Why turret complexity rises faster than gun count

Is there a rule of thumb for the efficiency and difficulty of twin, triple, and quadruple turrets?

As a rough guide, problems double with each added gun, making triples a common balance and quadruples much harder to perfect.

Adding guns to one mounting increases more than the number of barrels. Ammunition handling, interference, machinery, and failure modes interact inside the turret. A rough rule in the discussion doubles the integration problems with each added gun, which makes triples a practical compromise and quadruples much harder to perfect. The Royal Navy often preferred twins partly because its doctrine also relied on fielding more ships. Turret efficiency therefore belongs inside a fleet-wide design choice rather than a simple count of guns per mounting.