When analyzing music, each diatonic triad is identified by a Roman numeral.
Four different types of roman numerals exist - one for each triad type.
Let's apply roman numerals to the C major scale.
Since the first triad is major, its roman numeral is upper-case.
The second and third triads are minor; therefore, their numerals are lower-case.
The fourth and fifth triads are major; therefore, their numerals are upper-case.
The sixth triad is minor, making its numeral lower-case.
Since the seventh triad is diminished, its roman numeral is lower-case and a little circle is added.
Finally, the last triad is a repeat of the first.
Next, we will apply roman numerals to the C natural minor scale.
Since the first triad is minor, its roman numeral is lower case.
The second triad is diminished; thus, we will use a lower-case numeral with the little circle.
Since the third triad is major, its numeral is upper-case.
The fourth and fifth triads are minor; therefore, their numerals are lower-case.
The sixth and seventh triads are major; therefore, their numerals are upper-case.
Again, the last triad is a repeat of the first.
Finally, we will apply roman numerals to the C harmonic minor scale.
Since the third triad is now augmented, its roman numeral is upper-case with an added plus sign.
The fifth triad is now major - making its numeral upper-case.
The seventh triad is now diminished - making its numeral lower-case with the little circle.
The roman numeral system can also be used to indicate inversions.
First inversion is represented by a small 6 after the roman numeral. This is due to the root being a generic sixth above the bass note.
Second inversion is represented with both a small 6 and 4. This is due to the root and third being a generic sixth and fourth above the bass note.
The fifth triad's numeral is also lower-case.
