limits during a public speech, which is the most important and risky context of communication for leadership.”

And it gets more complicated. These leaders adopted an entirely different tone when speaking to other high-ranking politicos or when the subject strayed from political topics. “They stretch their voice less when they speak to other leaders, keeping the vocal pitch very low. They stretch the voice limits even less when they speak about nonpolitical topics,” Dr. Signorello said.

Just to confuse matters further, when Dr. Signorello acoustically modified the speakers’ pitches, he found that if he moved the voices up in pitch, they were rated as less charismatic.

So what’s going on? Is it variety of pitch? Is it the low voice? Is it talking in a limited range mano a mano?   Or is it something else altogether?

To understand what’s really happening, we have to think about what’s signaled by variation in pitch. And we can draw first on common sense, and then on some research in the real nature of the human voice that trumps most of these rather superficial attempts to base authority on pitch alone.

A higher pitch – within your vocal range – indicates tension, passion, and, if it’s high enough, panic. It makes sense, then, that the lower voice signals authority. But it’s not just the lower pitch that matters – it’s the positioning within your own range that’s important. If you have a higher voice range than the person standing next to you, your higher pitch will not signal as much tension as the other person. Correspondingly, you don’t need to go as low to show authority. This use of vocal range is the key to understanding all these apparently contradictory research findings, and the key to managing the authority and passion in your own voice.

Go low in your range when you want to indicate authority. Go higher for passion. I explain the technical reasons for this in my new book, Power Cues. The short version for this post is that the research shows that your voice puts out more authoritative vibes at the low end of your range, and more passion at the high end. So learning to control and manage your voice is essential to successful leadership, and leadership communications.

And it works for the horses, too.