hey, welcome to 12tone! last week I did a video on the Axis Progression, also known
as the Four Chords of Pop. you probably already know what they sound like: (bang) and you
may also know that hundreds of hit songs have used this exact same loop over the last couple
decades.
if you didn't know that, well, now you do.
but working on that video got me thinking about another chord loop, one that doesn't
get nearly as much attention even though it's quietly established itself as one of the most
important progressions in modern music, especially modern rock.
it sounds like this: (bang) and as far as I know it doesn't even have an official name,
but I call it the Plagal Cascade, for reasons that will hopefully become obvious pretty
soon.
so how did this chord loop come to dominate the airwaves, and what can the Axis Progression
tell us about how it works?
(tick, tick, tick, tick, tock)
let's start with a little history.
the earliest song I could find that uses the Plagal Cascade is Pictures of Matchstick Men
by Status Quo in 1968, although they do a slight variation on it, playing the first
chord as major instead.
(bang) there's also Throw Down The Sword by Wishbone Ash in 1972, which does use a minor
I chord, but it's not really played as a loop: the Cascade is just the first half of an 8-chord
progression. if you want the full, minor Plagal Cascade, played as a self-contained loop,
the earliest I could find is Mad World by Tears for Fears, released in 1982.
there's some other examples dotted throughout the 90s, including Man In The Box and Wonderwall,
but the progression didn't really come into its own until the 2000s, ironically coinciding
with the Gary Jules cover of Mad World.
I don't want to spend this whole video listing songs this loop was used in since the year
2000, but just to prove that it is, in fact, popular, here's a quick sampling: Nosebleed
Section by Hilltop Hoods, Boulevard of Broken Dreams by Green Day, New Divide by Linkin
Park, New Romantics by Taylor Swift, Scream and Shout by Will.i.am, Pumped Up Kicks by
Foster The People, Piece of Me by Britney Spears, and Radioactive by Imagine Dragons.
that's far from a complete list, but hopefully it demonstrates that this chord progression
is kind of a big deal.
so how does it work?
well, fortunately for us, it's actually really simple.
it's a minor progression starting on I chord, then it hops up to bIII. these two chords
share two notes in common, so this motion is relatively smooth, like the calm before
the storm.
once we're on the bIII, though, the real fun begins: we just keep falling down by perfect
fourth over and over and over, until we wind up back at I and start again.
the resolution from IV to I is called a plagal cadence, and it's probably the most common
resolution in rock and pop 'cause it feels satisfying but it's not completely final,
so you don't get the same sort of awkward stopping point you might get with, say, a
V-I resolution.
this loop decides to go all in on that one chord motion, cascading through a series of
plagal cadences, hence, plagal cascade.
the only break is that move from I to bIII, resetting the cycle and making it clear that
this chord sits at the bottom of our slide.
songs that use the plagal cascade tend to have this sort of meandering energy to them,
chaining together a series of mild resolutions to sort of drift back to I while making every
chord transition feel like its own miniature event.
the plagal cascade has come up in a couple of my song analysis videos, and that's always
been roughly how I've explained it, but last week, while working on the Axis Progression
video, I realized something new, something that as far as I know, no one's ever noticed
before, at least not in any scholarly publication I could find.
in order to explain what I found, I'm gonna have to reference some stuff from last week's
video, and I'll put a link in the description if you want to see the full version, but this
is YouTube, I know most of you aren't gonna go watch a whole other video and then come
back, so I'm also gonna summarize the important points here.
basically, the Axis Progression comes in two different forms, the major axis: (bang) and
the minor axis. (bang) they've got the same chords, in the same order, we're just starting
in two different places. and, amazingly, both of these forms are stable: that is, both of
them sound like they start on the I chord, which means the loop as a whole actually has
two different I chords, and we can influence which one you hear as stronger by playing
around with their metric positions.
in last week's video, I argued that this happens because of the interaction of two competing
biases. first, there's major scale bias: that is, we tend to assume that music is in a major
key until we hear something that can't easily fit with that assumption.
this is especially relevant for the Axis Progression, because these three chords are the I, the
IV, and the V, collectively known as the primary triads.
they're the three most important chords in G major, and including all three of them effectively
supercharges our major scale bias. we really want to hear this loop in G major.
on the other hand, there's destination bias.
y'see, the Axis Progression is what I like to call a Cascade Loop, which means that every
chord approaches the next one by strong harmonic motion, except for one.
when we go from E minor to C, we're moving by 3rd, which is, again, weak, and much like
in the Plagal Cascade, breaking the chain of resolutions makes this E minor chord feel
like our destination, the point the loop wants to fall down to.
this makes it the most harmonically prominent chord, so while we may want to hear this loop
in G, we also want to hear it in E minor.
both roots are valid.
that's roughly where I ended the video, but it got me thinking about theories.
I'm sorry, I'm a music theorist, I can't help myself.
but as a theorist, once you have an explanation for something, the next step is to try to
generalize it.
you look for other things with a similar structure and see if your model explains them too.
my theory was that the Axis Progression's bimodal behavior was a result of the fact
that it was a cascade loop with a minor destination, where the other three chords were the three
primary triads of a different major key.
if that's true, then we'd expect the same behavior from other chord loops that also
fit that description, which brings me back to the Plagal Cascade.
now, the Plagal Cascade is, as you might imagine, a Cascade Loop, and as we saw earlier, the
bottom of our chain of resolutions is minor, so we're off to a good start, and if we look
at it again: (bang) we see that these three chords are the IV, I, and V of D major.
we've got our primary triads. it's the same structure, so if I'm right then we should
be able to rotate it into a major-sounding progression by starting the loop in the middle,
and if we do that: (bang) yeah. it sounds good.
but is it stable? it's hard to tell: lots of progressions sound like they start on the
I chord if you only play through them once, but the real test of a chord loop is what
happens when you, well, loop it, so if I play it again: (bang) and just let it run for a
while, you should start to get a sense of whether that D chord still feels like the
root, and to my ears at least, it totally does.
ok, I'm gonna stop it now.
so… great, we've got a stable loop, but an important part of the Axis Progression
is that not only do these two forms exist in theory, they exist in practice too.
that is, since the '80s, lots of hit songs have been written using both forms, so if
we want to show that the Plagal Cascade really behaves the same way, that musicians treat
it as though it has the same structure, what we really want is to find an example of this
major rotation in the wild. if only somebody had written a song like that.
