Back to Nonesuch (3)
NONESUCH . English, Jig (6/4 time). F Major. Standard tuning (fiddle). AABB. The melody first appears in print in Henry Playford's Second Part of the Dancing Master (London, 1698), and was subsequently printed in the 12th edition (1706), 15th edition  (1713), and finally in the 16th edition (1716) of the Dancing Master. London publisher John Walsh published the melody in his Compleat Country Dancing Master (London, 1718), and in his 1735 and 1754 editions of the same work.
Graham Christian (2015) suggests the piece was possibly named not for Nonesuch the palace (for which see "Nonesuch (1)") but Nonesuch the flower, also called "Flower of Constantinople" or "Flower of Bristol."
Source for notated version:
Printed sources: Barnes (English Country Dance Tunes, vol. 2), 2005; p. 92. Christian (A Playford Assembly). 2015; p. 80.