It is probably unfair to characterize a religious vocal composition as an oddity. I include Cecile Chaminade's "Angelus" in this series because of its surprisingly early use of neo-modal harmony.
The duet is in two verses, musically identical; all of the first verse is shown here. At (a) the ^1-^5 frame is established; at (b) it is inverted and ^2 replaces ^1; at (c) the change is repeated, but as an echo in the same register: ^1-^5 -> ^2-^5; at (d) a play between ^2 and ^1, where the second vocal part goes down by step (circled notes) and the first part returns to ^5 to end the phrase. After this the Angelus bell rings the same ^2-^5, but an octave higher [at least, I assume that's correct; this is the only edition I have access to at present; registers may well be more complicated if there is a prior edition in a different instrumentation].
The ringing of the bell prompts a brief Angelus prayer. At (f), the oscillation between notes shifts to A4 and G4 (circled) with F major 5/3 and G minor 6 harmonies. A steady movement upward first reaches Bb4, then -- at (g) -- continues upward to close on F5. Note, however, that the leading tone is missing and the cadential progression is plagal: IV-ii7-I. At (h) a quiet "echoing" coda.
The "oddity" then is the "incomplete" rising line; whether it starts on A4 or its companion at (f), G4, is unclear, but I'll assume A4, and so the line is ^3-^4-^5-^6-^8.