A solis ortus cardine, the hymn for Lauds in Christmastide

Here's a really lovely version of A solis ortus cardine, the Lauds hymn for Christmastide. The hymn has 7 verses, each beginning with a different letter of the alphabet (in sequence).

The text comes from a 23-verse alphabetic poem, Paean Alphabeticus de Christo, written by Caelius Sedulius (died c. 450); the poem is the story of Christ's life, birth to resurrection. The first seven verses - the ones in this video - make up the Christmastide Lauds hymn; verses 8, 9, 11 and 13 of the poem are used for Hostis Herodes impie, the Epiphany Vespers hymn.

Here's the Latin text of the entire poem.   Below is the section used for this hymn, with an English translation by John Ellerton below the Latin.

A solis ortus cardine
Adusque terre limitem
Christum canamus principem
Natum Maria virgine.

Beatus auctor seculi
Servile corpus induit,
Ut carne carnem liberans
Non perderet, quos condidit.

Caste parentis viscera
Celestis intrat gratia,
Venter puelle baiulat
Secreta, que non noverat.

Domus pudici pectoris
Templum repente fit Dei,
Intacta nesciens virum
Verbo creavit filium

Enixa est puerpera,
Quem Gabriel predixerat ,
Quem matris alvo gestiens
Clausus Johannes senserat.

Feno iacere pertulit,
Presepe non abhorruit
Parvoque lacte pastus est,
Per quem nec ales esurit.

Gaudet chorus celestium,
Et angeli canunt Deum,
Palamque fit pastoribus
Pastor creator omnium.

From east to west, from shore to shore,
let every heart awake and sing
the holy child whom Mary bore,
the Christ, the everlasting King.

Behold, the world's Creator wears
the form and fashion of a slave;
our very flesh our Maker shares,
his fallen creature, man, to save.

For this how wondrously he wrought!
A maiden, in her lowly place,
became, in ways beyond all thought,
the chosen vessel of his grace.

She bowed her to the angel's word
declaring what the Father willed,
and suddenly the promised Lord
that pure and hallowed temple filled.

He shrank not from the oxen's stall,
he lay within the manger-bed,
and he, whose bounty feedeth all,
at Mary's breast himself was fed.

And while the angels in the sky
sang praise above the silent field,
to shepherds poor the Lord Most High,
the one great Shepherd, was revealed.

All glory for this blessed morn
to God the Father ever be;
all praise to thee, O Virgin-born,
all praise, O Holy Ghost, to thee.

From the YouTube page, describing the video:

EN: Schola Gregoriana Monostorinensis performing in the Calvary Church from Cluj (RO) HU: a Schola Gregoriana Monostorinensis előadásában, a kolozsmonostori Nagyboldogasszony (Kálvária) templomban
www.hhrf.org/schola

Here's Guillaume Dufay's 15th-century version of the hymn; he uses chant and polyphony in an alternatim style.  [EDIT:   Raven notes in the comments that this may be a Binchois composition instead - which would mean the video is mislabeled.  I'll see what I can find out - but mainly I'm interested in showing off the chant as used in a polyphonic piece!]