Hi, all: There's a very interesting research paper available online, complete with imbedded (MIDI) tunes and analyses -- the result of a study done by a musicologist a few years back in an attempt to resolve this very question. (Interestingly, its title matches this topic's exactly.)
"And the Band Played On:
Hypotheses Concerning What Music Was Performed
Near the Climax of the Titanic Disaster"
presented at the October, 1999 meeting of the Southwest Regional Chapter of the
American Musicological Society, Rice University, Houston
by
J. Marshall Bevil, Ph.D.
http://home.earthlink.net/~llywarch/tnc02.html.htm
If you haven't already seen it, it's well worth the read (and listen). It delivers a pretty thorough analysis of the "Autumn" versus "Nearer..." contentions, and also investigates in depth the issue of *which* NMGtT tune(s) would have been likely. Quite an admirable and convincing piece of research, I think.
Myself I think it's quite possible that *both* "Songe d'Automne" and "Nearer My God to Thee" could have been played (in that relative order), but that Harry Bride was too waterlogged to *hear* the final, brief hymn. (I believe that was also the paper's conclusion, though it has been a while.)
I definitely think accepting Harry Bride's singular assertion of "Autumn" as THE final piece too readily dismisses *numerous* other witnesses who clearly recalled "NMGTT". And that's just way too unbalanced, from my perspective. (But I *can* see that it might have been Harry's "last" song.)
Cheers,
John