In a discussion at TheOneRing.net's forums, Firiel50 commented that there was a short phrase in the first movement, (Allegro moderato), of Jean Sibelius'  Symphony No. 3 that sounded quite similar to the Fellowship Theme. This is especially interesting since we know that JRRT was interested in the Finnish language and sagas and Sibelius is a Finnish composer who composed from the sagas.

Grendel's Mother said this:

The recording I have is 10:50 long.
The first time is at about 8:50 (there's a section of very quiet pizzicato that bounces from violins to cello/bass, then the whole orchestra chimes in majestically (with the horns on top) to accent on 3 chords ..Bb..F..C. That's it.

Sibelius, part 1 ~ 8:50

About a minute later (9:45) there's a section of slow scales up and down that hold on a long "A" (horns over viola, I think) Then the horns slowly scale up into another majestic statement of the same three chords ..Bb..F..C.
It's not the whole theme, just a few bars of it... those three chords with practically the same grace notes.

Sibelius, part 2  ~ 9:45

When I listened to the Sibelius phrase, I could immediately imagine the Fellowship Theme. Finding a comparison clip was harder than I thought, however. I don't have more than a rudimentary musical knowledge, so bear with my simplistic attempt to break this down a little. The Fellowship Theme has an opening measure with 5 notes... two slower, three quicker. This opening measure is often used by itself as a little reminder of the Fellowship. But when the phrase goes on, it continues with a series of three quick notes repeated three times followed by two slower. Then it all repeats. The opening 5 note measure is heard again followed by the three repetitions of three quick notes (with same rhythm but different notes)... the last note being held out (with maybe a declining phrase of some sort to finish or to segue into the next bit of music). Now, this gets changed for every iteration. The rhythm, notes and/or key may change.

By my ears, what sounds familiar between Sibelius and Shore is found in those three repetitions of the three quick notes as heard the first time through the phrase. In fact, it is the second and third trio of notes. So I've isolated those 6 notes from the two Sibelius clips (as heard above) and then from one iteration of the Fellowship Theme (as heard in the final moments of the FOTR credit music - Track 18 on the CD ).

	Sibelius, part 1 segment ~ 8:50
	Sibelius, part 2 segment ~ 9:45
	Fellowship Theme - 3:51 - 3:55, FOTR, Track 18, May It Be

Jean Sibelius, Symphony No. 3 in C Major Op. 52, Movement 1, Allegro moderato - recording information for audio samples is unknown.