From what I could gather by looking at a few sources of the album, listening to the whole thing in its entirety, and reading the lyrics, I have come up with a summary of the album Kid A by Radiohead. I'll give you the general scope, and then support each part with examples. Note that these analyses are simply my interpretations; they're not set in stone. Let's begin!
As far as the main binary oppositions, there are quite a few in a range of perspectives.
Opposing sides are:
Pitched music (guitars/synths/keyboards) vs. Drum and other Rhythmic devices.
Being one with the world vs. Being one with society
Monotony vs Chaos.
Right vs. Wrong
As a general rule of thumb, the melodic portion of the music emulates physical action of a character, while the rhythm portrays the thinking/speaking (the lack of physical action). Upon looking at wikipedia, it analyzed the songs individually, and even said where Radiohead was coming from with its creations, but lacked a sense of analysis of the album as a whole. I tried connecting the pieces together, and though it has some bumps, I think ties it all together. Each one adds on to a greater story.
Track 1- Everything in its Right Place
This one is a personal story about the main character. The lyrics state "I've got two colors in my head", which follows right into a binary sense of the overall concept. This could be his sentient knowledge of good vs. bad. With a lack of drums in the background, it has somewhat of a lack of thinking, and our main character is just going through his life. The song fades out at the end, suggesting that this process is continuous.
Track 2 - Kid A
The piece has the same texture and sound color as the end of the first track. Only at 0:28 does a rhythm pattern enter. It's not hard, but definitely present. The lyrics talk about 'a little white lie' and ventriloquists. These are huge images of political power going corrupt. 'Rats and children follow me out of town' is clearly a corrupted leader leading his blind followers for selfish gain, reminiscent of the Pied Piper of Hamelin. Again, the subtle gears are turning, and the corrupted society is being built.
Track 3 - National Anthem
This one was a personal favorite. The repetitive bass figure on the intro is wonderful in its depiction of even modern society. People hustling and bustling around just 'doing their job'. No one thinks outside the box. In fact, at 0:23, the drum kit stops for a bit (saying the thinking process stops), yet the bass line (the physical action) still continues. Very clever. The texture becomes more complex with extra sounds from about 0:50 until the vocal entrance at 1:36. The bass line keeps going, but the vocal line is the main character (not the pied piper character; but a person in society, now mentioned by me as 'Kid'). And he's looking around looking at the way society works. "What's going on?" and "Everyone has got the fear" speak for themselves. Blind, repetitive action as the bass line continues without stopping. The chaos builds up in the 3rd minute and just stacks and stacks. Finally it shortly recedes a bit (the lesser of two chaoses really) at about 3:42. The drums stop, but the bass line of course continues. There's another hiccup in drums at 4:50. The drums stop all together at 5:12. And the bass line finally stops on an abrupt blaring of horns at 5:17. Perhaps this is signaling the quitting bell. Unrelated music plays at 5:30, and then dies quickly into a sound of wind blowing. This could be the emptiness of the workforce for the day; each gone home until tomorrow.
I was blown away by this piece. Not because I thought it was pleasing to listen to (the monotony and I'm not the biggest fan of brass), but its symbology as it plays into the story and mimics modern society too is fantastic. "The National Anthem" is a perfect title. Whether we're aware of it or not, most daily life globally marches to this beat metaphorically.
Track 4 - How to Disappear Completely
The words give the mood of this one. They deny all. The speaker is feeling disconnected to society; to everything he has grown up with. "I'll be gone" shows his idea of escape from the society. Through the whole piece, there's a very melodic line - peaceful like the first and second tracks. The main difference is that it is a different speaker from the second track (Kid again). The drums pick up at 2:15, right when he says "In a little while, I'll be gone". His action has cognitive thinking. This solo-subject piece has a substantial beat, the volume of which shows the level of thought used. This track is about a thinking individual denying his society. At 4:38 the vocal line turns into a higher register. This is the speaker screaming at the top of his lungs as he is reborn spiritually into a world outside of his society.
Track 5 - Treefingers
The first thing that struck me about this piece was that there were no drums. None. Not one. No words either. This one is strictly the peace after the rebirth process that is Track 4. I'm thinking this is the night after he runs away from home, past the outskirts of town; into the unknown. It's a peaceful sound though, so it's a piece of reflection and welcoming, I'd like to think. Also a very wonderful contrast to The National Anthem.
Track 6 - Optimistic
The beat and the melodic lines start together. The vocal line talks about very pastoral things - vultures, big fish eating little fish, trying the best you can. And the best you can is good enough! Very uplifting. But I think that last part might be said in sarcasm, because the speaker is then saying "This one's optimistic. This one went to market." Like the one being observed is shopping for something new (a new way of life in this case). This is the most together piece so far, having the rhythm and melodic lines together at all times. Action and cognitive thinking are together in harmonies like we haven't seen before. The words move onto "I"d really like to help you man." Perhaps he's speaking from an observer's perspective (like you). You're watching it all happen, and you can scream at the TV screen, but he's not able to hear you and you can't alter his fate. The last line says "Dinosaurs roaming the earth", which shows that this escape from society has proven that there are mysteries happening that the main part of society had no idea about.
