mutter vs sound off

mutter is a noun but sound off is not a noun.

Word	Noun	Adjective	Verb	Adverb
mutter	Yes	No	Yes	No
sound off	No	No	Yes	No

As verbs, sound off is a hypernym of mutter; that is, sound off is a word with a broader meaning than mutter:

Other hypernyms of mutter include complain, kick, kvetch, plain, quetch.

mutter (noun)	sound off (noun)
a complaint uttered in a low and indistinct tone
a low continuous indistinct sound; often accompanied by movement of the lips without the production of articulate speech

mutter (verb)	sound off (verb)
make complaining remarks or noises under one's breath	express complaints, discontent, displeasure, or unhappiness
talk indistinctly; usually in a low voice	express one's opinion openly and without fear or hesitation
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