As a proponent of notation, I'll add the following (looking only at the second and third system), referring to each of the circled pieces of notation by the red letter below it. Chords are not just displayed above the music, they're inherently part of the written music.
A is a D major chord, root position. The second D (an octave lower) is part of the same chord.
Between
A and
B is a passing note. It's not part of either chord, but provides a little bit of movement connecting the two chords. In this case, it's an E.
B is an F major chord, also in root position. In this case, you just hold the chord for the entire measure.
C appears to be a much more complicated piece of music. However, it's really all just an F minor chord, also in root position. First you play the chord, then you arpeggiate (roll) the chord as a triplet against the first two beats of the measure. The half note in the second half of the measure is still part of the F minor chord, just a note that wasn't initially played. And the F at the end of the measure is similar to the D in beat three of the first measure I looked at. Part of the chord, but dropping an octave cause it sounds nice.
D is incredibly simple. It's a C major chord, root position, that's just held for two measures. The only interesting part of the measure is that there's a passing tone in the base at the end of the second measure, the D.
E is also just an E major chord, root position. I don't know what it's doing after the first measure since it wasn't included in the scan. But if you're following the score, you're going to hold it through at least the beginning of the next measure. It wouldn't surprise me that it's also a two measure sequence just like
D,
I keep saying "root" position. Basically, a root position chord is one in which the lowest note played is the root of the chord. A C in a C major chord. An F# in an F# dim chord. Etc. A lot of popular music likes root position chords, which is why bass players hate the rest of us.
But the chord doesn't have to stack up with the root at the bottom. For example, a C major chord has a C, and E, and a G in it. If the bass player plays a C, then it's root position. If the bass player plays an E, then it's a first inversion. (You can do this on a piano by playing an E, the G above it, and the C above that. It's still a C major chord, but it has a different feel.) If the bass player plays a G, then it's a second inversion. (Again, do this on a piano by playing a G, the C above it, and the E above that. It's still a C major chord, but the feel is different, again.)
Why bass players? Because generally they play the lowest note. An open E string on a standard bass guitar is the bottom E on a piano keyboard. Very seldom will a pianist use the notes below that E, and other than pipe organs, I don't think any other instrument goes lower. (And if the pianist keeps stealing the bass from the bass player, the bass player can respond with a five or six string bass. At which point the pianist is going to need a Bosendorfer, and the band's budget just got blown away.)
As for how chords are written, that's an interesting question. In popular music, the three versions of the written chord are C, C/E, and C/G. (There's an example on the first line of music.) In classical music it gets more complicated. In most cases rather than starting off by saying it's a C chord, it refers to it by the scale position of the chord in the key of the piece. (And may include the effects of modulation, etc.) If the piece was in the key of C, then the C major chord would be referred to as I. (That's a capital roman numeral 1.) But if the C major chord being looked at was chord D in the scanned music above, it would be referred to as III. (that's a capital roman numeral 3, since the piece is written in A minor and C is a third above A.) Minor chords are lower case roman numerals. There are multiple ways of referring to inversions, which is probably WAY to long to write about here. Also, without my books in front of me, I may get it wrong. (I haven't even started studying figured bass which throws more complications onto the picture.)
I've always wondered about the guitar tab in written popular music. There are multiple ways of playing the same chord on a guitar. But the tab is almost always the base position of the chord. How long does it take a guitar player to learn the fingerings of the chords? I suspect that for the vast majority of guitar players, the tab (which indicates where to hold down each string) is ignored, and they go straight to the symbol, and then play the chord where it sounds best. Seems like a waste of ink. But what do I know.
And after I wrote all this, I actually looked at the music, and realized that I know the song. (I saw them live on Long Island when they went on "tour" for the album.) As is usual for them, the written music tends to not display what makes their music so great.
