The use of fife and drum as part of a military battlefield communications system was developed in Western Europe during the 16th century. Geoffrey Parker discusses this (briefly) in his well-known work The Military Revolution: Military Innovation and the Rise of the West, 1500-1800, in the section on changes in communications and logistics during the 16th and 17th centuries.

Small fife and drum bands (in fact that's where we get the word "band" to refer to a musical group -- prior to this "band" referred to the smallest level of military organization, what we would call a fireteam or squad today) we attached to most military units by the 17th century, and by the mid-18th century even small local militias had a fife and drum corps.

For some example of modern performances of military fife and drum perfomances, the U.S. Military actually still maintains a Fife and Drum Corps that play original 18th century tunes: http://www.fifeanddrum.army.mil/

For some more examples of late-18th century fife and drum music: https://www.youtube.com/watch?v=yTDOoXd6EXs

I'm only familiar with 18th century American and British military music; I've no idea how similar or different the Spanish or other Continental European equivalents of the same or earlier period are, although my instinct is that it was probably pretty similar in style, but probably used different tunes.

The fife and drum music (sometimes just drums, since fifes were more expensive) was mainly used for keeping cadence during marches, and also for communications both regularly and especially during battles. While there may have been some psychological benefit to the soldiers, this was not the main goal.