Today is the feast of St. Sylvester I Pope & Confessor, it is of double rite.
Mattins has three nocturns and the usual nine lessons. The antiphons and psalms being taken from the Psalter for Wednesday. At Lauds a commemoration of the Octave of the Nativity is made.
At Mass the Gloria is sung, a commemoration of the Octave of the Nativity made, the Credo is sung and the preface and communicantes in the Canon are of the Nativity.
Vespers are first Vespers of the Circumcision without any commemorations.
In the 'liturgical books of 1962' today is a day within the Octave of the Nativity. At Mattins the antiphons and psalmody are festal but there is only one nocturn of three lessons. At the Little Hours ferial antiphons and psalms are used(and as noted below the hymns do not have the tone or Doxology in honour of the Incarnation). The Mass is Puer natus with a commemoration of St. Sylvester. Vespers are the same as the Old Rite.
In pre-1911 practice in addition to the Octave of the Nativity the Octaves of St. Thomas (in England), St. Stephen, St. John the Evangelist and the Holy Innocents would have beem commemorated at Lauds and Mass.