Channukah in Summer? (a note on Mahler’s Eighth Symphony)

Gustav Mahler in Maiernigg, summer 1906

As I write this, it is the last day of Channukah, 5776 (2015), and it occurrs to me that Maos Tzur, sung at Channukah, begins with a most unusual melodic progression:

E-flat, B-flat, E-flat, A-flat: Down a fourth then up a fourth. I searched in my mind for other instances of this combination of intervals, and all I came up with was:

If you replace the third note/syllable of the first line of Maos Tzur by a rest and transpose what remains up an octave:

you have the main theme of Gustav Mahler’s 8th Samphony — the first choral entry, given above.

To go further — perhaps too far — the second theme of Mahler VIII, sung by the men in unison, begins with the next two notes of Maos Tzur:

Which Mahler spins into:

Ignoring the question of whether Mahler was a Jew or a Christian, he undoubtedly knew the Channukah tune, which was apparently already used by Jews in the 15th century (See here) and was copied by Martin Luther in 1523 for his chorale “Nun freut euch, lieben Christen g’mein” (See here)

Was this tune running through Mahler’s head when in June 1906 he decided to set the 9th century Christian hymn?