April 5, 2016

#10 Circle of Fifths

by Surprisingly Awesome

What one idea from music theory can tell us about culture, biology, math, physics and The Simpsons.

The Facts

Surprisingly Awesome’s theme music is “How We Do” by Nicholas Britell.

Our ad music is by Build Buildings.

This episode was edited by Alex Blumberg and Annie-Rose Strasser. It was produced by Kalila Holt and Rachel Ward. It was mixed by Matthew Boll.

Eric Mennel and Robyn Wholey provided production assistance. Special thanks to Emma Jacobs.

Where to Listen


RACHEL WARD: Adam, where have you been?

ADAM MCKAY: I joined the Air Force. And it did not go well. Terrible inner ear issues, afraid of heights… No, I did not join the Air Force. I actually was promoting The Big Short. But I am happy to be back at Surprisingly Awesome with you Rachel, Adam Davidson, our whole amazing team.

RACHEL: I feel like I should give you the honors, you should introduce our guest.

ADAM: Our guest actually is from The Big Short, he’s our composer, Nicholas Britell. Was a concert pianist, degree in psychology from Harvard, who’s also done music for 12 Years a Slave, Gimme the Loot, and… he wrote this.

[Music: Surprisingly Awesome theme song]

RACHEL: From Gimlet Media, this is Surprisingly Awesome. I'm Rachel Ward.

ADAM: And I am Adam McKay and joining us is Nick Britell.

NICK BRITELL: I am incredibly honored to be here.

RACHEL: And Nick, we brought you here to help us understand this very specific idea from music theory. You proposed this as the topic of our episode because this concept is everywhere. It’s this tool that composers are always using because it evokes a very specific set of emotions in us. And it can help us understand what exactly it is that you do for a living. It’s called the circle of fifths.

NICK: The circle of fifths for me is this incredibly, it's a very beautiful chord progression and hopefully by the end of the episode, it will be clear what it is, how it feels when you hear it, and also I think it's a cool lens through which we can understand a lot of issues around music theory, starting with things like pitch and intervals and chords, and leading all the way through kind of how composers and songwriters write music. So that's why the circle of fifths I think is pretty amazing.

ADAM: I actually had a horrible musical education when I was in school. All I remember from my musical education was like “tah tah ti ti tah rest rest,” and then like all college kids I learned like five chords on a guitar and aggravated future girlfriends by playing horribly on it so I come to this world having been betrayed by it, but I am open-minded.

NICK: Do you want to hear the circle of fifths?

RACHEL: I think so we know what we're going for, let's hear the circle of fifths

NICK: Okay. Here's a circle of fifths.

[Musical clip: “Fly Me to the Moon”]
RACHEL: Okay, and it’s also here:

[Musical clip: “You Never Give Me Your Money”]

RACHEL: And apparently it is also here.

[Musical clip: “Love You Like a Love Song”]


ADAM: Wow.

RACHEL: So, I understand that we heard a circle of fifths in there.

NICK: Yes. Yes.

RACHEL: I'm totally incapable of identifying it.

NICK: That’s okay, that’s okay.

RACHEL: So, in order to understand this concept we're going to-- I think we have to start at a very, very basic level.

NICK: For me, I think the most basic element to begin with is pitch. So I think by starting with an understanding of like what a note actually is, we will sort of build up to what the idea of chords are and eventually to what chord progressions are.

ADAM: Could I confess something which is very embarrassing? Although I love music, all I know about pitch, if I'm really being honest, is Randy Jackson on American Idol tells people they're pitchy all the time.

RACHEL: Pitchy, dog. I believe “dog” is also a music theory concept.

ADAM: That was a little pitchy dog, that's all I know. That's pathetic. I'm embar- I'm 47.

NICK: Basically a pitch is actually what your brain perceives when it hears a repeated vibration that's regular in nature. So I'll unpack that a little bit. There are a lot of things in nature that repeat, but repeat kind of slowly, so let's imagine a propeller of an airplane for a second.

RACHEL: A natural phenomenon—

NICK: A natural phenomenon like a propeller on an airplane. So when you imagine a propeller, when it first starts up, it's repeating not very quickly.

