Musically, "Baba O' Riley" represents a successful fusion of the old and the new—it's The Who's signature sound mixed with some innovative musical concepts that circulated within classical music during the 1960s.
The song begins with a simple, repeated pattern played on the organ. Here, Townshend was influenced here by California composer Terry Riley, who explored the musical possibilities lying within simple non-melodic patterns that were repeated and overlapped. His composition, "A Rainbow in Curved Air," seems to have been the most influential in shaping Townshend's introduction to "Baba O' Riley." In "Baba O'Riley," Townshend was trying to replicate the sound of a synthesizer. Townshend had other ideas, too, that didn't show up in the song. For example, he theorized that an individual's biographical data fed into a computer-driven synthesizer would construct a musical portrait of an individual.
Back to the song itself: after about forty seconds of Riley-influenced patterns, some classic Who power chords (played on the piano) are laid across the top. The bass and drums soon enter, and eventually Townshend echoes the piano with the windmill guitar power chords that we're been waiting.
The organ/synthesizer pattern continues to run along the bottom of this standard rock instrumentation, surfacing periodically during gaps in the chords and vocals. But about two-thirds of the way through the song, this electronic track is abandoned and the power chords give way to an increasingly frenetic violin solo. Now we've got a different sort of fusion. The violin plays what sounds like an Irish jig melded with some traditional Indian music. This is a final tribute to Townshend's spiritual mentor Meher Baba.