So what did Lincoln's voice sound like? According to this article, the new movie, Lincoln, has it right.
This article, also from Smithsonian Magazine, discussed Lincoln's voice in detail:
“Lincoln’s voice, as far as period descriptions go, was a little shriller, a little higher,” says Holzer. It would be a mistake to say that his voice was squeaky though. “People said that his voice carried into crowds beautifully. Just because the tone was high doesn’t mean it wasn’t far-reaching,” he says.
Lincoln’s accent was a blend of Indiana and Kentucky. “It was hard to know whether it was more Hoosier or blue grass,” says Holzer. The way he spelled words, such as “inaugural” as “inaugerel,” gives some clue as to how he pronounced them.
Despite his twang, Lincoln was “no country bumpkin,” Holzer clarifies. “This was a man who committed to memory and recited Shakespearean soliloquies aloud. He knew how to move into King’s English. He could do Scottish accents because he loved Robert Burns. He was a voracious reader and a lover of poetry and cadence. When he writes something like the Second Inaugural, you see the use of alliteration and triplets. ‘Of the people, by the people and for the people’ is the most famous example,” he says. “This was a person who truly understood not only the art of writing but also the art of speaking. People should remember that, though we have no accurate memorial of his voice, this is a man who wrote to be heard. Only parenthetically did he write to be read.”