Track 7 - In Limbo
Melody starts the piece off for a few seconds, and then a thickened (almost too thick to breathe) texture comes in with the backing beat at 0:08. This piece struck me as a blurring between the new and old. What seemed so clear as good (the seek for a new way of life) and bad (the old society) is now close to one and the same. "You're living in a fantasy world" shows this. It goes on to say "I've lost my way" and "I got a message I can't read." The clarity is muddied. The action represented by the melodic lines becomes very chromatically inclined, adding to the "what exactly am I doing anymore" feeling. The beat is there, so the actions and head are working overtime, and the dissonance of the chordal structures adds onto this blending. At the end, the music kind of turns into nothing from 3:00 till about 3:07 where the music just fades out. Perhaps this is an overload of the main character, as he's again questioning who he is and what his purpose is.
Track 8 - Idiotique
The beat kicks this one off. The first melodic concept at 0:12 is quite random, spastic, and frantic, as if he's slapping some sense into himself out of desperation. His actions become as frantic as his thoughts. The vocal line talks about "Women and the children first." Perhaps he's salvaging his people from the society that finally capsized. I can see the panic in his mind. "Ice age coming" means something bad's on the brink. "Let me hear both sides" could be him trying to lead his people to better places. And "Throw it in the fire" is him giving orders to a lost people needing a leader. "Everything all of the time" means all hell is breaking loose. It's about a group of people escaping as he did before, only under more time-pressured circumstances. The constantly present uneven beat line is emulating the chaos in his head, and the melodic lines are broken up through the piece. His mind's on overdrive, but his actions aren't able to keep up because he's thinking too much. The last 13 seconds of the piece are eerily droned out. I think this is the sound of the dead city / society devoid of its people.
Track 9 - Morning Bell
The uneven beat comes on again. But the melodic line is calmly put together similar to the first and second tracks. The actions are then just kind of droned like a person in autopilot; unaware of their daily life, just like in the society we escaped from. The 5/4 meter is putting a strain on the new society's image. The Morning Bell is a society concept. "Release me" is not a good sign for this newly formed society. The dialogue in the vocal line are typical things that could be said between a couple that's lost the will to stay together. Not all new things end well, sadly. "Sleepy jack the fire drill running around around around" adds to the chaos in this new society. The last three parts are kind of disturbing - "Cut the kids in half", "I wanted to tell you but you never listened, you never understand", and "The lights are on but nobody's home". These aren't promising things you want to have occur between any two parties of a new society. The very last line of "Everyone wants to be a friend, Nobody wants to be a singer" is dangerous for a new society as well. Everyone wants to keep everyone else happy and won't speak up to speak their mind. Sheep aren't a good way to make a profitable society. This song is saying how the new society is just like the old one in so many ways. It sounds different, but there are problems anyway.
Track 10 - Motion Picture Soundtrack
This is how it all comes down. There are no beats in this one. Just a soothing, dead sounding, melodic line. The lines have lost hope with images of red wine, sleeping pills, cheap sex, and sad films. "I think you're crazy, maybe" is a way to say he's not sure of his values anymore, though he's quick to judge. "Stop sending letters, letters always get burned" means that though someone can say sweet things and make promises, they never last forever and aren't set in stone. And "They fed us on little white lies." Perhaps they never actually left the grasp of society and just transplanted it instead. The song ends with "I will see you in the next life" at 3:15.
Then silence for a minute.
At 4:19, the melodic line comes back as a thin note. This reminded me of a flat-line heart monitor. Perhaps the Kid died; or rather the essence of him died. But from 4:19 - 5:08, the melodies swell and grow into beautiful harmonies. Perhaps this is the life after death. A sort of "to be continued". There are no drums, so we don't know what he's thinking, but there's something going on for sure.
From 5:08 to 6:57, we're left to wonder what exactly that ending means to us. Very zen.
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Schenkerian Analysis for Kid A by Radiohead:
I wasn't able to find the music itself, so analyzing the vocal line in collaboration with the harmonies would be very difficult. I'll proceed to just do the chordal synopses.
Track 1 - Everything In Its Right Place
The whole piece is easily in Db Major or Ab Major, but it stresses heavily on its seventh chord ( C ). This leads me to believe it's more of a Phrygian on C, with the scale then being allowed for C Db Eb F G Ab Bb C.
The main chords throughout the piece are F C Db and C/Eb. It's repetitive to say the least.
