Augustine's definition of a "hymn" as referring to a category of psalms

"Hymns are praises of God with singing: hymns are songs containing the praise of God." 

Three elements:

1. Not only of praise,

2. but of God,

3. and singing. 

Here is a link to Augustine's commentary on Psalm 73. You can read the quote [see v. 1] in its context.

http://www.ccel.org/ccel/schaff/npnf108.ii.LXXIII.html