The original version of is for voices, with a text to be sung, but the common medieval practice of performing music involves using whatever instruments were at hand.
a. "behold, spring"
b. "eagle dance"
c. "he who gladly serves"
d. "i can all too well compare my lady"

i'm not sure i completely understand your question, but i will do my best.

i think the answer you are looking for is sequence. (see below)

a repeated melodic fragment would be best defined as repetition, while repeated chords (different or the same) could be a chord progression. however, you then mentioned the chord and melodic fragment beginning on higher or lower pitches, in that case, the answer could be best defined as a sequence. the definition of a sequence is as follows: "the restatement of a motif or longer melodic (or harmonic) passage at a higher or lower pitch in the same voice."

let me know if this !