Don't know why "chuck" won't let me log in to Mudcat, but a guest posting will have to do for now.

From the original post, this thread had two objectives, stemming from one recorded performance. As detailed in my 06 July 2016 post, this is a recording that was first released as an HMV 78 RPM vinyl single, and has since been subject to more than one re-release, the most recent on Gael-Linn's CEFCD201, a compact disc published in 2011. This thread's second post has a link to a "video" containing this recording sung by Máire Ní Scolaí.

Working from the recording of "Eibhlín a Rúin," the first objective was an accurate version of the song lyrics. In this regard, Mudcat's Digital Traditions disappoints, because the lyric as given in more than one "Eileen/Aileen Aroon" file is inaccurate, spelled out phonetically rather than with the correct Gaelic spelling. Later posts to this thread improved the matter, without changing what is in the Digital Traditions files, by contributing more accurate lyrics for what James Hardiman's "Irish Minstrelsy" called "Old Eibhlín A Rúin." Thus the first objective is attained.

The second objective was the tune as recorded by both Máire Ní Scolaí and uillean piper Tomás Ó Canainn.

If you have an allmusic.com account, which I have not, you can listen online to a tune as follows:

title: Robin Adair / folksong arrangement
first words: O had I a cave
poet: Robert Burns
composer: traditional
arranger: Franz Josef Haydn
composition: no. H.31a/202
arrangement: voice, violin, violoncello, keyboard

http://www.allmusic.com/performance/robin-adair-o-had-i-a-cave-folk-song-for-voice-violin-cello-keyboard-h-31a-202-mq0000870845

This latter song, the melody of which I have referred to by such names as "Robin Adair" and "Lady Keppel," also has Gaelic lyrics. It is often heard with an English translation. Is Robert Burns' lyric independent of this tune originally? That's a question in itself.

From the original post on this thread, my position has been that the Haydn/Robert Burns/Lady Keppel/Robin Adair melody is distinct from the melody in which Tomás Ó Canainn so clearly plays what would be called, in the American vernacular, a "blue note."

To each his own judgment, and from that post to this, I still hear two distinct, albeit related, melodies.