"Pilgrimage" is the ninth track on the Left disc of The Fragile. It is an instrumental track in a 3/4 time signature.
The "Buddha Boys Choir", credited for background chants on this track, was actually (with the exception of Keith Hillebrandt, Clint Mansell and Steve Duda) a random group of bar patrons who were brought in from Igor's Buddha Belly across the street from Nothing Studios.
This is the album version. Its abrasive guitar riff fades in from the end of "Even Deeper," joined at each repetition by new layers of mechanical synthesizers and percussion layers. These layers are soon subsumed by the main theme, played on synthesizers. After its repetition, the layers halt to simply a distorted guitar playing the same riff, which is then joined by drums, bass synth, and wordless vocal melodies. These layers soon crossfade with a return of the main melody, played this time on brass instruments accompanied by marching drums that fade in. Eventually, the horn and synth layers stop, leaving only the marching drums to repeat and stop suddenly, leading into the opening ambient pad of "No, You Don't."
On the vinyl version, the song does not fade in at the start, rather beginning with the guitar riff and building at its natural mix volume.
Released exclusively through Apple Music as part of The Fragile Instrumental, this is a very different mix, though the arrangement is very close to the album version. Its intro, like the vinyl version, does not fade in.