Anonymous: Puer Natus Est

Our recording of the chant can be found here.

The fullest resource I have found to medieval Christian liturgy can be found here

A history of Gregorian chant can be found here.

History
As claid out in the Rule of Saint Benedict, the chanting of Biblical passages and other religious texts became central to medieval worship. Each daily Mass and office was filled with song. Chant was divided into two parts, the Ordinaryand the Proper. These words refer to the texts: texts for the Proper changed each day, while texts for the Ordinary remained the same.
Puer Natus est is the Introit for the third Mass of Christmas Day. In a medieval Mass the Introit was the first item and would be sung as the celebrants entered the sanctuary. Its text changed daily and featured a dialogue of sorts between the choir singing the Antiphon (in this case the repeated section beginning at Puer Natus est) and verses from the Psalms sung by the cantor. In the medieval church the cantor would also sing the first word of the chant to establish the pitch. Our recording, however, does not follow this tradition.
As one might expect for the Mass of Christmas Day, the spiritual import of the chant is one of overwhelming joy at the birth of the Christ child and the theological ramifications of this birth. Owing to the obvious importance of this day in the church calendar, the Proper texts were not used again until the following Christmas.
As tradition grew Introits began to be replaced by newly composed songs that were poetic reflections on doctrine known as Conductus. (e.g. Perotin's Beata Viscera) In other instances the Introit chant would be extended with newly composed music at its beginning or at points within the chant itself. These extensions became more elaborate over time and on particularly important feast days such as Christmas and Easter grew into small dramatic scenes. The version of the chant on the recording includes no such extensions.

Things to Note
Studying the actual melody of this chant its age becomes clear. The first line of the antiphon is very conversational and seems to focus around one note. The high pitch of the antiphon relates also to the state of great joy inherent in the theology.
The melody itself is not overly complex and unlike Kyrie IV, does not make use of multiple notes for a single syllable of text. This is particularly evident in the Psalm verse sung by the cantor. Chants that have relative correspondence between pitches and syllables are referred to as being syllabic. The texture of the chant is also quite simple: there is no accompaniment to the singing and all voices sing the same melodic line. This kind of texture is known as monophony.

To the right, you'll notice a copy of the score of this chant. The notation is similar to modern music notation, however, the staff or stave (the lines on which the notes are written) is comprised of four lines instead of five. Further the notes themselves are square shaped and grouped in odd ways. Below the staff are the words of the chant. Above the staff is a device for scholars. These squiggles (neumes) are duplicates of the squiggles that would have appeared in the earliest manuscripts of this chant. It is uncertain as to what benefit these squiggles had. Some argue that they served as a mnemotic device for early singers, while others suggest that it was a form of notation in itself and could be read from like an alphabet. The transcription from which the monks sing in the recording is based on an interpretation of these markings.
The small "c" at the left of each stave is known as a clef and provides a pitch reference for the singer.
The score should be read from left to right from top to bottom. Where there is a small indication "Ant." at the right of the fourth stave, the score returns to the beginning. After the second hearing of "angelus" the chant continues on the fifth stave where the small Roman numeral "VII" is, returning again tot he beginning at the indication "Ant." You should try at some listening to the chant to follow the score.

To see other examples of early chant notation, click here.

Translation

Puer natus est nobis, et filius datus est nobis: cuius imperium super humerum eius: et vocabitur nomen eius, magni consilii Angelus		A child is born to us, and a Son is given to us: Whose government is upon His shoulder: and His Name shall be called, the Angel of Great Counsel.
Cantate Domino canticum novum: quia mirabilia fecit.		Sing ye to the Lord a new canticle: because Hehath done wonderful things.
Puer natus est nobis, et filius datus est nobis: cuius imperium super humerum eius: et vocabitur nomen eius, magni consilii Angelus		A child is born to us, and a Son is given to us: Whose government is upon His shoulder: and His Name shall be called, the Angel of Great Counsel.
Notum fecit Dominus salutare suum: in conspectu gentium revelavit iustitiam suam.		The Lord has made known his salvation; to all nations he has revealed his justice.
Puer natus est nobis, et filius datus est nobis: cuius imperium super humerum eius: et vocabitur nomen eius, magni consilii Angelus		A child is born to us, and a Son is given to us: Whose government is upon His shoulder: and His Name shall be called, the Angel of Great Counsel.

Listening Chart

Anonymous: Puer Natus Est (before 1200)

Puer natus est...	0:00	Antiphon: (A)The beginning of the antiphon.
Cantate Domino canticum novum...	1:18	Psalm Verse: (B) A soloist sings a more syllabic line of music.
Puer natus est...	1:37	Antiphon: (A)The choir reenters with the Antiphon.
Notum fecit Dominus...	2:50	Psalm Verse: (B') The soloist returns with a slightly varied version of the melody of the previous psalm verse.
Puer natus est...	3:17	Antiphon: (A) The chorus reenters with a final version of the antiphon.