I don't think that anyone really knows where 2-6 heave! comes from. Web 'sources' repeat the story about running out guns. The number of men manning a gun depended on its weight, but number 2 would either be the 'second captain' or the 'loader'. Neither of these would be employed in running out the gun. So that's just a guess then!

On the subject of ships' complements, merchant ships would have a crew of a quarter to a tenth of that of a warship of similar size. Even an East Indiaman, big ships with big crews compared with other merchant vessels, would have had crews at least three times bigger had the been warships, and quite a number of the Indiaman's crew would have been stewards/servants rather than seamen.

So the twin reasons of 'not conducive to discipline' and not needed because of very much larger crews meant that shantying was not used in the Royal Navy. That isn't to say there was no singing though. 'Spanish Ladies' - the original, not the later American whaling version - is mentioned in contemporary accounts, and Dibdin's songs were as popular on board as they were in Drury Lane.

Mentioned earlier in this thread are the use of fife and drum. This was taken care of by the Royal Marine detachment carried on Royal Naval vessels. Drums were also used to issue important or urgent orders - as in 'beat to quarters'.