These three tunes do share some characteristics. Personally, I would not say that SLOW TRAVELLER is a variant of THE COVENTRY CAROL or Niles' LULLE LULLAY specifically because of these characteristics. What they have in common is that the first and third phrases end on the seventh scale degree. Also, LULLE LULLAY and SLOW TRAVELLER use an ABA'C form. However, I do not think that this would qualify them as being related (see the link below for the scores of the COVENTRY CAROL and LULLE LULLAY).
Niles' LULLE LULLAY -
http://www.folkinfo.org/songs/displaysong.php?songid=291COVENTRY CAROL -
http://en.wikipedia.org/wiki/File:Coventry_Carol.png#fileLet's take a look at the pre-1820 incipits for these tunes:
SLOW TRAVELLER (1805) -
111(d7)u12(3)4(3)2(1)d7 u21d7u125 54212(3)4(3)2(1)d7 u43d57u21
COMMUNION (1810) -
5u11(d7)u1343(1)d7 u3(4)54(3)12(3)4 2(1)54(3)1343(1)d7 u321(d7)57u1
LIBERTY HALL (ca. 1801) -
5u1d7u12(3)42(1)d7 u353(2)12(3)4 353(2)12(3)42(1)d7 u321(d76)57u1
SINCERITY (1820) -
111(d7)u1343(1)d7 u354(3)13(4)5 354(3)1343(1)d7 u311d57u1
Though the second phrase does differ between Ingalls' setting and the others, the first and third phrases are almost identical, especially in the latter half of the phrase. SLOW TRAVELLER also resembles the fourth phrase of the other three settings. Because of these similarities, I believe that they are related.
Now let's look at the COVENTRY CAROL and LULLE LULLAY
COVENTRY CAROL
11d7u1321d7 u123421 5432321d7 u1d7u1423
LULLE LULLAY
33(1)35(4)54(3)4d7(u1) 23(4)56(5)47 7u1(d7)u1d5(4)34(5)2d7(u1) 23(1)34(3)d7u1
Comparing these tunes with the earlier sources, I don't see that much of a connection here. The LIBERTY HALL/COMMUNION/SINCERITY variants all use the same form: both an ABA'C or an ABB'C as seen with the first half of the third phrase basically replicating the melodic material of the first half of the second phrase, and the second half of the third phrase replicating the second half of the first phrase. SLOW TRAVELLER deviates a bit from this form because of the way Ingalls set the second phrase, though it does provide an overall ascending shape as in the other variants.
COVENTRY CAROL differs from the pre-1820 variants in several distinct ways. Its form is not the ABA'C/ABB'C form. Rather, it's in an ABA'B' form. Significantly, the final phrase echoes the second, but concludes with the Piccardy third. Also, the second phrase does not ascend as in the pre-1820 sources. LULLE LULLAY does not include any phrasal repetition like the other tunes. What remains similar is the emphasis on the seventh scale degree at the ends of the first and third phrases. Otherwise, it really shows no similarities between them. Niles said he recorded this from an old lady. She also happened to be a shape-note singer. She could just as easily have set her own words to a pre-existing sacred tune, thus nullifying the "traditional" aspect of her performance. This tune could have been her own modified variant of one of the book tunes and not a traditional melody that accompanied this text.
Niles's attributions and sources are often confusing (sometimes deliberately I would argue). Then there is also the problem of taking a recording from 1934 and applying it backwards to an 1805 source, to prove a connection. Without a known name, source documentation, and other necessary information, this application seems impossible to state with authority. Maybe I'm missing something here.
The Niles tune resembles more a S.M. tune by John Cole called CHESTER. Though the meter is different, the melodic contour seems closer.
CHESTER - A minor
5u1(2)32(1)d7u1 23(4)56(5)45 55544332 23(2)14(3)21
CHESTER did make into at least one shape-note book, Freeman Lewis'
Songs of Zion from 1824. FWIW.
Nikos Pappas, Lxgtn