The People's Parts
I believe I've lamented before that church musicians are often hired and expected to execute their function properly without qualifications or training, or even guidance. Well, the good news is that there is an actual instruction manual out there: the General Instructions of the Roman Missal (it's even online for free!) or GIRM. Here is laid out, in very clear terms, whose job is what, the order of the rites, the cues to begin and finish singing, and so much more. If you can afford your own copy of the whole missal, so much the better! Once you find your way around it, it is the single most useful and important book for a cantor or choir director to own. (I bought two copies - one for my use at home planning and practicing, and one to keep in the choir loft, because I am that disorganized and can never remember to tote a copy around with me from place to place.)
In the GIRM, there is a lot of language talking about "fostering participation" by the people. It emphasizes that the liturgy has a "communitarian character," which is emphasized by the people taking part especially in the acclamations and responses, and those parts of the Mass assigned to the whole gathering, especially the Penitential Rite, the Profession of Faith, the Prayer of the Faithful, and the Lord's Prayer.
Those parts of the Mass which we refer to as the "Ordinary," consisting of the Kyrie, Gloria, Sanctus and Agnus Dei (and sometimes also including a memorial acclamation or Anamnesis), the GIRM calls for to be "sung either by everyone together, or by the people alternately with the choir, or by the choir alone." I have always considered this phrasing to be indicative of the order of preference. Note also that although in other places, "sung by a cantor" is laid down as an option, it is not for these parts. These rites are not intended to be solos, they are the role of the congregation.
What helps encourage a congregation to fulfill their part in the liturgy? Simplicity, familiarity, and clarity. Anything that makes them confused or unsure will make them be silent. Therefore, the ideal Ordinary settings will be ordered to singing in unison, by people of average musical ability, without needing training in reading music. The settings will be familiar (by constant repetition), simple, and reverent. Chant being proper* to the liturgy (as once again emphasized by the GIRM), chant-based melodies are preferable to forced metrical settings. (Settings with words added or taken away are specifically ruled out.)
Why is this important?
After some remarks on the hierarchical nature of the liturgy and the nature of the "ministerial priesthood," the GIRM states in paragraph 5:
"Moreover, by this nature of the ministerial Priesthood, something else is put in its proper light, something certainly to be held in great esteem, namely, the royal Priesthood of the faithful, whose spiritual sacrifice is brought to completion through the ministry of the Bishop and the Priests, in union with the Sacrifice of Christ, the sole Mediator. For the celebration of the Eucharist is the action of the whole Church, and in it each one should carry out solely but totally that which pertains to him, in virtue of the place of each within the People of God. The result of this is that greater consideration is also given to some aspects of the celebration that have sometimes been accorded less attention in the course of the centuries. For this people is the People of God, purchased by Christ's Blood, gathered together by the Lord, nourished by his word, the people called to present to God the prayers of the entire human family, a people that gives thanks in Christ for the mystery of salvation by offering his Sacrifice, a people, finally, that is brought together in unity by Communion in the Body and Blood of Christ. This people, though holy in its origin, nevertheless grows constantly in holiness by conscious, active, and fruitful participation in the mystery of the Eucharist." [emphasis mine]
There are those who denigrate the emphasis on participation by the people as a callous disregard for the respect due to the priesthood. Indeed, the general lowering of the status of priests and over-familiarity with them to the point of dispensing with the title of "Father," is bad for the faithful and sad to see. However, this does not mean that clericalism isn't also a problem. Ordained priests are not the only ministers of the church. We all have a role in the salvation of the world; theirs may not be ours, but ours is still crucial! When it comes to the liturgy, the participation of the people encourages them to see it as their work, to hold a stake in it. When one Does the Work, one cares more about its execution and its outcome.
(If I might be permitted a personal story here, a few years ago I prepared the music for an ordination, a first for me. It was a Big Deal, as it was also the first ordination to the priesthood to take place in our parish. If you don't know, there are a lot of extra parts to be sung in an ordination Mass, and there were all kinds of dignitaries visiting, and everyone wanted everyone to be impressed, so I worked hard. And I did a great job. At the end of it, a dear friend said to me "I saw the priest in you today." It was the best compliment anyone has ever paid me, as I finally realized my childhood ambition, one I dreamed up before I was told that girls can't be priests.)
What about polyphonic or orchestral Mass settings?
Does this mean we can't sing beautiful polyphonic Masses? Well, I don't think so, but one must take the occasion and the needs and culture of the congregation into consideration. I work in a conservative, fairly well-educated parish in which many of the people are more than just passing familiar with Latin. We sing one of the Masses linked above at Midnight Mass and on Easter Vigil, and I am just beginning to feel ready to move forward with another on other high Holy Days (we would have done one for Epiphany this year if it had not fallen in the middle of cold-and-flu season and I was missing too many voices). These occasions seem suitable for raising the bar, in coordination with the celebrant's use of incense, longer prayers, fancier vestments, and so on. A visit by your bishop might be a good occasion as well, since the GIRM specifies in paragraph 22:
"For the Diocesan Bishop, the prime steward of the mysteries of God in the particular Church entrusted to his care, is the moderator, promoter, and guardian of the whole of liturgical life. In celebrations that take place with the Bishop presiding, and especially in the celebration of the Eucharist by the Bishop himself with the Presbyterate, the Deacons, and the people taking part, the mystery of the Church is manifest. Hence, solemn celebrations of Mass of this sort must be exemplary for the entire diocese."
Orchestral Mass settings, though, are better left for the concert hall.
* By "proper," I mean that it is designed for the Liturgy - not only is it suitably solemn and beautiful, but it is not used for other purposes, like the vestments and linens set aside for use at Mass. Indeed, the first ever papal decree regarding Sacred Music was to stop singing liturgical songs at parties. Ever since then, they have been pleas to stop singing party songs at Mass.