The Dutch, French and early American Christians sung Psalms when they went into battles fighting for their liberty. The book of psalms was considered a "little Bible" by Martin Luther. Psalms were sung exclusively in churches until about 100 years ago because they created strong Christians. Psalms are also full of political issues and battles with examples of godly responses to those situations.
The word "Psalter" is the term for a book of psalms arranged for singing. There are many different ones. The one we have is the Trinity Psalter (words-only edition). Reading the introductory notes is inspirational in itself. One year, as an introduction to singing one psalm each Sunday School, I read a paragraph from those notes and repeated them three times in a year. That was a very helpful technique to impress the importance of the Psalms for everyday and political life.
Many different tunes with the same meter (syllable pattens repeated per line) can be used for the same psalm. For instance, if you know Amazing Grace, then you can sing over 40 psalms using a Psalter.
For Psalm 44, my favorite tune is Immortal, Invisible. You don't even need any audio, if you already know that tune. But to remember the tune, here is an audio of Immortal, Invisible. Try singing along for the eight verses below as a starting point!
(Note: Requires download to play until we connect it to a stream. Singing starts immediately)