During the run of the series there were three MT (main title) themes, one by Sydney Lee which was replaced by a new theme by Riddle and this one, the first MT theme (I think, the best, most exciting of the three). IMDb indicates Jerry Fielding scored S1 eps yet he’s not credited at the end of any of the episodes. So, I’m guessing either he or Walter Greene (who is credited on most shows pre-Riddle) composed it:
It's interesting the different themes are written to only a slightly altered film collage.
First S1 MT Theme (Greene? Fielding?) to 1:29 S2 Theme (Nelson Riddle) 1:30 to end
Second S1 MT Theme (Tarzan’s March, credited to Lee), theme begins 1:33 (at 3:07, though Greene/Lee are credited, we hear Riddle's ET).
To me it was always Sydney Lee who wrote the Tarzan march. It was also covered by Al Hirt in 1966.
Yes, he's credited as writing the second one, 'The Tarzan March' (theme heard in the second video posted) which replaced the first theme about seven or eight eps into the 1966-67 season (S1). The first theme intrigues me because Walter Greene is the only 'music composed and conducted by' credit (in S1), yet imdb indicates Jerry Fielding scored a dozen S1 shows including "Eyes of the Lion" and ""The Ultimate Weapon," the first two shows aired (but not necessarily the first two produced).