This makes the intro simply: i II i
and the verses are: iv i II i
Track 2 - Kid A
Our chords are F, g and a, all in first inversion (the third's on the bottom)
The bridge switches up. Until then, we have in the key of F Major: I ii iii ii
The bridge is just C heavy, so it's just V
Track 3 - National Anthem
This is just D heavy, with a little C involved. For the most part, it's just
I and then I VII
Track 4 - How to Disappear Completely
The chords are D major, f# minor and A Major with a little E major in there.
Intro is simply, in D: I iii
The verse is then I iii as well, until the chorus of V iii
The bridge is simply II iii.
Track 5 - Treefingers
F#, E, B, C#, G#
In the key of B, this one is V IV I ii
And then IV V vii/V V
and finally V vi V
It ends on a nice half cadence
Track 6 - Optimistic
g, a, Bb, b, C, D, d. D is usually in the bass of the majority of chords. I believe this one fluxes between D minor and D dorian. I'll be doing this in dorian to start.
Intro is: v vi i vi VII i
Then: i vii ii I i vii ii II
The verse is: i VII iii I i VII ii I i VII ii I i VII ii I
The chorus is: ||: v iv I i VII ii I :|| I
The bridge is: i VII ii I
Outro is then: i VII ii I, v vi I, VI VII I, i VII ii I
Phew long song.
Track 7- In Limbo
Chords are: d a e G F and c
The intro is cute. If in D, it goes like this -
i v ii IV III which is lovely. 1 5 2 4 3. It narrows down on the middle chord. Very systematic and works. It's in limbo, after all. You're stuck in the middle, with no where to run
It looks like they're still in the D minor/dorian thing from before though.
Verse is in c though, then back to d for the chorus:
Verse: i v iii I
Chorus is the same as the intro
Outtro is same as the verse.
Track 8 - Idiotique
Chords - g Eb
The entire thing is just: i VI
Track 9 - Morning Bell
Chords: a G D
The entire thing is just: i, VII V
Track 10 - Motion Picture Soundtrack
Chords: G C b C D e
Intro: I IV iii IV
Verse: Same as intro
Chorus: vi IV I V
And that's all for the chords.
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As for the discussion of the ambiguous key centers, there are a few examples that I think fit your request.
First up is track 1!
The first piece is unique for a beginning with phrygian scale. I bet this is their way to get a hook and be original. I'm pretty sure being in a phrygian scale is an odd choice to start with.
Track 2 is interesting too in that it's just a rocking from the 1 to 3 chord, via the 2 chord the whole way. We then go to the dominant (rather far away from the tonic) in the bridge, which could be foreshadowing for the plot of the whole story.
Track 3 stays within a step for both of its chords. The monotony of the daily life is emulated clearly by this lack of chordal diversity. It's not very easy to define a key with just two chords, so it's teetering on a thin line with just sticking to these two chords.
Track 5 is unique on the soundtrack because it ends on a half cadence. It also doesn't stress what key it's in and kind of floats freely through the whole thing. The ambiguity makes it seem like home (tonic) is "somewhere" but we're not exactly concerned so much to find it. Very nice imagery for the way this piece functions the the grand scheme of things.
Track 6, despite its many chord progressions, is rather stable. The only interesting thing is that it goes from D minor to D dorian with a very wishy washy Bb/B.
Track 7's intro is nice and clever, like I already stated. It goes from the 1 to the 5, then back towards the 1 to the 2, then back to the 5 and hits 4, and then settles its rocking into 3. 1 5 2 4 3.
Track 8's harmony is made up of a pair of double chromatic mediants. That's pretty unique as far as the rest of the album goes.
A common theme in these pieces is that they establish tonic (more or less) and then try to get away from it and never come back to it again. Quite poetic given the subject matter, I'd say.
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I'm not usually one to listen to Radiohead (I think all I know is their Creep song), but this was a very intense and gratifying process to analyze, and I feel like I learned a lot and had a full experience while diving in. I hope this enlightened you and answered your question, GuitarBizarre. This is quite a detailed question. I didn't just give you highlights for a final or otherwise semester project, did I? o.O
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As for the Tristan Und Isolde, I think what you're thinking of is, appropriately named, the Tristan Chord. This chord, made famous by Wagner's opera of Tristan Und Isolde, is a large part to Tristan's 'leit motif', or theme motive. It occurs every time he's introduced audibly, and is simply a misspelled half-diminished chord of F B D# G#, this can be 'correctly' respelled as F Ab Cb Eb chord.
The thing that makes this chord so obscure is that it's found in such an unrelated key. A typical F half-dim 7 chord should be in the key of Gb major. Instead I believe the key was a minor (don't quote me on this). Several composers since Wagner were interested in replicating this chord and have used it since.
Interestingly enough, to tie everything together, an artist named Paul Lansky used the Tristan chord and inversions of it for a piece he made named "Mild und Leise". Radiohead then used Lansky's interpretation in their 8th track, Idiotique of Kid A.