Roman Numeral Analysis

Roman numeral analysis is a way of naming the notes and chords of a scale by their position instead of their letter. Count to seven in Roman numerals, I, II, III, IV, V, VI and VII, and you have the whole system.

The point is that the numbers work in every key. In C major, I is C and II is D. In D major, I is D and II is E. The letters change; the numerals do not, which is why theory books and teachers talk in numerals. One explanation covers all twelve keys.

Why Roman numerals rather than 1, 2, 3? Because plain digits already mean something on a piano page. They are fingering. A numeral can only mean a scale degree, and that is the only job it is ever given.

It also settles which note is home. I is always the root, and everything else is measured from it.

Each of the seven steps has a formal name as well as a numeral. The names turn up in theory books; the numerals turn up everywhere else, because they are faster to say and to read.

Two of these earn their keep. The tonic is home. The dominant is the note, and the chord, that pulls hardest back to it.

A numeral can name a whole chord as well as a single note, and the way it is written tells you the chord quality.

Uppercase means a major chord. Lowercase means a minor chord. Three extra marks cover the rest:

In C major, for example, iii is E minor, the chord built on the third degree. V is G major, built on the fifth. vii° is B diminished, built on the seventh.

The case is also how a numeral shows a chord that came from outside the key. See diatonic chords, and the ones you borrow.

The most common use of roman numeral analysis is the set of triads a scale contains. Every note of a scale has a three-note chord built on it, and those seven chords are what chord progressions are made of.

In a major scale the triads run I, ii, iii, IV, V, vi, vii°. In a natural minor scale they run i, ii°, III, iv, v, VI, VII.

Read the pattern once and you never have to work it out again. In a major key, I, IV and V are major and the rest are minor, except the last, which is diminished.

Those seven are the key's own chords, and diatonic chords, and the ones you borrow covers what happens when a song wants an eighth.

Every scale on this site has a page of its triads, playable in the browser with Chordzy. The links are at the bottom of this page.

A seventh chord has four notes instead of three, and the numeral says so with a small 7: I⁷.

You will also see a small M. That marks a major seventh.

Inversions have a notation of their own inside roman numeral analysis, and it is called figured bass. The small numbers change their meaning: they no longer say "seventh", they say which note is at the bottom.

The numbers are intervals counted up from the bass note. Take the C major triad in first inversion, E-G-C. From E up to C is six steps, so it is written 6. In second inversion, G-C-E, G up to E is six steps again, but G up to C is four, so both numbers are written to keep it clear: 6 over 4.

The chords in a key are the seven built from its own scale, one on each degree, and nothing else. They are called diatonic chords, from the Greek for "through the notes": every note in them comes out of the scale, so no accidental is needed to play one.

That is the whole test. In C major the diatonic chords are C, Dm, Em, F, G, Am and B°, and every note in that set is a white key. Add an F sharp anywhere and the chord has left the key. The key of C major works the set out note by note, and every other key has a page of its own.

A borrowed chord is one a song uses anyway. It comes from the parallel key, the one with the same tonic and the other quality, and it keeps its own accidentals. The commonest example in pop is iv in a major key: in C major that is F minor, borrowed from C minor, with an A flat that the key does not own. It sounds like a cloud crossing the sun, which is exactly why writers reach for it.

Borrowed chords keep the numeral of the degree they sit on and change case or gain a flat to show what happened. Write F minor in C major as iv, not IV. A major chord on the flattened sixth degree gets a flat in front of it: ♭VI.