to be fair, Vivaldi lived and composed in the Baroque period (1600 - 1750), not the Renaissance aprox 1400 - 1600).
During the Renaissance, there were many different and varied styles of lutes with no widely accepted standards for size configuration or tunings. And tho the word 'mandolin' or variations of the term were used in the 17th and 18th centurys, The "mandolin" we know today really didn't catch on till the 1750's - the very end of the Baroque period. So it's more likely that Vivaldi composed for some sort of small double coursed lute not unlike the examples shown.
it's a box with strings. If it's a well made box, It'll play?
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