[Soundbite of a propeller starting up]

NICK: So it sounds kind of like this mechanical whooshing sound. But what's interesting, and I think everyone will recognize this happening, when you hear a propeller start spinning very quickly, as a plane might be starting to take off… You ever notice that the sound of that starts changing, and you starting hearing almost what sounds like a droney note?

[Soundbite of a propeller changing to a droning sound]

NICK: So you see there starts to be like a drone note in there that you hear that doesn't sound mechanical—it actually starts to sound like a sort of weird note. And what's happening basically is that once something starts repeating at a certain level of speed, your ear and your brain start perceiving this as a note.

RACHEL: That if rhythm repeats in rapid enough succession, eventually it becomes a note.

NICK: The threshold of where we start hearing pitch is really around 20 hertz. Which, hertz is a unit in science that has to do with frequency, so how many times something happens, how many cycles something happens per second. So twenty hertz is twenty cycles, twenty somethings per second. And what's interesting too is actually that the brain may have something funny about that area of frequency. Because for example, it's approximately that same area where frames in film start looking like fluid motion as well.

ADAM: So that's fascinating, so that twenty vibrations per second threshold is really interesting. Ao that seems to be where our mind orders things and looks for commonalities and structure.

RACHEL: That's the point where our brains sort of just get tired and we’re like blahhh, I don’t know, music.

NICK: Exactly! Yeah, exactly! So your brain just summarizes a lot, it's just like so much information your brain is like actually that's a sound now.

RACHEL: So hertz is a measure of how many times per second something vibrates. And when we’re hearing pitch, our brains are processing those vibrations—they’re converting them into a note. And what that note is depends on how many vibrations we’re hearing.

NICK: There’s thousands of all these different frequencies, there’s all these different ways of making these sounds. So one of the interesting things is different cultures have different frequencies that they've chosen that to some extent sort of matter to them for their music. And in Western music we have certain frequencies, there's these conventions we've agreed to, and we say okay, this is that frequency. The most famous one is A, which is defined actually as 440 Hz, so 440 vibrations cycles a second, this is A. So we choose this frequency and we say hey, 440 Hz, that pitch is A, which actually I can play right here. So A is this:

[Nick plays an A note]

NICK: That's A. The air molecules here when I hit this are vibrating at 440 times a second. So that’s what you hear.

RACHEL: Right, so A is 440 vibrations per second. What if you've got like 441?

NICK: Yep, totally, totally. So that would be, you know, there's a certain range around notes where the brain basically feels it's still the A, and that would be a little bit what in music we call sharp. So things that are a little bit higher than a set frequency, we say they're a little sharp, and things that are under a frequency, we call them a little flat.

RACHEL: In other words, pitchy, dog?

ADAM: So what, how to octaves fit into all of this? So if you're at 440 vibrations per second with A, like what happens when you jump up an octave, what's going on?

NICK: Exactly, so basically when you double a frequency, it's what we would call an octave.

ADAM: Oh okay, so it's that simple.

NICK: So basically A is 440, when you double the frequency of that and you say okay, I just want to double that frequency, I want to hear 880, you hear that.

RACHEL: So just to be clear, pretty much every human, when they hear a 440 or an 880, it’s going to sound like the same note. But what they call it -- and what they consider a “scale” -- those things will vary across cultures.

NICK: Exactly.

ADAM: Okay, so we understand pitch. We understand vibrations. So now how are we bending towards this magical circle of fifths?

RACHEL: We're only playing one thing at a time.

NICK: Exactly.

RACHEL: Which is not how most music sounds.

NICK: Most music doesn’t just do one at a time.

RACHEL: Alright, so the second note.

NICK: The second note. So we're going to start with the most basic one we've already talked about to keep it simple. What if we play the A and then we play the other A one octave up at the same time? And Adam, you already said it, that's an octave. So we got an octave. So we're already playing what's called an interval, two notes at once. That's an octave. It sounds really consonant, really stable.

RACHEL: And an interval can be any two notes at once?

NICK: Any two notes. I could play…

[Soundbite of Nick playing a series of notes]

NICK: All of these things are intervals, and each interval is related… It's just the ratio of these frequencies. So this one we know is 2 to 1. So now what if we chose another…

RACHEL: Wait, back it up—that's 2 to 1, so what you played is the octave and it's 2 to 1 because … ?

NICK: Because the frequency of this one is 440 Hz. And the frequency of this one is 880 Hz. So if you take 880 and divide by 440, that's two. It's doubled.

