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. you can also join our mailing list to find
out about new episodes, like, share, comment, subscribe, and above all, keep on rockin'.
