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Many of the effects that make up Radiohead's trademark production and arrangement qualities are in "Paranoid Android." The computerized backing vocal "I may be paranoid, but not an android" is a widely-used effect on OK Computer; it comprises the entire vocal track to "Fitter Happier" and also compliments the general yuppie-culture criticism of the album. The style of vocal sampling seen in the beginning of the word "ambition" during the bridge has remained prominent in later Radiohead works. The layering of vocals in the third section is something else that the band has kept in their musical style, as well. Plus, the choir-like arrangement of the voices reveals the classical influence on the band; as the third section builds to its close, not only does the song have a choir going on, but Yorke's vocals (beginning, "that's it sir, you're leaving") act as a counterpoint to the progression of the choir (that is, the two melodies play simultaneously while being completely different).
The three sections of the song are all distinct rhythmically. The first section has a Latin feel, with a 3:2 clave in each measure that syncopates the third and fourth beats. (There's a lot of music-theory jargon in that sentence, but if you listen for the bass drum and the clap along, you'll find you'll clap three times in the first half of each measure and two times in the second half, which is a defining feature of bossa nova rhythms.)
Aside from a more standard rock rhythm, the second section features several three-measure parts in which the song shifts to 7/8 time, which is incredibly unusual for contemporary rock music (most pop songs are in 4/4 or 3/4). Unusual time signatures are pretty characteristic of Radiohead's music. As further examples, "15 Step" and "2+2=5" feature 5/4 and 7/8 time, respectively. In 7/8 time, instead of having four beats per measure, there are three—two normal beats (which are a quarter note long) and one "compound beat" (that's a quarter note plus an eighth note long). Try to follow the beat to these 7/8 sections in "Paranoid Android." You'll find that the first two beats are easy to hear, but the third is different.
7/8 time is not something that's typically heard in pop music, so it immediately draws the ear and almost by necessity the listener must work hard to grasp the rhythm. With the increased sense of pace in these sections, the rhythm—and even Jonny Greenwood's guitar melody—feel cut off too soon as the measures frantically go by. This style recalls the historical appearance of 7/8 in traditional Greek and Bavarian dance music and jazz, as it builds an incredible tension that finds release only in the song's slower third section.
That slower final section is the song's most straightforward, in rhythmic terms. The tempo drops to near 60 bpm (beats per minute) and the drums move into the background of the piece. This standard 4/4 feel involves the emphasis of the bass and the drums on the first and third beats while the guitar takes the second and fourth beats (strumming every sixteenth note on the second and fourth, rather than just every eighth note).
This short laundry list of the defining characteristics of "Paranoid Android" illustrates the most important musical quality of the song: that it's a Radiohead song. While Radiohead has been copied time and time again in recent years, there's still no band that sounds exactly like Radiohead. Their style is defined abstractly by their willingness (and musical capability) to be experimental and unconventional in non-superficial ways, while also managing to incorporate standard pop elements. The band's style is defined by Thom Yorke's unique vocal genius, Jonny Greenwood's guitar work—which often travels into the atonal and dissonant spaces, only making the resolution of that dissonance so much more powerful—and the rhythm section's far too often unappreciated subtleties.