RACHEL: Okay. I feel comfortable with that amount of math.

NICK: That's as much as we will need. It’s just doubled. So, and let's keep it simple here. What if—I'm just going to throw a number out there—what if I said I wanted to increase the ratio here, I wanted to take this ratio here and I want to increase the frequency by 50 percent. That's all I want to do, I just want to say, what does the note sound like if I increase it 50 percent. So that's E. So that's the ratio of A to E, is 3 to 2, and that's how you define it. It's basically 50 percent more frequency, is a fifth we call it. And the name in music theory is, you call it a perfect fifth.

RACHEL: Okay, so that’s a lot of math for me to have to manage in this setting but it sounds sort of like what you’re saying is, the relationships between notes in an interval can be summarized mathematically? And our brains tend to like it when that math is pretty simple?

NICK: In Western music we’ve chosen very simple relationships between frequencies, and the fifth is this one.

RACHEL: So that's A…

NICK: To E. Yes

RACHEL: And that's an interval. It's two notes.

NICK: Two notes, it’s an interval. Certain types of intervals tend to feel certain degrees of stable or unstable and this is to some extent due to culture. maybe the numbers are just easy for our brain to process, this sort of relationship. So if I do this for a second...


NICK: That feels a little bit, little different right?

RACHEL: I mean my response to that was like that got darker

NICK: It got a little darker, it got a little different.

ADAM: The fifth is like a reveal in a movie. Like the... turns out the wife is alive and she steps in the door with a fifth, the second one feels like she's not alive and the guy is going to commit suicide.

NICK: That's interesting you say that because the second one, this is a very famous interval called the tritone. And uh, in fact, in the Middle Ages, it was referred to as “diabolis in musica,” which is “the devil in music.” This ratio. And was forbidden, and it was actually forbidden to be used in certain contexts. And it wasn't until really until the 1700s that people started using it.
And the funny thing with the tritone is it's actually not… on its own it sounds less, potentially less stable than the fifth, but when you use it in the context of other types of music, it's great and actually can be used in so many different ways. So for example, just to show where the tritone is very clear: the beginning of this theme song has the tritone almost right away.

[Musical clip: The Simpsons theme]

NICK: That's a tritone. [sings: “The Simpsons…”] That's a tritone.

RACHEL: And in the 1600s, you would have gone to jail forever.

NICK: You would be burned at the stake for that for that, for the tritone. So even in The Simpsons that you just heard, it starts with the tritone but right away, goes to a fifth. So it's…

[Soundbite of Nick playing “The Simpsons”]

NICK: So you have that right away, and funny enough, the tritone there is almost like the step to getting to the perfect interval which is the resolution of that, let's call it dissonance. Which is similar in like Bernstein’s Maria. You know, that:

[Soundbite of Nick playing “Maria”]

NICK: So there you go you have the tritone, and then it goes to a fifth right away.

[Musical clip: “Maria”]

ADAM: Nick, what would happen if you did a tritone at the beginning of our national anthem? Like if you added a tritone that resolved with a fifth. What would it sound like?

NICK: So if we do it where it actually, if we start out it would be something like this...

[Soundbite of Nick playing a tritone in the national anthem]

NICK: Or it would be this.

[Soundbite of Nick playing a tritone in the national anthem]

NICK: That would be interesting.

ADAM: The Civil War would have happened 40 years earlier.

RACHEL: You’ve told us there are a bunch of these intervals, these sequences of notes, and they’ve got all of these funny names. But the one we’re really focusing on is the “perfect fifth,” a building block of the “circle of fifths.” And what makes a fifth a fifth, is basically the relationship between the notes in the interval. Basically, in the scale, if we’re thinking about a piano—they’re just five keys away from each other. 1, 2, 3, 4, 5, perfect fifth.

NICK: Mmhmm. I like to think in a way, if you think of like composing as sort of this, you know, like a chef mixing all these different intervals and chords and rhythms and pitches together, different intervals to me have different almost, like, flavors, you know?

ADAM: So we're getting intervals. We're getting two notes at a time. So now we’re, it feels like we're on the threshold of chords right?

NICK: We are right on the threshold of chords. We are exactly there.

ADAM: Rachel, there's no way I'm ready for this. Can we take a break? I'm going to go take a shower, have a cup of tea, take a walk around the neighborhood and then we do this.

