Radiohead is clearly a thinking-person’s music, but which of their songs are the most thought-provoking, and why? How do we make sense of their often surprising, even shocking music? If you’ve ever found yourself pondering Radiohead way too much, here are some clues, a few answers, and even more questions.

9. Chord substitution in “Motion Picture Soundtrack” (2000-10, 2:44)

This Kid A finale couldn’t be any more in G major. Why then, when Yorke sings his final high G (“I will see you in the next LIFE”), is the G chord we expect replaced by a crunchy C-sharp half-diminished seventh? This dissonant uncertainty regarding our “next life” (C# half diminished) creates tension until the “Amen” cadence (C major–G major) alleviates our anxieties about the afterlife.

8. Displaced Guitar Rhythm in “Let Down” (1997-5, 2:11)

In the first chorus the lead guitar plays a three-note melody starting on a high A (A–G#–E). It happens right on beat 1, but in the second chorus, it gets moved back a beat early, beginning on beat 4 of the previous bar. Why? To my ears, the misplaced high A actually foreshadows the song’s climax: Yorke’s heroic ascent to that same high A in the third verse (“one DAY”).

7. Deformed Timbre(s) in “Daydreaming” (2016-2, 5:51)

Jonny and Nigel are both geniuses at taking normal sounds and deforming them into something spooky. After hearing both cello and Thom’s voice throughout this track, which is making that spooky sound at the very end? Voice, cello, or some sort of voice-cello Chimera? What’s being spoken is one thing, but how they slowed, reversed, and processed Yorke’s voice to sound like an aggressively bowed cello is even more fascinating.

6. 5-against-4 handclaps in “Lotus Flower” (2011-5, 0:01–0:14)

The drum and bass groove of this song is clearly in 4/4, but what’s up with that repeating 5-note handclap pattern? [clap-clap-rest-rest-rest]. Like so many anomalies in Radiohead’s music, this one has a clear mathematical explanation. Because 5 and 8 are co-prime—no smaller number other than 1 divides both evenly—those 5-count hand claps will actually complete the cycle of all possible eighth notes in 4/4 [34…12…78…56…] before starting over again.

5. Minor-major 7th chord, “Life as a Glass House” (2001-11, throughout)

According to classical music theory, seventh chords come in 5 flavors. This isn’t one of them. It’s a minor triad (A-C-E) with a MAJOR seventh (G#). Still, it’s oddly familiar. Where have we heard that chord before? Really just one place: Bond films. After we hear this association with spy/espionage, Yorke’s lyrics “but someone’s listening in” at the end of the first chorus make a lot more sense.

4. Runaway drum machine, “Idioteque” (2000-8, 1:52–2:34)

This song begins with a 6-count drum machine. But how is that 6-count drum part supposed to work in a song with a 20-count chord progression? Verse 1 is easy: the drums just fill in the remaining 14 beats with hi-hat and snare. But in verse 2, which has 100 total beats, the drums run out of control, playing the 6-count beat over and over. What’s weirder? There are a few 4s and 2s thrown in just to mess with you. See if you can count all the 6s, 4s, and 2s to make 100 beats.

3. Quarter-step detuning, “No Surprises” (1997-10, throughout)

As if they knew that every sappy singer-songwriter would be trying to learn this for their next coffee shop gig, Radiohead basically made it impossible to play along to. It’s not in F, it’s not in E, it’s actually halfway between the two. Whether you call it “E quarter-sharp” or “F quarter-flat”, your tuner doesn’t have that note. So, should you just start on 4th fret and bend everything up? (please don’t). Want a hack? Offset your tuner’s calibration down 50 cents and tune to F.

2. Creepy backwards singing, “Like Spinning Plates” (2001-10, throughout)

What’s Yorke saying, and why does it sound so weird? Believe it or not, this trick was taken from an early Twin Peaks episode. Agent Cooper meets a dwarf voiced by an actor who recorded his speech, played it backwards, learned his backwards-speech phonetically, recorded that, and then the sound engineers reversed the reverse, creating a simulacrum of regular speech. Because the backing track for “Like Spinning Plates” is an ill-fated circa-1997 “I Will” demo reversed (!), Yorke’s strategy actually makes perfect sense.

1. Euclidean rhythms in “Pyramid Song” (2001-2, throughout)

Why has more ink been spilled on this rhythm than any other moment in Radiohead’s catalog? Like the Golden Ratio in music, it’s because of a special geometry. The five chords are arranged unevenly over 16 beats as 3+3+4+3+3. It’s longer in the middle than the ends, just like a pyramid, and, just like a pyramid has four sides of 3 angles and one side with 4 angles, this rhythm has four chords lasting 3 beats and one lasting 4 beats. Coincidence? Maybe not: both of these pyramid shapes can be explained through the Euclidean algorithm—a mathematical formulation nearly as ancient as the pyramids themselves.

Listen to the full playlist below.

Featured image: “Radiohead” by swimfinfan. CC by 2.0 via Flickr.