If Mary resembles Billy Holiday then Zechariah is more like Nat King Cole. The Benedictus (Lk. 1.67-79) at it core is a love song in which old Z sings about how "Unforgettable" his God is. The first word says it all, "Praise." (i.e. to bless, to adore)
Zechariah shows us that jazz is not all improvisation but composition too…
Because he had been sentenced by the angel Gabriel to over nine months of silence he had plenty of time to work on his song of adoration. As you read it you will notice that it is a list of reasons why he loves God. You might also see a minimum of 16 references to the Old Testament. Finally, it is structured like a chiasmus (a form of poetry that makes use of inverted parallelism).
While Mary was improvising, Zechariah had the time to compose. Duke Ellington and Charles Mingus where great composers but no less magnificent jazz musicians.
A jazz-shaped faith has room for both. A jazz-shaped faith needs both.