Marching songs such as the British Grenadier march or the occasional Prussian or French march were both famous and notorious back in the day - and still are - and had the power to incite fear into the enemy.
But were they ever used by a different faction, than the one it originated from, to incite confusion and fear into the enemy?
I.e the British Grenadier march used by, say, the Prussians to plant fear in French hearts?
EDIT: Or would it be too unpatriotic and dishonest to use the songs of the enemy or even your ally?
EDIT II: I should probably elaborate on the fact that I meant the marches to be played out of sight of the enemy, instead of in the open field as the colours of the ones playing the songs would most certainly give away the ruse.
I am also not limiting the question to warfare between 1700 - 1850, but to the use of marches and battle songs throughout all of known history. The example of ''The British Grenadier march'' is just for the sake of convenience, as most people interested in history most likely tend to know that one.
This documentary talks about how the Prince of Wales regiment in Yorkshire decieved a french force by adopting it's tunes.
Lilliburlero seems like an ok example of this. I think the original was sung by the Irish who supported James the II, and then it was taken in by the English as a mockery to Jacobites (Although i could totally be wrong on this).
Another one that im thinking of is not necessarily a Battle hymn, but folk songs. Its probably only a legend but the story goes during the Chu-Han contention in China, while Xiang Yu and Chu troops were besieged by the Han troops led by Liu Bang, Liu had his troops sing the Chu folk songs, deceiving the Chu troops and Xiang Yu in to believing their land had fallen and thus dropping their morale to the point of desertion.