As far as I can tell, the four tunes (Clifton's "Send Back My Barney", French & White's "My Barney Is Out on the Ocean", Watersons' "Barney", and "My Bonny Lies over the Ocean") bear little or no relation. White's tune appears entirely original (even though French's lyrics look somewhat pirated), and is in the nature of a march—which doesn't exactly complement the feeling of the lyrics.

Here's a quick ABC transcription of White's tune, which you can feed to Concertina.net's Tune-o-tron or Folkinfo's ABC converter to get a MIDI. I'll also send a MIDI to Joe Offer, who can post it with Jim Dixon's message, if he feels so moved.


X:1
T:My Barney Is Out on the Sea
% melody only
C:Words by Arthur N. French
C:Music by Charles A. White
S:Period sheet music at the Library of Congress's American Memory site.
Z:Artful Codger
H:Published in Boston: White, Smith & Co., 1876.
M:4/4
L:1/8
Q:1/4=120 " Andante" % transcriber's estimate
K:G
D2 |G2F> GE2F> E |E4D2zD |G2F> GA2E> E |F4 z2 D2 |
G2F> GE2F> E |E4D2zD |D2F> GA2F> F |G6 D2 |
A2^G> AA2B>A |G4B2zD |A2^G> AB2 c> B |B6 B2 |
d2d> dc2B> B |A4c2zc |B2{d}c> BA2G> A |B6 B2 |
d2d> dc2B> B |A4c2zc |B2D> BA2D> D |G6 ||
%
% Refrain
d2 |d2d> dd2{f}e> d |f6 zd |d2d> dd2{f}e> d |g6-g g |
f2 e> d c2 B> A |(e4 d2) z2 |f2 "^ad lib." e> d c2 [Be]< [Af] | [G6g6] x2 ||


(I dropped the fermatas, which make the MIDI playback sound mistimed.)