Since "We Wear the Mask" is a rondeau, we can assume that we'll have a few more literary devices circulating in this already highly formulaic poem. And since this sort of poem is supposed to be lyrical and memorable (considering that refrain) we can expect those devices to help amplify the sound even more.
You want proof? Let's start at the beginning, then. Stanza 1 has quite a bit of consonance (repetition of consonant sounds) in words like "grins," "lies," "cheeks," "shades," "eyes," "hearts," "smile," and "subtleties." Whew. That's a lot of S sounds for one stanza. So, what's up with that? Well, that repeated sound not only helps to accent the first rhyme of the poem ("lies" and "eyes"), it also gives us an underlying sense of multitudes.
It's subtle, but think about it: most plural words end in S (like, um, "words") and most of these S-sound words are indeed plural words. So, the poem is using sound to underscore that the central phenomenon of mask-wearing is not just limited to the speaker or even his best buds. It's something to which nearly everyone in the world can relate.
Also, in line 5, we get some alliteration (repetition of initial consonant sounds) in the words "mouth" and "myriad." Just like before, the repetition of that M sound helps to accent the words even more and gets us thinking about that mechanical sound of "mouth[ing]" subtleties.
And finally we get some more alliteration in line 11 that repeats that T sound in "To thee" and "tortured" souls. Here we really feel the connection the speaker is trying to make between himself and Christ by using similar sounds to address his savior and the tortured souls that need his help.