Knights of Cydonia is a song from Muse's 2006 album Black Holes and Revelations. I first heard it played incessantly on the radio while going to and from work around that time as well. I found it to be a catchy and genuinely interesting rock hit, but it wasn't until I started taking a closer look at it that I noticed it had some neat compositional features.
The work doesn't have a typical song structure for starters. It's not your average AABA or ABABCB song form which so many pop tunes are built on. It can be broken down into this general form:
Intro - A - A' - A'' - Intro - B - Coda
I've omitted any indication of how many times the Intro, B, or Coda is repeated, instead just choosing to show how the basic formal divisions are mapped out. It may seem a little peculiar to have the recurring "Intro" lodged within the middle of the piece, but I didn't want to call it a letter name, which I thought might imply it being more structural (it functions like a slow intro, and is merely repeated after A'' concludes). You can see from what I've organized above that the song is therefore a kind of binary form.
The three instances of A is where I find the most interesting part of the song takes place. It's composed around a key modulation scheme which is derived from a classical tradition rather than learned from any pop school. Most pop/rock songs don't even modulate; this one traverses paths which are seriously atypical of a mainstream work! I can think of a few pop songs like The Police's "Every Breath You Take" which modulate to [bVI], but it's brief, in a major key, and bounces right back up to [I], rather than boldly modulating even further like Knights does.
I've placed to the right of here a visual representation of the way the keys change within the three instances of the A section (circle of fifths graphic shamelessly stolen from a GIS).A starts in Em and modulates to C minor
A' starts in C minor and modulates to G#m
A'' starts in G#m and modulates to Em
The keys divide the octave into major thirds, something which you may be familiar with in a piece like Beethoven's "Waldstein" Sonata, where the second theme modulates to [III] instead of a more typical [V]. It wasn't until composers like Schubert and Liszt came around that there would be more extensive 3rd related key modulations which divide the octave up totally. Knights of Cydonia mimics this latter method. Using roman numerals, here's a way to show the chords progress within each A section:
[i]: i - III - VI - III - V - VI -
[vi]: I - III - V - i - V - VI - III - V* - VI - III - V - i
[vi]: I - III - V - i - V - VI - III - V* - VI - III - V - i
I don't think I can totally convince myself where the exact pivot chord is, but I'm sure this is comprehensive enough. Where I've placed the asterisk is a point I found noteworthy; while the chord is a dominant V, the guitar melody on top plays the flat-third of the V chord, creating an interesting false relation. I figure this is some kind of subtle blues derived idiom; either way, it's not too jarring because the background chords only have the root and 5th notes of that chord primarily perceptible. It's only at 1:53 do we hear the brass play the raised 3rd (F-double sharp) right before the guitar plays the regular unaltered-3rd (F-sharp) of the V-chord.
Since I've just mentioned a point in the song relating to a specific time, here's an embedded version of the song to follow along with:
When that elaborate chord progression of the A section outlined above is applied three times, as occurs in the piece, the keys come full circle (or in the case of the graphic, full triangle) and return to E minor, where it all began. One thing I particularly enjoy about the modulation is how seamlessly Muse is able to go from [i] to [vi] within each A section. The lead guitar provides a motion from VI5-6 to #VII (reinterpreted as III in [vi]), and it is performed without my ears hearing it as abrupt or foreign. I would wager to say that your average listener is unaware that the keys cycle through this anachronistic scheme.
The piece also harbors some harmonic motivic unity -- a chromatic line that outlines a major second. For example, in 1:03 a III - V - VI progression occurs with the guitar outlining D-D#-E (decorated with an F# neighbour), and once we reach the modulation to [vi] at 1:07, we hear the guitar play A-A#-B. How convenient that they are a perfect-5th apart.
I hope this analysis was informative. I feel compelled at the end of it to say that it's not an attempt to elucidate the value of the piece. I have not included many things which contribute to the quality of this song, but I think showing the objective harmonic features give an impression that this is different from the more common pop/rock songs one hears on the local radio station, certainly more interesting from an analytical perspective, in my opinion.
