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What a fascinating thread!
I can understand why there is so much confusion.
According to pre-Vat.II rubrics, High Mass is always sung, and Low Mass is never sung. That's the SIMPLE story.
Since Vat.II, we've been in a war zone, and during war, some things get changed. That's because a lot of stuff is getting destroyed and a lot of people are doing WITHOUT.
What has developed in Canonized Traditional Latin Masses since the wreckovation of Vat.II, is that Low Mass (which is sometimes the only Mass a person ever gets to attend in a lifetime these days) might have a few hymns, that is, on Sunday and perhaps Holy Days (of obligation or not -- but in these days, a "Holy Day" might be a WEEKDAY that happens to be the only day during three months when you get to have ANY Mass!). Generally, there is a Recessional Hymn, which happens after Mass is over, and there might be some organ music during the Mass. The choir can consist of several voices, men and/or women, or it might consist of very few voices. It might consist of ONE voice. Allow me to explain!
Don't be shocked when I tell you that one experienced singer can provide the ambiance and texture that would seem to be only possible with several voices, and not unrelatedly, a very well-coordinated and artful small group of two or three men OR women can sound like one voice. In Latin the phrase is "una voce." That has nothing to do with the Indult organization by the same name!
In case you don't believe me, I'll say it again:
One experienced singer can provide the ambiance and texture that would seem to be only possible with several voices, and conversely, a very well-coordinated and artful small group of two or three men OR women can sound as if they must be truly one voice.
By extension, it is quite possible for a small group of two or three gentlemen and two or three ladies to sound as if they are one man and one woman.
I know this to be a fact, because I hear these comments at least a dozen times a year. So I'm not making it up.
When there is only one singer and his or her head is as big as a beach ball because he thinks his opera training makes him an expert, he should not be singing in Church at all, IMHO. He (or she) will never be able to render the holiness and devotion necessary and appropriate for Holy Mass. Operatic style is not conducive to prayer. If you cannot sing without a vibrato, you should not sing in the choir. Of course, if you're a priest you can do whatever you like or are capable of, and the choir provides the background.
During Low Mass, the Kyrie, Gloria, Credo, Sanctus, Benedictus and Agnus Dei are never sung. Nor is there any Vidi Aquam before Mass begins.
Also, in this chaos of post-Conciliar liturgical battle, there are now Low Mass venues for Sunday Mass (and perhaps Holy Days of Obligation) where an Entrance or "Processional" hymn is sung until the priest begins the prayers at the Foot of the Altar. Ideally, the singing should be over before he begins, and usually the priest will wait for the singing to stop before he says, "In nomine Patris et Filii et Spiritus sancti. Amen. Introibo ad altare Deo..."
Such Low Masses might have any combination of Entrance, Offertory, Communion and/or Recessional hymns, but generally if there is only one it will be the Recessional, and if there is only two, it will be the Processional and Recessional, and if there are only three, Communion hymn would be added, but other combinations are possible, as this is not a strictly rubrical question. If you were going to stick to the rubrics hard and fast, you would have no singing at Low Mass, except for perhaps a Recessional.
Then comes about 6 minutes of silence during the Offertory, during which a collection is taken up, which commences after the priest recites the Offertory antiphon proper to that Mass, and during which time a nice, short hymn can be sung, preferably one that lasts about 2 to 4 minutes long, but should never keep going until the priest says, "Orate fratres..." The congregation should have a minute or two of silence before hearing that said.
Then later, after the Minor Elevation and the second Confiteor, when there are communicants to receive, the priest turns to face the nave of the church and says, "Domine non sum dignus,..." three times, immediately following which a Communion Hymn may be sung. When there are 50 or more people receiving Holy Communion, there can be 7 or more minutes of silence before the priest reads the Communion Antiphon proper to that Mass. That's plenty of time for the choir to receive Communion and return to their place to sing for as many as 5 minutes. That's long enough for two short hymns, or one hymn with 3 or 4 verses.
Finally, there is the Recessional, which is a hymn that begins after the Leonine Prayers After Low Mass, and any additional ones such as the Angelus or Soul of My Savior or one of the many prayers to the saints, such as the patron saint of the venue where Mass is being said. During the Recessional it is improper for the congregation to make a B-line for the exit, although it's understandable if some particular people have to leave due to pressing concerns. Nor is it appropriate for anyone to CLAP after the choir sings. To do so, they would have to turn their backs on God and proceed to give praise to man, instead, which is a venial sin against the First Commandment, and perhaps a mortal sin, if done with malice, spite, or hatred of God.
When possible, Latin should be used during Mass, such as the Offertory Hymn and Communion, but it's not obligatory. Gregorian Chant is always preferred, but at the same time, polyphony most certainly has its place, especially when it is done well. Some two part works in English are most conducive to prayer and contemplation for everyone who hears them, when the singers are well-rehearsed and stay IN TUNE. It is absolutely UNNECESSARY to have an organ accompaniment to keep a good choir in tune. The problem of intonation is almost entirely based in the TONE QUALITY being less than beautiful, as well as technical deficiencies such as proper breathing, diaphragm support, soft palate, posture, projection and ATTENTION TO DETAIL.
At all times, the singing must render the ambiance of the Mass conducive to prayer. The singing should not demand attention. The singing is not entertainment. Everyone in the congregation should be able to ENTIRELY focus their attention ON THE MASS and their prayers, with the singing providing a backdrop, an atmosphere, a setting in which the Mass is the centerpiece. In this way, the choir is most analogous to Our Lady, as she is not the center of attention in the Mass, but she provides an essential framework for our human shortcomings to reference, such that our complete attention can be directed to Our Lord Crucified.
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