Isn't that the... adjectival form? Something like that. I think this is covered and Tae Kim somewhere?

The original sentence ...ではなく近代的な... and the て version ...ではなくて近代的な... mean pretty much the same thing. You'll come across the former pattern more often in written text and formal speech while the latter is more common in everyday conversation. Also, you might want to see them as a conjugated version of a set phrase "ではない" rather than the ない -> なくconjugation because 〜ではなく and 〜ではなくて are almost always interchangeable while 〜なく and 〜なくて are usually not, i.e., ない has various grammatical functions and meanings, but when it follows では, the little word て most likely doesn't change anything aside from the slight difference in nuance.

For example, なにも言わなくていいよ。(You don't have to say anything.) is ok, but なにも言わなくいいよ。sounds unnatural. So the function/meaning of ない here is different from that in your example.

The ないs in the first and second sentences in your post may be the same. But I can't say anything for sure without context.

@magamo:
Thanks for the explanation - it makes a lot of sense now. I was kind of suspecting it something was along those lines, but didn't want to learn it incorrectly.

@jarvik7:
Ah, did not know that. I thought it was only a negative conjugation of ある. Good thing to know.