*sigh* somebody.
someBODY.
...oh my god.
(All Star plays) that's right, All Star and Boulevard of Broken Dreams use the exact same
loop, they just start playing it at different times.
and this is far from the only example: I could've also used Irreplaceable by Beyonce, Hot N
Cold by Katy Perry, Just Like Heaven by The Cure, or Wildest Dreams by Taylor Swift, but
when life gives you Smashmouth, you don't ask questions, you just go with it.
and if we take a step back and look at the progression we've made, this result isn't
that surprising.
let's compare it to the Axis Progression: if we take the minor forms of both loops and
play them back to back: (bang) they're not that similar.
we've got a couple of the same chords, but they're not in the same positions, and the
motion through the loop feels pretty different.
but if we do the same thing with the major forms: (bang) suddenly the entire picture
comes into focus.
they're almost identical: they both go from I, to V, to a minor chord, and then to IV.
the only difference is which minor chord we use.
the major rotation of the Plagal Cascade is just a slight variation on the most famous
chord progression in popular music, but when we rotate it back into minor, it becomes almost
unrecognizable, taking on a completely new musical identity.
how cool is that?
that said, they're not exactly the same.
one thing I said in last week's video is that part of what makes the Axis Progression work
is that the two possible I chords are a 3rd apart, which makes them both stable chords
in each other's keys. this creates a sort of tonal overlap where the major axis always
has a shade of minor and vice versa, because no matter which key you're hearing it in,
they both sound resolved.
in the Plagal Cascade, though, our I chords are a whole step apart, so whichever one you
hear as the root, the other one becomes dissonant.
I think this helps explain why it's harder to hear the similarities between All Star
and New Divide than, say, Where Is The Love and Africa.
it's still there, just with a little more camouflage.
now, I'm always hesitant to say that I discovered anything.
after all, I'm only human, and I haven't read every theory paper ever written, so it's very
possible someone else found this connection first.
but loop theory is a relatively under-researched area, and I could barely find any scholarship
on the Plagal Cascade in general, let alone this specific connection to the Axis Progression,
so there's a non-zero chance that, by watching this video, you've become one of the first
people in all of human history to be aware of it.
or maybe not.
I mean, probably not, statistically speaking, but as far as I know it's possible, and that's
pretty neat.
so where do we go from here? can we generalize this model even further?
well… maybe.
I do have some more questions.
like, in both loops, the major triads are arranged in a series of plagal cadences.
what would happen if we turned that around, doing authentic cadences, or V-I resolutions,
instead?
like, take this loop: (bang) is that stable?
I mean, I can't find any songs that do it, in either rotation, but in theory it should
be.
I think.
or maybe not: again, the V-I resolution is a lot stronger than IV-I, and that may bias
us too much toward the major interpretation, making the minor one feel incomplete.
so is it stable?
I dunno, try it out.
write some songs with it and let me know how it goes.
or here's another question: what if our two I chords were right next to each other?
like, in both the Axis Progression and the Plagal Cascade, the minor destination and
the major root are on opposite sides of the loop, so we get this see-saw motion between
them with the other chords filling the gaps, but what if, instead, they were back to back
like this? (bang) is that stable? and how about the major rotation?
(bang) again, I'm not sure.
it's a really weird loop, and I couldn't find any songs that used it either, but again,
if you want to try it out I'd love to hear the results.
all in all, I think this connection is fascinating, but more importantly, it's pretty solid evidence
that the model I built for analyzing chord loops is on the right track.
I've said before that music theory isn't a science, and I stand by that, it's absolutely
not, but it's still really cool to be able to form a prediction based on a model and
then find the exact results you predicted out in the real world, being used by actual
musicians.
my model will never be the only way to explain four chord loops, but I think it's a pretty
good one, and I'm not sure I would've ever found this connection without it.
these sorts of videos are only really possible because of my patrons on Patreon: 12tone is
my full-time job, and this isn't something I expect to get a lot of views.
it's a pretty obscure topic that most people don't know or care about, but, well, I care,
and if you've made it this far I hope you do too.
Patreon support helps me make videos like this anyway, covering the things I actually
want to talk about instead of having to chase whatever's going viral right now, so if you're
a fan of the channel and you can spare a couple bucks, I'd really appreciate your support.
there's a link to my Patreon in the description.
that said, I know money's tight for a lot of people right now, so I really want to stress
this: no matter how much you like my work, you don't owe me money for it.
I choose to publish all my stuff for free because I want people to be able to access
it even if they can't afford to pay.
Patreon is completely voluntary, and if you're not financially secure enough to pledge right
now I would honestly rather you didn't, but if you are and you want to, it really helps
keep 12tone freely accessible for everyone else.
plus patrons get to help pick the songs we analyze, and they've chosen a really great
one for next week.
anyway, thanks for watching, and extra special thanks to this video's Featured Patrons, Duck
and Howard Levine.
if you want to help out, and help us pick the next song we analyze too, there's a link
to our Patreon on screen now.
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