Roman Numerals

Every key has seven notes, and you can build a chord on each one. Roman numeral analysis gives each of those chords a number, one through seven, written as a Roman numeral: I, ii, iii, IV, V, vi, and vii. Some are capital letters and some are small ones, a difference the next part explains; for now, the numeral tells you which step of the scale the chord is built on.

In the key of C major, the chord built on C is I, the one on D is ii, the one on E is iii, and so on up to vii on B. So instead of saying "a C chord in the key of C," you can just say "the one chord," the I. The number pins the chord to its spot in the scale.

Write the seven numerals in order, I, ii, iii, IV, V, vi, vii, and next to each the note it lands on in C major: I is C, ii is D, iii is E, and keep going.

A Roman numeral is an address, not a spelling. A chord letter like G names specific notes to play; a Roman numeral names where a chord sits in its key and what it does there, which is the information analysis needs. The numeral points to a position in a system.

The payoff shows across a whole repertoire. The same progression written in C and in E-flat gets the identical string of numerals, so an analyst can compare pieces, spot shared patterns, and describe a convention one time for every key at once. The numeral records a chord's place in the key.

In classical music theory, Roman numerals do a second job at the same time: their case tells you whether the chord is major or minor. A capital numeral means a major chord, and a small numeral means a minor chord. So I is a major one chord, and ii, written small, is a minor two chord.

Two special marks cover the other qualities. A small circle after a small numeral means diminished, and a plus sign after a capital means augmented. With just the size of the letters and a mark or two, a numeral tells you both which degree the chord is on and what kind of chord it is.

Write these three and say each one: capital I, small ii, and small vii with a little circle. That is a major, a minor, and a diminished chord.

Folding quality into the case of the numeral is a piece of notational economy. One symbol carries two facts, the root's scale degree and the chord's quality, so an analyst reads both from a single mark instead of two labels. Uppercase marks a major triad, lowercase a minor one, a small circle diminished, and a plus sign augmented.

Quality shapes how a chord behaves, so keeping it in the symbol earns its place. Whether the chord on a given degree is major, minor, or diminished affects where it tends to lead, and putting quality in the same symbol as the degree holds the two behavior-setting facts together. A reader never reconstructs the quality separately; the case already states it.

If you build a triad on each note of a major scale, using only the notes of that scale, you get a fixed set of seven chords with a fixed pattern of qualities. In every major key the pattern is the same: I major, ii minor, iii minor, IV major, V major, vi minor, and vii diminished.

Memorize that pattern: it never changes from key to key. The one, four, and five chords are always major; the two, three, and six are always minor; and the seven is always diminished. Learn it once and you know the built-in chords of every major key.

Say the pattern out loud in order: I major, ii minor, iii minor, IV major, V major, vi minor, vii diminished.

The pattern of qualities in a major key follows directly from the scale's spacing. The major scale places its half steps between degrees 3 and 4 and between 7 and 8, and stacking thirds within that fixed arrangement of whole and half steps yields one quality on each degree. Change nothing and the same seven qualities fall out every time.

Every major scale has the identical step pattern, so building triads on it always produces major chords on I, IV, and V, minor chords on ii, iii, and vi, and a diminished chord on vii, in that order. The chords a key offers are fixed the moment you choose the key, and Roman numerals read them off.

Minor keys use Roman numerals too, but the pattern is different because the minor scale has a different shape. Built on the natural minor scale, the chords are: i minor, ii diminished, III major, iv minor, v minor, VI major, and VII major. The lowercase i tells you the home chord is minor, which fits minor's darker sound.

There is one common twist. Composers often raise the seventh note of a minor scale to get a stronger pull home, and that raises the quality of the five chord to major, written V. So in real minor-key music you very often see a capital V even though plain minor would give a small v.

Write the minor-key home chord as a Roman numeral. It is a lowercase i, because the tonic chord of a minor key is minor.

Minor keys make Roman numeral analysis more fluid than major because the sixth and seventh degrees are variable. Natural, harmonic, and melodic minor supply different versions of those two notes, so the chords built on and around them come in more than one quality, and the numerals reflect whichever form the music uses at that moment. Minor offers a larger, more flexible set of diatonic chords than major does. Its tonic is still a lowercase i, since the home chord of a minor key is minor.

The raised leading tone is the most consequential of these choices. Tonal minor keys need a leading tone a half step below the tonic to cadence strongly, so composers raise the seventh degree, which converts the weak minor v into a major V with real dominant pull and produces the diminished vii as well. Reading minor harmony means watching the sixth and seventh degrees to see which form is in play at each chord.

The real payoff of Roman numerals is that they show what each chord does in the key, its function. Chords fall into a few families. The I chord is home, the place of rest. The V chord is the one that pulls back home. The IV and ii chords set up that pull. Music moves among these roles, and the numerals let you see the roles at a glance.

That is why analysts label music this way instead of just writing chord letters. A string of numerals like I, IV, V, I shows the story of a phrase, leaving home, building tension, and returning, no matter which key it is in. The letters would change from key to key; the numerals and their story stay the same.

Take the numerals I, IV, V, I and describe the journey: start at home, move away, build the pull, come home.

Roman numerals are the entry point to functional harmony, the theory that chords behave in categories. Grouping the diatonic chords into tonic, predominant, and dominant functions captures a real regularity in tonal music: chords within a function substitute for one another, and the functions tend to succeed one another in a preferred order toward the tonic. The numerals make that syntax visible.

Function labels transpose while the specific pitches change underneath, which is what lets a whole convention, a cadence type, a sequence, or a phrase model, be described one time and found again in any key. Cadences, progressions, and chromatic harmony are all spoken in this language of functions.