A funny thing happened the other day. I chose Gustate et Videteby Asola (1588) to teach to my family/choir. It's scored in 3 flats, which to the semi-modern theoretician should mean that the piece is in E-flat major or C minor. The last two "chords" are, in that reckoning, a tonic followed by a dominant -- which is to say that the piece ends on a b-flat major chord.
I had some music theory back in the day, but it's been a while. Can anyone help me answer the question "What key is this piece in?", with enough thoughtful background so that my non-specialists can understand why the piece doesn't end on the tonic?
If you consult the CPDL page for Asola's Gustate et videte, you'll see that the piece (with three flats in the key signature and presumably edited by Christoph Dalitz) is in B-flat Mixolydian mode. It is transposed up a minor third from the original (which is in G Mixolydian mode). The Anthony Cekada edition at CPDL has one flat in the key signature and is in C Mixolydian mode (transposed down a perfect fifth from the original work).
In terms of chant modes, think Mode VII (or VIII).
Also, in terms of cadences in renaissance polyphony, the real cadence happens in mm. 38-39, where the soprano has the 'cantizans' role (ascending to the tonic from the semi tone below), and the bass the 'tenorizans' role (descending to the tonic from the step above), an authentic cadence, fulfilling what we think of as the V-I function---in renaissance theory, the so-called 'plagal' cadence (IV-I) is not a true cadence. (The alto has the 'altizans' role, scale degrees 5-4-3, with a 4-3 suspension.) Everything after this point is merely an ornamentation of the tonic triad: for all intents and purposes, the piece ends on the second beat of bar 39.
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