The music which developed in the Age of Faith was Gregorian Chant. It fundamentally is a sung prayer used in praying the Psalms or in chanting parts of the Mass. It was vocal music in Latin, without musical accompaniment. This is still done is some monasteries today.
Regina caeli, letare, alleluia,
QUEEN OF HEAVEN
Queen of heaven,
During the first half of the Middle Ages chanters relied on memory or placed simple marks to indicate when to go up or down, etc. over text words or syllables. The square notes on a four lines stave you see on illuminated manuscripts were developed by a Benedictine monk named Guido d'Arezzo (Italy 990-1050). Here is a sample of Gregorian notation and its English equivalent.
To this day Gregorian Chant has become the norm for Church music. The reason for this has been given by St. Ambrose as follows: "The fundamental power, animating all music which is not made but which grew (as is the case with the folk-music), belongs pre-eminently to Gregorian chant." For this reason Gevaert considers the most characteristic quality of the chant to be the fact that it never grows stale, "as though time had no power over it". Not the most conspicuous, but the most simple artistic means produce the deepest and most lasting impression, when skillfully employed. The first requisite is that the sentiments contained in the text be given true expression, and be not obscured by obtrusive external forms. (New Advent: The Catholic Encyclopedia)
In the 12th century, sacred composers started experimenting with Gregorian Chant at the Cathedral of Notre Dame in France. They started by adding the same note an octave higher or lower to notes of the plainchant. This doesn't really change the harmony, but it adds a richer texture to it. Then, they began adding this additional voice to the plainchant at the interval of a perfect fifth or fourth instead of just at the octave. Hence, the birth of organum, the first form of polyphony. Once the concept of adding other notes to a plainchant was realized, there was no stopping the possibilities that the newly discovered concept of harmony would allow. From this evolution, the major sacred forms of medieval music were created: the medieval motet and pieces composed for the various parts of the ordinary and proper of the Mass. (Webpage/Medieval Music: Birth of polyphony)
At first this music which merged secular music with sacred was not accepted. But "in 1364, during the pontificate of Pope Urban V, that composer and priest Guillaume de Machaut composed the first polyphonic setting of the mass called La Messe de Notre Dame. This was the first time that the Church officially sanctioned polyphony in sacred music". Although Polyphony has the ability to uplift the human heart to the realm of divine glory, it has its limitations because the congregation cannot vocally participate in it.
Today's hymn singing in liturgical functions does engage each person in the singing and the Church admits the used of modern music in Church, however, since secular melodies are at times combined with the doctrinal text, care must be taken that it be free from the profane and theatrical aspects.