I can't help much, except that I agree it's 'muse' rather than 'goddess' and Greek mythology rather than Roman. It might be intended to be 'Calliope', the muse in Greek mythology who presides over eloquence and epic poetry, so called from the ecstatic harmony of her voice, like this one:
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That one is from an antiques website, measuring 9.64 x 12.2 x 5.11 Inches, said to be a French spelter piece c.1920 and priced at $200, which I think is overpriced even though it's a more skilfully made piece than yours. If the paint on yours is indeed original, that's an indication it's made from a cheap metal such as spelter. I would think yours is also from sometime around the 1920s, or back to the end of the 1800s at the very earliest.
You say it has "a hole on each end probably for mounting". I presume you mean on the plinth, such that it could have been screwed to something. It looks like a mantle ornament to me and may have been screwed to a wooden base, but I wouldn't rule out it having been on top of a clock, depending on how big it is
