You are right on the first two points...
- Roman numeral indicates the scale degree
- Upper case means major triad, lower case means minor (also include suffix
o
means diminished triad and +
means augmented)
But the important thing is the scale in question is given by the key signature. And there is a sort of matching and alteration that can happen with the symbols depending on the key signature and the intended chord qualities.
Keep in mind there is a system that simply labels scale degrees with all upper case Roman numerals regardless of chord quality.
Also, you should give key signatures with Roman numerals for clarity.
- a sharp, flat, natural prefixing the Roman numeral means a chromatic alteration from the key signature.
So... in C
major, just III
could mean simple the third scale degree, E
or any triad rooted on E
.
In case-sensitive style iii
is used because the diatonic triad on the third scale degree is minor. If it were given as C: III
the chord would be E
major. (A small aside: that chord could be considered a secondary dominant to chord vi
A
minor. To clearly convey that secondary dominant sense, you would write C:V/vi
. The secondary dominant is sort of the standard harmony analysis way, changing the letter case to alter diatonic from the key signature is more of a jazz way to label chords.) Finally, you could prefix the number with a flat - ♭III
- and that would mean the E
is altered from the C
major key signature to become E♭
. Conventionally this is conceived as "borrowing" from the key signature of C
minor which has three flats A♭, E♭, B♭
, and the diatonic triad in C
minor on the third scale degree is E♭
major. So...
C:♭III
is the chord "borrowed" from C
minor E♭
major
If the music was initially considered to be in C
minor, the key signature already includes an E♭
and so no alteration or prefix is involved:
Cm:III
is the diatonic chord in C
minor E♭
major
Notice the difference in symbols depending on whether you give the key signature before the Roman numeral symbols.