(This is my handout mentioned above, except I added a couple of notes I'll include the next time I use this. I might have also cited Pope John Paul from Redemptionis Sacramentum, but I wanted this to be on a single sheet of paper...)
Latin and Chant at Mass: What Vatican II said:
From the Constitution on the Sacred Liturgy, Sacrosanctum Concilium, promulgated by Pope Paul VI, December 4, 1963:
36. 1. Particular law remaining in force, the use of the Latin language is to be preserved in the Latin rites.(1)
2. But since the use of the mother tongue, whether in the Mass, the administration of the sacraments, or other parts of the liturgy, frequently may(2) be of great advantage to the people, the limits of its employment may be extended. This will apply in the first place to the readings and directives, and to some of the prayers and chants, according to the regulations on this matter to be laid down separately in subsequent chapters. (3)
3. These norms being observed, it is for the competent territorial ecclesiastical authority mentioned in Art. 22, 2, to decide whether, and to what extent, the vernacular language is to be used; their decrees are to be approved, that is, confirmed, by the Apostolic See. And, whenever it seems to be called for, this authority is to consult with bishops of neighboring regions which have the same language. (4)
54. In Masses which are celebrated with the people, a suitable place may be allotted to their mother tongue. This is to apply in the first place to the readings and "the common prayer," but also, as local conditions may warrant, to those parts which pertain to the people, according to the norm laid down in Art. 36 of this Constitution.
Nevertheless steps should be taken (5) so that the faithful may also (6) be able to say or to sing together in Latin those parts of the Ordinary of the Mass which pertain to them. (7)
116. The Church acknowledges Gregorian chant (8) as specially suited to the Roman liturgy: therefore, other things being equal, it should be given pride of place in liturgical services.
But other kinds of sacred music, especially polyphony, are by no means excluded from liturgical celebrations, so long as they accord with the spirit of the liturgical action, as laid down in Art. 30. (9)
What Pope Paul VI said in Jubilate Deo, a booklet of chant issued by the Sacred Congregation for Divine Worship, April 14, 1974: (10)
This minimum repertoire (11) of Gregorian chant has been prepared with that purpose in mind: to make it easier for Christians to achieve unity and spiritual harmony with their brothers and with the living traditions of the past.
Hence it is that those who are trying to improve the quality of congregational singing (12) cannot refuse to Gregorian chant the place which is due to it….
In presenting the Holy Father's gift to you, may I at the same time remind you of the desire which he has often expressed that the Conciliar constitution on the liturgy (13) be increasingly better implemented. Would you therefore…decide on the best ways of teaching the faithful the Latin chants of "Jubilate Deo" and of having them sing them…
What Pope Benedict said, in Sacramentum Caritatis, March 13, 2007:
42. In the ars celebrandi, (14) liturgical song has a pre-eminent place. Saint Augustine rightly says in a famous sermon that "the new man sings a new song. Singing is an expression of joy and, if we consider the matter, an expression of love." The People of God assembled for the liturgy sings the praises of God. In the course of her two-thousand-year history, the Church has created, and still creates, music and songs which represent a rich patrimony of faith and love. This heritage must not be lost. (15) Certainly as far as the liturgy is concerned, we cannot say that one song is as good as another. Generic improvisation or the introduction of musical genres which fail to respect the meaning of the liturgy should be avoided. As an element of the liturgy, song should be well integrated into the overall celebration. Consequently everything – texts, music, execution – ought to correspond to the meaning of the mystery being celebrated, the structure of the rite and the liturgical seasons. Finally, while respecting various styles and different and highly praiseworthy traditions, I desire, in accordance with the request advanced by the Synod Fathers, that Gregorian chant be suitably esteemed and employed as the chant proper to the Roman liturgy. (16)
62. ….Speaking more generally, I ask that future priests, from their time in the seminary, receive the preparation needed to understand and to celebrate Mass in Latin, and also to use Latin texts and execute Gregorian chant; nor should we forget that the faithful can be taught to recite the more common prayers in Latin, and also to sing parts of the liturgy to Gregorian chant. (17)
1 "The Latin Rite" means the Roman Catholic Church, i.e., not the Greek, Lebanese, or other branches.
2 Emphasis added, and so throughout.
3 Note it never mandates that the vernacular must be used, but rather that it may be used.
4 This language does not envision a complete elimination of Latin usage at Mass.
5 Who should take these steps? Clearly bishops, and those who act for them, pastors. What steps? Not specified, but some steps are envisioned.
6 The faithful also—i.e., not just priests, not just choirs.
7 "Parts of the Ordinary" refers to prayers said every week.
8 Gregorian chant, by definition, is in Latin.
9 This makes clear the music needn’t be all Gregorian chant, only that it have "pride of place."
10 Although what follows was issued by the Congregation, it clearly represents the pope’s own desires.
11 Note the wording: the pope intends a "minimum" understanding and usage of Latin, Gregorian chant.
12 Note: this is for congregations, not just the priest, or for choirs.
13 I.e., this is linked to what Vatican II said about Gregorian chant, and tells us the pope’s understanding of its meaning.
14 I.e., the art of celebrating the liturgy.
15 Note how this echoes what Pope Paul VI said in Jubilate Deo, quoted above.
16 The pope is referring to the Synod of bishops, held October, 2005; his request to use Gregorian chant reflects their recommendation as well.
17 The first part of this paragraph (not quoted) refers primarily to international celebrations of the Mass, at which the pope requests and encourages the use of Latin; this part goes further, and speaks to more ordinary settings. I.e., the use of Latin and chant are not only for international gatherings, but as Paul VI made clear, parish settings.