RACHEL: I think that sounds fair.
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ADAM: And I'm back. I've just taken a shower, I've had some chamomile tea, I read a little bit of Kahlil Gibran’s the Prophet, I feel very centered. Let's do it. Let's go into chords.

RACHEL: Alright. From Gimlet Media, this is Surprisingly Awesome. I'm Rachel Ward

ADAM: And I am Adam McKay. And we're joined by Nicholas Britell and we're talking about the circle of fifths.

RACHEL: And so, we have been made to understand that a note and pitch and a frequency are all pretty much the same thing. So we're going to use all those words pretty interchangeably.

NICK: Absolutely.

RACHEL: And another idea that's on the table here is the idea of an interval, which is two notes played at the same time

NICK: Exactly.

RACHEL: And a type of interval is a fifth.

NICK: A fifth is a type of an interval, exactly. So it's when you go from one note and you go up five notes. So if you're on the first note here, you could say we define the first note as 1, the second note is 2, going up the scale 3, 4, 5, so it's up a fifth. That's how we would count it in music theory.

RACHEL: Okay. Where do we go from here?

NICK: Okay, so we have these different types of intervals and an interval, again, we're saying is basically two notes at once. So chords are when we add more notes. So it could be three or more notes, you get chords. Before that when you're dealing with intervals, you're just talking about, the sort of flavor of intervals isn't quite as complex, let's say, as the flavors that you can get when you have full chords. You know, you can really cook all this crazy stuff once you have these three-note chords. Um, and just to make it very, very clear when we talk about chords, we also talk about the chord based on that first note.

RACHEL: So that means there’s more than one A chord, right?

NICK: So an A chord is basically any notes you stack on top of an A. So here, that's A major. A minor. You could have A dominant 7th.

ADAM: That was my nickname when I played basketball in college. I was A Dominant 7th.

NICK: I heard that.

RACHEL: Can you compose us some walk on music for him real quick using his nickname?

[Soundbite of Nick playing fake basketball music]

ADAM: Ladies and gentlemen, from the University of Kentucky, at power forward: Adam A Dominant 7th McKay! Weirdest basketball nickname ever. So you're saying A dominant 7th, you're saying A minor, you're saying A major… Is it always the note on the left of the chord, is the one defining it?

NICK: Absolutely. The lowest note, generally, is what we would call the bass note on the chord. People have different terms for it. People call it the bass note, people call it the root. People call it the fundamental. All these different terminologies, but basically when you're thinking about chords and harmony, the simplest and most fundamental way of thinking about it is that it's the bass note that sort of determines a lot of western harmony. And that's why when you think about in a band, the bassist is such a crucial thing because the bass is actually going to help you know what chord you're on at any given time.

RACHEL: It's almost more BASE than BASS.

NICK: That's a great way to think about it actually.

RACHEL: As in like a home plate.

NICK: It's the base, like the basis, the basic.

ADAM: Alright, so we're in the realm of chords here. I feel like I have a vague caveman like knowledge of chords now.

NICK: Basically chord progressions are just when you play two or more chords in a row, you get a chord progression, it’s just like this sort of parade of chords. So for example, there are these very famous and very often used chord progressions in Western music. We were talking about 5 1, like the perfect fifth, you know, going from a 5 to 1? If you build the chords on top of those notes, you then get that thing called the authentic cadence, the 5 1 progression which is this. So basically, here's 5 and here's 1. So you hear that sound… Very common sound. It’s feels very much like you’re, like almost at the ending of something, you're like, and we are done. You know?

[Musical clip: Beethoven’s 5th Symphony]

NICK: And then another one actually, here's one that, well, I'll play this and you tell me what you think. So we're very used to this right? 5-1. What if I go…

[Nick plays a deceptive cadence]


NICK: So that's called deceptive, that’s called deceptive.

ADAM: I like that.

RACHEL: That's a deceptive cadence.

NICK: Exactly, that's a deceptive cadence, because your brain is like, “Oh, I'm going here.” But actually we're like, “No, we're going there.”

RACHEL: Okay, so, now we understand that this a chord progression, it’s just one chord after another. So this feels like now we are poised to understand the circle of fifths, yes?

NICK: Exactly.

