So I know that typically if an HDO is on a Saturday or Monday, it’s abrogated. But what about Vigil Masses?
Say the Assumption’s on a Saturday. If you went to Mass that evening, would it be those readings or the Sunday’s? Or what if it was on a Monday? Would evening Masses the day before use those readings or the Sunday’s? Does this change if it’s during Lent or Advent and ranks change?
First it’s important to note that your obligation to attend Mass is fulfilled regardless of the readings used. If you attend any valid Catholic rite the day of the feast or the evening before, you have fulfilled your obligation. Hence, if it were a feast in the Latin Church but not in one of the Eastern Catholic Churches, for example, your obligation is still fulfilled even though you didn’t hear the same readings or celebrate the same feast.
That said, if the Assumption were to fall on a Saturday or Monday, the obligation to attend Mass is no longer present, but the feast is still in the calendar. Were it to fall on the Saturday, you could expect that there might be a vigil Mass for it on Friday evening (I don’t remember right off if it was one of the major feasts which had a proper Mass for the evening before or not) and then another Mass would be possible during the day on Saturday. If you went to Saturday evening Mass, however, it would be the anticipated Mass for Sunday. Were the Assumption to fall on Monday, there would be no Vigil, as that would be overtaken by the rank of the Sunday, but then the feast itself would still be celebrated on Monday.
It depends upon the particular Sunday and the particular Solemnity.
Whichever day ranks higher in the table of feasts in the calendar is that one which begins on the evening before.
So if the Solemnity is a Monday and the Solemnity ranks higher than the Sunday, then the Solemnity begins in the evening.
I won’t go through all the possibilities, but the point is to look at both days, and see where each day falls in the ranking. Then compare the two. The evening in-between goes to whatever is the higher rank.
Note that the Sundays of Lent and Advent are #2
Solemnities of the Blessed Virgin Mary are #3
Sundays of Ordinary Time are #6
It also depends on particular law for that country (as determined by the conference of bishops) because sometimes, a solemnity is moved—for example, the Annunciation on March 25 is usually moved to outside of Lent (at least in the US).
To your example, the Assumption (#3) outranks a Sunday (#6) in Ordinary Time (since it’s in August, it must be Ordinary Time) Therefore if August 15 is a Saturday, the Assumption takes precedence and Saturday evening is still Assumption.
If the Assumption falls on a Monday, then Assumption begins on the evening before (ie, Sunday the 14th).
Easter triduum of the Lord’s passion and resurrection.
Christmas, Epiphany, Ascension, and Pentecost. Sundays of Advent, Lent, and the Easter season. Ash Wednesday. Weekdays of Holy Week from Monday to Thursday inclusive. Days within the octave of Easter.
Solemnities of the Lord, the Blessed Virgin Mary, and saints listed in the General Calendar. All Souls.
Proper Solemnities, namely:
a. Solemnity of the principal patron of the place, that is, the city or state.
b. Solemnity of the dedication of a particular church and the anniversary.
c. Solemnity of the title, or of the founder, or of the principal patron of a religious order or congregation.
Feasts of the Lord in the General Calendar.
Sundays of the Christmas season and Sundays in Ordinary Time.
Feasts of the Blessed Virgin Mary and of the saints in the General Calendar.
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 a region or province, or a country, or of a wider territory.
d. Feast of the title, founder, or principle patron of an order or congregation and of a religious province, without prejudice to the directives in no. 4.
e. Other feasts proper to an individual church.
f. Other feasts listed in the calendar of a diocese or of a religious order or congregation.
Weekdays of Advent from 17 December to 24 December inclusive. Days within the octave of Christmas. Weekdays of Lent.
Obligatory memorials in the General Calendar.
Proper obligatory memorials, namely:
a. Memorial of a secondary patron of the place, diocese, region, or province, country or wider territory, or of an order or congregation and of a religious province.
b. Obligatory memorials listed in the calendar of a diocese, or of an order or congregation.
Optional memorials; but these may be celebrated even on the days listed in no. 9, in the special manner described by the General Instruction of the Roman Missal and of the Liturgy of the Hours. In the same manner obligatory memorials may be celebrated as optional memorials if they happen to fall on the Lenten weekdays.
Weekdays of Advent up to 16 December inclusive. Weekdays of the Christmas season from 2 January 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.
That’s not how it works. The Assumption is always during Ordinary Time (since it’s in August). The Sundays of Ordinary Time give way to the Solemnity of the Assumption, since the Assumption has the higher rank in the table of feasts.
So if the Assumption is on a Saturday the feast continues through all of Saturday (including the evening). If it falls on a Monday, the Sunday of Ordinary Time gives way to the Assumption and the Assumption begins on Sunday evening.
Now, if it’s a feast that happens during Lent or Advent it’s reversed. The Sundays of Advent take precedence over Solemnities. That’s why the Immaculate Conception always yields to the Sunday of Advent.
Whatever applies to “the whole” applies to “every part of the whole.”
Since the liturgical day itself begins in the evening (whatever day that might be, so long as it’s a solemnity) everything about what happens on that day pertains to that day. Therefore, every part of the Church’s liturgy is that day: every part of every Hour, and every part of the Mass (readings, collect, post-Communion, etc. etc.).