Sorry for the levity.
This from Claud Simpson's The British Broadside Ballad and its Music not an easy book to scan – (excuse the errors) Not particularly helpful to the questioner but it provides some background
Jim Carroll

THE SHEPHERD'S DAUGHTER
This tune appears in all save the first edition of The Dancing Master (1652, p. 83 = Fig. 426), usually called "Parson upon Dorothy" or "Parson[s] and Dorothy," but in the 1670-1690 editions called "The Shepherd's Daughter." Under the former name the tune is also found in three ballad operas: Momus turn'd Fabulist and Gay's Polly, 1729, and Lillo's Silvia, 1731.
The traditional ballad known as "The Knight and Shepherd's Daughter" (Child No. 110), licensed as a broadside in 1624 and again in 1656, is preserved in an edition representing the second of these entries and published by Gilbertson: "The beautifull Shepherdesse of Arcadia," beginning "There was a Shepherd's Daughter/came triping on the way" Roxburghe III, 160).1 This issue and another of not much later date (Douce I, nT, 14) bear the tune title "The Shepheards Delight"; in issues of c. 1700 the tune is called "The Shepherd's Daughter" (Lord Crawford, Douce, Chetham, Roxburghe; reprinted in RB III, 451). The stanza is a ballad-meter quatrain with a burden "Sing trang dil do lee"; music in The Dancing Master and the ballad operas, however, is designed for a six-line or (with each strain repeated) a twelve-line stanza in this meter, and there is no provision for a refrain. It may be doubted, then, that the tune as we have it was used for singing the ballad. Chappell "adapted" the tune by eliminating the second strain which nearly or completely repeats the first, and adding a two-bar coda for the refrain (PMOT 1, 1927). This reconstruction, while it has no textual validity, is probably sound: as the tune passed from ballads to country-dance sets, a two-bar refrain would almost certainly have been discarded, in order to allow the conventional four-bar phrases to flow unimpeded.
"The forsaken Damosel: Or, The Deluded Maid," beginning "Abroad .is I of late did walk," is to the tune "A Shepherds daughter once there was" (Rawlinson 24). The tune name may be a paraphrase of the opening line of "The Beautiful Shepherdess"; except for the absence of a refrain line here, the stanza, patterns are identical.
The earlier tune name, "The Shepherd's Delight," is found as the title two ballads whose metrical patterns are so widely at variance with the leasure of "The Beautiful Shepherdess of Arcadia" that neither can be seriously considered as a source of the tune title.
Most of Child's traditional texts of "The Knight and Shepherd's Daughter" lack a refrain, but as B. H. Bronson shows (The Traditional Tunes of the Child Ballads, 1959-…, II, 535), "every copy collected with its tune has strong elements of refrain." A Somerset version which Cecil Sharp included in his One Hundred English Folksongs, 1916, p. 6, supplements the ballad quatrains with a burden "Line twine the willow dee, phonetically reminiscent of the "Sing trang dil do lee" of the seventh-century broadside; the two-bar tag at the end of the tune is characteristic of several Sharp recoveries in which the last line of each stanza is repeated or a single-line burden appended.