Christie commented, "The Editor arranged this air from the way it was sung in Buchan". I don't have the relevant volume of Bronson, so can't quote him just now; as a general rule, though, he was suspicious of Christie's second strains, considering them to be mainly editorial. However that may be, here is the tune from Christie in abc format:
X:1
T:The Earl of Mar's Daughter
S:Traditional (Buchan); perhaps modified by Christie.
B:Christie's Traditional Ballad Airs, vol.II, 1881.
L:1/8
Q:100
M:2/4
K:F
F3/4G/4|Ac (d3/4c/4)(f3/4d/4)|(d/c/)(B/A/) {A}G(F3/4G/4)|Ac ~d(f3/4d/4)|{d}c2 z (c3/4B/4)|
w:It_ was in-till_ a_ plea_sant_ time, Up_on a sim-mer's_ day, The_
{B}A(G3/4A/4) c(G3/4A/4)|{G}FD C(F3/4G/4)|{B}A(G3/4A/4) c{A}(G3/4F/4)|F2 z (F3/4G/4)|
w:no-ble_ Earl of_ Mar's daugh-ter Went_ forth to_ sport and_ play. As_
{B}A(G/A/) c(G3/4A/4)|FD C(F3/4G/4)|A(G/A/) {A}c(B3/4A/4)|{A}G2 z (c3/4B/4)|
w:thus she did a-muse her-sell Be-low a green aik tree, There
{B}A(G3/4A/4) (c3/4A/4)(G3/4A/4)|(F/4A3/4)(D3/4C/4) C(F3/4G/4)|A(G3/4A/4) (c3/4B/4)(G3/4F/4)|F2 z|]
w:she did see a spright-ly doo Set on a tow'er sae hie.
The tempo setting is a guess; Christie specified Briskly. I've also made a midi, with the graces omitted for clarity. Until it gets to Mudcat Midis, it can be heard via the South Riding Folk Network site: