This is the song of my divorce, both a sad and happy moment frozen in this song. (dependent clause/phrase no conjunction)

Some dependent clauses or phrases work with or without conjunctions.

You could use a conjunction:

This is the song of my divorce and both a happy moment frozen in this song. (same meaning/different sentence)

What defines the dependent clause or adjacent element as needing the conjunction versus the examples that don't or can use them or not use them eitherway, apart from just testing to see it it takes one. Like:

She ran all the way to the playground, her friends following.

Doesn't take a conjunction.

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