An air of conviviality (8,4)

'conviviality' is the definition.
Although both the answer and definition are singular nouns, I can't understand how one could define the other.

'an air' is the wordplay.
I cannot quite understand how this works, but
'an' could be 'i' (Roman numeral for one) and 'i' is present in the answer.
'air' could be 'song' (air can mean a piece of music) and 'song' is present in the answer.
This explanation may well be incorrect...

'of' is the link.

Can you help me to learn more?