I have a small schola that sings for a Tuesday evening Mass. We use plenty of chant, a bit of Renaissance polyphony, but I would love to work in some more medieval music (something more than just parallel organum).
Not quite medieval, but take a look at the music of Guillaume Dufay (if, indeed, you consider fauxbourdon more than "parallel organum") Much of it is in three or fewer parts.
Dufay, Binchois, Dunstable (or Dunstaple, take your pick) and there are others. I would call them 'late' mediaeval harbingers of the renaissance. Their music is much neglected and deserves more renown than it receives. It should be a staple in a group such as yours.
Stella Splendens! Nobilis Humilis! Alle psallite cum luya! Laudemus Virginum! Whatever the sacred version of Sumer is ycumen in is!
These can all be found at Nancho Alvarez's online shrine to Victoria, under the "Other" heading, at the very top of the page. Except maybe the last one.
I have those. Second is based on the works of Marcel Peres. Third is my own restitution with invocations adapted to my parish. Harmony is in the same trend as Peres work.
Thank you, Etienne. Please post more if you've got any... Things are getting a bit stale with my various Scholae. We've burned through so many "Mr. Motet-Head's" (my term for late Victorian "quick and dirty" compositions which, like the children's toy Mr. Potato Head, just seem to be constructed in 5 minutes or less from common, programmatic musical gestures, predictably rearranged.
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