In music roman numerals are used to index the diatonic chords associated with a scale. The way the chords are indexed is based on the root of the chord.
Given a major scale we would denote the different diatonic triads like this:
| Numeral | Root | Anchor Inteval Collection | Relative Interval Collection |
|---|---|---|---|
| I | 0 | 0 4 7 11 | 0 4 7 11 (Major 7th) |
| ii | 2 | 2 5 9 0 | 0 3 7 10 (Minor 7th) |
| iii |
4 | 4 7 11 2 | 0 3 7 10 (Minor 7th) |
| VI | 5 |
5 9 0 4 | 0 4 7 11 (Major 7th) |
| V |
7 | 7 11 2 5 | 0 4 7 10 (Dominant 7th) |
| iv | 9 | 9 0 4 7 | 0 3 7 10 (Minor 7th) |
| iiv | 11 | 11 2 5 9 | 0 3 6 10 (Half Diminished 7th) |
Note: We write lowercase roman numerals for minor chords, so instead of writing IIV we write iiv.
This process may be repeated for any other scale which forms triads, like the natural minor
| Numeral | Root | Anchor Inteval Collection | Relative Interval Collection |
|---|---|---|---|
| i | 0 | 0 3 7 10 | 0 3 7 10 (Minor 7th) |
| ii | 2 | 2 5 8 0 | 0 3 6 10 (Half Diminished 7th) |
| III |
3 | 3 7 10 2 | 0 4 7 11 (Major 7th) |
| vi | 5 |
5 8 0 3 | 0 3 7 10 (Minor 7th) |
| v |
7 | 7 10 2 5 | 0 3 7 10 (Minor 7th) |
| IV | 8 |
8 0 3 7 | 0 4 7 11 (Major 7th) |
| IIV | 11 | 10 2 5 8 | 0 4 7 10 (Dominant 7th) |
Thus when we talk about roman numerals we usually have a scale in mind and each roman numeral references a diatonic traid build on the root of the scale degree.