The Classical & Romantic Ages at least hint accurately of what they are all about.
Not so the Ages of Modernity & Post Modernity.
Because the Romans no doubt thought of themselves as fully modern - as will humanoids a million years from now, if our species is still around by then.
I think it much better to tag each of these slices of history as "the Age of Exclusion" (culminating with Auschwitz's exclusionary fires of racial purity) followed by "the Age of Inclusion" (beginning with the American Civil Rights Movements' biggest success, 1965's inclusive Voters Rights Act).
Only time will tell, if these terms have any legs....