The most important objective of any pop song is to deliver the same high with each listen. The quality of that high is what defines the artist. Quality is subjective, of course, but it's ruthlessly so. You may or may not enjoy songs written by Smokey Robinson, Joni Mitchell, Billy Joel, or Linda Perry, but it's at least possible to understand how their songs have managed to earn repeated listens by millions of people.
You may not like The Doobie Brothers, or Michael McDonald for that matter (or Kenny Loggins, for that matter), but I'm here to tell you that What a Fool Believes is one of the greatest pop songs of all time.
The song is amazing on so many levels, but I'm limiting this discussion to the scope of songwriting. Let's consider the final product: track 2 from The Doobie Brother's 1978 LP, “Minute by Minute”. The track itself was co-written by Loggins and McDonald, and in fact Loggins released an earlier version of the song that same year. We'll stick to the Doobie Brothers version. It's considerably better (sorry Kenny), and I believe it fully realizes the potential of the song.
First, a quick primer on how I'll be notating chords. To keep things simple, I'll be using this notation style:
I, ii, iii, IV, V, vi◦, vii
Uppercase roman numerals signify a major chord; lower case, a minor chord. The above example is for a major key (the first chord is therefore major), and those seven chords are just the usual set — other chords are possible. More info on Roman Numeral Analysis, here. When I refer to roman numeral I, I'm referring to the key that we're in (in this case, C♯ major; oh, and the “♯” symbol means “sharp“, or one slight step in pitch higher). It's also called the “Tonic”. Thus, if I mention a V chord, I'm referring to what's called the “Dominant” chord, which in the context of pop music, usually acts as a signal that we're about to return to the I chord. Your brain understands this. It hears a G♯ major while in the key of C♯ major and it begins to need that C♯ chord once again (it's almost a form of cruel and unusual punishment to deny the listener of this kind of resolution). There are other chords, of course, and I will explain more as we go. Just understand that your brain expects certain chords to come after certain other chords.
Now, in terms of harmony, the verse section of Fool moves very fluidly. The first four changes are:
IV -> I/iii -> ii -> I
So, you can see what's happening here: we're stepping down like “4-3-2-1”. This kind of passage is found in a majority of pop songs, but the second chord change is a nice choice. A lot of songwriters may use an actual iii chord, but it's a bit more harmonious to use a I chord with the root key of the iii chord at the bottom (as is happening here). The brain doesn't get the V to I resolution it loves, but instead it's gently walked down from the IV chord, or “Subdominant”. You should feel a little bit at peace now. You've gained some peace for a brief moment.
But then it's over, because the song walks you right back up:
ii -> I/iii -> vi -> ♯v+
First, the walk back up is quicker than the stepping down in the previous passage, by half. That's so cool! It's so playful and whimsical. The passage starts walking back up in familiar territory (II and I/iii chords) but then jumps up to the vi chord, where we have not yet been before. In the context of western pop music, the six chord has a magical property in any key: it's the serious version of the “happy” key, harmonically speaking. It's the same person, but it's their pessimistic self. The song briefly lands here but then quickly descends down a half step into an augmented chord, which is the equivalent of saying, “I'm serious! Just kidding!”. Because then we start the walk-down all over again, as in, “see, I'm silly again”.
Each verse, harmonically, contains two walk-down, walk-back-up blocks. Since harmony dominates the verse structure, the melody just follows along, as you'd want it to. The highest note he sings is an A♯5, of which A♯ is the root of the sixth chord we previously learned about. It's that pessimistic tone we briefly visited. So once Michael McDonald starts up, we've got four verse-lines before we move onto what I'll call Bridge 1.
There's nothing fancy about Bridge 1 as a standalone part of the song, but it's a perfect bridge in that it breaks the pacing of the preceding verses. Harmonically, it's pretty simple:
vi -> vi -> V -> V
But we left off in the melody of the last verse on the A♯, sounding all serious. And so the beginning of Bridge 1 melody just starts here and reaches higher. Love that. It's a hopelessly optimistic, whimsical move while oscillating back and forth between the confident, pessimistic vi chord and the dominant V. Remember that the V wants to resolve to the I, but we don't let it. We keep coming back to the vii chord while the melody repeats its struggling climb for hope, which we find in Bridge 2…
Bridge 2 returns harmonic changes back to the dominant structure, but yet it adds a new and yet differently-syncopated pacing. This bridge only half-repeats itself:
ii -> V -> I - > ♯vi -> ii -> V
The harmonic framework underneath finally gives the brain what it's been wanting: classic resolution. ii / V / I is songwriting 101, but then it's nicely altered by dropping a ♯vi chord at the end before it returns to ii / V/ I.
