A number of readers have written me in agreement with Terry Teachout. A few of them also included recordings (here for instance) & I’ve listened. A tenor, definitely, but I wouldn’t say squeaky. However, it may be that 1912 audio technology couldn’t capture squeakiness.
Gore Vidal got the thing about Theodore Roosevelt having a squeaky voice from the Washington insiders he grew up amongst, any of whom had known TR personally. There are other sources, though. A reader passed on this snippet from “Rough Rider in the White House: Theodore Roosevelt and the Politics of Desire,” by Sarah Watts:
For an Easterner to cross the divide into essential manhood, he must somehow appropriate the amoral energy of the American West that Mark Twain had described. Roosevelt’s own cowboy-soldier life testified to that, but first he had to create a persona that he most surely was not born with. He entered the New York state assembly in 1881 at age twenty-three, having overcome poor health just like his idol Abraham Lincoln. He still appeared unmanly, and newspapers and his fellow assemblymen ridiculed his ‘high, squeaky’ voice and dandified clothing, referring to him as ‘Jane-Dandy,’ ‘Punkin-Lily,’ and ‘our own Oscar Wilde.’ The New York World proclaimed him ‘chief of the dudes.’ Duly insulted, he began to construct a new physical image around appropriately virile Western decorations and settings, foregrounding the bodily attributes of a robust outdoorsman that were becoming new features in the nation’s political iconography.