However, the common usage of modern implies contemporary - and that's determined by the age of the observer. I can just about call the 1960s modern, but the shifts in technology that have driven such immense social change might mean that anything before the rise of popular internet use is, like, ancient. Modernity has been cool - hence the Mods and their sharp suits - and uncool (see the Green Party Manifesto for anxiety about modernity, or the Conservative's fear of change).
And that's not to mention post-modernism. Good luck with that.
Jacque Samson (Modern Strategies for Pictorial Enunciation in Comics) offers two ways of interpreting the modern. It's either diachronic (concerned with time and history) or synchronic (about the modes of production). His definitions - in brackets - don't quite match the ones that I found in the study of linguistics.
However, his diachronic definition locates 'modern comics' as beginning in the late 1960s, 'contemporaneous with the extraordinary movement towards diversification that transformed it'. Since he is talking abut bande-dessinee, I'll flip it back to the early 1960s, and claim the Stan Lee/Jack Kirby revolution as the first moments of modernity.
Moving to theatre, it also allows me to include the antics of the 1960s - Peter Brook, The Theatre of Cruelty at the RSC, that kind of stuff. And I immediately realise that Samson's markers for modernity happen at different rate for theatre. It might be nice to imagine that the 1960s were a pivotal moment, but the harbingers of modernity - Artaud, Beckett, Brecht - were working earlier.