So I was analyzing "Yesterday" by The Beatles when I got to the word "Why". How come it has Em7 over the note when the score doesn't feature the note E? It doesn't look like an Em7 chord at all to me.
Quick answer: The chord symbol is wrong.
Want a long answer?
This is what is normally seen in song copies.
This is what The Beatles actually played - according to 'The Beatles - Complete Scores', which is usually reliable.
That's OK. Song copies are frequently only approximate. The usual published version and your version are not quite accurate, but they sound nice. Possibly even nicer than what the boys actually played (now, there's a can of worms!)
The chord naming in all three versions is a bit approximate. A7sus4 - A7 often gets changed to Em7/A - A7. Maybe 'sus' chords are too hard to be put in published song copies? And your version shows a (correctly labeled) chord box for Em7 - but that does not take account of the A note in the upper stave!
I could go on. But the main point is that published versions of pop songs are often sloppy and chord naming is often even sloppier. Your primary source is what was played on the record. Both song copies seem to get it wrong. But if you're GOING to play that copy, believe the notes, not the chord symbols. Chord symbols can't always fully describe the music. That's why we have notation.
(I just dialled up the original recording. Funny how it's now possible the LEAST familiar version of the song :-)
The chord is Em7 and you’re right, the piano part is playing all the notes in an Em7 chord except the E. Paul plays an Em with the E root on the guitar but the cello in the string quartet plays a low note of A at that moment both times. The A dominates the low register because the note is sustained and it seems the piano part is likely based more on the string arrangement than the guitar part. That chord ends up sounding more like a G/A or an A7sus4 than an Em7.
Another interesting thing, Paul plays this song in G on a guitar tuned down a step. You can tell by the low D’s he plays at the ends of the verses. The Em is actually played as an F#m and on some videos you can see he uses his thumb to play the low F# (that sounds as an E).
The Em7 label pertains to (is part of) the guitar chord diagram, not to the score below, and is accurate. The diagram shows a standard open-string Em chord with an alteration to the minor seventh.
The guitar chord diagrams in pop music sheets like this are almost always rubbish. If at all the original pop music recording has any guitar part in it at all those diagrams rarely represent anything remotely similar to what the guitar is actually doing.
Also, even in situations where the chord fits, the name is sometimes wrong in that it doesn't reflect the true function of the chord in the music. For instance, maybe a chord shown as Em7 is functionally a GM6. The chord diagrams, name and all, are just canned symbols from a chord diagram library.
If you're not playing guitar, just ignore that. If you are, ignore it with greater fervor.
The chord names above the staff are not naming the total harmony but the part to be played by the guitar, as indicated by the fretboard diagram. This is an excerpt from a version intended to be playable by piano/keyboard and guitar in parallel. It usually also works as mere piano instrumental (containing the melody voice in the piano chord sequences) or as singing accompanied only by guitar. But the guitar chords/voicings are not fully included in the piano parts, so the chord names will not necessarily coincide with the piano part when it is not duplicating the guitar.
Looking at the original example given, I’d lean towards an A9(sus4) as a more accurate chord. You’ve got the A, the B natural (9th), the D (sus 4), and the G (dom 7). Don’t really need the E, and the C (3rd) is replaced by the suspended 4. The Beatles don’t use the B (above) so the 9th would be out of place in their score - the A7(sus) works.
There's nothing wrong with the notation, if you see it as instructions for players, instead of an analytical description of all of the pitches heard in the song.
Even if you look at this as a transcription of the original recording, it's not far off. (well this is a "remastered" version, but I guess the remastering didn't change the notes that were played)
The part in question is at 0:39.
If you listen to the right side with headphones, you'll hear only the vocal and the guitar, which is clearly playing an E bass note.
If you listen to the left side with headphones, you'll hear only the vocal and the strings, which are clearly playing an A bass note.
Out of these two, the guitar's E is actually the lower pitch. Let's confirm it with the Transcribe! application:
So, what you have in the notation, isn't it quite close to what you should have, if the piano part is mimicing the string section? Did the music copy, song book or something, come with instructions on how to read it?
If you want to be picky about the chosen guitar fingering diagram from a transcription point of view, they could have left out the low B note on the A string.