I get plenty of criticism here for being attentive to intonation, so, discount my comment all you like. But are you sure you are being true to Josquin? This, again, does not seem right to me. The second measure already looks wrong, it would imo have to be a G# in the key you have chosen.
I have a special affection for Josquin, he is up there with Mozart, Bach, and Beethoven for me.
I presume you're talking about the AB version with 2 sharps . . . I'm not sure what the problem is with the G natural.
And I can assure you that I'm not taking liberties with the music. No, I don't have a scholarly edition in hand, but I'm trying to be careful to eliminate all typos before I post. If you're incredulous about some of these items, you'll need to take it up with Misters Soderlund and Scott (editors), or with blessed Josquin himself.
Yes, the AB version. The first bar, E is a perfect fifth above A. The second bar, in your version, the E would have to be a major sixth above the G, and then, either the G goes higher to make that interval pure, or the E goes lower. If the former, then the D in the higher voice is out of tune, a mis-tuned fifth. If the latter, then the higher voice is expected to change intonation on a repeated note. That might happen in Mozart, sometimes, but I don't think it would be Josquinic.
A very simple fix, for the second measure, is provided by 'musica ficta': the G is a sharp.
The piece in question is in the pure Dorian mode on E (transposed down a step with no accidentals, it would be D Dorian, the scale beginning on D and using just white keys) ... or think (plagal) Gregorian Mode II (same as Mode I except for range).
The tonic is E, the subdominant is A. The step up E to F# is 9/8 (wide), and the step up D to E is 10/9 (narrow). Similarly, the step up A to B is 9/8 (wide), and the step up G to A is 10/9 (narrow). Thus, at the beginning, both the Bass and Alto descend (from A and E, respectively) by a narrow whole step. Thus, the G in the Bass tunes to the E in the Alto with the (correct) ratio of 5/3. The Alto descends by a narrow whole step from E to D, which tunes with the previously sung G in the Bass as a pure fifth, while the Bass descends from G to F# by a 15/16 half-step, and the F# in the Bass tunes with the D in the Alto by the (correct) ratio of 8/5.
CHG, you are getting good! And even better, you are right. My apologies, Heath. Sorry to waste your time rechecking. I misled myself with the modern key signature. Had I seen it rightly as modern E minorish, one sharp, it would have fallen into place better, with the opening A and E as Chuck says, tuned low a small whole step above the respective G and D (or if you prefer the G&D high near the A&E).
Seems almost moot now, but I passed along the ficta issue to a mentor of mine, retired musicology professor and early music specialist:
"I looked at the Josquin and can find no plausible reason for applying ficta. The b-flat is signed, there is no tritone that needs fixing and no alteration required to make a cadence."
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