Is "convivial" a formal and uncommon word? Can I say "a convivial community"?
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You can use it whether or not it is uncommon or formal, as long as it means what you intend it to mean.
- Fond of feasting, drinking, and good company; sociable.
- Merry; festive: a convivial atmosphere at the reunion.
If your intention is to say the community is "fond of feasting, drinking, and good company" Or "a very sociable community" or even "a festive community", they "a convival community" would be correct. Though if you are asking if it is rare...somewhat, I would say.
Step by step
"convivial" comes initially from cum - vivere = to live together
if you live together, you eat together
if you eat together, you like feasts and drinking in common
These meanings are generally weakened nowadays, towards merely "sociable", "friendly".
This word is neither formal nor uncommon, but somewhat hackneyed by commercials.
"Enjoy one hour of relaxation in our convivial parlour". (parlor in US-English)
"Come and see our full range of products in our new convivial super-market".