We use it as the third repetition with Mass VIII. So it's 1st time cantor, 2nd time choir/congregation, 3rd time choir singing the Byrd. Then we repeat the process with the Christe's and Kyrie's.
Sort of a germane footnote to the question - Many (most) English polyphonic masses do not include kyries at all, for reason: in the Sarum custom kyrie was always sung as plainchant. The glory began with a glorious gloria.
Which raises an interesting question - has anyone ever encountered a polyphonic trope? Such would, I think, be rather surprising.
It is worth noting that our late mediaeval ancestors likely knew what they were doing, drama-wise, with the juxtaposition of plainchant and polyphony throughout the mass; that and the calibrated addition of boys' treble voices at dramatic moments both in chant and polyphony.
This is all very well implied and represented in Paul McCreesh's wonderful CD of a Sarum Easter Day mass, which also illustrates the sound of English-pronounced Latin in the late XVth century, before the great vowel shift. I recommend this to anyone who can find a copy - it is likely 'out of print'.
Cleobrury and King's did a recording, for EMI, of Sarum Plainchant Mass for the Nativity of Our Lady, and Vespers for the Octave (or was it the other way round?). It's Choral Scholars only - no boys. It's good and very interesting from a historical perspective--uses a reconstruction of 15th century Anglo Latin--but the chant is a little stilted for my taste; it's too equalist, you can almost hear them counting Mocquereau : 1-2, 1-2, 1-2-3, 1-2-3, 1-2, 1-2-3, ... . Also, I found the pause at the half-verse (which seems to be "Ave Maria, gratia plena, Dominus tecum") to be absurdly long for the acoustic of the chapel ("Ave Maria, gratia plena" would have been long enough).
I don't have the CD you mention, Salieri. Do you think it would still be in print? What is the title and number of the album?
Your critique of the chant performance is valid, though such performance, being dreadfully slow and sounding even worse than poorly done (so-called-but-not-really) 'Solesme method' chant, is probably closer to chant performance of that time than scholarly interpretations of our time, influenced as they are by a greater understanding of Carolingian notation. Chant of the XVth century was performed quite slowly and almost definitely rather equalistically. The McCreesh disc also presents chant in this style. I'd really like to get the CD you mention.
I find it odd that the disc is called "Gregorian Chant" since what it actually presents is Sarum Chant - though I suppose most people know what "Gregorian" means but not "Sarum".
It might well be an 'historically accurate' performance tempo-wise since Dr. Berry was involved in it (I believe she created the performance editions, I'd have to check the liner notes), but there is something about ensembles, no matter how good generally, that sometimes just don't seem to "get chant" - their performance is cold. It's as if you can't just read it off the page and give it a reasonable performance like you can with say Palestrina or Mozart (BTW, I'm talking about trained/professional musicians here, like The Tallis Scholars). You have to live and breathe and pray the chant in order to really "get it". Incidentally, I've found that The Sixteen seem to really "get chant".
There's also a recording of the Salisbury Cathedral choir singing the Mass of Christmas Day according to the Sarum use. Though it did have a prophecy reading in addition to the Epistle, which was strange at first sight, and I can't comment on the quality of the chant, sadly.
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