Got it largely wrong about "The Grey Cock" - all 7 notes do occur, but the B flat is only just perceptible. (It sounds odd if you put in a B natural instead, which suggests it isn't genuinely hexatonic as I thought).

X:1
T:The Grey Cock
S:Penguin Book of English Folk Songs
M:3/2
L:1/8
K:DMin
 G|        A2  A2  f6    ed |[M:4/4] c2  e2 (dc) A2-|A6
F2|[M:3/2] A A3    f6    e2 |       (dc) e2  d6
de|        f2  d2  c2 d4 B2 |        A2  G2  A2 D4
E2|        F2 (Ac) d6   (AG)|        F2  E2  D6    ||\
                                   "^original"\
                                     F2  G2  F6    |]