This tune (notated with cut time, and in D minor) is given in the introduction by George Farquhar Graham to John Thomas Surenne’s "The Songs of Ireland, without words, for pianoforte" (1927). Graham writes that this "singular dance air" has "no settled mode of tonality; and, therefore, it is not susceptible of any regular harmony, not even a regular bass." The tune itself was taken from the 2nd edition of "Ancient Melodies of Ireland" by Edward Bunting, published in 1809.
By the way, it is thought that Graham may have taken some lessons in harmony with Beethoven.
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