That's an interesting question. First, it certainly seems like the Sunday obligation would be satisfied by attending Mass on Saturday evening, regardless of which liturgy is celebrated, since Canon 1248 §1 merely requires attending Mass "anywhere in a Catholic rite either on the feast day itself or in the evening of the preceding day." Now, under the General Norms for the Liturgical Year and Calendar, "the observance of Sunday and solemnities begins with the evening of the preceding day." And Sunday, January 2 is both a Sunday and a solemnity (in the U.S., at least), since the Epiphany is transferred to it. So unless I'm missing something (which is a big if), I would certainly think that the evening Mass on the 1st ought to be the anticipated Mass of the Epiphany.

Wouldn't it all be simpler if Epiphany were celebrated on January 6?

SkirpR is correct. We already received notice from our diocesan Office of Worship. Mass in the evening of January 1 this year (in the USA) is to be the Vigil Mass of the Epiphany.

I'm not old enough to have experienced this as a music director, so maybe somebody can answer another one for me. If the 2nd Sunday of Advent is December 8 (which it will be in 2013, but hasn't been for a while), do you celebrate the Second Sunday of Advent or the Immaculate Conception?

One would assume that Masses for the Solemnity are during the day. Isn't the anticipated Mass considered the beginning of the next liturgical day? I remember when they started, they were usually done later in the evening, but now they start as early as 4:00pm. How can one do 1st Vespers at the right time with the next day's Mass already done?

In case anyone else dreams up any interesting calendar conundrums, here:

Table of Liturgical Days
from the General Norms for the Liturgical Year and the New General Roman Calendar, nos. 59-61

The order of precedence for liturgical days is governed solely by the following table.

- I -
1. Easter triduum of the Lord's passion and resurrection
2. Christmas, Epiphany, Ascension, and Pentecost, Sundays of Advent, Lent, and the season of Easter
Ash Wednesday
Weekdays of Holy Week, Monday to Thursday inclusive
Days within the octave of Easter
3. Solemnities of the Lord, the Blessed Virgin Mary, and saints listed in the general calendar, All Souls' Day
4. Proper solemnities, namely:
a) Solemnity of the principal patron of the place, city, or state
b) Solemnity of the dedication and anniversary of the dedication of a particular church
c) Solemnity of the titular saint of a particular church
d) Solemnity of the titular saint, founder, or principal patron of an order or congregation

- II -
5. Feasts of the Lord in the general calendar
6. Sundays of the Christmas season and Sundays in ordinary time
7. Feasts of the Blessed Virgin Mary and of the saints in the general calendar
8. Proper feasts, namely:
a) Feast of the principal patron of the diocese
b) Feast of the anniversary of the dedication of the cathedral
c) Feast of the principal patron of the territory, province, country, or more extensive territory
d) Feast of the titular saint, founder, or principal patron of an order, congregation, or religious province, observing the directives in no. 4
e) Other feasts proper to an individual church
f) Other feasts listed in the calendar of the diocese, order, or congregation
9. Weekdays of Advent from December 17 to December 24 inclusive
Days within the octave of Christmas
Weekdays of Lent

- III -
10. Obligatory memorials in the general calendar
11. Proper obligatory memorials, namely:
a) Memorial of a secondary patron of the place, diocese, region or province, country, or more extensive territory; or of an order, congregation, or religious province
b) Obligatory memorials proper to an individual church
c) Obligatory memorials listed in the calendar of a diocese, order, or congregation
12. Optional memorials, as described in the instructions indicated for the Mass and office, may be observed even on the days in no. 9
In the same manner obligatory memorials may be celebrated as optional memorials if they happen to fall on the Lenten weekdays
13. Weekdays of Advent up to December 16 inclusive
Weekdays of the Christmas season from January 2 until the Saturday after Epiphany
Weekdays of the Easter season from Monday after the octave of Easter until the Saturday before Pentecost inclusive
Weekdays in ordinary time

Celebrations on the Same Day
If several celebrations fall on the same day, the one that holds the higher rank according to the above table is observed. A solemnity, however, which is impeded by a liturgical day that takes precedence over it should be transferred to the closest day which is not a day listed in nos. 1-8 in the table of precedence, the rule of no. 5 remaining in effect. Other celebrations are omitted that year.
If on the same day vespers of the current office and first vespers of the following day are to be celebrated, the vespers of the day holding the higher rank in the table of liturgical days takes precedence; if both days are of the same rank, vespers of the current day takes precedence.