The transition between the ♯vi chord and the ii chord is a major third jump. The transition from the ii chord to the V is a fourth. And the transition from the V to the I chord is, well, a fifth. So, here the harmony has two different geometries occurring simultaneously: the outlining of two-five-one, and the underlining of three-four-five. Lines are converging; tension is building.
Over this, McDonald sings “As he rises to her apology” on a melody that itself rises and falls. That's clever. But it's more clever than it looks: he's reaching, climbing upwards to the very top, a high C♯ (C♯6), the root note. This is now the highest we've been. [insert Doobie Brothers joke here]. Will we ever get that high again?
So now we land on yet another segue, the brief but necessary Bridge 3. Here, we return to the pacing of the first bridge, and almost the same harmony. However, you'd be expecting that, so let's not do that. Instead we'll just duck under the the V chord like this:
vi -> vi -> ♯IVø7 - ♯IVø7
A diminished chord is a freak chord. It's a perfect molecular structure made out of minor thirds that can endlessly repeat. If the flatted V chord here were a real diminished chord, it would have less in common with the vi chord, and that wouldn't make sense. Keeping an F note on top allows the chord change to occur while keeping the right amount tension. So instead we use a “diminished 7” chord. That's two minor-third intervals plus a major third jump up top. We're really building towards something big now.
Bridge 1 was perfect. Bridge 2 was necessary. Bridge 3 is genius, and here's why.
Remember when I wrote earlier that the brain needs the V chord to resolve to the I? Well, the brain will take any kind of resolution, and if you're close enough to a V chord (like our friend, the ♯IVø7 chord), the brain still wants the I chord next. It'll make do with a flatted V chord or even a ♯vii chord (which was the harmonic point of the climax of the Barbara Streisand / Neil Diamond song “You Don't Bring Me Flowers”, so there you go). And in fact, the more tension the better. And now we most certainly have tension.
Finally, we reach the Chorus and thus resolve to the I chord right? Nope. We change keys from C♯ to A (stick with me, music theory nerds). There's a new I chord in town, and the brain technically gets what it was asking for. But the song cheated by switching keys on us. We now have about two seconds to appreciate our new harmonic landscape before we realize we've been tricked, yet again.
After we finish hanging out in A major, we move to a B major chord. This would technically be a II chord, not a ii chord. It's major when our brain is expecting minor.
It's here where the song hooks you, and delivers the high.
See, they never went to the key of A major. They switched from C♯ major to E major but used the A major chord as as a harmonic pivot point. We actually get our V -> I change, but we have to jump through a harmonic portal to get there. Essentially, for two whole chord changes our brains don't know what's going to happen next. That's pretty awesome. That's why this song works so well.
While our ears are busy figuring out which way the earth is moving under our feet, the melody achieves its original goal of sticking the landing on that high C♯(6). But we're not in the original, key of C♯ major anymore, we're in E major. The melody couldn't get what it needed in C♯ major, so it took what it needed in E major.
It gets better, because the chorus melody repeats itself, and the harmony just subtly changes, yet again (not the key signature though, just the chords in the key of E major). The first harmonic movement is as follows:
IV -> IV -> V -> V -> I -> I -> vi -> vi
…while the second harmonic movement of the chorus is (with the same melody over the top):
ii -> ii -> V -> V -> I -> I -> vi -> vi
I never, ever realized that until I studied it closely. It's subtle but it's necessary. Moving to that A chord earlier was so awesome that you don't want to remind the listeners how we got here in the first place. It's the object of misdirection in the card trick. Don't give it away, because we're about to repeat everything all over again…
Now, I highly doubt Loggins and McDonald thought the song through like this as it was being written. But to some extent, they must have. Any good songwriting session includes some amount of critical thinking, or else you end up with fragments of pieces of songs laying around in your head. That's one of the reasons songwriting is so much fun. It's a game of logic that must require emotion.
Hopefully, this overly-thorough analysis I've provided shows only what skilled songwriters they are. They did much of this on feeling, but were well-trained enough to actually channel those feelings into a very complicated, yet unbelievably catchy pop song.