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not understanding the gravity of the situation
nonchalant?
Cavalier? Ignorant?
Also, why is this in music. Are you writing a song?
The closest that I could think of was "inarticulate". I doubt this is what you're looking for, however.
Synonyms for speaking casually include babble, chit-chat, and ramble. (With ramble being the closest to what you're looking for.)