a sharp or flat before numeral mean raise or lower the chord root from its normal diatonic spelling
In the usual Roman numeral analysis we have these conventions:
First we have to give a label for a key like
E: for E major or
Em: for E minor. Then we have these points...
- capital numeral means major triad
- lower case numeral means minor triad
- 'o' after numeral means diminished triad
- '7' means a diatonic seventh above root
- a sharp or flat before numeral mean raise or lower the chord root from its normal diatonic spelling
That last rule is the crux of your question.
E major the diatonic chord of the sixth degree is
C# minor and gets labelled
E minor the diatonic chord of the sixth degree is
C major and gets labelled
E minor is used in
E major the chord root is altered from
C natural. (This is called chord borrowing.) When in
E major that change in the chord root is made explicit in the Roman numeral figure by using the flat to show the change of chord root:
The reason your book's example is confusing is because the key signature on the staff is
E minor, but the analysis key shows
E which is read as
E major (it should be
Em: to mean minor) and then the Roman numeral figures are labeled with flats which makes things seem like the assumed key is
E major. Basically the labeling is a mess and it makes confusing the use of sharps and flats on Roman numeral figures.
As others point out, the book doesn't even label the chords as 7th chords!
The book seems sloppy.
@Tim makes a good point that Roman numeral analysis can be tricky with rock music. The real conundrum to me is the final chord. It's an
E dominant 7th with a
G natural on top. That is a very bluesy sound. It's a very familiar sound, but Roman numerals are a poor way to label it. There is no way to indicate the simultaneous
G natural... and the minor 7th. About the only thing the
I label gets right is a root on
E and a perfect fifth of
B. Tread carefully with harmonic analysis of rock music. You might find a lot of inappropriate labels.