The early Gaelic Christians sang their Psalms. In the monastic communities one who was a Psalm singer was called a salmchetlaid. We don't know what the music sounded like, just like we don't know what tunes David used with the Psalms.
St. Benen, one of St. Patrick's Irish converts, was known as his Psalm singer. It's said that he drew thousands of souls to Christ with his sweet voice. Compare the modern Psalm singers (track above) to this YouTube video of Psalm 79: 3-4.
"Their prayers were songs, and as they crooned or intoned them, they seem close to the continuous prayer the Orthodox describe as a murmur in the heart."~Esther DeWaal in God Under My Roof