Well I talked to this Historian on Roman Army Talked and he said the Spartans had Trumpeteers, Fluteplayers and Drummers. The Trumpeteers were a Spartan clan and were Spartan so perhaps the other positions as well.

Spartan Phalanx marching with the music and the Spartans singing the Spartan Paen with the Spartans marching like the Grenadeers in perfect unison must have been intimidating.