ADAM: So we have arrived. We have arrived at the circle of fifths. I feel like I'm in 7th grade and I'm playing Dungeons and Dragons again, and we've just gone through a great adventure—a module as they used to call them—and finally we have arrived at the stony gates of the circle of fifths. Nick Britell, as our dungeonmaster, please lead us into this magical realm.

NICK: So exactly, so we're simplifying this a little bit, but essentially a circle of fifths is a very common type of chord progression. Let's imagine instead of just these two note chord progressions, like going from the 5 to the 1, where the bass note goes from the fifth note of the scale to the first note of the scale, what if actually we keep going? And we play more chords after that? And what if every chord that we played was just this sequence, related by moving the bass note a fifth?


NICK: Okay.

RACHEL: So this, you're going to play something that's basically just adding five.

NICK: I'm basically moving the bass note by a fifth each time. So if you take the bass note, we start on C and I go here, so you'll hear these sounds, so this is the bass going down a fifth, you see these things can move by fifths? Or if I go up, I go up, I go—see, those are just fifths.

RACHEL: And I'm actually in the room with Nick playing the keyboard and I can see that on the keyboard it’s just counting. Just five keys down the row.

NICK: Exactly. We're just moving these things by a fifth, right? So if I do that, and then I just put chords, just build basic chords on top of each one of those, you get this sound.

[Soundbite of Nick playing a circle of fifths]

NICK: And you see, so you get this thing called a chord progression. And you can do it in different types of tonalities. That’s the major circle of fifths, you could do a minor one.

[Soundbite of Nick playing a minor circle of fifths]

RACHEL: Ohh okay. So it’s like, more complicated. So we had that Beethoven-y cadence, that’s sort of like and it’s end of something. And the deceptive cadence, the one that’s like a fakeout. And then this one is just, there’s a lot more to it, it’s not just ONE chord to ANOTHER. It’s one, after another, after another. A series of chords that follows a pattern.

NICK: So this one's interesting because basically the bass notes when you do the circle of fifths, you hit every basic chord of the scale in the process of going through it. So in a cool way it's this sort of summary of the chords of a scale. And you know, to use that number terminology we were using where we start on like 1…

[Soundbite of Nick playing a circle of fifths]

NICK: And you're back at 1. And that's the reason it's cool, because it's this weird identity of the scale, and it has this type of sound that because you're sort of coming back to the 1at the end but you're going through this interesting journey of the chords, I think different people feel differently about that progression but I tend to almost have this nostalgic, sort of wistful feeling. So here's a circle of fifths.

[Soundbite of Nick playing a circle of fifths]

ADAM: It's funny it has… It a little bit feels like graduating 6th grade. Yet it's got a little bit of grooviness to it.

NICK: Exactly.

ADAM: It's got a little bit of life to it, so it is, I sort of have a similar feeling of like nostalgia, yet it's dynamic at the same time, like a dynamic nostalgia, is almost what it feels like. Let me be a real like a tone-deaf non-musical person: how is that in “Fly Me to the Moon?” I still can't quite hear it.

NICK: So here's the thing, this is where it's cool. So in “Fly Me to the Moon,” it's actually doing that exact thing. “Fly Me to the Moon” is in A minor, and when you hear the melody so the melody is…

[Soundbite of Nick playing “Fly Me to the Moon”]

NICK: Right? So if you look at our bass notes, it's exactly doing the circle. Watch, so…

[Soundbite of Nick playing “Fly Me to the Moon”]

RACHEL: Yeah, so I’m watching him play this… and I can see that his left hand, the hand playing the bassline, is sort of just climbing up and down the keyboard and it’s making this pattern, and then it repeats.

NICK: Absolutely. So basically the left hand is just our circle of fifths and so that sound…

[Soundbite of Nick playing “Fly Me to the Moon”]

ADAM: Wow.

NICK: If you just look at the bass note you see the whole thing.

RACHEL: Can you play us another example. I think—you've actually prepared something for us that shows us how truly similar lots of music is.

NICK: Yes, yes! So another very famous piece that happens to use the circle of fifths is the song “I Will Survive.” So here's a quick example of that.

[Musical clip: “I Will Survive”]

NICK: So that is the circle of fifths basically, where it's the same—and actually it's even in the same key as the “Fly Me to the Moon” example! Where it's…

[Soundbite of Nick playing “I Will Survive”]

NICK: See, the left hand is just doing the same exact thing.

