I'm doing a Haller 3-voice Mass for my EF Parish. The edition I have doesn't really have the tripling on the Kyrie, but it does on the Christe. I know it's kind of a grey area but I was wondering what everyone else does or if there are more EF-friendly editions out there. I could easily repeat the first Kyrie, but the last one seems like it would only work as the FINAL final Kyrie. In that case I'd repeat the first Kyrie twice again, but then the chord progressions are wonky between sections. Happy to take any input, including if your favorite trusted priest said if it's 3 voices it counts as 3 and not to worry about it.
I don't know the Haller Mass, but my choir recently learned Hassler's Missa Super Dixit Maria which has a similar "problem". I asked around, and discovered that one choir uses Mass IV to fill in the "gap", but that was with an Agnus Dei.
I wouldn't be surprised (but this may change if I look closely at the Haller Mass) if a similar patch would work.
The strict adherence to "triples" in the Kyrie in polyphonic settings isn't required, settings range from each text once (cf. Byrd a3) to many (cf. almost every polyphonic Mass from Ockeghem to Poulenc). Don't overthink it.
In general Salieri's point holds, though sometimes (e.g. Byrd's Mass for Three Voices) the Kyrie is so brief that some repetition with chant is called for. In the case of the Haller, it seems like a borderline case, though you may want to add chant if only to make it long enough to cover the action at the altar.
Salieri, Conceding the general point you're making, I think it's fair to take account of the fact that Byrd's a3 is conceived for a place and time when it is illegal to be Catholic.
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