Roman numerals

Also called Roman numeral analysis

A Roman numeral names a chord by the scale degree it is built on: I is the chord on the first note of the key, V the chord on the fifth. A capital means major, lowercase means minor, in any key.

What does a Roman numeral name?

Number the notes of the scale 1 to 7 and build a triad on each one, using only notes of the key. The Roman numeral is the number of the note the chord starts on: I is the chord on the first note, IV the chord on the fourth, V the chord on the fifth. It says where the chord sits in the key, not which notes it contains.

The case of the numeral gives the quality. A capital letter is a major triad, a lowercase letter a minor one, and a small circle after a lowercase numeral marks a diminished one. In a major key the pattern never changes: major, minor, minor, major, major, minor, diminished. Minor keys have a pattern of their own (natural minor, with the raised seventh used only inside V and vii°): i, ii°, III, iv, V, VI, vii°. Of these i and iv are minor, III, V and VI major, ii° and vii° diminished.

The seven triads of C major with their numerals: I ii iii IV V vi vii°.
NumeralChord in CQuality
ICmajor
iiDmminor
iiiEmminor
IVFmajor
VGmajor
viAmminor
vii°Bdimdiminished

How do you read I–IV–V–I in C and in A minor?

To read a string of numerals, find the note of the key that each number points to. In C major, I–IV–V–I is C, F, G, C. Move to G major and the numerals stay put while the letters follow the key: G, C, D, G. That portability is the whole reason for using numerals.

Minor keys use the same system with one catch. In A minor the main chords are i, iv and V: A minor, D minor and E major. The V is a capital because the seventh note of the scale is raised (G becomes G♯), which gives the chord the pull back to the tonic. That raised note is why V is major, where the natural minor scale would give a minor v, while i and iv stay lowercase. Leave the seventh natural and the chord on it is VII, a major chord (G–B–D in A minor); vii° is the diminished chord built on the raised note (G♯–B–D).

i–iv–V–i in A minor: A–C–E, D–F–A, E–G♯–B, A–C–E. The G♯ in the V chord is the raised seventh.

What do °, ø and the small numbers mean?

MarkMeansExample in C
°a diminished triad (with a seventh, a diminished seventh chord)vii° = B–D–F
øa half-diminished seventh chordviiø7 = B–D–F–A
7a seventh added on topV7 = G–B–D–F
⁶ ⁶₄an inversion: which note is lowestI⁶ = E–G–C / I⁶₄ = G–C–E

Small figures such as ⁶ and ⁶₄ are the same numbers a figured bass uses: they say which note of the chord is lowest. V7 and V⁷ are one chord, the raised figure being only a way of typesetting it. In a pop or jazz analysis a plain 6 after a numeral (I6) is a sixth chord, not an inversion; the small raised ⁶ of classical figures (I⁶) is the inversion.

How is a numeral different from a chord symbol?

A numeral names the degree a chord is built on, while a chord symbol names its notes outright. The reference has an entry on chord symbols, which sets the two side by side.

Common questions

How do you find the Roman numeral of a chord?

Find the key, count the chord’s root up the scale to get the number, then write it in capitals for a major chord and lowercase for a minor one. In C major, A minor is built on the sixth note and is minor, so it is vi.

Why are some Roman numerals lowercase?

Lowercase flags a chord with a minor third, and adding ° makes it diminished. In C major the lowercase ones are ii, iii, vi and vii°, whose third sits a minor third above the root.

What chords are I, IV and V in C major?

C, F and G major, built on the first, fourth and fifth notes. Together the three use all seven notes of the C major scale.