RACHEL: So again it's the bass...

NICK: The bass is driving this, and you're just building chords on top of that progression.

RACHEL: Using that progression.

NICK: So, this was something that actually I discovered over the weekend: If you take the “Fly Me to the Moon” audio file and you mash it up with “I Will Survive,” the bizarre thing is they actually fit on top of each other perfectly. Which is kind of crazy and shows that they're really using the same harmonies. And this, and this is something that people do in mashup culture, this is why a lot of this stuff exists, so I'll play this example and you'll see they literally are the same.

[Musical clip: “I Will Survive” and “Fly Me to the Moon”]

NICK: And then here's a piece by Mozart that does the same thing.

[Musical clip: Mozart’s “Piano Concerto No. 17”]

NICK: See? They're all the same!

RACHEL: It's incredible. It's totally incredible.

ADAM: That's cool. That's really cool.

RACHEL: DJs are really just scammers, they're just exploiting a fundamental component of music theory. When you're composing, do you sit down and do you say to yourself like ah, I think this is a moment where I'd like deploy a fifth? Like do you actually have that internal conversation?

NICK: Yeah, absolutely. It depends. Especially where you're writing film music where you're really trying to think about things that are happening dramatically in a film and you're trying to imagine the way that your music can emotionally relate to those things, absolutely there's this sort of there's a toolkit and vocabulary of different types of chords and different things, and you have everything from… These different types of chords feel like different things, so minor chords have their sort of feel and augmented chords have this sort of feel and major chords have that sort of feel… You know, so everything has its own feeling and composing is that fun experimentation and search for different types of emotional journeys.

RACHEL: And the circle of fifths is a tool in your toolkit as a composer.

NICK: Sure, I love the circle of fifths. And in fact, uh, as we realized recently, there is a partial circle of fifths in the Surprisingly Awesome theme music!

[Music: Surprisingly Awesome theme song]

NICK: So basically, I do a little circle of fifths sequence inside, and that gives it that same kind of feeling of you’re cycling through these different things but then coming home in the end.

ADAM: That's really cool, man. Wow, once again, whenever we do this show I always feel like, why didn't someone tell me this in 3rd grade?

RACHEL: Um, this has been amazing. My mind is officially blown. I'm going to be looking for the circle of fifths everywhere. I'm going to become a circle of fifths detective.

NICK: Amazing.

RACHEL: Surprisingly Awesome’s theme song is obviously by Nicholas Britell. Our ad music is by Build Buildings. We were edited this week by Alex Blumberg and Annie-Rose Strasser. We were produced by me, Rachel Ward, and Kalila Holt. Matthew Boll mixed the show. Robyn Wholey and Eric Mennel provided production assistance. Special thanks to Emma Jacobs.

ADAM: And a huge thanks to Nick Britell. If you want to hear more from him, the soundtrack he did for The Big Short is on iTunes, and it’s incredible.

RW: And we’ve got something new that you might really like. Every week we have to leave cool and weird facts on the cutting room floor, and we find it very wasteful. So now we’re doing a newsletter! Every episode we’re gonna send out more stuff. So if you want in on that, head to Gimlet Media dot com slash awesome, and look for the signup box. It’s down on the lower right hand side of the screen. Gimletmedia.com/awesome

ADAM: If you’re enjoying Surprisingly Awesome, you should rate and review it on iTunes. That’s the number one way you can help more people discover the show.

RACHEL: And you can tweet at us @surprisingshow, email us at surprisinglyawesome@gimletprod.staging.wpengine.com. We’re also on Facebook. Our website is gimletprod.staging.wpengine.com/awesome. And our Tumblr is True Shark Attack Stories dot tumblr dot com.

ADAM: Surprisingly Awesome is a production of Gimlet Media.

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ADAM: Thanks to our sponsor Squarespace, the easiest way to create a beautiful website, portfolio, or online store. When you decide to sign up for Squarespace, make sure to use the offer code AWESOME to get 10-percent off your first purchase, and to show your support for our show. Squarespace … build it beautiful.

ADAM: Thanks to our sponsor Ford Motor Company where Ford engineers bring new and innovative ideas to life every day. Go to Ford.com/awesome to learn more.

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NICK: And we are done.