I will return to Jamieson and his Danish source later, though that song isn't particularly relevant here. Meanwhile, a little more on an earlier question.

The tune noted by Andersson is in Bronson and (slightly differently) in Thomson. Bronson describes it as 'an authentic Mixolydian variant of the air particularly associated with "Hind Horn" (No. 17), but met as well in a good many other British and American connections.'

The DT file The Grey Silkie of Sule Skerry includes a midi (SILKIE2.2.MID) of a mutant form of it, presumably made by ear from Jean Redpath's recording of the song. Here is an abc of the tune based upon the form printed by Bronson:

X:1
T:The Grey Selchie of Sule Skerry
B:Bronson II, 564-5
S:John Sinclair, Flotta, Orkney, 1938
N:reproduced from Otto Andersson, Budklaven, XXVI (1947), 115
N:time signatures of individual bars not specified in Bronson
N:words fitted notionally, following Bruford
N:tempo approximate
N:authentic mixolydian
L:1/8
Q:1/4=120
M:4/4
K:G
A2| [M:3/4] G3/2E/ D7/ B,/ | [M:4/4] B,3/2D/ E4 A2 | [M:2/4] G3/2E/ DE/F/ | [M:4/4] G3/2A/ B4 d2 |
w:I am a man up-on the land, I am a sel-chie_ in the sea And
[M:3/4] dc B3 A | [M:4/4] GD E4 EA | [M:3/4] AA B3 A | [M:4/4] GE D4 |]
w:when I'm far from eve-ry strand, My_ dwell-ing is in Sol-sker-rie.

Whether the John Sinclair of Flotta from whom Andersson got it is the same John Sinclair of Flotta from whom Sean Davies (not Peter Kennedy, as stated in another thread; though Kennedy may perhaps have recorded him later on, in 1964; as usual, the information he provided was ambiguous) recorded a version in 1955 isn't clear, but it seems likely enough. Alan Bruford may not have been aware of the recording: at all events, he didn't mention it in the article cited above.

A brief sound sample can be heard at http://preview.mp3fiesta.com/disk11/a/alan_lomax/sailor_men_and_serving_maids/12_the_grey_silkie_john_sinclair.mp3

For further comments on the North Ronaldsay text, see thread Silkie (as sung by Anne Lister) (links above). At some point I will have to post the genuine text there, to replace the mediated one given (the second text there is apparently taken from a revival arrangement, so tells us nothing useful about the song).