Green Bird by SEATBELTS/Gabriela Robin is a fantastic example of music that's a bit inherently moody but nearly everyone familiar with it has a strong emotional tie...

Julia...

I think your question is a difficult one - the common answers are likely to be tied to shared media moments as a multimedia experience creates a much stronger memory than sound alone.

Did the radio happen to be playing "Little Green Bag" as you pulled into the parking lot of the church for your father's funeral? Well then "Little Green Bag" might make you break out in tears. When my partner's mother was passing away she was listening to Dancing Queen on loop by request... my partner has difficulty listening to Abba now.

So we've got three ways (maybe) songs can get emotional - they can be inherently emotional, they can have a curated multimedia experience or they could have a personal multimedia experience. The last factor is absolutely where you'll find the strongest emotional ties - the middle factor inherently produces softer associations but ones that are more likely to be shared experiences (and dip into personal experiences... i.e. I was watching Cowboy Bebop when my girlfriend was growing more distant and I associate it really strongly with loneliness)... as for inherently moody music, I'd argue that's just a more vague form of a curated experience. We have cultural associations with instruments and chords and those "written to invoke X emotion" songs are playing into those associations.

Anyways, I did want to clarify that it's still super interesting to see other people's emotional associations. That dive wasn't meant to lessen the question or be dismissive in anyway - I just find the why extremely interesting.