Since apparently there are no placquards in the exhibit to identify this piece, I shall chime in.
It has been misidentified often on the web as "an early machine gun", "an early volley gun", and "an early gattling gun"
It is brieflydescribed here:http://palazzoducale.visitmuve.it/en/the-museum/layout-and-collections/armoury/
"Room III. .... The twenty-barrel harquebus, with 10 long and 10 short barrels, may be considered a predecessor of the modern machine-gun."
Thu we find it is a 20 barrel ( 10 long and 10 short) matchlock, revolving/repeater, wall gun.
The swivel base would be mounted on or behind a wall or rampart to provide cover.
Each barrel is fired individually, then the operator re-cocks the matchlock hammer, manually advances to then next barrel,
"blows on the slowmatch" to ensure it is burning well and not covered in ash, then opens the cover to the fresh barrel's flash pan
and he is ready to fire again.
The barrels are common "part round part octagon" fowler barrels, (tang and all) mounted on a rotating frame .
the frame then attaches to the buttstock, and the entire mess mounts on the "swivel frame"
this allows for removing the assembly for (tedious) reloading .
The only advantage is that a single operator can offer 20 aimed shots before reloading. But then he is hosed.
The disadvantages are legion. a Better method is 1 musketeer, and 2 reloaders - then they only need 3 or 4 muskets (instead of 20 barrels) and the rate of fire is nearly the same, but continuous; and the reloaders do not need to be skilled marksmen.
With flintlock muskets ( as opposed to matchlock) one shooter and 1 loader can keep up about the same rate of fire.
It differentiates from a volley gun in that a volley gun fires all barrels at once. It only vaguely resembles a gattling or machine gun to the uninformed.
Why "short and long" barrels is beyond me. I hazard a guess that the "short barrels" may not be musket barrels at all, and have been misidentified by a museum employee uneducated in firelocks ( it is more common than you might think).
ah . a search for this device reveals this prior threadshttp://brassgoggles.co.uk/forum/index.php?topic=31984.0