Thorny question and again we struggle with the GIRM.
In a nutshell, a polyphonic Mass setting is appropriate at anytime for the greater glory of God. This is famously stated in Sacrosanctum Concilium as well as the GIRM itself. It is also restated by Bl. John Paul II in 2003.
Whether or not it is the best idea with your Parish is another question. Further to that, when to use one must certainly be a matter of prudence.
The problem (manufactured problem in my mind) is that we have confused the term participation. Actual vs Active. Whether I am right or wrong on the issue. We are very far from convincing people not to be upset if they can't do stuff at Mass.
So when you pick a Feast or Sunday to do a polyphonic setting of the Mass. Do so with care and preparation not just of the choir, but the people as well.

I would add too, and say that chant ordinaries (in Latin) ought not to sit on the pine for too long.
If we are always polyphonic, or vernacular for that matter, we are still making some of the mistakes we made pre-council and post council GIRM warfare.

Peter

M. Jackson and Liam,
I heartily agree.

CGM et al
It seems we are more legalistic now than ever. Instead of a real immersion in the Roman Rite and true study and understanding of it, spiritually, historically and so on, we end up treating it like an operation with an operations manual (the GIRM). I'm all for rubrics, but I think we can see that it is not so easy to take up the manual without first understanding the language it is written in. (I mean to be metaphorical, not literal about the language)
Be assured CGM, that doing a polyphonic setting is always in continuity with the Church. That she has loved and treasured polyphony and that if we could start to think of the immensity of God, what heights some polyphony could help us get to.


Peter

As a further reinforcement here, considering that the documents praise polyphony almost on the level of gregorian chant (GIRM no. 41, SC no. 116, etc...), it would be odd to argue that the ordinary could not be sung in polyphony, even if it appears that's what the GIRM wants.

Thanks to all who have replied thus far, and thanks, Mark, for your note referring to your earlier post. There is no question about the beauty, or the liturgical origins, of polyphonic settings of the Ordinary. However, Jeffrey Tucker raises good points about the structure of the Ordinary Form and the challenges that arise from that in respect to polyphonic Mass settings, which were, after all, written for an earlier and different form of the rite. This echoes your original quote from Dr. Mahrt, that "these problems will be addressed in a later article." (Did he ever write that article?) The thing that I began this thread with was a quote of his from the mid-1970's; the quote you mention is from just a year ago and is probably a better representation of what he thinks now.

It seems incredible that there should not be a definitive answer to this - after all, the "new" liturgy has been around for 40 years now. But maybe there isn't! I refer to the GIRM because it seems that the official "book of instruction" on how to celebrate the rite ought to be the most binding word on, well, how to celebrate the rite.

But I'm open to being schooled more...

I can assure you... they sing polyphony in heaven's liturgies...

And PMulholand is spot on with this one:

"The problem (manufactured problem in my mind) is that we have confused the term participation. Actual vs Active."

The Latin phrase is Actuoso Participatio. Do a google on that one and you will find some very interesting discussion.

I have the extreme good fortune of heading a music program where the professional choir is capable of singing different polyphonic ordinaries each week, and the pastor would support their use. So my question is really, what does the liturgy require?

I know the whole actuoso participatio thing - I've brought it up with my pastor in relation to the non-big-choir Masses, where I've been introducing the SEP (with a wee choir of me, my wife, and two of my kids) and he wants me to go back to hymns. As Jeffrey Tucker, Adam Wood, and others have said, the template seems to be that the Ordinary is for the people, and the Propers are for the choir. If this is normative for the Ordinary Form, then just using polyphonic settings of the Ordinary for special feasts seems appropriate, since the rest of the time the congregation will have congregational ordinaries. On the other hand, this seems to contradict what Dr. Mahrt says in his book: "One performance a year of a polyphonic Mass, while a laudable endeavor and an enrichment of the liturgy, risks being removed from the context of a familiar practice, and being seen as an exceptional or even esoteric happening." (p. 33, emphasis added)

Contrarily, the use of the SEP means that the congregation can actually observe the liturgy unfolding around them, instead of ignoring what the priest is doing whilst singing a hymn - or ignoring the hymn and trying not to feel guilty about it!

We currently use the stuffed Mass that PMulholland suggested. I also agree that it's not ideal, but so far there are much fewer complaints.

We only use polyphonic ordinaries for greater solemnities.

Last year I had the good fortune of talking over this issue with another musician who runs an exceptional music program in a large church. He has a professional ensemble who does complete polyphonic ordinaries every week, and I said to him, "If the Ordinary is supposed to be 'for the people,' how do you justify this decision?"

His answer: "We are fortunate to have the musical forces (and the clerical support) to be able to do this, and we are the only church in the state so endowed. So we offer it, to give people another option as to what liturgy can be like. We aren't necessarily prescribing it as normative, just as normative for us here, and as an example of liturgical diversity and tradition at the same time."

What a wise and comforting answer, I thought.

My practice presently is that we sing a complete polyphonic ordinary on about twelve major feasts in the year; the congregation sings a complete Gregorian ordinary the other Sundays, using some six different settings through the year. This means that the congregation has ample opportunity to sing the ordinary, but also enough opportunity to hear a polyphonic ordinary that its conventions are understood and well-received. Moreover, that fact that they sing a Latin ordinary regularly means that they know those texts well and are ready to hear and appreciate them sung by a choir.

There was a time when I had the singers who could manage a polyphonic ordinary every Sunday, and I considered doing this; it is something that some exemplary choirs in large cities do. But then I considered our congregational singing of the Gregorian ordinary that was well established and had years of tradition, and decided that I could not take that away from the congregation, so I kept the practice we have today.