As a former melodeon player I found WP's claim to be able to tell the ages of songs by whether they ended on a draw interesting/dubious. This is quite apart from questions such as whether he was correct (probably not) and whether the tunes he had were the same age as the songs (another question).

On his melodeon he had basically the notes for G major and D major. By definition he also has the notes for the relative 'natural minor' keys (E minor and B minor). He has basically one octave in each major key and a few added notes either end.

Modes found by Sharp included mixolydian, aeolian and dorian and some tunes he found to be a mixture of/undecided between both. To play in E or B mixo Pardon would need but not have a major third (g# in Em; d# in B minor). This is does not have. Attempt to play in aeolian would founder on the lack of a major 6th (c in Em; G# in Bm)

Of course, he didn't have to limit himself to those keys: he might have attempted to play a modal tune with its 'tonal centre' on a different note, not G E B or D. He might have tried to play tunes using fewer than 7 notes. I don't know whether he did this. None of his mediators appear to have interested themselves in such things. In any case, the attempts would be problematic.

I'll leave it to somebody else to explain which modes and which sorts of melody in terms of the way the tune goes above and below the tonic centre in each mode you can and cannot get on a GD melodeon.

The problem with WP is that what we know about him is so very heavily mediated that it is impossible to know what ideas got into his head through his long and close association with revivalist enthusiasts, some of whom had/have clear ideological agendas.